Unification/nomu-tcs.ps
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%!PS-Adobe-2.0
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%%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software
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%%Title: nomu-tcs.dvi
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%%Pages: 29
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%%PageOrder: Ascend
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%%BoundingBox: 0 0 596 842
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%%DocumentFonts: Times-Bold Times-Roman CMR10 CMR8 Times-Italic CMMI10
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%%+ CMMI12 CMSY10 CMTT12 CMR12 CMSY8 Courier CMBSY10 CMMI8 CMTI12 CMEX10
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%%+ CMTI10 CMMIB10 EUSM10 CMR6 CMMI6 CMSY6 CMTT8 CMBSY7
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%%EndComments
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%DVIPSWebPage: (www.radicaleye.com)
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%DVIPSCommandLine: dvips nomu-tcs.dvi -o nomu-tcs.ps
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%DVIPSParameters: dpi=600, compressed
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%DVIPSSource:  TeX output 2004.04.09:1442
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%%BeginProcSet: texc.pro
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%!
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/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
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N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
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mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
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0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
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landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
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mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
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matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
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exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
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statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
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N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
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/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
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/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
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array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
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df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
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definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
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}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
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B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
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1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
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1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
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0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
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sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
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rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
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gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
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/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
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/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
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A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
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get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
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ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
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fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
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{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
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chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
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1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
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forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
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/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
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}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
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bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
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mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
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SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
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userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
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1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
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index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
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/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
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/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
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(LaserWriter 16/600)]{A length product length le{A length product exch 0
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exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
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end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
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grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
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imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
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exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
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fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
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delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
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B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
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p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
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rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
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%%EndProcSet
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%%BeginProcSet: 8r.enc
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% File  8r.enc as of 2002-03-12 for PSNFSS 9
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%
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% This is the encoding vector for Type1 and TrueType fonts to be used
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% with TeX.  This file is part of the PSNFSS bundle, version 9
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% 
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% Authors: S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, W. Schmidt
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%
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% Idea is to have all the characters normally included in Type 1 fonts
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% available for typesetting. This is effectively the characters in Adobe
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% Standard Encoding + ISO Latin 1 + extra characters from Lucida + Euro.
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% 
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% Character code assignments were made as follows:
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% 
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% (1) the Windows ANSI characters are almost all in their Windows ANSI
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% positions, because some Windows users cannot easily reencode the
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% fonts, and it makes no difference on other systems. The only Windows
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% ANSI characters not available are those that make no sense for
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% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
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% (173). quotesingle and grave are moved just because it's such an
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% irritation not having them in TeX positions.
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% 
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% (2) Remaining characters are assigned arbitrarily to the lower part
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% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
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% 
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% (3) Y&Y Lucida Bright includes some extra text characters; in the
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% hopes that other PostScript fonts, perhaps created for public
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% consumption, will include them, they are included starting at 0x12.
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% 
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% (4) Remaining positions left undefined are for use in (hopefully)
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% upward-compatible revisions, if someday more characters are generally
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% available.
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% 
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% (5) hyphen appears twice for compatibility with both ASCII and Windows.
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%
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% (6) /Euro is assigned to 128, as in Windows ANSI
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% 
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/TeXBase1Encoding [
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% 0x00 (encoded characters from Adobe Standard not in Windows 3.1)
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  /.notdef /dotaccent /fi /fl
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  /fraction /hungarumlaut /Lslash /lslash
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  /ogonek /ring /.notdef
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  /breve /minus /.notdef 
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% These are the only two remaining unencoded characters, so may as
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% well include them.
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  /Zcaron /zcaron 
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% 0x10
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 /caron /dotlessi 
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% (unusual TeX characters available in, e.g., Lucida Bright)
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 /dotlessj /ff /ffi /ffl 
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 /.notdef /.notdef /.notdef /.notdef
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 /.notdef /.notdef /.notdef /.notdef
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 % very contentious; it's so painful not having quoteleft and quoteright
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 % at 96 and 145 that we move the things normally found there down to here.
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 /grave /quotesingle 
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% 0x20 (ASCII begins)
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 /space /exclam /quotedbl /numbersign
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 /dollar /percent /ampersand /quoteright
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 /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
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% 0x30
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Christian Urban <urbanc@in.tum.de>
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5c816239deaa added Unification subdirectory
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Christian Urban <urbanc@in.tum.de>
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5c816239deaa added Unification subdirectory
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
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5c816239deaa added Unification subdirectory
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
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diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
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diff changeset
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/FullName (CMTT8) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   529
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   530
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   531
/ItalicAngle 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   532
/isFixedPitch true def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   533
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   534
/FontName /CMTT8 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   535
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   536
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   537
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   538
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   539
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   540
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   541
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   542
/FontBBox{-5 -232 545 699}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   543
/UniqueID 5000830 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   544
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   545
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   546
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   547
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   548
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   549
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   550
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   551
2BDBF16FBC7512FAA308A093FE5F0187316F83DDE3E2D27FCDF6C5CE4F95B6EE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   552
3317BD91B7921F3039DD35FEA387D5CFB6C6E9DC84C178F3432994FC7FAC6E5A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   553
ED41A1E2EBA350178FBFEB45944511731BA827167DDAC238FC69A5486B995477
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   554
C469E2E27493B0B711DF8E267D3D5613B450011921685147114106C9472580BD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   555
F531022F6DF5432B2A4EBC51A8032C7F9689B6FA942D849B29709631613DA68D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   556
4DF7B6F059A19304F40A3C3580CE3B51D79D42984194D4F178801720892FB6E7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   557
61FF43C63F9256B5E9F4227B1378222BAAD4D52C77462DF01892220E11129C16
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   558
6C9E45BB9F01ED7C1AD5D8B4D72BE0E12969AFEA90FEF170603CDB91CB243173
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   559
B19A56084D10293B80A35275F41BF78A054DDC98F4A1FFF592463D944960FB31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   560
6BE5F03960F9B1F213CBCC7FD448657FE388F10104D42B0715FC9571CC60CF23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   561
C72560CBB8835A0CA208FE06676B3B48B093CB7FB2C0C53AF17EC5B372A9771B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   562
BFD52FFB7062B4FE0106A01A2A1A1DD4EF5C8C7623EC9324A2CB3B402FCC1FCE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   563
52BFC8662F8A39D5F1B41C97E7CE34E16AC28A1E94007AEA7D4C519399F1B7A9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   564
48FA7DDB671067244F09C29F95DD60668223F45BBDA8B1C452E930A9F3F341C5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   565
351D59EA87462FFB30277D3B24E2104D4AAB873BB2B16DA5B23BEE25BE2C8128
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   566
C4CF2F4F438A4E520CD932BAC455BF8775C27AEA6C73EED3EB2F8DB5E356AE27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   567
41B35C8AEFE73C4CD6A591AAE4F45762EBD6D3636C03F08C552BBFD0A13D11D5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   568
491F8369B4BAB8ED9D6F1DE7DB7AFD383986C4338D3AA71C9AF2B8A0955CFD86
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   569
0345F16D9798B25156DDF826A7CB6A0CC4CB43078BEBD3E499DA95562A08EED9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   570
7CA27B7A0CE3FA7EBDAA87A6042231493B69CFEA7AE1992BCCF33B408CD50C7B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   571
8665EF678BB3B42D17D703B63DD8B76E3ECA117D3DE545A88A49AD0CB49D1B5A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   572
C920F89299DEBA6CA0B38D0131DE51CC2652D597386B659849699B7AB3465F93
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   573
256D9CCF0A07891D6F310750D72ACFE1A498583FE2C167B057FB3EA6EC057AF4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   574
0A96B2399719B8902403E7833B7EB6F117C3F96FB7ADC2490E680A7ABA9BEA84
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   575
49BD1D4307AB6F6401F913F85D9DDF0B414F1FF79BF7C5788A5EFF60CEA9B2F7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   576
5436EADECABB4C56C2E6BDFB6DB26AF884D590E545ECBDFD7425DB89C6B078AE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   577
FABE6479DC4F184445D71C052BCCEDD9A85AB9C94431E2BC305564F43C9BD36C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   578
BEB52E69ED948933A791CA47FC35625B97BF321BA9118DE302F526C7728194D2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   579
69622B146974D1D5105DC891279E8B0F7BF7CDEED7005AACDF972745E6290F2E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   580
38EFA0EA88D22A366FDC299883554B30D1A9C0EC5F4BEBBB72BF069E84EE3460
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   581
1FEABC64557779EA9871F92473F25DB12E53EB4E0067D72EF60BF798DD4B96C4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   582
A051F4877F9040EA9881602F814996038FD60CB721B2BC34DB5115DCCBE09322
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   583
43C75F2148B8CED5D250932CF91235019CF81300388EA235D0B0CD180A8D7ADD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   584
FE8EEDBAC7828A02B86A150FC415179B8083B3AD2D8C438E19CBC1C110E132CE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   585
7ABD9C28BD953636EE20FE72F56DE320C2E85690F15B774B89A0046F4EFC2D2D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   586
160FF39BFF8E71F2E5096F2B9464257703DA24538BB4764A43AD58A1C66CDEBE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   587
570D84E2EFC62A29274AF650A0843276C6A1EB4257704655EE1D11BBE8B8A0FB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   588
7AA7E93971EEF39F3EF2DC11B795D10581F89850C8E691C759B266E4DFDA8006
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   589
AFDE411B07E822021E27BB6608F9206F239DA5E3F743D8780428809AE6649CC8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   590
628853E96C15B56223DC454EAC9750BB27457FBE40C34149848E11320BF06883
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   591
1A1BA06C3A2BCD716E52AC4FA9DF97F82203CEC315A046C215A7A474A7BE6CA2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   592
D837D6CA08651D247FE2132CF89A530EC5CE24309CD42A63B38BD42B4B9DF104
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   593
64A32984AC2DC3B4285D54815EC8D0702A1CAE2D0B1B42BE55E56EABC131D8C4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   594
282C11C95997CA005109CF71D8D277A468E23D101DB285250AEC26A778A2F3B4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   595
007A88C1B7FE3B4CB4DCE318824700203E4555816ADEFFD13A1C4D2A3485D1C2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   596
681482F0606BA2936543A623E121D140B70AAA459B0060FEABC5DF65C2470511
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   597
07277A4E5B30B31A1DF870B571EC276A8EC80A11794DC5F1D444218690D89DCA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   598
4501F78C16A3118BF6A557F5A1A30E38A52145A545BC101DF51A51DE563001FC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   599
DB2773064DE8EB005CEF2D1F822E85B889104DB7DFB72D7E93068495531315EA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   600
C4983BFA1186ACE72A45E709B846D2D5861AF4745D360B8E39F14E37575041C4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   601
F72697AF00EC75F46C4021E4B03A6E1FE26326667B08F6FB584F6B7E0133D5FC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   602
DC9CB6C5B67BB5C7C52D115D189B796C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   603
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   604
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   605
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   606
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   607
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   608
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   609
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   610
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   611
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   612
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   613
%%BeginFont: CMSY6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   614
%!PS-AdobeFont-1.1: CMSY6 1.0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   615
%%CreationDate: 1991 Aug 15 07:21:34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   616
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   617
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   618
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   619
/version (1.0) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   620
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   621
/FullName (CMSY6) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   622
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   623
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   624
/ItalicAngle -14.035 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   625
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   626
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   627
/FontName /CMSY6 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   628
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   629
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   630
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   631
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   632
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   633
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   634
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   635
/FontBBox{-4 -948 1329 786}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   636
/UniqueID 5000816 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   637
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   638
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   639
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   640
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   641
A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   642
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   643
221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFB7605D7BA557CC35D6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   644
49F6EB651B83771034BA0C39DB8D426A24543EF4529E2D939125B5157482688E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   645
9045C2242F4AFA4C489D975C029177CD6497EACD181FF151A45F521A4C4043C2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   646
1F3E76EF5B3291A941583E27DFC68B9211105827590393ABFB8AA4D1623D1761
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   647
6AC0DF1D3154B0277BE821712BE7B33385E7A4105E8F3370F981B8FE9E3CF3E0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   648
007B8C9F2D934F24D591C330487DDF179CECEC5258C47E4B32538F948AB00673
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   649
F9D549C971B0822056B339600FC1E3A5E51844CC8A75B857F15E7276260ED115
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   650
C5FD550F53CE5583743B50B0F9B7C4F836DEF1B263DB260571DCE3DFEC496E93
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   651
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   652
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   653
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   654
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   655
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   656
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   657
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   658
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   659
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   660
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   661
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   662
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   663
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   664
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   665
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   666
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   667
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   668
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   669
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   670
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   671
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   672
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   673
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   674
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   675
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   676
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   677
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   678
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   679
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   680
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   681
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   682
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   683
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   684
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   685
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   686
/version (1.100) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   687
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   688
/FullName (CMMI6) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   689
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   690
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   691
/ItalicAngle -14.04 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   692
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   693
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   694
/FontName /CMMI6 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   695
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   696
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   697
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   698
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   699
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   700
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   701
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   702
/FontBBox{11 -250 1241 750}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   703
/UniqueID 5087381 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   704
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   705
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   706
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   707
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   708
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   709
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   710
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   711
D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   712
5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   713
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   714
6AD6FB2DC4C13F077F17789476E48402796E685107AF60A63FB0DE0266D55CF1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   715
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   716
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   717
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   718
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   719
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   720
70BCD9C063B63B561EF165BF3AF11F8E519F37C6FDA2827685739DE2C48B5ADE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   721
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   722
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   723
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   724
3B5BC75FB53B55D72AF4A6A7BB613FA235B11BB37D059FD87127CEF73D5B3FBF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   725
9F91ABAD78BD9240BD9525EBA78095EA0BDB25D1A19E876F292882EAD5619D46
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   726
D20317A345D931F4FF4EAE6216C27044CBA525E3B917CEA25A04C120466C4B93
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   727
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   728
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   729
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   730
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   731
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   732
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   733
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   734
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   735
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   736
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   737
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   738
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   739
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   740
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   741
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   742
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   743
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   744
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   745
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   746
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   747
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   748
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   749
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   750
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   751
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   752
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   753
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   754
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   755
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   756
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   757
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   758
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   759
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   760
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   761
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   762
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   763
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   764
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   765
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   766
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   767
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   768
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   769
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   770
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   771
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   772
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   773
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   774
%%BeginFont: CMR6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   775
%!PS-AdobeFont-1.1: CMR6 1.0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   776
%%CreationDate: 1991 Aug 20 16:39:02
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   777
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   778
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   779
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   780
/version (1.0) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   781
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   782
/FullName (CMR6) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   783
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   784
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   785
/ItalicAngle 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   786
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   787
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   788
/FontName /CMR6 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   789
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   790
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   791
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   792
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   793
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   794
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   795
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   796
/FontBBox{-20 -250 1193 750}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   797
/UniqueID 5000789 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   798
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   799
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   800
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   801
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   802
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   803
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   804
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   805
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   806
68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   807
3645B82392D5CAE11A7CB49D7E2E82DCD485CBA17D1AFFF95F4224CF7ECEE45C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   808
BFB7C8C77C22A01C345078D28D3ECBF804CDC2FE5025FA0D05CCC5EFC0C4F87E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   809
CBED13DDDF8F34E404F471C6DD2E43331D73E89BBC71E7BF889F6293793FEF5A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   810
C9DD3792F032E37A364C70914843F7AA314413D022AE3238730B420A7E9D0CF5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   811
D0E24F501451F9CDECE10AF7E14FF15C4F12F3FCA47DD9CD3C7AEA8D1551017D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   812
23131C09ED104C052054520268A4FA3C6338BA6CF14C3DE3BAF2EA35296EE3D8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   813
D6496277E11DFF6076FE64C8A8C3419FA774473D63223FFA41CBAE609C3D976B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   814
93DFB4079ADC7C4EF07303F93808DDA9F651F61BCCF79555059A44CBAF84A711
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   815
6D98083CEF58230D54AD486C74C4A257FC703ACF918219D0A597A5F680B606E4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   816
EF94ADF8BF91A5096A806DB64EC96636A98397D22A74932EB7346A9C4B5EE953
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   817
CB3C80AA634BFC28AA938C704BDA8DC4D13551CCFE2B2784BE8BF54502EBA9AF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   818
D49B79237B9C56310550BC30E9108BB06EAC755D6AA4E688EFE2A0AAB17F20FE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   819
00CD0BFF1B9CB6BDA0FA3A29A3117388B6686657A150CE6421FD5D420F4F7FB5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   820
B0DAA1BA19D638676E9CF159AC7325EF17B9F74E082BEF75E10A31C7011C0FFA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   821
99B797CE549B5C45238DD0FADD6B99D233AC69282DF0D91EA2DBD08CE0083904
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   822
A6D968D5AE3BD159D01BDFF42D16111BC0A517C66B43972080D9DD4F3B9AE7FB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   823
11B035CE715C1218B2D779761D8D7E9DEBE277531BD58F313EBD27E33BEF9DC5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   824
50C7821A8BBC3B9FDF899D7EAA0B94493B97AFEAC503EB5ED7A7AB62FBEFBEFA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   825
AD08ADD6648E354B05E584C970AACB6E015F56F3482678504279F10E01CDA446
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   826
6F6E039511BE0576EC00ACDBBDE8DAD593121F1D855D175D616711DB93645AB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   827
03227673BAF4CCF593EB7EF23AFEB7B2CB7AB053C26530E564BC01C2F74A3D1A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   828
4C1279D91F1EF1383E34E8218B3A9918341FE9E346EB3EBFE627E7518D6AB787
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   829
8DC227C39FAF27D969769756B98A0A078058A6D04DBC5A18344ED6EC71C98E00
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   830
7996DD675B953CBDA5AAECA2AB8819E1FFFE61F2A2C48F13B70F8334E9A2CDAB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   831
4603C68292AD8A93E29A04D262AFE205293FC10AD70F360DC07DC03E00CD12A1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   832
5213BFEA869BE17CB485E81907A09B54E11FDBD10D0F96A93331A1C67F567735
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   833
D8103CDD80521A2ECBDFD5300A52A807A0CDFC1682A8152B969A4BB552C7F749
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   834
B1CF7DF736594BF66F8BDA9AD556CDE9B1A7DB9D925BE2A6126ECFC9B5840DA9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   835
8DC33CE9E081A081726EA759DB1CD8D17674EC2EBD19ECB3EDA97CE76919BBF6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   836
FD8D8EDEA1CC16A552224B6B237450E93F953A3E5A831F9D56FF8A56EE011489
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   837
F11F4770859118A61EB7F9D552E3AF26BF4C061D136A25969FA4F98524DE2B29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   838
37048AF15112C33E0A209BBE2BB660CF3690CB633122473A607E181FCAB6684A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   839
4EEF2C8B40869EBA5F3A9DC7384DA16DF2EE07986F86C00F0780117B1A6CEBA0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   840
0345A6B9F709B463B1AADEDB5A76FCD5D08EDECBB366C248EDFB02EF6EF4D5FE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   841
8EC92B011698C86A817B703C9E08511938C5E824C2A78E8F20D59F6F38471D6D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   842
C886487193C3742947E4DF31A01F89512E74344EA515FE8F3F0B5B2D0EAEAEB5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   843
79EE7DD825B87AB1BE8AF331DF5F087A8E61D9A606D684CA34BDD91BA76FE680
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   844
C29D2AB77B8A513C259CEFB5CBA26071E55E0C5B17DB0A9E4476F79C84F2676F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   845
79B8C7AB8CCC4EBABFAB37BC961DC469FF21F3B212506E0CE29947219C2D2375
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   846
1FEC3209D22EF95488F584655D7389E90204DD39E0C5938EB49107B49EA6343B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   847
D6ADC868BF393850973F912AA46ED3D4E11362DFAF19AC312F216FD5960FBA17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   848
8C5F89F51AE749F73150F077DADBA20BEE3A1B7DA363F34CF6F477B411EB5129
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   849
1DBA86E8D7AFD4916A10FE2113FF2177E31F9456DB39984F2A123D51D26B36E3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   850
BE132D008D884BA2A44FF04031BA21A47AD823B57BE67B44116E7A7003EBC2E6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   851
97F17FFE8B65AD781E0AD24885FA94CADF751D2DB2BCC33DA1CC7C49843EBA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   852
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   853
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   854
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   855
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   856
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   857
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   858
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   859
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   860
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   861
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   862
%%BeginFont: EUSM10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   863
%!PS-AdobeFont-1.1: EUSM10 2.1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   864
%%CreationDate: 1992 Nov 20 17:36:44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   865
% Euler fonts were designed by Hermann Zapf.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   866
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   867
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   868
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   869
/version (2.1) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   870
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   871
/FullName (EUSM10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   872
/FamilyName (Euler) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   873
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   874
/ItalicAngle 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   875
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   876
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   877
/FontName /EUSM10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   878
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   879
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   880
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   881
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   882
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   883
dup 85 /U put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   884
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   885
/FontBBox{-8 -194 963 738}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   886
/UniqueID 5031988 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   887
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   888
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   889
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   890
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   891
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   892
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   893
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   894
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169DE483FC3C5DBA587E58D683
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   895
9E11948C1A3E8B5360ADE57410E9F910E561F679EBFBEB0730125606CD072EB1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   896
0A975FC5186A70BA3CAA77642D606B57469AD72289DA911758623D8C66DCB000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   897
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   898
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   899
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   900
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   901
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   902
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   903
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   904
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   905
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   906
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   907
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   908
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   909
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   910
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   911
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   912
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   913
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   914
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   915
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   916
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   917
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   918
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   919
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   920
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   921
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   922
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   923
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   924
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   925
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   926
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   927
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   928
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   929
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   930
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   931
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   932
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   933
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   934
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   935
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   936
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   937
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   938
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   939
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   940
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   941
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   942
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   943
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   944
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   945
/version (1.100) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   946
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   947
/FullName (CMMIB10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   948
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   949
/Weight (Bold) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   950
/ItalicAngle -14.04 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   951
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   952
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   953
/FontName /CMMIB10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   954
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   955
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   956
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   957
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   958
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   959
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   960
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   961
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   962
/UniqueID 5087392 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   963
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   964
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   965
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   966
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   967
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   968
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   969
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   970
D919C2DDD26BDC0D99398B9F4D004B836D34E88C25F6CE738846C8E2E59A2BCF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   971
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   972
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   973
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   974
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   975
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   976
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   977
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   978
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   979
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   980
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   981
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   982
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   983
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   984
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   985
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   986
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   987
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   988
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   989
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   990
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   991
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   992
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   993
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   994
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   995
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   996
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   997
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   998
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   999
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1000
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1001
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1002
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1003
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1004
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1005
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1006
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1007
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1008
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1009
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1010
%%BeginFont: CMTI10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1011
%!PS-AdobeFont-1.1: CMTI10 1.00B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1012
%%CreationDate: 1992 Feb 19 19:56:16
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1013
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1014
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1015
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1016
/version (1.00B) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1017
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1018
/FullName (CMTI10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1019
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1020
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1021
/ItalicAngle -14.04 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1022
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1023
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1024
/FontName /CMTI10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1025
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1026
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1027
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1028
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1029
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1030
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1031
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1032
/FontBBox{-163 -250 1146 969}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1033
/UniqueID 5000828 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1034
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1035
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1036
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1037
3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1038
532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1039
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1040
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1041
D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1042
9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1043
21EC3643079EECE0C9AB54B4772E5DCA82D0D4ACC7F42FB493AA04A3BF4A1BD6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1044
06ECE186315DBE9CFDCB1A0303E8D3E83027CD3AFA8F0BD466A8E8CA0E7164CF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1045
55B332FAD43482748DD4A1CB3F40CB1F5E67192B8216A0D8FE30F9F05BF016F5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1046
B5CC130A4B0796EE065495422FBA55BEE9BFD99D04464D987AC4D237C208FA86
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1047
0B112E55CE7B3782A34BC22E3DE31755D9AFF19E490C8E43B85E17ECE87FA8B9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1048
1485831624D24F37C39BF9972D74E6EC4784727AC00B9C4A3AD3DA1C22BD6961
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1049
7E0ADAF55422F22ACA5E4DCD4DF9FCD187A566B7FB661D0530454D0DD6C6C50A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1050
7A3875C6CBF8EC7769F32A1F3F7FC1C072BADEC97794D4E90E0035282A170402
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1051
356E5A9CD9ABD80AC4342A5283E458A7269252F4541CBB6452B39ED54D336D0B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1052
19928E9CD1AB26AD83EB209E2EC75011A2643813053B5DBB0246097C4821B5F2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1053
C92554E9140BE35B2DBFCD98809A8EC9FC910FDE9E0D86457C70ACB056EBF90F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1054
244DC0A5BBD455E15D6E3180311D52CF50B0BF7D0A7F64F3A1821E0AEDBC2E7B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1055
AEB549FE1D51088C153799C6E089B5D5D65E1C4E2D2B430CDF1FFA23CCB25D95
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1056
592943209E846E55B4CB54F6658CBA3C0B29796D69D0435D5431ABECF3448C15
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1057
98CA2F36F3659E29AEB79355EC2ADF835CF0886C21B766B9DEBC3950B5B3B496
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1058
2E06D980A8C60305B273232D4604F12632FB4F1B2F9703952C823C098543AED1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1059
CFB4ECF259A11985F0C944A57B5AFD853374FCF12305601200C2A393E2FC77FD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1060
F78C2BEAF545FB34D38EED3579B16A9724302E591A2F873A766ADD5572E32935
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1061
1FC9784C66AF7E2E13D92D32C0C48F82D45BFACCC2BCAFA04B854CEC608FBCA9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1062
643028338C2CD69ACB53C7E6AC418FC6F1635EA2702668C3B98AA439066990B4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1063
CE74A7C22B992987625D2EE48EDB70865F9E4A1270E31FAC2D3E53A8439B7B53
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1064
8B9EEA7FE7A10F17C39BB7B59B378048D647E7262FF36D2F50AD1585CF7A329D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1065
ACB0AA69E4B9237A38B34F678D425DDC223513DBB24647F26DC9AE1F4D32A65D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1066
D8BF0FB2E22E0F124BD5E2BCDD118AB22573E6F6F222B66E06B1A978C9351185
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1067
5D92E88E5EFD2A2F0C7409E7EFAFCD2068698E376056B34D26EF1B9B3F8F4939
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1068
8B78507CDB2784F367825A6FF7966F91A2484D81D88EB29C28C177F614C9CBE1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1069
9742FEFAE2EF8986837A44A7DA8ECD775F92A67B241F371B0C510DDB9FC04380
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1070
40699EE66D74DB29E2A42542325DE900C6C3D5F2AC32856B2E8750F907434487
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1071
CAA85339DFC689CF96323EEF28D4EB5EE0F89503D5E7BBE1BE59E2731F7CC5FB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1072
EA68224C8049A7657367AF2D50CA834854EFAA771B90D92397A137D8F54C31DA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1073
6F2911B0806BC00DF1123C0C48095FD5B31BF2BD2DDD55A6AC84C7C7C406D5B4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1074
6D0BCD5FE8E3EE46CA12B533AD713F8D50C53D95B489599443D342DA57291846
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1075
EEF677D1B88EF3EE1BA20C0BD3445E9F1384AD7C487CA413C486C95FED100038
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1076
814926A1BC8B9CD3C6073F80096255FACDEA9C2F50B38E9FEE14053A2788D98B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1077
C49EF4098B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1078
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1079
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1080
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1081
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1082
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1083
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1084
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1085
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1086
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1087
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1088
%%BeginFont: CMR10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1089
%!PS-AdobeFont-1.1: CMR10 1.00B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1090
%%CreationDate: 1992 Feb 19 19:54:52
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1091
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1092
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1093
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1094
/version (1.00B) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1095
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1096
/FullName (CMR10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1097
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1098
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1099
/ItalicAngle 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1100
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1101
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1102
/FontName /CMR10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1103
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1104
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1105
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1106
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1107
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1108
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1109
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1110
/FontBBox{-251 -250 1009 969}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1111
/UniqueID 5000793 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1112
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1113
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1114
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1115
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1116
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1117
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1118
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1119
2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1120
87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1121
D1F017CE45884D76EF2CB9BC5821FD25365DDEA6E45F332B5F68A44AD8A530F0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1122
92A36FAC8D27F9087AFEEA2096F839A2BC4B937F24E080EF7C0F9374A18D565C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1123
295A05210DB96A23175AC59A9BD0147A310EF49C551A417E0A22703F94FF7B75
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1124
409A5D417DA6730A69E310FA6A4229FC7E4F620B0FC4C63C50E99E179EB51E4C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1125
4BC45217722F1E8E40F1E1428E792EAFE05C5A50D38C52114DFCD24D54027CBF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1126
2512DD116F0463DE4052A7AD53B641A27E81E481947884CE35661B49153FA19E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1127
0A2A860C7B61558671303DE6AE06A80E4E450E17067676E6BBB42A9A24ACBC3E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1128
B0CA7B7A3BFEA84FED39CCFB6D545BB2BCC49E5E16976407AB9D94556CD4F008
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1129
24EF579B6800B6DC3AAF840B3FC6822872368E3B4274DD06CA36AF8F6346C11B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1130
43C772CC242F3B212C4BD7018D71A1A74C9A94ED0093A5FB6557F4E0751047AF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1131
D72098ECA301B8AE68110F983796E581F106144951DF5B750432A230FDA3B575
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1132
5A38B5E7972AABC12306A01A99FCF8189D71B8DBF49550BAEA9CF1B97CBFC7CC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1133
96498ECC938B1A1710B670657DE923A659DB8757147B140A48067328E7E3F9C3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1134
7D1888B284904301450CE0BC15EEEA00E48CCD6388F3FC3A307A1A4455646E1F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1135
B73047F2C36AB0DE64B2660795139BF3E491E7329C6804B62E7607010C423008
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1136
37F93F3851E472BD8F6D8DD9DFC1577C04A9531F8BEF1154F701F3FE438FD25D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1137
0B9C4EB4E2132F3094A166D7D2D3D877B0447947E929A44135D567DFC946AC97
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1138
E6EDD4B4ED1204D5D2402C351212FC96C0EACEF4222FD9A271D0C3DB27CEA5D1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1139
81D7E6BEDC9CE8937288DBC4F96661C812D31312FDBD0E680C6EEF544CCF26CD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1140
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1141
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1142
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1143
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1144
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1145
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1146
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1147
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1148
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1149
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1150
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1151
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1152
6E370390407746B9D3B77BF54FD908650F54EDCFF07F1FDC473ABE8F145314B4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1153
872D158E88EE3F59090FB93A5747EDA57889E69C9114F441822FB770581BB0AB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1154
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1155
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1156
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1157
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1158
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1159
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1160
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1161
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1162
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1163
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1164
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1165
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1166
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1167
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1168
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1169
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1170
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1171
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1172
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1173
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1174
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1175
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1176
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1177
D5F6F5EE98AE202933787B589790A31AF611C1DF720B6ADA6BC239A59134DC30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1178
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1179
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1180
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1181
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1182
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1183
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1184
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1185
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1186
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1187
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1188
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1189
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1190
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1191
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1192
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1193
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1194
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1195
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1196
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1197
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1198
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1199
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1200
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1201
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1202
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1203
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1204
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1205
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1206
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1207
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1208
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1209
%%BeginFont: CMSY10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1210
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1211
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1212
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1213
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1214
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1215
/version (1.0) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1216
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1217
/FullName (CMSY10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1218
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1219
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1220
/ItalicAngle -14.035 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1221
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1222
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1223
/FontName /CMSY10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1224
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1225
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1226
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1227
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1228
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1229
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1230
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1231
/FontBBox{-29 -960 1116 775}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1232
/UniqueID 5000820 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1233
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1234
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1235
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1236
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1237
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1238
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1239
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1240
27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1241
5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1242
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1243
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1244
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1245
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1246
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1247
75082A9BF73D0F7781F7541D64AFD7C99AF409D4E2AC42AAD5E7E86A6728D134
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1248
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1249
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1250
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1251
A77116CBB7195E4878BA2A6FB4357ABDB89FE940218335675846DB18868A9658
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1252
F864B1C438AE6915FED20CC3B3D962688F2164C457EC13BF26FC61A44616F51D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1253
DAB0FBBF3C98676F7304B5455CFD65C6ED21E582AE8B78F1C125E2ECC603264C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1254
8E9FB3B50411FD6841462547085A6D3AC4CBBAD10256CCBA55C42F96A5E87169
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1255
CDBB40425B321CA17301122CA7AE90856685EDE8D4704BB2BEAC91F21DAC869A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1256
B64D1FE0B556727B875474C6C5BE660E82BDA7BBE25DEDF6E59F50D001A04BBD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1257
31949F48B9A908E4F74FF36D64DCDCD30940FAE4063AB32FAE56BCC8B996E0F2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1258
5ACF051FF643C3058CC411CC3FD22DD50ED43678CCD2B9C06E1BEE5E686DF3F0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1259
E118322E30040BFC8AABC8C28B02FD1B7066DD7276BE23309C2AB3BC9BB2143E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1260
0F975F4985AA2299853DA5091AAD2D020FA8B10395055F0B865BD998A59F62BD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1261
DB8F6B8331B3C7FD5DFD51F2203CE018C9A5E227BF58FD9DE9CED50617EEAACB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1262
6D2F782763D019E192E75A4B5F3926A27E25076AEF787623542B6DFEB7FD03BC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1263
C8DEBB242D43EAF7F2BE14DB97A19CEA9750F83A0242AFE2F7BD980F4F84B1B9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1264
6825964503D6DD07FDE3A5C9B164446939A3AEFB5BEFCA4378452E96F54697ED
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1265
3397D66C7C1335DDCE8A506A6AE2B814233A86D07E525144A16F893AE18B9109
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1266
ECD1DBD22E41EBD0CBA00D36E7DA95C9B618442D334EE34DFEE461153FC05B6C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1267
65345748836A807FD360ABD721F7B17F8F84E9107FC7AB79E2485C692EFD19E1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1268
E45AB951588BC4065FBAB9FF0DB5CA542A2169A6974281C5D124A825820ADE16
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1269
FB335B7FF5DFE9C41CC767CD93A1664DFA6B4C2984CF604B5DDC02C74C8C5752
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1270
36596E8E546DB447A98BDCA476E85E92DCD9B80C85EB341547BC13E31C968AD2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1271
93663F93CAEBECB1F4F1D75D27873620E79A6A135C97219637E197E5E6AAC9F1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1272
47C833C5DB688992A57D5FB1C34B4C121ECF9EF5156E1BE4A1BC20C66B4E0072
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1273
FC928AA1CEF326B749F5D53E195083500DBDE786A988FAF8416F4B6C3BAE0F9D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1274
52D917726A9603A7F40F739B95086B4DF288FB06675AAA2EA3170498C04038DC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1275
6E978A18F766A4F788D0B5B5458FFCC73AE7FED1E1C04D7E661D44089DAB6987
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1276
66B6561C345F4984F3F157E1CCED47ED5631413B76474AC227F51E070DB3DBC6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1277
9491979366EC67BF5B58AAE64536791DDF799ACB35B5150120BCE6039B9E2B3C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1278
10A519113758AB57234ED0A65C93F5FE31F43D9A68BF854B74119ED124AD73BD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1279
16867EDC7EC72D90F6A9D5F92C9DF39C4E656D10CEEDECF90BCE0A2FC0D0F061
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1280
A4BEB82CB5B80BDE0B88299FFC951C81B0A911A640CDD5DE95F49DA12DF4F450
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1281
4DFC6BABED6B763AAFE899AE391C95EA11BB8651D4CC8F726DDF691D68A29778
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1282
C2E0126C7D43045437AA04551D3678D3B0B489C4F011DDCE04EA99EE049F1841
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1283
7FAED59BEF7472AA50F1A907689D55EAA79CD318D0CB64B5DE013AD23FCCD985
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1284
DA0D9FEDFA0E5FE24A74FD4004022BD6336B4504DC748170F9ECCFD748AD0DEB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1285
B1927F19412A1CE3839CE17CFDD9D5B75A00508B3F834E89D661CA49CD0B2644
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1286
E46BAD173B124969FDA2D2997DF28EA53FCDFA8EF90A58CA8A1189EFFDE1C05D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1287
B309373DD98A0E6AE0A78D9010A9213DD5C00445F9F3AD02D7D27772D5B3FE74
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1288
51915B6E3A2D62F00A30CC12D63309D7D1AAAC1B3F63CC1B4A7F9F86A9F7F501
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1289
DC057E9F9D496338FFAD12FDF008AAF5F7468F5732CACC68551CFB79A81354E2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1290
CFA6DADB0D8C1B55A3E76177F22876396240FC028BCC244CD579C3EDD4CC1827
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1291
BD83D19CE2D601AC195FEF8DC83EA390CA8994A1B023A3DD687FA1F34309A5AF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1292
BD413E7FBA11C14EAE026361A73B15A73C7D996F4277EFB81CBF47B45E42DE92
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1293
5BB41B1831CB5244B8FDA84ADC0A385B5B0AF56071DC5328B4EBF8AD10794635
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1294
62A25213ED5712720ADC12AC9C9949ACCC70B0BF203F5B20CFB472695165737B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1295
CE476E46A90CFEF299D9CACEB0C201C6275647B1C13122AEA330474907F82898
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1296
2A973D904FCA51DC76CE776D22E29AA16A34D5F5726B48FFCE740F6DD32005C8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1297
18FEA3FCD32A40A21F6D10ADCFAD8D71680FD430CBB25DA32A9F8190ED1DB32D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1298
A860D10063E80F6C35E0AB67BDB6A48D9BCDE145B0393265DE3264A7E6728B0B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1299
30B4AA7A7187786697D14D3A872D0018C1A6E4C507129E80751000025B55EF8A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1300
FC82E6D7178B4D88AAD67BBD5805B78F07238C092D4F66984D9E2B30DFFDF499
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1301
323AC5F0D66C45EC56A22DD28C8575E2E0A79AD1D999215D31402143643B45F0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1302
DE3522A9B77D1C7A3A0952939FF49E850FC5732D8F3DE9FE2C5894180EA559C8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1303
9D765620005B53AAC916C622752BB5B89B235B4AFF5847D79DA903DC63A61CB4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1304
9CC15243CD91A5F630FADAA2B18DD53D47C46D03F6DF6D9F9714F5A6276F4AC5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1305
881889E6978BDE4B668966F50268A8AE3544E5EC0C180134660265ED3ED0056D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1306
CC6C8C5B1131F09B123ED3A30F4F66B9D543281F1DA102F1AF10102BE7DBF169
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1307
0529DDAB30A9D3F3229BEF61635DF44920A81AE0F51A94CDE613D71F0A390A5B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1308
6BCBB27A0B5D903B5B36EDE600DD337D7F8D033556BA91EA4B9E219CA06951DC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1309
B22D5D48CBB3350DEC250430F610379866ADABD259ECE2690E013B586381A2E8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1310
37B7F0329E49B4C77634B145AC536D31E4DC898D004A444B91BE1773F27511A6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1311
EA602CE23131009BB2EF282AE6192FA96EC332F8C367B7774B67E656B7D9369B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1312
30C103179C5C4014517FA61E67BA37EF2045F7DB75B8BC35574727D7D2B0AE35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1313
2201033C51849454205F5F03FB4F7013E501E939A6575E0A88AD8F5AF850046A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1314
00002BF6BEB09160F4810BCF3AFFF7DF9E7489C0BAAC3DC8382562A649138FBD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1315
8C03984BDCB50246A5CA5ABBA1DA3B52E17D8646BCA357CF8F953D6E544D4086
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1316
1922FF9B526BC4CD28CB4400992CD2D171B3A1E530F27886B70D1A09C8AB416B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1317
ECB957171D0422C8A3E22845328E15D8B4DEBFF2EACAEC2B7B87A246EC52E3FC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1318
AA9395C7969ACB53C0208F761AC7952AC750403FFE9AD505562B52C37035BF02
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1319
4B69679BEC2D99FCE838148AC18A9C7B66614F07219C27C798709B7EB547E458
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1320
409F298F8D785145030DE7B04D0B0CF063D8A52EAA8445988A3D56A84755F473
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1321
7CC7137451275A5277A67B0319493CDC9FC3BF8A044B49120A4DB24427FDAFA9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1322
605D2F694C14252181C916322CFF65E89F1204B763BFD71429AF8453420757B5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1323
9628B1E88FF6DC865F4A2C8F2A5B56C546FDC866418A8C4E2F553E280BDCC690
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1324
770CE5C795674A0BF1D91322F9ED93865C156FC0F26FB37DB11A19BF933C5D4C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1325
E06230764344BEA35CA0C373D6BD355B3BB33431E870558DDAB64E9753BF51D9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1326
84ADDE6DA3E7153EE1CB62D87B581C6EFE8CCD5ABA12DBA85F88B576148F3B90
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1327
5D4D5247A654F0B9661B3DFB7E64108B1CF0FDB54053A4C8C7DB1518001934F8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1328
FCE735E41E8DB3B0D262491B8F99226EA9A7D53F57C45E96D923A4F5DB70AEAF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1329
C2319396CBB34361FC3127778A9532AD6DDA383C054EC66CDC2FC4B721D91EDF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1330
CDC41741107FA1F2B1790D1301413EDD316E150CA78FA6064F37D6E861E9C7F7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1331
DC68D5BED811E591E943EC6075BC28BA2255C3A8AF78C0FFAA66E419F13308F4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1332
6E9DDAA5BCC2392EFB7DC428D4D0C02DE85D7D817B2AC7BF147FE116D78B553A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1333
8E5D97242F4CB876E8714F3129A738A97C87FA74195FB25632D7B9F1150989C4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1334
FB47E8F53FA3532C0C1C80B218D9CBBB3DBF4C8E2EE3F678B52A8938B11B8A1A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1335
3F5A5A12A9DEA229F6F46395074344853E0C8C5DFCB75AB1CEE296F4D0DDA749
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1336
460E4A7D3509D652CF699BFDA5C0CEDA5FA37B14FE27E63E14C8B086265114A1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1337
5890D4A698A926C556609A2945C0A0FB1191052674731318F40DD5389134D0A9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1338
28174D9E62E6666C0F3D5404CC02D3496E09E24C3C6569F9E0F571B10882FB51
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1339
189BE89BB40D4785C77B46B5B1A2B2100804169DBD745EC72B0CD11747BAAE0A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1340
2630741C3D9FCB0895AB91FFADD9E0417DBED8FE3A9CD1934F027CF89E0953BC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1341
4E4EEADDE09BF03864666976A9E2767F55D28E27FCEDF94A89893DB833AB55B0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1342
C032380A851D80C78F2ECB63A2BAD5D3DDB02439FC64A5DEC2C0C1B41BF0760F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1343
0CF6D654898119F9AFE2C18412AB91650F6582756A3FE4CA590BF665B3BF2CD3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1344
79EDDC1B8D3DAEBB8E5AD3E6DFDAC57265E2E4B293BC95D561734B14959B889C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1345
0A336506ACE8BADE4470D37F5777FE74399AF45A2FBF18140473080B787549EF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1346
DCE93E30D2679353D50D5EC7A9A9A8373D74A59C5A01FAA002CFD455DA63F61C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1347
C09BD1DE5155FA9DE2F42B0CA08ABC391B2B5A431470E3040D2F15A65E0464
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1348
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1349
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1350
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1351
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1352
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1353
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1354
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1355
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1356
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1357
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1358
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1359
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1360
%%CreationDate: 1992 Jul 23 21:21:18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1361
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1362
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1363
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1364
/version (1.00) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1365
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1366
/FullName (CMBSY10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1367
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1368
/Weight (Bold) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1369
/ItalicAngle -14.035 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1370
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1371
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1372
/FontName /CMBSY10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1373
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1374
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1375
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1376
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1377
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1378
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1379
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1380
/FontBBox{-27 -940 1332 825}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1381
/UniqueID 5000762 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1382
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1383
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1384
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1385
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1386
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1387
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1388
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1389
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1390
A8CD93F7195D5A07BA2F18CB3FD5FFEDA4D83BF758062134D84AC0100187A6CD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1391
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1392
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1393
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1394
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1395
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1396
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1397
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1398
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1399
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1400
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1401
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1402
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1403
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1404
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1405
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1406
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1407
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1408
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1409
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1410
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1411
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1412
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1413
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1414
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1415
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1416
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1417
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1418
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1419
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1420
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1421
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1422
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1423
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1424
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1425
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1426
%%BeginFont: CMEX10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1427
%!PS-AdobeFont-1.1: CMEX10 1.00
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1428
%%CreationDate: 1992 Jul 23 21:22:48
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1429
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1430
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1431
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1432
/version (1.00) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1433
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1434
/FullName (CMEX10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1435
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1436
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1437
/ItalicAngle 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1438
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1439
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1440
/FontName /CMEX10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1441
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1442
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1443
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1444
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1445
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1446
dup 56 /bracelefttp put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1447
dup 57 /bracerighttp put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1448
dup 58 /braceleftbt put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1449
dup 59 /bracerightbt put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1450
dup 60 /braceleftmid put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1451
dup 61 /bracerightmid put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1452
dup 62 /braceex put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1453
dup 88 /summationdisplay put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1454
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1455
/FontBBox{-24 -2960 1454 772}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1456
/UniqueID 5000774 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1457
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1458
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1459
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1460
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1461
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1462
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1463
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1464
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1465
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1466
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1467
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1468
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1469
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1470
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1471
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1472
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1473
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1474
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1475
4A978B98483A63FCC458D0E3BCE6FD830E7E09B0DB987A6B63B74638FC9F21A5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1476
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1477
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1478
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1479
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1480
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1481
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1482
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1483
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1484
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1485
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1486
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1487
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1488
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1489
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1490
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1491
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1492
882C2F4B63BAD251898BCC685375E570DBA2C04D3E872E2BE6B9203CED0D1B26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1493
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1494
1C04C62B3365A9C659D15184ED588B4CFB1058533B750551C0DA0A1905D05464
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1495
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1496
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1497
500C61BA95CAEE78EE77A3EDDC18DF93A39C90B9B8A46C98645655592F74DBB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1498
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1499
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1500
2369A4DE0DD5C86591E9434DEF0712D2C94DAACE050342DE5EE1DD8F26E61487
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1501
584ED5C920D3A2F9E847A1B95A1F447AC25BA73C51B8C49A8020CEA53FA2E798
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1502
2A34B72678DF15A9D68D2081ECF22AD4C2D4B595573D3E5669A5BB6598C106E5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1503
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1504
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1505
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1506
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1507
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1508
412FE717E5F3F497CAC904547C40ABABFAE91F27949DBFABC7CD202934B52C43
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1509
A84A7D78F406B7AC6C08EF1BA039297D21421F56E7E11B9E6371893718AF99FA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1510
577613AACE689420859429DCC763A560E9D33EB916B86AA6FCB152E09716FCB7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1511
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1512
40A8B0E7333A8F5E127AB78DD6E3D9B657325A789F66977C2CBF700AE95C73F9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1513
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1514
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1515
8FA925408C0C610948186A51C654D822846577405B76A798877B03B72A14F4AE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1516
230E6DCA55112699A001AF1B18D754EC91F1DDC21263714CF6F12EAF5101EDB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1517
55AAD1C7946CA0BF585B84DE0F4A3A331DAC2CA46B33EE3E39303D00CD7FFF5B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1518
95B93241312DFFE16F96A6F75AD4D2480ABA8A4274F149DCE287D10CAD57C712
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1519
272AE67B59E4EC9EA31DBB4C052B03C7B89F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1520
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1521
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1522
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1523
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1524
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1525
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1526
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1527
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1528
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1529
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1530
%%BeginFont: CMTI12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1531
%!PS-AdobeFont-1.1: CMTI12 1.0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1532
%%CreationDate: 1991 Aug 18 21:06:53
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1533
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1534
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1535
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1536
/version (1.0) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1537
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1538
/FullName (CMTI12) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1539
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1540
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1541
/ItalicAngle -14.04 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1542
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1543
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1544
/FontName /CMTI12 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1545
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1546
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1547
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1548
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1549
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1550
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1551
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1552
/FontBBox{-36 -251 1103 750}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1553
/UniqueID 5000829 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1554
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1555
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1556
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1557
3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1558
532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1559
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1560
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1561
D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1562
525003F3DBE5BF07B2E83E66B7F97DDD7CE0EEB75A78BD9227BF359D002B6ADB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1563
8AC57A33FED4EF021A7085B1E2B933DE602F0FF71467ECD501744AE338AF29A0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1564
26F7D368AC6F25CCB882DB7B7343566192BD687E1349225982823027D3B66703
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1565
3B0DB7A7E680A682B98023D39C7FAE81A5D5B867A0A66C8AA0DBC83B1596A84F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1566
0436AC6A7900B767BDCCE0060A4811003C79FDCC71D73F7F2D0A6675E93AD21A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1567
56B4CD8EF75EED3DE8C0A18BEBF7B9D1BE72504872D56EDB272F1E97FC726CB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1568
68C85C713059DA19F6C2E0F3E12710A59B6FC4699AE883DE8C8615B7292AC25C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1569
D5714B6CFB14EF0EF11EB13009BEBA4F345A5D3D6D9926ABC2BAD7DB1328651E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1570
437BFB3C46DA7B62219660FC368CF3D3704DAD3AB461C28F711665BF484BF61C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1571
052093D231CA65618EA463D63E406ECE858D180A6C0589B2FEDC321371C28E77
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1572
DE974D655DF5FF7D41ED01FE717D928A885F6FA6CFE4D2C0807F8E7F937916E0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1573
96EDD1A3BA67802B1F4A49100E75613BA0356D9DCBBAD4DAB3C59E70A47058F5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1574
2163D1730F0EE4D1F87C3A4AE723A23CFD7986FC4FBD399347E9F5946354E013
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1575
D860FC446AFF0B0744F5DA27CC777C96ADB388D1E835DDCBE123FB517679B9B7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1576
EF696E091A9D51510BE264701A41C04FA8125A48F306ACA7A83E35D5BA0C296A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1577
BC594ECA2CB27E92FED95B595C21E5BF0DA724D40761CB377BDE5FB98C9D152D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1578
6C0DC98C4083E9656321BFC445CD6FCC142DEF16E27DD6FAD0B3185223B1A7D6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1579
779F39C70793184F2C3B721FD0AE6D8E063BD47804785DAEA74AF8C75483B713
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1580
6506165055CD1430305941C5813EA8BDB4832B3A8BEDBA91DF61C9B419499D4D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1581
AF7C963D310E2C7E1A518F02ECB659C98DF4C85AB936BA60DCDD34876F39D496
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1582
156BB1D255FBFF4BDAE741475D832B26C856987EDEACCA657E02B639B51D49E5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1583
90B07711F5671EE3238DB9D65DFD5E754AE2169D9496BBEA59461FE7727BC69D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1584
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1585
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1586
24856D394AD5E63B25733FE09A8C3C666CC8A64FD99F499D40D6228A6238BC6F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1587
3A911B5115CF7CA1C35B7D2BCF64F1D2F493EF6DD1A35F5254DCE35890FC0C3D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1588
9559CDFEBE196E420722FEF2A069B21127ED777FCD8F16EC42F1BBFAE47C3C7D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1589
CF69CAE2BCE88BCE6D6209003DD375B7179E72FF5569D4BF61F48EA554EC93E2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1590
AA6B34F8C8C3D284F59163830163F79ECA604121F302B6AC2100DDEFCB16EC88
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1591
7213D4C1A50FD6812F87E141794710B486F7FD1397BB9C30C74A71AE92AA3695
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1592
F044A1915E1382FCB0014AC0D3E99B81EF0BD4BD76E0FA30145CC20192A8116C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1593
3F8118FDCF9C435204A62F2A1E83BA523EED32B5BA95700622C01F7F967EE294
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1594
276BA0E7C69A0482950F448B979A41828D6B12B5E6AC43B858398EA55F73FBB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1595
26891E76A1482C6DDAA342C1A3AA820AAC1AB929217ED7A1CDA01D60963E57B6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1596
1BD432BF4056F68CA42FDF5F18A7CFED79874BD4DBC6FD3B35C981509D418136
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1597
A9270E2A10EBE47D765316AF230A6B163F9C6680182BACC5BE0A3058B76C26A2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1598
DB53917DFE062E25C7BAE60B76E10709EDCA549D15C0937F03C764F67987CA5A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1599
FD1448002CBF50EEDF9FB48420E428CD0ACEE827EF5BD787DDF8A1818DC179FC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1600
D456F5407CDC66D62E0CBFAEBE33ABEEF8E7DFD5537DB011982B6D4BBE97C603
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1601
21FFC4CA284D58D691AD00828A45ED0977934283E2975C73E72F40CF56086FCD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1602
765A63351A467EC2934FD8F589AECC3C642F150609CD9D57D37156E2ABC312CB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1603
FB74EFBBD19ED616CBA9F4816C5C43124A471EE1878F43131020D9C412EB6616
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1604
A127925DC2930C85664F69A5E3FD3F0E309BFD1B2C12EDA9C306E8388154F65D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1605
1CB5F6BD4EBF0CAFF85B71B918A6D484CA516A4E9D1622807134B70339670CD6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1606
6738B1FEF6ED55E4B34ABDFC895F12CD274BF400CB59252D2D89A53C2BBF3FE7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1607
6FE7CB1A22362F48895F708C0B9B8D337843A72571DED644CA95947CAA30E039
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1608
FA4D92805AE2EB6038D47ABBEAB734B84DD328BE04AFAD44044FCF73ACBC872A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1609
94E0A3DF54E3BB5A1651369F49A0ACABF563D99EA8DD5FF8FDC25F1AEF22A778
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1610
C3CCA8EFC27E8D5A09AAE53A75323B2242D7A90F3E95E79739FDE2EF0AB8CCED
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1611
EDFAAC033B3F30C70896C5476F848C7725E7D41FEB138D57EAC8349B170ED1A9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1612
C7942F505B448638C41C42770C71AE85FAD42D28B70B6F239E4A22ED34AC2842
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1613
218B9B7F2873C7F506F524F1C9694C0F9EAD60C373AF0FC4427B72FE05527369
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1614
3B4E89E9754A0965F83765EA0BB93933FEBA181EE2B146A50EA42CFB2D7D86AE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1615
17592EB4800B0CFDB7023DBF884321799F0A17D31F563AAB1146C8E1A2266285
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1616
7F534DF2570B0B11285570C6360F1EF95D3FD9F23316060374CA16161B2D20DE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1617
8A7B0E65491BBF78DF1D732949C7311EC4FFBB683349E15527750A9B27C4E417
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1618
EAA25D8961DECFA7A2CA45AB2AF0F8E6B65DD8C6557BF244F8FCD3D290F9E881
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1619
976CBE6F1088F8D0D77864C8D2E5D4C814CFC0DD061CE01CAAE307ABEA03F24D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1620
C3E7D0E8DE72804B3E809FFD5E1AEA18F30368D6F44CBCABBDF2E25EBF8F3B79
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1621
07FA918238ADE92C689E221B04EDA99AC82A2DA5FB9E4B79F652D2B1C76A6761
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1622
59E93AFC467D1C1D184B72D3321B45A0BCD7E3832547FD7E188F7AB8DCC8A31A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1623
21362FF0C9EDC038C9BD97FDC7FAC046EB43690F4A307259627D37B7AFFDFE13
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1624
3323D22CE53D7ECE119CBD846E565317B661BDE2BABCB4C741A5E2928B21EC69
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1625
EE0BBD2E95EB445CE7468A3C49AAA05CC4D71E5151B3E8FE4D083833A63BD1C0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1626
A2802E9D5245DD9DDBCF17CD152796E0B25C3E1E139ED27BC17B2254E869312D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1627
C1CD9E23B672E95081F19EB2A944D5ECE09418E462FDDE0BE52BEFFF750F9550
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1628
84D97E7BD8C9BC2254966DB0076BA4AF9E4D4C17107954EBA5A443136C5E833F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1629
400080D557C81A74144CE2684C5B880325DD8F1F46CFCB6A2141886F72D458AB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1630
956EC1FA948112B45D0A6BA8D9109C615DD25D7D0E0E63CCF08FFD02E57D0168
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1631
D392904E7F0105158885A3D27F4EE4BB1C852A4CA3CE642F8437A8E4349FB1CB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1632
4F7F395AC011354CF9DDED270E76941F5E154803ECF8071FE81F97D87D494235
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1633
965C3A15592B3BC875CC61A96F7789FEE005295FBAF9FF791C3D786E9576A384
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1634
C87F0C762618B1B5870C2545F357F17B9EA745DCEE514A0A7DF9245499280C8E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1635
98E3FE24327B75CEBCF4E767692D4DD670A5EB0BB4F285D57CCCFBD2836683D6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1636
65C7CE73EB96F1B371B7C8E256F3BDCB14A1732B28BAE44D1F2C8FD73B10BF9D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1637
5DFB41F493635A07D14D16064BBD5E136836E9C0AF7F0398B1C2B836EFFEA517
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1638
71A5102BD3A2D43FA3BE41B1B0D728E7D3206D9CD112D419AB04515051899BBA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1639
CDA524535E3A139E60C2157F1AEEE84E3C6A7CBA48D47AE1EE23C8825B4A5651
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1640
3FD5BA4E8D36D4BFCE02AD80A2801CA7184258B2A9E0A11B1E7AF262C17D17DC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1641
23527DDF7848B139B10F645B60022E755137BDCC72870FF2D962E0099D4087E3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1642
06B966FB88AF83C4A113728471048A8D2B1B043CD9B14BE2430CA6E41F4CC674
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1643
10F14CEC66FC0032D9B0324A946909D957B8011002314080296A3D7270FD1EA9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1644
5E4796CBF1640BA3FED68739BA35CB4FCEED6FDDEAA49C56A697C55C11BB7CEA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1645
61351288A39ACAF3DE7532DF6F9236A35C42D7C6171053CD76AD990A1633329D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1646
1330160138953911C0A1AB1AE87BE040A6180A2B836553F71D4D6460B5E8AD7B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1647
5036FF166854C4BA98C8A3B9B9D7767D3D580D1163A93881ADFBBB6B6120DF4B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1648
11BD6401DB9AE68EB8EEDBC67D73D0681D97376778C192626FB25745B95DC03C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1649
F4E8F6E6A42C4FAD12194583DBEC5BC0798ECB6C4A5F4EF40AE1AAF7DB06EEB5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1650
99F2E0C6AC662D4874885E6A30CA6D735AB0268D56301681A14A6F94BC8D7B03
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1651
86C61520D5FE8749000B1C2DB39884C7BC98ED8611A55F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1652
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1653
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1654
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1655
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1656
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1657
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1658
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1659
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1660
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1661
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1662
%%BeginFont: CMMI8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1663
%!PS-AdobeFont-1.1: CMMI8 1.100
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1664
%%CreationDate: 1996 Jul 23 07:53:54
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1665
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1666
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1667
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1668
/version (1.100) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1669
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1670
/FullName (CMMI8) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1671
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1672
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1673
/ItalicAngle -14.04 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1674
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1675
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1676
/FontName /CMMI8 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1677
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1678
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1679
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1680
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1681
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1682
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1683
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1684
/FontBBox{-24 -250 1110 750}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1685
/UniqueID 5087383 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1686
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1687
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1688
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1689
3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1690
532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1691
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1692
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1693
D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1694
5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1695
4391C9DF440285B8FC159D0E98D4258FC57892DDF753642CD526A96ACEDA4120
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1696
788F22B1D09F149794E66DD1AC2C2B3BC6FEC59D626F427CD5AE9C54C7F78F62
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1697
C36F49B3C2E5E62AFB56DCEE87445A12A942C14AE618D1FE1B11A9CF9FAA1F32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1698
617B598CE5058715EF3051E228F72F651040AD99A741F247C68007E68C84E9D1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1699
D0BF99AA5D777D88A7D3CED2EA67F4AE61E8BC0495E7DA382E82DDB2B009DD63
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1700
532C74E3BE5EC555A014BCBB6AB31B8286D7712E0E926F8696830672B8214E9B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1701
5D0740C16ADF0AFD47C4938F373575C6CA91E46D88DE24E682DEC44B57EA8AF8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1702
4E57D45646073250D82C4B50CBBB0B369932618301F3D4186277103B53B3C9E6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1703
DB42D6B30115F67B9D078220D5752644930643BDF9FACF684EBE13E39B65055E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1704
B1BD054C324962025EC79E1D155936FE32D9F2224353F2A46C3558EF216F6BB2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1705
A304BAF752BEEC36C4440B556AEFECF454BA7CBBA7537BCB10EBC21047333A89
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1706
8936419D857CD9F59EBA20B0A3D9BA4A0D3395336B4CDA4BA6451B6E4D1370FA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1707
D9BDABB7F271BC1C6C48D9DF1E5A6FAE788F5609DE3C48D47A67097C547D9817
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1708
AD3A7CCE2B771843D69F860DA4059A71494281C0AD8D4BAB3F67BB6739723C04
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1709
AE05F9E35B2B2CB9C7874C114F57A185C8563C0DCCA93F8096384D71A2994748
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1710
A3C7C8B8AF54961A8838AD279441D9A5EB6C1FE26C98BD025F353124DA68A827
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1711
AE2AF8D25CA48031C242AA433EEEBB8ABA4B96821786C38BACB5F58C3D5DA011
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1712
85B385124F409FE733070651C9B7A2D6E683A2BFB681080792962AE48EE5B3F8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1713
820BC9D61F438E027AC3EECE10A7FCDB529C856728E86A8025D8948EB0F9740D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1714
1BAB41670C54AE8925698A6A197B742196487461F7DCF7B0F53E94A3B37653DB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1715
5AFCEF96E05DB75B724F80154FC91C8C08313775EEB7ADA99399A20868A061F2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1716
E758C49383633ECDC5A408D25937F6556EEC505365FCE73745BE8578229C92A6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1717
12A4678795EC2A4407445222CFBD0837A31C421DB9B03F92FE3FA72193D1C65D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1718
F69E9CFD70B658B4F5F43129259D35A83360363E8841758AF61DF261CE0A82F8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1719
A5A0D3FC91A95C52C118B02386AF037DC75FC6A3C6D2D25FBB80C0EAAEDE0A90
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1720
6DF9E23B18C238C8A4662687467EEA19643150ECFAB377FEDCE630B7D135E079
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1721
6B7F0BB23926CC6BB9AD8F6E7F0C7705EFE760845C1E65F0AC6AE2B18A2B4CDD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1722
8DE291E4880F20FE65E0AD26A4C5B27B74BB4FCFBDB787E29869A8EBB6EC7ED5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1723
BB72CF73852F836B3BFC6355086F6A210B45056B9C3D8A0A2BEF49D119A6A7BE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1724
D6F617379DD0D6A467C416BBBDA2ED9DF4ADF5AE13E344DF608358C6DE2DAB4F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1725
989A2258E664FD0EDAC5C0E873EA27B64FE1DFAB4D03F1747F9FF11D75076BE6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1726
C7390F000890FACB9FAB28118A9867BF50CB37CFD50F7541C53DDE4E9E24E898
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1727
E5F8013278BAF060F416A18BEB37D50410DE02817988F4DF20D557EF0A026946
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1728
EDB6F2E3627F1E6AC26B178724B4343524E02E533491295EC532C4D896A38C81
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1729
6EE508D6F9CDA8DDDE8372222BFD274D26A5969F0F38E622B0FB3967B5CF27C9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1730
AB9FAD864C26219A662985E2282EC6E3B920CD62828458F8A67AE7D26724ED66
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1731
8F68B5492ED92F4E035AED8A9AD60FA22577DC7D7350A90D63F771964844713B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1732
AFD5C85ED0C3FDBC3F3C2DBAE3E578BA78A9B79E09132CB86BED3EE46CBA86D1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1733
784D3D1AA674AFF374EAE08628054F185917EA3A9F03701932C9CC44B6685EA5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1734
57C276AD9F7CDFF5E4C75374935B0FCF3BB87027FF75315181E02DAFFF2DEF22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1735
E1B01499E82D56CF546DD27273AD0D585F290C4F54115D7AD5BF508C20EFB0AD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1736
33A20B023EDA3F5D430946A3026DF418B626C5676D613B03CA34AF1F9DBA89E7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1737
A4E48A754BD9E03A7605EE37F20D162D4BBCC3734A037CC81188BABCF691016E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1738
7B9B9888742CD6D71C04F38762D1431A660773E553FA3B6CE5D42FC89AEDF9B2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1739
96D2DB8B65E94C425DC5BA65309CD1B247939D4FD70E9175524DA0A334DBDF2D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1740
72465A5A87018167CCD26DC491D7E9519C67D6D135C485C45DF9388F5747BD83
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1741
A4B64490EB211AC050EC0C906FFC9687F5CA42875E9938112B7BDAC56546F9FC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1742
084099AA0864BF7C789CF2218CF7592059B02DFA9DB5600BC10CE4BC76C4056D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1743
DB7F88A52D82B050D82EC132F835D194A1C4EE98ACD2260D234FD25C9F5A1A20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1744
A666ED5C5A7D26E75B9069C860928739B5851460B37E73AE1AD568C071A88F3C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1745
A3EA67E6DBF60156F3DB90E2E390D5115EBBB918C67AAB291DE9B2E79E2E501E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1746
02547B4A9BF1112286740E9ED6FFEDD9781B3029C4FB95B480B86F532569784A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1747
61D8FE161C1B9A9E8A8DDA8A8411E244CA11C210B38D90C5803380DA4AF29382
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1748
D31C7B40C022005B866BA920A50FEF87F7FCBF02EF5CB44EE712391D2D8A6028
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1749
99E20908FDA20065E1F75D114CFC64D8EDCA860669961FEDC7E8883ACF6576C9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1750
256EB11023D756A7EE06DDAFF16B701633333EBD5A635ED4E320724F643169F2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1751
800CDC46F79DB8A69CC6DA7FB1E6B370EC8C9DAB9FB2C989E46A924BF183B92C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1752
A4C7C042E841232FE398586CC7EB55B14D4200B65353A27CCD066F2175F9206E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1753
553F6550A2A5CC8A701EC01CCA4EEECFDAA9E4065E6FDB8710CF42D80303B88B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1754
A7613784015CC08BFBC6524993479CF4FBCB223E714D2A47A34DAD4B0FF35147
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1755
348D0A6FD407092D7B218106414BE9FABD0921104A2F3A8124AA5E3DE161EC2F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1756
70F86A50C9432A0935200505F56DD433514D0C94D72922C941C122FEA1051403
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1757
D913325F733D9DEE3D7F3334C422E569A2ED3C47CB53BCFE21CDD39FF6D5137B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1758
FE1664C591846FFD8433DC240C95D90AFAB0DD29792EA8345BDFC9EF17230967
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1759
9F0974FEC656E93F64EFE7589BE7FD159DC167E0DC1C46781EBBD9A51D48DF27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1760
462B4D1F491A4D671F0CAF11E7545F78F2E0624006CFE650BF435FC8FC2A7992
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1761
5C43B7F51AF90DD5BE9A7B08744C681459D8078A61A14F556DE2926907DF7B6F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1762
C037CE01772DEDB0FFD81A298FEBDBD2196AF5EDA93AF7D5B5E96C4FCA5A6538
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1763
B1A999956633854B5900DEA2BC4ED3D89185DE9EDACD18EDA620D4A6337853DC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1764
352C0BFDC6FA40B3FA7332B1189EA2372DB4346116D6C34F68F1B7422EEB5453
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1765
5456AB3377FCB21B440322996A8F99EF4784167AA0316665B14A7862EB573310
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1766
86ABBCEFE41B39ECDE38553380DC808E7E821F646FF5EB73776C25084FBA6432
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1767
4A5BD37F30DCCCDFF78D50E6A94D8816BC6A3549BC407C2D9290778D44A6BDB8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1768
F2F2812BC145AD649586C9014C4BA89945CC0FFB99C311F7F60208600AA9A803
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1769
DA78A3CA0A23A3F2B87FDE73D51310635DA106B4000FAFD8D7FC830EAA57DFAE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1770
5F2D9A08CC2D663A6E1FCF075ED17DD7569DDF2F0939C642989C85F475A9AA1B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1771
30D5B7ECBA17C9FC2367E97E37B79B23BFD20082811F75DBBC3714257D309AFC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1772
217A352E802B5EC49D19306526E27AAF4D6EC2D0CE4DB379D5FF9298F878A999
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1773
06EBCD32E4E1336ACB9E6558FD63DB6924C8C604FB4C725AEC0D00CD27CB00A4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1774
48ECF6464EF9A6585D4C48C4DC5743FE01F77889934FF05CBF5A5AAA110A0D7A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1775
E3DC96EF096228D53EF63A752118CEE758E3B4EA072434C99CE5A80E34BA2328
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1776
E8B4BF9915226EB470D2F07B6667E236C644D90BE033E9DD1FF1C8DBD118CDA1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1777
CB1A40478AB4907D1CD6AAAC0869ABD917C5E7B1A71FE79488FE16F48AFB22D8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1778
207FF6C4D6456EA280F1CF924671E4E11220EFEEC49E547D764FD6F7DC3B03D0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1779
38DC4EAC7B3D3E5161F3CF10E62531A8C88548AD04A4E64CAF6FC648238E6AF1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1780
C07188AE52FDA6CFB83F975BB9F78B94A600A82CAB470E333C5E3F66B43FDE5A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1781
ABAC621C1C158B0265D10C20ADDE8B3A91CEBFCED8864060265DFCF65FDF47A8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1782
FA5A55F153E43DD7D08D18C2BE1E13B9BD9D9DBA8679943B83749D7AC27A2210
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1783
8AAFB25C425DE39C9EB74BD0615D4ECB7B2B88D01C694ACCC711BB687686CF83
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1784
6530F6681C91CE58B14E7267E321BDA7878F2E843A8A8523BFDAFB66402223C3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1785
AAA823E5337C21B9B6BBF91FD2D16387DA0CF2E5B440510900692A1D941429E0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1786
68F62E5E8374D3D55D6ECBA044CC7DA50FD22F447C76EB1299249D6F2850122B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1787
9F54D7B21692CBAFD00DECAC0C775B745C7EBE1336564CC4D05208087C33F584
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1788
188703D73B2C12D023F5F821706ABD93D7F9227682D871772477F83773F8FA78
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1789
CA5B9A1A7B1663960D58B5673CCF9ED40F60B2BBEBF61AC5322AF56FB683C114
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1790
677D292978E9EA4FE621E00CB0980E34A13ECEA5905A6150DDCCD826AB7AFE74
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1791
DF462EA0FEDD0195DD34F073878F19C2981FC4B3D71E647594528FC7AACC5D18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1792
FDE91646D19289A9400A626BF395C7DE1CDB2996E3F9DE9880A433BC111D5B31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1793
8332DF2D4B5975D29319F75A764C31B6580210D082DA1EC3D23F674BCD955982
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1794
19EDC2DEEE18979E3FCB9E308075D630E8D1DB9589FB82CCDBE7B5044740F857
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1795
EB4ACF1964B91A654E85FE7C1D81205E238A62041825EC820F6073C0A6E4531A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1796
792CBAD8466CC895E8331A750209136C2B9645E8B011EE3F566759D644BAD46D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1797
4DF543EAD466DB7A94CA21A617B3FDD06062D984180E0FDC00B4E0E6462DA4A0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1798
B6009352F1DAE2C798B09228CB4DAF70EDE9F947406814EB1AC8347BB647C6B6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1799
71FC2C0564D8AC2337E43B257F42D2E5AB72E90D5CA6FC4691C974B85E1346E8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1800
3AEC45511086E40677D9379396ACAA0F18262DD2A13377F8DD93CA31AF8B34BA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1801
C34B09BF79239B8F7F29EBDB3C3D2B165B3024E013305585778A5D738FC6DAF1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1802
C61100A1286DF275E751E5315C4030A621723A39D41D418C5EFF417FD72814C4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1803
4E036349270C48C15D75AAE80CCF97FC484BE3027B49C237873505ADD46280C6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1804
00CAAD68E99B2391B062C085CBD8D0184E9BDB479A1E6490CA9E8D376ECA6919
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1805
C4D8A169C75CBA9E709587579D6886BF96FFAFB682E6863E0BD138236388DAAF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1806
7D64E649204B7A1C6FC224D36C53E5DBF34B22B9644442156D8F5CFDE07CC59E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1807
1F1A867CDDFDA80D52E32DB46191107D8238C5E1A06BAD964548463AD011C0E4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1808
A44ADBAC88927E91923199A64A04B118965833D4FF4E1408AEBB086E0FC3418B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1809
75D644EA6430AA1E4950CDD3823B1D2363EABBFFDB23F58ECD990247DBA7E4A9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1810
0103ECDB8970478C23B5700C351E17B4D4BE1303E9320050FC651EAEA684D24D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1811
DA4D91BEC4B5D12EEE2EEBCDEB18C7951961A1202FE12FDEF1FE286CC2E3A0BF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1812
C9DB9C55FD16F0A7E8BDE50819891875657C2B867704FAE7E0EEE20DBB445CE3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1813
B7CB48D20BF8CC14ABB1310013472C9B919AED96B7FC4205C09FD98B5DDA07C1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1814
DEA9CDE6983E579C72B03506B10BC01770953BEE9BCC403BAD053C4822A85FB4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1815
245DB868CB4B82BB4185274ABC3DA78207E4811D5C8696277D02B5D80EC22DC6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1816
491FF010A925BE7ACF100A6261E04071E939D1A86B87C1C0C33BE53FE0E2DA1F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1817
0B96E84A761045
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1818
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1819
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1820
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1821
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1822
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1823
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1824
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1825
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1826
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1827
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1828
%%BeginFont: CMSY8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1829
%!PS-AdobeFont-1.1: CMSY8 1.0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1830
%%CreationDate: 1991 Aug 15 07:22:10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1831
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1832
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1833
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1834
/version (1.0) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1835
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1836
/FullName (CMSY8) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1837
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1838
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1839
/ItalicAngle -14.035 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1840
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1841
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1842
/FontName /CMSY8 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1843
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1844
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1845
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1846
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1847
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1848
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1849
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1850
/FontBBox{-30 -955 1185 779}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1851
/UniqueID 5000818 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1852
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1853
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1854
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1855
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1856
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1857
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1858
221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBB2A7C1B5D8E7E8AA0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1859
5B10EA43D6A8ED61AF5B23D49920D8F79DAB6A59062134D84AC0100187A6CD1F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1860
80F5DDD9D222ACB1C23326A7656A635C4A241CCD32CBFDF8363206B8AA36E107
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1861
1477F5496111E055C7491002AFF272E46ECC46422F0380D093284870022523FB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1862
DA1716CC4F2E2CCAD5F173FCBE6EDDB874AD255CD5E5C0F86214393FCB5F5C20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1863
9C3C2BB5886E36FC3CCC21483C3AC193485A46E9D22BD7201894E4D45ADD9BF1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1864
CC5CF6A5010B5654AC0BE0DA903DB563B13840BA3015F72E51E3BC80156388BA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1865
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1866
53AD5F3D9983B036D9202C8FCC4FA88AF960E1E4992ED4D358A43D0B625E7B8F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1867
2CB5599132B9E31EC3421EBBF4BBEE085CFDD794E0B4B694DEC1FA0F4659EBB4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1868
8519781FC955ECFB19C20E94CACA623E755471ECCF677190C3C26822E97567AC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1869
2CD723A5F65DE62EF0E103658C4E94456BD12851C89BBB7D042FDAB8B6D01DE0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1870
7B930D1F63DCD59628371A2EA482EB65A6BAC43680C318427A70B844D313DF5D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1871
12D35D89990DDC7033205197EE96F3C0596AB0B69AD48366BBF98E8022AE9282
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1872
B803D6E86273FF3C739031C6C8D90DBD12501A684A2B37AA83D5C9946CF8A671
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1873
76B4B3A04AA295986963279D3B3A30E9F815CE728FD4DCAEE31A95C15FA0491B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1874
54F936970A892E2C72A09A834F40736240602C872CFDA6AF79468AFD10481A35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1875
5E6527A2792F33A15CD2EBA335139CFDA1F4F43B9F3646BE3DCDDA0C799ACEF0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1876
38B1A979ACAE33810F684A2D364F44A77C3B67085A51DF9192170244582F3201
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1877
53004DB0A58D4952A9D6615553F92599238469AA282D6DABC50B0DA0FB785D84
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1878
3F40FE2695F4338B905FEBC0F8B5FC0DA2A9B924C25BBE03CB87E0D4F7FB291F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1879
0E16C58370CEC38D1BE34CA95E305A158F902A7DE77CB0AF321518BBCC89BE81
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1880
1867C8B603D935813902769CB2E7FAF7EABA0129F40156E5B35F8A698194464B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1881
BFBA5E4F12F6D6C336EF50B7EE05B2CB80B723CFD68623969253A157EE2B0E00
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1882
CEAC662C7FFD809A69C633ED8A64DA0ACB640C74B44DBE77E2495E6C40CC44DC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1883
EEF07CB15CA136E69353A19A15815FC945DF68F9F0883D0920148EC50368A357
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1884
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1885
3F69C034B754A575180A3465992D2B78A3EFE66941BE8A4A4D54AAE2BA022A1F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1886
5B5FA60658D9BE08F1004961C5F665274BBAC4C94F9D14BD56E911F421427863
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1887
408D498BAC667AE754B80CF6D0E431EA431961E97BD4C7F270C64A99BC24F97A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1888
7882E5EB5A0371FAF10A16D13CAB75B23E068B8CD528A420D0C49527626F9484
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1889
5269CA342605A606D420108564B66DEC54CC3EAA7D11E6A49A6522C7C7DE5731
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1890
74A674E37DBA9223F9D27233388F892FED220811CB368D97046D529CAF13FC9E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1891
965A0DB8038B071C371675C2457B48E7FFD22A04486C07594E6DA373B2F03077
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1892
E6F90F905F4E1702F4DD117DD7F6454B51BD634CC7763D5C007AD05875CB33C6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1893
0103D78D3D2BD8250DAA8E67C4F31F2B3DD1297B15F4DE37B0531CB58BC5019F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1894
9E7B6F9D1A683726BCC64F4772665AC3DD5CB75CCD44B95D3F5B3B687DE89B70
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1895
762F6EBA2A961C74AF1DE7718B122B25409C9A75C8C2C097894ECFCBCF9D0348
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1896
0A4B286938E345E1ACDC8DC473CC5B08317104462E0EF60B15EEEA321FDFC485
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1897
F076087EF16578D1552C9D164A61AFB915545C7FA1F06599991DD5C55A565246
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1898
67FFDE8AE5AB35634EE4ACDA69485F522A0EFF1F15D7488EBDCA0A3BF4B5A92D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1899
A13A5D3F02B55E6E83751F21F990AF1E7D4E1AD6AA7D6E46A374BB7757C2EDF7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1900
9C1D73D2151014798FB74829ABE5CBD7F42E8F115CF8F5252922768B39B50449
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1901
55B26CB872ABC2F37203A14B871B9E1CC24A85E8236374697DB1BEA09C40A44B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1902
50F3D99F3B227F1A43D8F425FF2E83D55D1D6F636F4A4686825928EE89E8A295
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1903
57DDE3C523F603C4AD47FD831B09D6AB3B90ABEF5293F0093B34A50011053BD5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1904
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1905
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1906
328F31993B8F9F1B5B8E685273901237F150183D89E5D6647499F37A416E2FE5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1907
A3AD0B08741D1DEA18E73CA3E5276786512CBEE5BDFA6146A78A92885CA7098F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1908
2D892E738AE230EC834CEF5258D3C1CDE61CFC1346767C51466CCA684E7CEE32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1909
9BB5081348C9131154300A1370EF67F5BC9EF51E9764A14DB5291FF72D0821D8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1910
2D74FD12CB12E17B3B87384E01EFD8F4B48D691030FD220A7343C85F31D2B4AB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1911
3866B32BE68DA800ADDFAC77640763491BA9EB2A38B556AB660E83A2233E5BD1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1912
99DE36CDAAF848D9D3AABD0E552FCFD2E924CE2D8A8E8ED37468A4C6AC4A4603
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1913
8B501CD0884C5D03FFA9D73D6485131C983ECE11F0BED9CED6EDEB14D7B070AB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1914
453EB129FA7FB31FFCFAB97BA677FC3603C1F85E34121EC8C31937978631EFF2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1915
04E80EE83EDCC0AF4F285B6DE20BD5C22E922A050C3FC5F756AD0A86B703C71C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1916
7A83A6BD77E41EAB2260DA0A8679EE46241190A0A0BBC32EE8A183EC0896988E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1917
5C52FD02B5772F55713ADA039464F9C3286E69DCE72B210FF5702BBF548967BF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1918
E9EFBCECF6D18BC47BA2FB658B8314C39CD60655C122C4C472BA45D17B7F339E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1919
FEE4E025310262CA496973E847138612A96B8695B9443E3C3CA6C736C7847C17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1920
8AC79F60062FFD7C93795129DA6A813F2BE35230CD27882FC2D2E673988B3171
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1921
1A59DA52493CDE64AD80B5E646EFF62658DC16B1E658E774AC53E9BD9670808C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1922
58684F567CDF9FD8168F13A7A9647E750962E7033AE8B5C0D412D4B08FF853A4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1923
3873FC51C7A9A3F841FD863607634233427B34BC1CA3BBCE45B1F1EA6FD5B3F8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1924
153AAAAEA0B58D737B6FBD372DB9B49918A1FC0D6FE38640291D0AA2510C8AEC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1925
E0CD2A0A42D0B20F6731390F0BC3A1DF2B867390885CC89FCEAAEE182C4BCFF8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1926
5E6C0771996EC36B4354057AB0E9FA30F5C364B7A6EA958A06A47D7C4DD143C1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1927
2269AFF37CAF54351E1C88B34115438E6D613F6E27CD26DB65ED59C057B1B343
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1928
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1929
617F72239B7D99A97E75361DB327CF433774DDA8FD32908B0D977A53A2604DDD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1930
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1931
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1932
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1933
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1934
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1935
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1936
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1937
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1938
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1939
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1940
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1941
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1942
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1943
%%BeginFont: CMR12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1944
%!PS-AdobeFont-1.1: CMR12 1.0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1945
%%CreationDate: 1991 Aug 20 16:38:05
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1946
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1947
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1948
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1949
/version (1.0) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1950
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1951
/FullName (CMR12) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1952
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1953
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1954
/ItalicAngle 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1955
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1956
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1957
/FontName /CMR12 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1958
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1959
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1960
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1961
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1962
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1963
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1964
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1965
/FontBBox{-34 -251 988 750}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1966
/UniqueID 5000794 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1967
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1968
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1969
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1970
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1971
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1972
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1973
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1974
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1975
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1976
3645B82392D5CAE11A7CB49D7E2E82DCD485CBA04C77322EB2E6A79D73DC194E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1977
59C120A2DABB9BF72E2CF256DD6EB54EECBA588101ABD933B57CE8A3A0D16B28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1978
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1979
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1980
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1981
45C4C068AD7EE867398F0381B07CB94D29FF097D59FF9961D195A948E3D87C31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1982
821E9295A56D21875B41988F7A16A1587050C3C71B4E4355BB37F255D6B237CE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1983
96F25467F70FA19E0F85785FF49068949CCC79F2F8AE57D5F79BB9C5CF5EED5D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1984
9857B9967D9B96CDCF73D5D65FF75AFABB66734018BAE264597220C89FD17379
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1985
26764A9302D078B4EB0E29178C878FD61007EEA2DDB119AE88C57ECFEF4B71E4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1986
140A34951DDC3568A84CC92371A789021A103A1A347050FDA6ECF7903F67D213
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1987
1D0C7C474A9053866E9C88E65E6932BA87A73686EAB0019389F84D159809C498
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1988
1E7A30ED942EB211B00DBFF5BCC720F4E276C3339B31B6EABBB078430E6A09BB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1989
377D3061A20B1EB98796B8607EECBC699445EAA866C38E02DF59F5EDD378303A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1990
0733B90E7835C0AAF32BA04F1566D8161EA89CD4D14DDB953F8B910BFC8A7F03
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1991
5020F55EF8FC2640ADADA156F6CF8F2EB6610F7EE8874A26CBE7CD154469B9F4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1992
ED76886B3FB679FFDEB59BB6C55AF7087BA48B75EE2FB374B19BCC421A963E15
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1993
FE05ECAAF9EECDF4B2715010A320102E6F8CCAA342FA11532671CEBAC7808842
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1994
A680E4250DD66FFE6EBEAF7EDC45B5F1765BE4BE4563AB9399932FE758F01BB4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1995
ABA03C0ABEADD1E3BC6430DA54E9BB7CE8E0B9C43755BF7C8DAB08C3E064C7BA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1996
676348BE1E40EB030B29B8918B8B9B9C6422DF15891BC607868ADEF2A9966F27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1997
40D6CB4F3AA8E715A5AD53F83CA9A5307F749D7BF47FCA32FEF324C5D4BC494D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1998
DD4CFFE171B658F7C368A959DB70BF553CC32E1A1D4794529596125BDE09516B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1999
FBDC0EF45E0E7E8740481A03D8672AEBE59812724401EFBE3D6F225E5BEFE06A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2000
57CE7183B9C8D2EDB0CF134DDC6BE5CE05FBE1B2149C1F9E3CDBFE13A94DEE0D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2001
535145F0520FA5E8BBD9A4FBDCF821B005F814E1226F40FAD7590DB1D1D4FA2A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2002
9DC75D06C9BB5A168D535A5EA58D90299B92051301F3C23A17D85495EB9BFBAC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2003
C395FD5EDF9B4A65641CE5443756CE71F7F8727DBF2C90C62BFFE9F83310006B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2004
8E6F252CCF78AF2B3B93F8E86C115A621956A3E6CD67FC2864DF3B4F4E7DED18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2005
91EC2503E05396403D0322DED2972C5E76AB1FDF5A503CC51227C069DCAE7127
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2006
24937D598A25377470D62C3441CFEA23257BCCCE4146B2CEBE0C72A8FE9DE1A0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2007
60C389B022B65DE4371A3D735344F6DC941FAEC4FB84FCCDD9D4C3C21085ABB4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2008
F816D0A93C7717FB08DAFDD30860A89DFDF14B347868251F774943A4F074DA18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2009
EBCD1D12440837D7DAA821460091232940B90A029AE9F5D24128C328335EE33B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2010
ED847B428AEC894DAAE93FEC51015085CD55D14FB43CCFCE3F59401B36065C6C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2011
348F7165980AB56DD6FBA1C3E0A77A6C4C8231C6D1E8E62CFC424746DDE1B1B2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2012
BE1AE4B944239E0E203FFE952F72BD1D3F6C25DCCE2B3F49030FCC3C72D94D4D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2013
61A7CD54E3E01EAADA5A128D409C164F5ED5ABBB9E845922248F405572ED695E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2014
5354F4B0D11C320475051405D488790D3897ACF237ACD6743E4901D4F425B1E5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2015
1BB473420C6EEBE25F67CF2DBBDFED2CBB5AD309FC4766B21159AF475A1CFDAC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2016
80FBCBDD1B3C1E6D554C460A1C113FAC7A13ECDC5DC97BD64C4B4104FC52CDB5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2017
0746A8A6E5FD2D8686C4B003263BEF16DED50283876144FE31288DF758055FE6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2018
8E52FE1F58F099E2D572A8CA07C2FEC43992773F7091218A4E2215F876C4F4B6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2019
E36D9C898D89F5343E1943CB748401E44699934A97FF332CAA115266C8368F01
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2020
B04049FA3CF67D4102E49D803FE79CCB0D240FF69C3E8AA197C012225F8A9CAA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2021
AA5976F3047FA0820983E0C642F60D49EEB47AF4BF93425E2F13F53073366A74
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2022
3BDD0AAA9FCBB80177232703181613D12A6114BC827D003923B43D0293BB6B90
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2023
FDD4724AB6B30104199D7742FA5F020A0218200ED323482CAA2012294A590C43
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2024
547FABD566C46C01FACDF88DB60BF4D8B3C017A4755EE076EEA8059B7D8ABBB8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2025
35C4A15875FD9EEF3A1EA350DE4B3E393CBC64437608AB396AD4F630D91C4F66
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2026
EDBC0013E7D15B22FA62B4936FB6BECE464730B594D041C217D29B51FCB4289E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2027
79FE3BC9441F1C1D91FD6DE98639D207923497E0209FB56FD59E23D0A44DB80D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2028
76E82E78F6B44132C4051295731D3907F7B0BAF39B3BA5C73615C72CA1491482
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2029
FD7BBB9113D4575D1A7F5C4830AEF9D20FE552EEF2A02BEF35CF7E8D39BE47E0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2030
C0907FF2E373BA034AA39D51029FF938AD3D1EAC4740F5E35ADB893E07807273
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2031
65C18F7D0CFBCA8BB8600386C6294B9EBC5CFCA07A8BEF89387582DCB555CD6A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2032
6627F4F242AF73124DF0D40224A3D85DD88900F4BB8A20E8BB23F21AA31618E8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2033
CA1B639A42CBC5C991433E8B1413A7317D87AAB3828C85240D60976D6A1854F1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2034
4A84BB02EDA57662E001C773DBE5F3B5AC234EC18D83EFF6C5AABB16C4ACBE91
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2035
F45A914AAAFC0DC42022A39AE77F1F8A7A8CD992368AA9C560E86C72806C70AC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2036
81DA1C74F597B3618E8488609CACF0AA351ABF1AE2890D86ED1F45F99CFCE700
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2037
205FF90931523AE6871084DBC316EF77A597A6B2461533F3FD57EEBD25FFD63E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2038
5B93760EB7F6EED86AB37A2EC44873602A0E5934F7665A295350DFDDA09049A7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2039
5513D47FE8D8522C528369B6141F7CB278B41763F98AADADFEBBC328C829CE41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2040
64370CA3F408D6A40A445093EE52229D579B30E72A3A517588676C8BAC358157
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2041
94A6079D23A8B88D6D072F026B58A9D6F7B440715828FAA57FFB80BBDF81B5EA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2042
B606FFF53DD4EA34B87B445F8E21F17114A51E1F1C9567A79F1606C1EDEA996A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2043
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2044
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2045
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2046
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2047
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2048
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2049
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2050
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2051
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2052
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2053
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2054
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2055
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2056
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2057
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2058
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2059
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2060
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2061
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2062
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2063
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2064
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2065
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2066
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2067
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2068
/FullName (CMTT12) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2069
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2070
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2071
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2072
/isFixedPitch true def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2073
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2074
/FontName /CMTT12 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2075
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2076
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2077
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2078
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2079
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2080
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2081
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2082
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2083
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2084
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2085
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2086
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2087
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2088
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2089
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2090
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2091
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2092
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2093
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2094
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2095
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2096
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2097
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2098
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2099
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2100
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2101
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2102
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2103
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2104
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2105
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2106
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2107
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2108
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2109
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2110
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2111
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2112
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2113
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2114
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2115
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2116
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2117
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2118
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2119
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2120
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2121
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2122
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2123
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2124
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2125
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2126
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2127
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2128
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2129
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2130
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2131
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2132
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2133
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2134
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2135
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2136
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2137
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2138
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2139
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2140
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2141
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2142
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2143
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2144
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2145
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2146
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2147
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2148
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2149
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2150
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2151
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2152
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2153
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2154
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2155
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2156
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2157
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2158
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2159
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2160
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2161
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2162
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2163
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2164
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2165
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2166
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2167
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2168
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2169
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2170
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2171
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2172
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2173
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2174
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2175
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2176
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2177
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2178
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2180
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2181
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2182
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2183
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2184
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2185
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2186
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2187
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2188
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2189
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2190
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2191
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2192
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2193
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2194
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2195
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2196
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2197
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2198
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2199
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2200
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2201
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2202
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2203
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2204
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2205
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2206
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2207
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2208
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2209
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2210
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2211
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2212
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2213
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2214
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2215
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2216
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2217
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2221
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2225
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2226
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2227
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2228
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2229
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2230
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2231
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2232
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2233
/FullName (CMMI12) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2234
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2235
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2236
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2237
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2238
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2239
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2240
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2241
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2242
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2243
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2244
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2245
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2246
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2247
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2248
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2249
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2250
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2251
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2252
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2253
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2254
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2255
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2256
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2257
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2258
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2259
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2260
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2261
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2262
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2263
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2264
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2265
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2266
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2267
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2268
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2269
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2270
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2271
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2272
02C28359A40AE66A6A6A8862CB17815B41E280313F0EFAA9981755611F7F683D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2273
35603984D60BB0C772054355A97A5E03C689E23B04DA79080CE4579CC90EF38B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2274
1A64CDD92B907AE83192C3C46C5FC40BB412F6656DC6349E6D29B5936DCE94CB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2275
98E3B465FFF7574095F57BB3750F1A525FDE28FB8FCA4F0DBD8BF16A3F1FD9A9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2276
CD52473E23A90E6632D39EBD39223004B2382EA7B1CE8E90BE77C69CB5B9F659
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2277
009CF2105EBACE0CF9BA0295F1937CDBF7F718B6B85C984490D1E560E9989B89
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2278
D7905696D5F64BFA604C5A93CA60A8C5C4A5AACDB6EF5562BF55E551CC048835
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2279
68743F501BB40ADB8DEC07D5975369A720A6D249F9A5AC91B1ED3896F2C6874D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2280
6C2EA8F580296EE177A97F5C50FF92FB804C7EE832FEE09D4975CE752F2D3CF7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2281
66AF8F6748D64821EB2DEAD1C5E50275E46460F6DBAAB372244C84107B983B1A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2282
5C7863DDF3174A09E363E92A1EAC874E4BF7544FC321A653D2995F020A0BC9F8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2283
959C4ABDF4FE7C245CA0CEDD499A368E7D55BACD328699AA3E465C41C19E8164
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2284
2B60DDF6CA62288E4E780F8614C7749C9406325C827EC8A67B3BA58728304A89
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2285
D56F596F0E1E2A35E4D40D70D5990DD9B4CA9726CAC5224C853F2229F0B337D0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2286
C9BECED9D75C25F5CDFDE290494439ED79D6305E42CAAAB1CD158975FF45AFC5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2287
6539492DE05FBC7E5D5A2A65C07D4FBCBB8FB94BE05DFF2B3C136D05597DC315
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2288
ACA725635AA768294B6319A6506C5CF42A65CA282CE66583F82EC2C242200FD1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2289
6C0FC15C0DCB4C59BBAE3A0C3B766E84C51DFE03A5AB4EEDFFA3A48F17115F0E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2290
B2991D13D9CDF6E18FCCE668886402A6534071AAE50D5ACDCB2163996299FA25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2291
E75395AAA60265F5F9C4FF8CAF1AE0D867CEDDB932C05F604C97248C54B5D684
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2292
D444577E6AA72F0BD08EADBB9EBE4B1EBF7091C0DDC1AC4A2265D10F6A7CEC42
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2293
FC81D1F4CBEE94ECDB043188968A9B764661916B832E25CE49A8B04A9DEAAB1B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2294
74EEB7B908245CDDB7A093C1AA3078E881AF16CD559F65C3FB88475B20A342A7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2295
D2D6623578765F8E3699C303C9830CA8AD726BD1E09FDC90F12AC14EF20726B9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2296
72C731CE019699113C009C09E30DB38B1B301F105C93E25C7CFA6A6EEA12BCD8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2297
F321C3B2A0DBFC4809AFEB576CEDDBFDADEB99A3D372154801D0D805E4A7DB68
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2298
DF780AC0F0FDEEA064AFBAAAF136F6723174414F05A93B7AE16CB40DA8C9DA8D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2299
0B4A7435075F9D69574A0C84EF7D0C0A78D24BCAFAD53F634FE29D5697CD01F9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2300
91022223D03A5F3EFC2F3D86EC4BD4B3929DC04C21A98E1D513948B7DE7D312D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2301
2517A932BE08DB51ACD11007AA194D3CD05F37F438576A773263485C12E6155D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2302
B7DB67F081430DB01F383937068CD274C150E1B8AA9E57D02C1F40DD537B72E1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2303
5DED842BAD6EDCB212D5ADB51AFEEF9E7582E79A147D57BF7E3139F4B3C8123D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2304
2F5C17982B8B744C9ED014BCEDA12390611DC885626AFC8538C1ADEEF2966B29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2305
BB6401A4DB94840169872A715D0016C6EFAE68F28D0FDAC830342469AA657EA4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2306
1F29AA9ED11B9B867C62289B740F40EB38E93B738E6D63328D3A9074A17A2C09
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2307
4A3E7A78C1C8EECD5DEC2A474476C58009BD295F9D9E809E7D9D355B321A0C93
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2308
E5B850FC4FD48BE9E990937F73D6FD830B08FBB36B93FAA9042DD30F34D3D73E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2309
9D0470832920A206ED263B64366AFDCEF245A6F1471D408EC3DF742F207A6C03
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2310
E8529C48F18F3F45B380A17E6E463455270B3804D1580B3B3C912E99F6BDB738
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2311
90310431B5235914531465DDFA1C281FF1B14EA956538AEF8E3C834935A5AA59
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2312
35BEA495EEEF110F88E32436635110BFD83E87566EB86F195D178DB1AA17A658
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2313
430FC620AF24EAFA7E04B1ADD4D278F02116933E00553D48F6C5309A317F5CC8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2314
23D267BB4FC6E690C02A85559FC1395372F20B5E94A540D1DD3A0FAC30D7A9C1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2315
1AF7BD0CA0746C30FCCA90F18C77D925D42B519BC6A8A7953C6B8F39D574798A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2316
F4748F74C50112E74092385CDB2671C13F560AF894695B0AE2E6CA4921D9AA39
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2317
D5A05EEFA079306C31ACCAD6C93C0612CEAFD042F73E9B914409EFE5EB437B9C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2318
91B2826084E5EF932FDF538E2DA4CEFDB262C03BFE9029B3C1B13DF4808B1C1D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2319
5A20E2925A91C134089A9F7420AE7228FE6809263DC9910DF38D8C619D6DA89F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2320
EDB6DE40C208D5C1635A6AA6ADF21ADE74FB9C8161C71B04AC1D980B0E53CFB5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2321
07BAC208F07CA9B23B0EFE63927395B6602A95FE14E435F4A37805CBBA6F9B03
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2322
037A58B5FE08E76A322E1D5163D55885DE4C2048C76FFE51ACAEFB5926BBD6E0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2323
DA9826016BF125909B215037FDB8E383AF4102A6E71A28CF70B642F2B3CAAECC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2324
6C0B89195F5CEA39FD16FF9C75A185A22F042614513829268295CF429D4E4F2A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2325
FB638A78265B8835EDB72EABA1F9A2D95D817F9EB7D9897F01260E957A7175B4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2326
C9EB4D27F2E53EFD6A9743244D04A8E7F05714F6F9F7169020E6E567F3928070
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2327
B865352893D17A0B71826154CA2714C1291BC04F60D62D5F7AB09B8A13D11F63
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2328
9C91CDD8496A128EAB280A341CED4918C091271694CE819432E7372333C188B5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2329
C5AA47A39B7740B93D1569D16F23F4E2DDB59158B3CA94B2E04CFBB4E8C8BEAB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2330
0F3C872C815227428ED415F4CE2CC9A1DEB3C082DC9368F2FB7681C056662EF8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2331
3FA26C2CD267ADD8AD2923062D2AC80052DA6ACCD4283F27D9D0C5513BC7F3CE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2332
DD6C771F8E50EC29BE58484968832F5C1F163F753702B577DA808488DEF8DB90
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2333
04CFFB431163D169BE5311F528E6D5A48F5576AEE3D0B7210FFEFDCCFD6B9CD1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2334
1B437FEA6A3FE0B563794EA424C59F8664A1E08DFFC4F94C3189B8D07CAE7F15
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2335
A49FDEDA1D4D6AC6E90C42A960C469498459DDD922971E8DEDF1079E15FE1F46
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2336
DFD74B0D697846D4E373838AB59EF1D82D7D739F3204E5230782D9B2BBB5C6A5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2337
8B41C50707B53FB29005896880F04CB2351AD1013C258DF77E9056193AE22780
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2338
3D422BB21A55C488244B73C1A4A7EA54AB24614E1507258686C3BB3C9D461EBB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2339
491C211503068B7EBA700000305757FAEE10251CECE5DFC98C355CBF29753649
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2340
FC90089F1E12E8EF350D06A8051A15E59790212519B5C83C8A0829D35B5CE001
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2341
65BADB38FAB29F8F159DCCC0C0D8D049C35F787AD7312783F9F3A38A30242A41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2342
331C327903EA3911786FED5AC82933A4388FD65D7A4AF9B626595D6DD8C36547
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2343
278ECC6A008EA12CF589EE3B310AB8BB4112BF8CC872E053DA11F406FE6EA79D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2344
57886D1716E84F5CEBF78F7268CB4D32A27175A6B60BEB1181A87727831C1B34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2345
965458F141151034EAD12FA27E9B9D9D8856CB6B7B828B836792899BA0CAE999
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2346
899FFA1499F7D04B9CCBC3BFAAEAD54B4032337E3E6C072128C9F9696C76CDD4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2347
81E5227E69F0DD18E2D266635A11F1C2B2E935BD1CA02ED6DF48E51B67659D9A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2348
45E7351DA161E55FD4D75EBC90361485A352D07BFB8F7F43E609C46040D122AB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2349
3845BB3D82DB86109DDE04E69925F82185892AE63390867A77D02B9BD6ED20B5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2350
14CE83662C2AACF619158B5985291D9585CB6F68CE9065F60A2B6A4AC0896F55
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2351
E99F078952898DACC3DBD2E0548A3503803A91478AFC6E7CC4A0F2BEAABA4106
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2352
20C860EEEFDB2ADCA7FE1FDEEDEFD040E769C6011E95209C8978E13350CA9D32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2353
B2C591BE1FCB5274C13454EE2B702E9904C29CFC05D57DAE08B9F5783D68F8B1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2354
ED657083C3F61D25100CFF02488EB8BE9EFE3A464D39F2FC92B701B286AE293F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2355
9DE7047431B97150EF0C1922A9F6842CC733CC58AF67299D635EC62F5D8AA537
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2356
20CA49D4EE3256E9A30A6175D2F4CA07DC0D44AD2F41802F4775E508762ACFA6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2357
A2C33DB8F2A10C49DF4AE412200A56BF9035A7A4769E27B5002BBA697E7F3EB5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2358
599C6D065BC86D514902A83D2799234B3C1C9C667CB8257DA1EADB70CD739432
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2359
B14B751DF7685573CB4B59E74D87AD8779879F42213CA7A6953A98A57402BBC2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2360
CCF1BCA977BC7462872347DB109E836A03D5BD956B0559D792F8F061786E71D5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2361
B66C0CD112D4002321B5C52B1C6EA8B86AED1FECC35CE62755551A0A26B3AC8A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2362
B80739D91220DFA13EA96CBB87CDA2693DD486D17E36CE79460196AAB90CC9E5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2363
731111BBBB2AD93D06E333941494044158E4ED44BCA2FD7D72CF35C5AF94567E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2364
878F3E74E668A17E5451A87F4076021D9BDA111674BD9A19D22EAC5EF915D038
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2365
03E3E2F58769B23E41CFE21B967491EE251C07E66F855A5FD1DABE027D415580
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2366
08A7F1469FC267772030E54CAC214F69D5BB99B48B85688E5A364D09D2EACE4B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2367
97DFD477EB843EF65A8302177C6D3A91A2EE8D1149E9F9FD09C2523A9F7C4AB8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2368
7B1249CF351CF15FE45DC9A918DAD2487EAC151A5F9B5470B0E91C2EEBDD86A6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2369
3B51AFAACA719DBC358FCC896F872886239D08B2E8E497A3334427D4A5B2C398
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2370
DEC67337A6BCFBFECFCF1A20D921AABB4259A81AFE89B4B580C1C87EDD8FBE24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2371
F60C75D407221CE179408672D4BF159AAF41FFAC4FE92A23C11A6DD8A1BF2559
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2372
B611FEA32F34B5E79A7FA81873494EA81ECCFCC3C3208AAF526E1FD72EA6B4F6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2373
395D8902DD0C37184ABED0C5A90851FB606197A2CC23ADA0B8BF20BBCFDAB7E4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2374
979ED53877C932686DD43756C50295A6048C8BDBF064585A613B556B97832495
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2375
A84C403188AEB3F9D1983F98E8CC781330EE164A6B1870F1E231D3E32FDD3B40
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2376
0C5EFD4125F34963FA1BE919F0C6D9588674140F1077558854B96ABA372D8E7C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2377
09E28C87CDD0A98944BBBF747489E145EFE86982F40C8EA7530B5A91961D9698
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2378
855A949436D5E5CC3CC8ED1EBBB83ACE2522FF09742FD41D6B5F249CAF451404
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2379
016C4206F2C0D2298D1A6ED64565DA36BB937D98DF80BA79E222EA057765FBBE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2380
96BE2BBD2F0C62B937612513B832EC7B07B3628E7B645211DA2E9BA62D5021B2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2381
916A596AC9340262A6823031CF7BA1832BCA926899EAE37B05B5DFE95E8BB9E0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2382
7CDC935F7A34613A9BD964576DB9992BEE8A18F3EC6D5B5AEDEF63DE5C67DF33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2383
1ECEAC31FB2A328A0E04706C972D67D6C471FB4BF24D0C2296BB4E98A9E92E28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2384
7F8198050A5DBAC2B06710C7F59571EF8BF1AB029CCE9C5B294B57421E6BC839
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2385
0514976305ADBE6658C6E679FD72220085A5E4F4422063262459B4A240B555EC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2386
E48987762ADB3B41E64B8BB3A667CEFC519B18AEBADE13EB92B93FDD429AB398
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2387
3FF7D45011BAE7E64C561D59085282B4E262AFB408F0F337D120554D1131EADF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2388
CBD9BF5DA98622EBC26D5413A632529407E5AB3F6A36338721FC8195A551F1A0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2389
2BA9F14B9540B1ACD633662D65D0D2857CCCF5C6EADFA081892107A1F0095617
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2390
971E1CEEF8AD80D7D97F6D6528D73371D51A1D50E2D4B0ABCCEEEEF213EAE057
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2391
34E7ADB3948A9C28D9582E51A211CFB426943C980ED2276FEC39DE88FB5DFF6C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2392
B5B25376237D8D97D24BD313C5450E8B0D2AC7F8CCA11428E2ADAF00C49F5691
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2393
B9206D77353908933412D4C66C3920B2D097ECDE735C6C7346D23B92A18D005C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2394
A2D40A8AE89DC0DF20EC2BA62FA047327C89027170369A2A556A41BCA1FEF6AB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2395
E1991DC453E46BFEC9A272F4DA2E5CCF8E33BC0F718422BAE65D913E5B72D0E8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2396
083B1CE88FB8889CBD38B0BF788FB57724F8A58AB57AE5E32F9CA84E5C50EE60
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2397
C0B94C3295D9085759BBBF1C7F1D9A4B01D832CAF556467AD054D0F7387B560D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2398
C4457FE90921F7B26011FB52C3E5F6D796819FCB2265971636B459D3CDD2D2CF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2399
2BD0686A5BCAC27A2175DE8489FD1C63524C6D56E2943B95EEF2AC331020C243
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2400
7714A5A486F10D689EDB5ECD530BBB8CA492A46DDA77F8FE5EF3697C8D950470
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2401
5985974925EB9AD2B5D7D5BD5CA31F5363452E2417BAB34D13F55F66AE145F6D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2402
E97EFAA58A17AC512DD5386587AA2E5B0B2D55F325CAE7D6B22CC80DF165FE84
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2403
E5B577CFC07A9EC7B8D60BACF393BED56AC64E1827880240467C2C17C942F467
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2404
F9DA255E9EAD277003E5607BD1FE24AE6400FC922C24083C8FD68B6D93A3997B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2405
CF16F3B167DC3AA5DAF2F68C386B781019D665E2A894DAAC96875007E44505F2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2406
38A44F198FD58A8F21961FE57A7122546D5F6EAB32D1903183A35F75579515F5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2407
8961CDA85B2E0C542105D15140BBED60730C2146DACD0A484E6A4672D0CDD5ED
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2408
028DD6BE49361BC87EBE7AF022FD60DC1CB7E39574C6C19DBF7758E3C60BB1F0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2409
ABAC9DBADF4D9416555630D540133CFB0E371FB8A268F5B055713D00FA48FB41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2410
F9F1E586E5DCFEA4CE89209BD4EA76ADDCA1DC3FC10C874FA4194801156666A2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2411
BD71A0D59764B595EE4C6B197C08EED7579B85B5800FACCC85D7165DCFDA5FC8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2412
FF25E237B7E19004524E7052007171B0DDEA436250351A5BB0CAD870D59D308C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2413
88347C7F5B4B9C61FEF57CE6ECD702202861C05062A355C63AFAE51A4A53E682
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2414
235F23142506EF797F86349DD9D1B744BB5C101BD76B65FE9AB98D835B35ED29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2415
AA4667062BDA956FA6DC687FD0980FCE3E7D8CA35DF28686FDF0B66D00B7B17B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2416
880A9BB199AA4415EABE5EE3C7ABBB298AD252FA077F5D499F865D7C3BB7428C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2417
F2A57E23D62E3E6408C41B0A25DB06C8ABA05F7DE811C9827D977DCA19B4589D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2418
C7E33F0DAEB66AE57F31C1444CBA850B19E0C1F4B909A228DF6228B0EF4A630B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2419
7ABF89866837A740C3B84321255FEC85E3D8818829EA4268D56C7A043BE05B35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2420
662E4FCDFCC9D2931944977E6505AB0E6B6F35BFB12823FCA4FFE700B73C1FBA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2421
A217EF67F1422A62DC24AA3D6907382EDEE0688CB40DB54315132B209825B621
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2422
0AB665D5CF74DF684FD7E06201B404218C91BF62012F230F1D49F365CE60E66B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2423
609B054EEFF4C271E9CB3C8634AF050D24583AE5400807ED15416940AC70892E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2424
E2A26AF83EFC90768B72AB256B399D782512622FE84D305AB089A1571FAD33F4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2425
D2C82D492549EB70034032898AF950BD8159FAC7F9578A8F0D0183FCBE85683E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2426
FBEFC3C013FA42CA534151C30A0FBC43BD37DFB2B2EBED0D86E1B643AB49C78C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2427
B8A8FE79AEBCF9DE2C577499C895232D210A36A8136D4BF29F04FBFC3CA9CEAB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2428
0DA5B89AA84438B619D92743F1B2D402108746C7A9B9AED068BCC8CD3FE8CA85
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2429
9BE65CFB9DCD8A7876EE15E091F318CE4BA5072EA842285809C20FC0165B6988
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2430
4159CDC475B2B03B318FB442A425871A99C4DE7150685A600377B623EAA013B1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2431
61C2B3E478D09E210FB7518C2ABDBF0201F03669C0D354AC24D1A2F82659978C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2432
A7A4FDBA9C66C380F67EBDBC20EDDC4124BB1E9BE310024551CD7FAB6D748E6A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2433
51005EB82A52DAC7747C4D2D589DDA746407865524E1119D4114FDE37130C51E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2434
17A6A0CC1B2674B5283E8529B22B32A87D515E4962EE4CDAF8053DFC83310121
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2435
01E0608E5E47BACDFEEA8A26AB5DB40D2FD00941B28BBBB1F548E359922F57C9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2436
DECE7F283036F828256AC28894A39E73287A3A8AD0FA351FF28C937798A089A8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2437
5E59FB7446B9503E726724F88070979D95AB07A09C2335E0A5A3F3EA49673C68
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2438
B273E056AB7FCE5EFBA00939A57606926457A7731472EB77E80E1BA182555E48
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2439
CAD63759D59B732CDB8944932D2DF1352890D8A1F22C28D25DD7EC543282489E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2440
52CC8039133728490D60D24B06BC5A2D76E4155E24DB5C0880F771187815E5C2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2441
03421093FE423D9C00F95630D25B9FF5FF43500CC8C4CA4BB70A0C002B6E4DB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2442
A9E693F6E710A6F94176DD1722BF60E6EAF7A96A67290B0DA2D2B538008C4192
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2443
13223F71D14EDE00E1C1B0CD1362B706E6CD4E3FF79FDFAB0AE7E906AFAD5E29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2444
093210FA9C129EF6CF9B6A39F879FE40DF5973518E88CAFB57CB3056EFF120C4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2445
2FE1CD8193C7F177C68F24A00006ABC4868FBB1FBB3A3E2B0063E2178B5BC4FA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2446
99977259BA94A75A657986483C425168340A7CD62C45D203882B3375861104BB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2447
46A26F492B1B5B2AB757BA6C5ECC8611E6BECBA2CBE4EE2EC6E6581122E9D05A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2448
706A3C9A9BE9DFECDD8E7052B188CD21B6D80E52A9BF7D13726D230660DEA9E3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2449
3DACE3480A24FD847908A52F9E8D7602DA473FD216AAD2827D22CF909AB21DEF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2450
3556BED769D8F0CB0579C095607723DB09E30E14803DE7DC635842F400069FB4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2451
A846D7C4D83E52BDBA554121290F76AE1200F2900E0F90BFC81EF640DDC111C5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2452
6B97F67BC0AD181F031A659B90FF37574869C2A6159B063B6B4D130084051406
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2453
250FEDE2162EC5C27A3CAFA5F9BA0EDE1D2A1B23A4B72C1C3C010D27CEC514CE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2454
9A773DA82A2D4A4A95DDF3B66D1C074ED8D39CF3484E1259420D43DEF233BA08
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2455
BB9595D9FF785A830EFA86EA451CB47D4A5529AFC3853090CDD68B6B144F8DE9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2456
45667F91417843B6C599C02355E650D7C73EEC61156D6EEB3BB310B1FBB444C3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2457
3B0974A987AFD8115FB870F9EAE580DB8080EF5EF316F73A7071D0DDED532F88
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2458
AF2CFCDDBC680EB5DD708FB070C44C54DE8F60946E0A637651F73A349B41974F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2459
CEF49787E442768431F9CF24936E3EA1644A701237A486AE1C676D3FDA92D0D0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2460
BA8B4EFDA8F4E2CA9BF95E915338EF0B71266022C5CFC338777607A38E0DACDB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2461
BFC1A46C1AD9216925333651F28CF857BB10022A585646152238FC1DA6A16F08
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2462
983EC45B808B60012C1ED1CAAAEA90513CCD663DB1DB1E75ADC05F1AF51D31BF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2463
BDDEAF4B6C2A6A775D74BE5CB1043471E38304A02CC73301F5FC71D02A412829
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2464
F1AE76628C0BE7006CBE98554AB631330A13B327799B83CD8C12D652C693ACF0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2465
242F727E4AC4E1EEE393904A72C48EEEAA45BB830B578643FAB0C227F6EEAFC1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2466
5295E99902A3DC49603BC567D3C0EE700DE1C01BB5721BE9B112AF5BEF20F4E8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2467
DE3E34640FDFCDEC5B8C3523756030B13B1896FF20B718BC2F59EFB980609129
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2468
9517B94BCD0972CCBE74BECBC818A2BDFE69C8285774C4E8274605AEDAC944FC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2469
5B310159F5D8013C00C9ED1C6A34495E3923F92827150634F018FCF91978E5DF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2470
DFE920B20B1605358D6447F9C0660D03DA8D86E98711465AC82DE46C9E20EE82
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2471
29755663A47FA70A59022342121396380C92C729AD26288830D12BF23DA68FFC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2472
1D84C22AC369E0424EA3D3F1CEC67E97C3BF268FA906DCEBBA1766562389D568
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2473
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2474
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2475
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2476
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2477
2482D18AE45F6DCC0EBACD44BCA8E157548A618313C215F1F92E13B52A87D4A0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2478
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2479
3B9D83E37115F60EF19F043A527C0E2A91149CE69FF10977E60D7E6DB95302FF
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2480
050A6A63B99A3E47A30EF26D394B95E6088EE398BD0220D0FA9E8AFD9D046FBA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2481
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2482
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2483
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2484
4D90F13068744FFA4B3728579E224249DE3692BEA1B4F238CD82E6D0D809984D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2485
2A9149DF0A028675659C10D0FF75BA77CBD0054A034122DFF0ADD9DB7C46511F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2486
0113B972BFB88C1DAF11F901C6E6B0D407566F026F3FC4A703511C6B0E65051F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2487
FA7FD005BE83A05138F2F1D24B2BE78D48C01ABC6F195779B6900643FC8AFB8B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2488
6FB2F0F1C09CC07F80A1F62FAB45A7BA874FD6A899F9E11C5155AAB1BB1BFBE8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2489
EE8A5BAFE8F2EAD4A2983ED2542AAEFE0BB1CE85DB67316BD7B05A8C7503ADB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2490
221BA9587108C6E7C7A6130C0CB111DBE7E4D6A71E6D8AA4C160F3BACBE9574B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2491
3932BF539AF8ABE02C42E2FC9BA9E99CB8635CE83555147F903218BD64972B64
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2492
AA75FB6B2327345805A9B464351ECC153588CE54413A5282A1315FF3285E9390
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2493
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2494
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2495
2F7B0086CE955F5E3562AB6F29AB5FB1C2C93CD4CBF1F71439E4C2FABFEF483A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2496
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2497
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2498
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2499
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2500
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2501
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2502
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2503
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2504
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2505
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2506
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2507
D9DDA32C6EB4D44B312DED7B0B75BE95C6675547AAE74B4E89E528A72DA5C1B5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2508
7EE26BD3062703E9EA1D388804331482E04927DBD05157B1896E01BD1DB8836B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2509
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2510
8899C9EC8A3921D13FB3AE0CB24B44167ADCAB8D23EC12567D07B2C882ABA823
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2511
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2512
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2513
26814F5EBA1EF483F52506CD21305D277EFEAD08B004EDE0E7D6B5576975E496
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2514
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2515
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2516
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2517
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2518
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2519
472C19F111332547559B10773FAF9E7DC9EDEF2B44ADE1E25A72A2C22F14C709
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2520
9BA62F470561EB4E2518ECE2E5C27FCDACD63ED67109EB0BE3A5DF06FB91554A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2521
1AC155C990E299D230B006CB40C881E6D3D11642C8B050C87B71CA76B532B1B4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2522
6B00DE4C5AE3CA8C29BA9972FC4885A1B0F93F898493E9C213D0E411C3563529
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2523
A89E7CFA0AEBE73A6F1CA1851C7C529A9AF79621CD69A47144CEB77CE9D6820A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2524
6F9CF55FDDCE90D61EE37AD3120A1D83159A54DA67994FA120312AC6D0AA2F04
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2525
B01E7B59BBEBF7670EC00296706235B72478F2618C5AB064A80C852AFD3CE8EB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2526
2DACBE43926F60D21D8DAB9C9EBF3FAE1550BB4FA2094D5070FEB8BE18DAD57D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2527
44A87E339425F94350E51CD3779968E7CDDC0F05750086D69A86100967D6D1E7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2528
908EE83F31857A27C0C725901D6634B74B4E0453C27361372D4C78EFFC245AB0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2529
8E59A9CF786F57B0081946634BB17ABCC31DBFDCD123652323FF192430631D92
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2530
A994339DB0BF3E94554CF953139A23F0010CB8391E2F96690A1A17248AD43B72
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2531
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2532
A94E233574A2B880E43D364646B254C6463F4E8FA104FC0BCBA60D8E000F9EDB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2533
BBEAD68A42CB1D669659DDD59AE8E16B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2534
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2535
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2536
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2537
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2538
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2539
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2540
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2541
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2542
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2543
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2544
%%BeginFont: CMMI10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2545
%!PS-AdobeFont-1.1: CMMI10 1.100
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2546
%%CreationDate: 1996 Jul 23 07:53:57
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2547
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2548
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2549
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2550
/version (1.100) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2551
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2552
/FullName (CMMI10) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2553
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2554
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2555
/ItalicAngle -14.04 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2556
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2557
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2558
/FontName /CMMI10 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2559
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2560
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2561
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2562
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2563
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2564
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2565
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2566
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2567
/UniqueID 5087385 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2568
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2569
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2570
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2571
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2572
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2573
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2574
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2575
D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2576
9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2577
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2578
6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2579
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2580
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2581
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2582
8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2583
6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2584
1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2585
03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2586
95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2587
74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2588
3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2589
47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2590
AFC0E2F840512D321166547B306C592B8A01E1FA2564B9A26DAC14256414E4C8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2591
42616728D918C74D13C349F4186EC7B9708B86467425A6FDB3A396562F7EE4D8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2592
40B43621744CF8A23A6E532649B66C2A0002DD04F8F39618E4F572819DD34837
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2593
B5A08E643FDCA1505AF6A1FA3DDFD1FA758013CAED8ACDDBBB334D664DFF5B53
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2594
95601766758D28AA39D6FF7952C9CF80458BACD8BE9F676B2D79F89AF3AECA49
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2595
FF0EAD54B11C7245097449D1931B719E828B09C0401C011AE1DCBDB313BBC8C5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2596
48130AF24A0969DFB53344C8A7C4F0ADEB3C8C87312571DB58E804DF5E773235
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2597
0DF5A07883F33603F1B1FE26A37124F0D26B911BBC0F5D294609395C92AA347C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2598
655BB711D63FEFD58CC0C617CD3BD9879A68E2C3B912C476CC561D9D007D66A7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2599
FB2006D9EA7027B292445002420703C8A6E0419D3AB9ECD7796861ECA6F39E44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2600
234E86830CDCC75E06AA1D4ABBFC66A23D25D432ACB057B1C37F481CAEEFE071
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2601
548358246B1443338BEB45C86BDA17C2B66938DB0A2B63BA76CCC63090764C00
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2602
5CDCA0A6F87E06DE95069C7855DFD334D509117033218BCB84D1313E21EE3323
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2603
349275E9A904B639B654FF72A9A78DA234EB42FF76EC262E6E0FD37E66ED3A5E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2604
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2605
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2606
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2607
78C674A79D148517FDAD94A67CC46E079940CC82B6AFB6ADF73AE1E6FC5E33C5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2608
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2609
43686A71A987944CB71AC052823FFAC41725525D4DD7258F9AFCD753D81756FD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2610
2A9050F4B765E258BDBBC5261B3CD7735E0CB80A60CDB4704063E50E195D090A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2611
1565D9271CCFEA85C95483A9DFF9C3ED8043D5F7346A25EF015A53266BD31A6E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2612
3F0F2C5E6C9AA71BE40EB7D6958F6517EDEBE27595E418EC7EC8B7388490A0BC
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2613
0FE992798E466C843E39D582E1BB1F0FA3C94FBF687980688F62C949A4CA13C8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2614
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2615
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2616
43F0B5343BA99AC7DD2EFDFBA09CB720569FD473A96C8B4F40E597818FD3E6A4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2617
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2618
587B4A491FAFC622ECC6B32390852AA419253E6522DA0F9BEBB675460F9DF0BA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2619
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2620
716A6F1F35FD69BA6846CEE3709E06820F9D6DEB78831C14BCF82A20508DE487
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2621
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2622
D96D1CE49AEEA9DA2E4A0364C685FB146C2F0183672E7804E9AE51C4003B8431
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2623
B17A7BFB4C094FF83804B9F9BAE23DB6081EF1C799E33708927126A933D7CBD1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2624
311D3A21F10F2E65FFD2EDD324F524FF593720C30E0A1A9ED3544595D18F9E82
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2625
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2626
EB5E4BD5F43CCF045E09892DEE140AA2694975AC9866EC303AEA2912133DF6C7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2627
24B2093BE47D28389FBAE9E2B4BE669CDEE068148243DC9D3ED36A9AE449B7B5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2628
95DB5815D7642CE1406A73FB777D6E3B4E76B195BFE7DE8997895A12EA03E3C3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2629
9326686B5A6E3A3D977DB8C5E2AEB5BCD5A1A076C750D9C7D1096948771DA578
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2630
58897A9685EBBCCEA69C886BC304844DD8C20A398611BC105EE2A785CFD1474F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2631
B47C1FC5AC8421C2454AEC68494A2DEE8F9671DECFBDC69C5CC72950BE6E0ED9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2632
C69F11B65EF7BC65AA9A281DE4B9C468AA4B9C7ACD76FCFA08AAA8932A644735
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2633
EB888350AC067BC06E41805FF544A33C10615C4060757A974388438988A309A6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2634
4B12A05503F5CE5DAE4ADD212DB7D9E2877CD8AC9B3C9C9AF2B44A91429E35D6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2635
BD77395B3A2D83D316212FBDD67A7100FCF8EAD473DC86DB2F07F71109335674
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2636
08A86E262847A6891C51BFB0DEF5EB561782261A45C590505EAE8FEDEC8F576B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2637
404ADF163D330388081B4001ADDFFEAFE47E67B39857D35BF0AB1C2178F17C37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2638
468ED2B7E82DE2B3CE84A581FEDF443132E22630D06B8E8B1AAB390DE6B8E4D4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2639
3C3FF490226D850D6CCDF24A401297DF0A9737EDA9CA827B7F0F36E096ECBB73
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2640
9E2DB239DE71F57A65E30D21E9D1A761BA216C7D9E7DDDBEE046CEC49E3B7B51
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2641
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2642
5572236D87DD7434C18804F3337C42B390E939E8788890EF607CCB2388EFC322
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2643
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2644
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2645
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2646
2E80464EB00C95AC41B2F9C9B1437D1B7156664AF7D347C3F1398EEC3244CEDA
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2647
C27CBBB44C6EB707B35383E4BCF02E8BCFAB5BB4FF1CB19C4AA719FF129E7000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2648
C18C315CEB710842B6A1EAD9A0C8EB8002A1A2BD82A6DA9BB24A367095B9A4D5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2649
2890C62ECFAC7BFEDD0AE71F679690CB8631FB182426DADA6DEDFCB0925A2669
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2650
3C22E7FB30F9156B03022CDB1C92FD7D5C71D4A4A4DB16F7C57FAA22A4745BE2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2651
900D2C1FFD557AB45AE34E6BAA68FDAA943A92FD0738D73D49FB363377481E84
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2652
67EEBB2B1B2027B4044343797E9ADDE6E7F92FAAD9795B5D48D2B892BEDABC7C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2653
22552F70716CDF9BB17BABEC606C657DAF3B4093863A7440DB3B6DAB06CEFA4B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2654
2302B25D9ECF7B5AF6EFDE56B107D4F6CCB5CF618054983E0B38DBB27B567646
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2655
E281C1DA9C72472C30063D65302AE24E63256FBB84BB1218A505FFCF64872FAD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2656
ED6D94E3D46DDFF42D70F5A6656417516E44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2657
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2658
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2659
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2660
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2661
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2662
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2663
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2664
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2665
cleartomark
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2666
%%EndFont 
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2667
%%BeginFont: CMR8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2668
%!PS-AdobeFont-1.1: CMR8 1.0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2669
%%CreationDate: 1991 Aug 20 16:39:40
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2670
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2671
11 dict begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2672
/FontInfo 7 dict dup begin
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2673
/version (1.0) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2674
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2675
/FullName (CMR8) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2676
/FamilyName (Computer Modern) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2677
/Weight (Medium) readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2678
/ItalicAngle 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2679
/isFixedPitch false def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2680
end readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2681
/FontName /CMR8 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2682
/PaintType 0 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2683
/FontType 1 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2684
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2685
/Encoding 256 array
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2686
0 1 255 {1 index exch /.notdef put} for
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2687
dup 0 /.notdef put
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2688
readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2689
/FontBBox{-36 -250 1070 750}readonly def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2690
/UniqueID 5000791 def
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2691
currentdict end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2692
currentfile eexec
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2693
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2694
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2695
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2696
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2697
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2698
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2699
68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2700
3645B82392D5CAE11A7CB49D7E2E82DCD485CBA1772CE422BB1D7283AD675B65
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2701
48A7EA0069A883EC1DAA3E1F9ECE7586D6CF0A128CD557C7E5D7AA3EA97EBAD3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2702
9619D1BFCF4A6D64768741EDEA0A5B0EFBBF347CDCBE2E03D756967A16B613DB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2703
0FC45FA2A3312E0C46A5FD0466AB097C58FFEEC40601B8395E52775D0AFCD7DB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2704
8AB317333110531E5C44A4CB4B5ACD571A1A60960B15E450948A5EEA14DD330F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2705
EA209265DB8E1A1FC80DCD3860323FD26C113B041A88C88A21655878680A4466
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2706
FA10403D24BB97152A49B842C180E4D258C9D48F21D057782D90623116830BA3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2707
9902B3C5F2F2DD01433B0D7099C07DBDE268D0FFED5169BCD03D48B2F058AD62
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2708
D8678C626DC7A3F352152C99BA963EF95F8AD11DB8B0D351210A17E4C2C55AD8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2709
9EB64172935D3C20A398F3EEEEC31551966A7438EF3FEE422C6D4E05337620D5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2710
ACC7B52BED984BFAAD36EF9D20748B05D07BE4414A63975125D272FAD83F76E6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2711
10FFF8363014BE526D580873C5A42B70FA911EC7B86905F13AFE55EB0273F582
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2712
83158793B8CC296B8DE1DCCF1250FD57CB0E035C7EDA3B0092ED940D37A05493
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2713
2EC54E09B984FCA4AB7D2EA182BCF1263AA244B07EC0EA901C077A059F709F30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2714
4384CB5FA748F2054FAD9A7A43D4EA427918BD414F766531136B60C3477C6632
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2715
BEFE3897B58C19276A301926C2AEF2756B367319772C9B201C49B4D935A8267B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2716
041D6F1783B6AEA4DAC4F5B3507D7032AA640AAB12E343A4E9BDCF419C04A721
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2717
3888B25AF4E293AACED9A6BDC78E61DA1C424C6503CC1885F762B92DCAD2A47B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2718
6B9A8DBEF5C9099E3D87CF31254B8FE1F02269893F6ED28045486321A2C89D4C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2719
401189A7E2BB7D6930806A94FD603E6F41A29BAB742D3B39EE5D466F01EAE670
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2720
ECE883C1A03319790D5485E89B210AA2DFB079A06037B590231088141C188224
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2721
41B36511D172B85BAC8DC4A5D8923DDFCCC7FB9E7139041A3987364398C6C4BD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2722
906A152728000BC1BFCE959CC41A31C5F856D1BDCC9670044E649159603C3686
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2723
06119C8A797D2B4CCD12980C936C8D6448AD5F636E500B7BCA12A228713F0C8C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2724
39271F7439E90049AC0BED962697D62B4FC578AB76B8ED3435466FFB06D0AB33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2725
99E38FEF539575C80A0A17B3234211136543862D0D08575ACDB45D4A9CBF03B4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2726
4EB9BC13D8285413C3CF8FE3483C5AD80C24405EB4F303AE4B53A840D8551717
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2727
998778B4E0150C6E2903DA6B66675F5FE94E4E459A8BE4F1115BF77891002D98
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2728
95D6CDFAEF4BE5742C180B9EFD08C447D622697B2DC3D4EEF36146000873341C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2729
C217B24F9CDCD7FCBBB737B9A1F9BF56B8691CFE3461E2D3AEEDE48635D3E88A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2730
7262691A41E07FB73F9F78FA6D4DC3C7183F3494A24FB2B832DFA7D8512EEE18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2731
CBBEAEDAAED794D087C950AD664BBB4A29C09BA4A2B39793494A6D9F3AFF11D5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2732
643EF3CE2D55D900B8A388440E9D842C7029262842398AB9B03E89CCA05CA341
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2733
4F13583239AFCE7DBBB890F37A443465D2A05A302167008364C6B767CFF820E4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2734
C49B152DF2425389B70353A66A18C0DD524DA5748F82CE00650FE1D7F8072587
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2735
6FE107E243BC593D46EE71968FF2642811F9AB469E8ABBCB546E60EC161A10A8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2736
C58F38D4CDF75319AFD62E478C9CC4D344C31768C0AA2F5A961B68BD7453B8B8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2737
E39E07BE521C9AC9CA1483358850175E6FAF41E2E5A417B83A81DB59BCB7E1A2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2738
1430C4505D383B21B83E51BBE0951D8C10F70DA67DCFA7CD923C1FBA6A30F384
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2739
60986F1405C92B3CDB376B83C4829F6A1331070798D832C1AEC4F3DDE65F6093
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2740
1BDB3D4F5A32015DAD95BEB0965C52D42492B3C4DBD5F7308E349A65C56E220B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2741
5C6B9F7146596C3E34F56612FB0DC2EB5EBD03E6DDDD34B3BCB88546E616C388
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2742
B33F8116C6780D766B93BD07261118700120B21B2C1C5839D96656F3A83166E6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2743
873FAB12C093EBE91D5BE747F2A40E2693A7A6A839F622B24CA1AA2400C3D615
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2744
F930A678F92FFBF61395EF917BE8E0FCF625BBD4C4CDC3A3A113AF556C34C137
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2745
6DAFAA08DFE2E05C5B50E3522EC0CE5BF62E6670969B11B6010685253BE2D38F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2746
43A30648E37FE431E144BA820B5EEEAD6E5E8BCF943EB26BD59BF70CD69FF6E5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2747
BEF8A70815D591B4848962B1D9FCBA27DD8F14E80B16DA66104EE470A5829668
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2748
401F537283ECBD11585A0CEDA647ED58003599FDD2B4A6833BA63AB7982A82D4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2749
475D2B398079D6170EADF48793A334611ABE0010E3FBCB38185C0409E70A86FB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2750
57D283A31176696DE8ED59B20605C4B9F3105F50FD362E9ABDC63BEDBE943859
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2751
4FE15ED4B2D958A3CCBCFE6B3A0A4B6DE4997FAB76A2E31AB780DDF0291118AE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2752
3061AA19BAA87E7A31BE9BA9947C3F4D5E7BB1DF7587BE990F3E888547AE7A3B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2753
4C9906D15B9C1EB902219D7F920BEC3C3FDA2B2C6411776033B3F82153A3F72A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2754
C35F6FC174E5F25651D097D172112BE48F882D092DF106E9E6121DB4EBA0D1F3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2755
1A7E9DDD48D1E7A08AF7BCE12F94AFBDF788C1E3F611AC8B85A981A198C06211
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2756
BB334D67280B3E981F090E93FAECE611C519ABB22E283033713312F9D5258BB1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2757
36C51A59BB216F2D752493A42C23218CBF62D844DAB3FCF38D0A01544F061F7C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2758
0E3CABF49097B5332A5C22A086566E3654352C3BDD609EB81C6222F5377E0AB1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2759
9B51F024F9A961A25C27759E2EB94E896378B189AE69CAA1A1CEDFE8BC5DF441
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2760
536637C800FFF0ABC3DCDAE48BB9B1B98B8C1B3EB1CECABA5E9C56811EEBD94E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2761
7363493E005F730AED8DC4391BDC2F2B6B9CAB02437A9233BE2B3EA9C7A20FA3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2762
2D5CDEFF1332C0196CA6A5043DA277D95305526B4B993D8797E802FC95284AED
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2763
D2F39E49462314FDD677169691D77EF89FF593FB70A7094F73E461148A4D309D
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2764
596BD21562FC266E915F09187590156AFEADDA857210DB29EF5ADFAC01D109B3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2765
0B8F1DBE1AD241752117650CEC4CCD5DD47FCAA50F772759B2D2B97A75C68500
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2766
A6775AD82109E38E40813FE41695D93B1D7EB8170A4C4BB08BAC9FDCC818C1A1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2767
ABBA03842FE42812EBCD0DEA9D37867BD1056F34A86067F9FF1E4559B1BC0DB8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2768
D05B7E59F3C6F8D0494148CE1411E0E15065ED1CE4AA0B1F4613DFFDBC55E08C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2769
6A99AE501DB257D8446F42CB04AFF7D32BC61C6746A8A82E14EAE912550CB4AD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2770
3D734E8EECBDC6FE06858017C139C3DD48B21CFA9FF32B713F5BFF5EBBBF7A51
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2771
2E9040F038DEF98B8A41E0A7D13129C70005B39C780942755AB01C60F7DB4ECB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2772
3A363B4897EE5E5ADABF06512B8EB62FEC96DB7BD5A40493A71F88EEB5704965
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2773
95981F7C78D2519DF1FE0FE6EA7121E14984B86FAF4CC4D6A610EC3D4C09F009
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2774
D6A1DCCC0400BC3FF557EFDDD8557E071F619D9016B0EEDA30DF51EF3C188534
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2775
0E2178DB5AF5E709432604CCEDF1533E678B0B8E03AAA58E35481579AC244D86
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2776
B1EABAEC15D2B160B385779338D3738A17467C4EDB75EA0B9ABFF35485B5887C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2777
65D05EC069E155E4F1A3F98CFBDA0F868E20DD1090C51278D1CB3625530DDFFD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2778
28217B4304D577CE3EC3F74A42C5665AA40514A08DE2B590EDBA6470AA13400E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2779
04822649CE07453764CF737429BF36226FF147FE1EE0BBFEB04D84F2C0C11FBD
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2780
2C7AA90CA94A8056E9CF45B93C204D21BACEBC5DF69C71D2AE65FC0D70F3BDF0
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2781
9EC2285CA3EA182E50997B31503665D0F26EB4814C408D851FA7B8CA0A2A6799
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2782
1C1119B911DBFE9C12E8A4182287F412FB4B382A7485165EC6629935C128F063
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2783
785FEFE52E1EDDA51BBDA48C4E64DF9E04A1C12A0C4700E26D1FE61CED5D75C2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2784
D4BF8D0CC925BF50C69820C2FD3C3EF37C1AA100AD2D838824F5DDC2DC861D67
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2785
48CF15EA2014475F236DAE3ECCB23363ADF3FB97849DF394FFC5062642E89F7F
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2786
D057989D509A61F896DDC6036910B4D159087CF9139961B417ACAFA20F4AEB37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2787
B7447C9CB920708F65A674C0C23829A7181743460930A08310CFCA1FF4110BBB
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2788
6E8AA33D0A67B365F26C74A372717BECC2F7D5A98E591DDF389E875834AA4099
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2789
CBF8320005B2DE88D643B578EAC66A4CE4E157C5BF620A61B30B6526CD129B00
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2790
157AA321C6A4F1A2A1AE6B10F9AAD30AFE39FDBEAB00ACBA4CD2FC345A350FB6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2791
94FE9EEAEEA0A71021F42B902C211C32B9F6968F6EF098C1A1662FFF10CECB40
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2792
B219D915DEB1D6ADB07E475D82E6A6631A370328B4C25DE35B0B8E6EA1A981D9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2793
12823E2B2822DD9930BAA09B41781ABD8AB66705864E5FB3534AFB834932677A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2794
C56BC76CAEAD09833FC7E9248D9C86CFCA8A26F02B5A92C005FA08D35B1B4BD7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2795
D431E0CD7052A9741EAB928D2694AF94693525C82036CC951F951778B791F717
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2796
662D25C6A91E66457310DF68CBC579818FA8DD6AE35FF96C3E1FF0CE4218C440
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2797
9CA8E53256CF78BB85834978F435919BCBAE9DC7E9BABD9B6B0D60D29BB28873
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2798
B3F089DC022E08A09B6C468E90210148A4A9152EC230DC8D7A1415B199C92211
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2799
D09BBCB2B38D47A8BA2837279C5862D90C7897B1C4DF3DED8B353B68481FBC9A
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2800
F9220D98A4747088434A2E576BA266D8DE6421B773831F637944348CD12C3B78
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2801
C1F9FCFD0975318DCF06FB621ED1D1AF36A09B3511271DF1B9009527EDF2C9ED
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2802
E97F76A3EB070C2F586662CF44AD631D85A09E3E11A32F24830EAA6B148F8C3E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2803
131407DDEBC04F78C1BCCBD59BB646F278F32216918A7DB4C322F527726887E9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2804
A5EEFDEC5F0915D70247CDEC0E6563800B9894F72895D20C8C19D137BF48E54B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2805
B02A58F4943CAC6A1AD120A1009DA6CBC9C4FF6E264C714AA529ECD30E64308C
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2806
41B29D416AA381F3F7FFAB311389AE51A0CCCA6EED45F27001DB9AE68E827159
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2807
90B64316DAE0467A1A518360469658C8713CA72DA0DC5DCBBBD4004C64C98D3E
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2808
50F4752CDB7C85556D4F3DDB3A50A0C77884C7808BC5F9718302BEF4D9904473
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2809
6F25C221B1B1D9AD73E187CF47B786A7FF29FC3843D11E77312ADBF799706084
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2810
1A44A21873815221AFF18593750515745D05A681189D65BF8412C64938CDE022
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2811
B230A41D0B5D143D75B2A4AED9210270B6D5B7EA4B8BBEBEACA0AD53C85F66FE
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2812
E7AED9EAB9D930BBD6802683965EFE9E99E427DB4986AFE4C63F0429389FBA41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2813
F588EC41010D14B04FEA34DF800CF8138DB21CEB194D40DF97B9CBD24392A524
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2814
06E1A813BBCBB1D44737E9F2844D7A12E56989113AD2E7E3F83F8D2E84678CE6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2815
2CA043ECBB799E064558132615B285D7C48C9FAC99490A593EE20C15768B2043
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2816
62226C1750374F5F75971BAC962D862DA4764C5AD03532EEE7370193F095FBD1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2817
6980C098AEB5CF08F1FE63FBD7FA377282096B13DB71941F5DD90BCF642AAD8B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2818
04813C462D9FA42ECEA19707E7BC6506B3002A42DCE293AC81583E5AB07E681B
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2819
2A79FCB1A08E9ACAC517E35578D1F466A60552DBB994D0573F2842C279C53424
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2820
E19C62ACA5BEBE45E11DCDF80D7D33F73676FB112B06CF1BD4FA5F06DC7EADE2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2821
76AF40BD241CD757E4BA428889D7B7536F6BB53C79FB1891F5EBD56030A9E6F6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2822
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2823
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2824
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2825
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2826
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2827
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2828
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2829
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2830
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2831
0000000000000000000000000000000000000000000000000000000000000000
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2832
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2833
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2834
TeXDict begin 39158280 55380996 1000 600 600 (nomu-tcs.dvi)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2835
@start /Fa 254[23 1[{}1 66.4176 /CMBSY7 rf /Fb 137[35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2836
3[35 1[35 1[35 7[35 4[35 97[{ TeX09fbbfacEncoding ReEncodeFont }6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2837
66.4176 /CMTT8 rf /Fc 141[51 54[32 10[18 48[{
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2838
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2839
/Fd 145[38 54 74[29 6[36 27[{ TeXaae443f0Encoding ReEncodeFont }4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2840
49.8132 /CMMI6 rf /Fe 200[30 30 1[30 2[30 30 48[{
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2841
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2842
/Ff 170[71 85[{}1 99.6264 /EUSM10 rf /Fg 153[18 29 33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2843
100[{ TeXBase1Encoding ReEncodeFont }3 66.4176 /Times-Italic
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2844
rf /Fh 244[76 11[{ TeXaae443f0Encoding ReEncodeFont }1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2845
99.6264 /CMMIB10 rf /Fi 136[55 1[55 55 55 55 1[55 55
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2846
55 55 55 55 1[55 55 1[55 55 1[55 1[55 11[55 26[55 7[55
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2847
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2848
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2849
90.9091 /CMTI10 rf /Fk 192[43 1[71 19[35 35 4[76 35[{
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2850
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2851
/Fl 141[76 8[35 35 7[56 41[0 3[61 24[71 25[{
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2852
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2853
rf /Fm 254[29 1[{ TeX10037936Encoding ReEncodeFont }1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2854
90.9091 /CMBSY10 rf /Fn 167[120 25[74 74 74 74 74 74
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2855
74 56[{}8 83.022 /CMEX10 rf /Fo 134[33 1[48 33 33 18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2856
26 22 1[33 33 33 52 18 2[18 33 1[22 29 33 29 33 29 46[33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2857
33 3[22 3[22 22 40[{ TeXBase1Encoding ReEncodeFont }25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2858
66.4176 /Times-Roman rf /Fp 135[45 1[45 2[40 2[50 50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2859
1[80 3[30 3[45 50 29[64 4[72 65[{ TeX74afc74cEncoding ReEncodeFont }11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2860
99.6264 /CMTI12 rf /Fq 139[25 5[43 62 3[24 6[30 37 8[58
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2861
7[45 20[20 20 23[33 6[40 5[41 3[35 4[40 45 11[{
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2862
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2863
rf /Fr 254[32 1[{ TeX10037936Encoding ReEncodeFont }1
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2864
99.6264 /CMBSY10 rf /Fs 134[60 60 60 60 1[60 1[60 1[60
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2865
60 60 60 60 2[60 2[60 60 3[60 8[60 3[60 5[60 60 5[60
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2866
4[60 60 6[60 10[60 60 60 60 2[60 60 4[60 35[{
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2867
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2868
/Ft 141[59 8[27 27 35 35 42[35 3[0 4[47 1[19 6[71 7[71
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2869
7[55 23[20 55{ TeXbbad153fEncoding ReEncodeFont }14 66.4176
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2870
/CMSY8 rf /Fu 162[27 1[27 26[76 46 1[76 2[27 8[49 5[76
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2871
1[38 38 4[81 34[61{ TeXf7b6d320Encoding ReEncodeFont }12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2872
99.6264 /CMR12 rf /Fv 135[51 51 51 51 51 51 51 1[51 51
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2873
51 51 51 2[51 51 51 51 51 51 2[51 46[51 51 49[{
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2874
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2875
rf /Fw 141[83 7[28 39 39 50 50 5[61 2[66 66 66 31[50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2876
4[0 3[66 6[61 1[100 7[100 5[77 1[77 9[50 50 11[77 28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2877
77{ TeXbbad153fEncoding ReEncodeFont }23 99.6264 /CMSY10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2878
rf /Fx 107[55 55 24[39 44 44 66 44 50 28 39 39 50 50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2879
50 50 72 28 2[28 50 50 28 44 50 44 50 50 12[55 50 1[72
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2880
61 6[33 72 72 61 1[72 2[61 5[33 33 4[50 1[50 50 50 2[25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2881
33 25 2[33 33 33 36[50 2[{ TeXBase1Encoding ReEncodeFont }49
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2882
99.6264 /Times-Italic rf /Fy 138[45 25 1[30 1[45 45 45
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2883
71 25 2[25 45 1[30 40 45 40 45 40 12[56 51 15[61 1[66
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2884
18[23 46[{ .167 SlantFont TeXBase1Encoding ReEncodeFont }21
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2885
90.9091 /Times-Roman rf /Fz 134[48 55 3[35 46 3[47 58
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2886
85 3[33 2[48 45 51 42 41 51 7[57 81 1[57 5[63 2[94 66
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2887
5[63 2[70 74 73 2[76 49 1[27 27 11[49 11[46 5[42 55 1[55
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2888
1[48 1[57 3[48 2[43 1[55 62 11[{ TeXaae443f0Encoding ReEncodeFont }39
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2889
99.6264 /CMMI12 rf /FA 87[33 16[100 50 1[44 44 10[33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2890
13[44 50 50 72 50 50 28 39 33 50 50 50 50 78 28 50 28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2891
28 50 50 33 44 50 44 50 44 3[33 1[33 3[94 1[72 61 55
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2892
66 72 55 72 72 89 61 72 39 33 72 72 55 61 72 66 66 72
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2893
1[44 3[28 28 50 50 50 50 50 50 50 50 50 50 28 25 33 25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2894
2[33 33 33 5[33 15[28 13[55 55 2[{ TeXBase1Encoding ReEncodeFont }80
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2895
99.6264 /Times-Roman rf /FB 87[33 45[44 50 50 72 50 55
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2896
33 39 44 55 55 50 55 83 28 55 1[28 55 50 33 44 55 44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2897
55 50 9[100 1[72 66 55 72 78 61 78 72 1[66 2[39 2[61
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2898
66 72 72 1[72 7[50 50 50 50 50 50 50 50 50 50 1[25 33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2899
3[33 33 22[28 14[55 2[{ TeXBase1Encoding ReEncodeFont }58
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2900
99.6264 /Times-Bold rf /FC 139[33 13[45 4[48 8[75 28[25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2901
25 32[52 3[53 8[51 58 11[{ TeXaae443f0Encoding ReEncodeFont }10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2902
90.9091 /CMMI10 rf /FD 75[30 11[30 17[45 1[40 40 24[40
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2903
45 45 66 45 45 25 35 30 45 45 45 45 71 25 45 25 25 45
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2904
45 30 40 45 40 45 40 3[30 1[30 56 66 1[86 66 66 56 51
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2905
61 66 51 66 66 81 56 66 35 30 66 66 51 56 66 61 61 66
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2906
5[25 25 45 45 45 45 45 45 45 45 45 45 25 23 30 23 2[30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2907
30 30 71 20[25 5[30 8[51 2[{ TeXBase1Encoding ReEncodeFont }81
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2908
90.9091 /Times-Roman rf /FE 139[30 35 40 14[40 51 45
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2909
31[66 65[{ TeXBase1Encoding ReEncodeFont }7 90.9091 /Times-Bold
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2910
rf /FF 134[40 40 61 40 45 25 35 35 45 45 45 45 66 25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2911
2[25 45 45 25 40 45 40 45 45 11[66 2[56 1[56 1[61 2[61
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2912
1[30 2[56 2[61 1[56 6[30 12[30 23 44[{ TeXBase1Encoding ReEncodeFont }
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2913
35 90.9091 /Times-Italic rf /FG 157[39 35 3[20 1[20 14[44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2914
2[25 2[46 4[53 1[33 1[55 2[20 2[35 35 35 35 35 35 35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2915
35 6[27 27 4[59 35[{ TeXf7b6d320Encoding ReEncodeFont }22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2916
66.4176 /CMR8 rf /FH 157[46 42 97[{ TeXf7b6d320Encoding ReEncodeFont }2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2917
83.022 /CMR10 rf /FI 134[60 1[86 1[60 33 47 40 2[60 60
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2918
4[33 60 2[53 60 53 60 53 11[86 4[66 2[106 5[86 3[80 1[86
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2919
65[{ TeXBase1Encoding ReEncodeFont }21 119.552 /Times-Roman
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2920
rf /FJ 139[48 4[72 80 120 40 2[40 5[64 1[72 11[104 6[104
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2921
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
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diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
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diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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FI(Andre)m(w)g(Pitts)2071 732 y FH(a)2146 776 y FI(Murdoch)f(Gabbay)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2934
3006 732 y FH(b)1018 948 y FG(a)1057 981 y FF(Univer)o(sity)d(of)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2935
(Cambridg)o(e)o(,)i(Cambridg)o(e)o(,)g(UK)1394 1094 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2936
FG(b)1437 1127 y FF(INRIA,)d(P)-7 b(aris,)23 b(F)-5 b(r)o(ance)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2937
166 1417 3288 4 v 166 1546 a FE(Abstract)166 1752 y FD(W)e(e)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(present)j(a)e(generalisation)k(of)c(\002rst-order)i(uni\002cation)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2939
(to)d(the)g(practically)j(important)f(case)f(of)166 1865
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2940
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2941
(ations)p FD(.)g(A)c(substitution)37 b(of)d(terms)g(for)f(v)n(ari-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2942
1978 y(ables)d(solv)o(es)f(such)h(an)e(equation)j(if)d(it)h(mak)o(es)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2943
(the)g(equated)h(terms)f FC(\013)p FF(-equivalent)p FD(,)j(i.e.)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2944
(equal)h(up)g(to)166 2091 y(renaming)21 b(bound)h(names.)d(F)o(or)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2945
(the)h(applications)k(we)18 b(ha)n(v)o(e)j(in)e(mind,)h(we)f(must)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2946
(consider)i(the)e(simple,)166 2204 y(te)o(xtual)25 b(form)f(of)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2947
(substitution)k(in)d(which)g(names)g(occurring)i(in)e(terms)g(may)f(be)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2948
h(captured)h(within)g(the)166 2317 y(scope)f(of)f(binders)i(upon)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2949
(substitution.)j(W)-7 b(e)22 b(are)h(able)h(to)f(tak)o(e)h(a)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2950
(\223nominal\224)j(approach)h(to)d(binding)i(in)166 2430
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2951
y(which)e(bound)h(entities)h(are)d(e)o(xplicitly)j(named)e(\(rather)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2952
(than)e(using)h(nameless,)g(de)e(Bruijn-style)j(rep-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2953
2543 y(resentations\))30 b(and)d(yet)f(get)h(a)f(v)o(ersion)i(of)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2954
(this)h(form)f(of)g(substitution)k(that)d(respects)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2955
FC(\013)p FD(-equi)n(v)n(alence)166 2656 y(and)23 b(possesses)i(good)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2956
(algorithmic)h(properties.)g(W)-7 b(e)21 b(achie)n(v)o(e)j(this)f(by)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2957
(adapting)i(tw)o(o)d(e)o(xisting)i(ideas.)166 2769 y(The)h(\002rst)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2958
(one)i(is)f(terms)g(in)l(v)n(olving)j(e)o(xplicit)f(substitutions)i(of)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2959
c(names)g(for)g(names,)h(e)o(xcept)g(that)f(here)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2960
2882 y(we)g(only)h(use)g FF(e)n(xplicit)h(permutations)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2961
FD(\(bijecti)n(v)o(e)e(substitutions\).)j(The)25 b(second)i(one)f(is)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2962
(that)h(the)g(uni-)166 2994 y(\002cation)h(algorithm)g(should)g(solv)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2963
(e)g(not)f(only)g(equational)j(problems,)e(b)n(ut)f(also)h(problems)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2964
(about)g(the)166 3107 y FF(fr)m(eshness)j FD(of)e(names)h(for)f(terms.)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2965
g(There)h(is)e(a)h(simple)h(generalisation)j(of)c(classical)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2966
(\002rst-order)g(uni-)166 3220 y(\002cation)i(problems)h(to)e(this)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2967
(setting)i(which)f(retains)g(the)g(latter')-5 b(s)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2968
b(pleasant)i(properties:)g(uni\002cation)166 3333 y(problems)23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2969
b(in)l(v)n(olving)i FC(\013)p FD(-equi)n(v)n(alence)g(and)d(freshness)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2970
(are)d(decidable;)k(and)d(solv)n(able)h(problems)g(pos-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2971
3446 y(sess)h(most)g(general)h(solutions.)166 3717 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2972
FF(K)m(e)m(y)e(wor)m(ds:)47 b FD(Abstract)25 b(Syntax,)f(Alpha-Con)l(v)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2973
o(ersion,)j(Binding)d(Operations,)i(Uni\002cation)p 166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2974
3823 V 166 4194 a FB(1)99 b(Intr)n(oduction)166 4537
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2975
y FA(Decidability)28 b(of)i(uni\002cation)e(for)i(equations)f(between)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2976
(\002rst-order)h(terms)f(and)h(algorithms)166 4658 y(for)20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2977
b(computing)e(most)g(general)i(uni\002ers)g(form)f(a)h(fundamental)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2978
(tool)h(of)h(computational)d(logic)166 4778 y(with)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2979
b(man)o(y)f(applications)g(to)h(programming)f(languages)g(and)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2980
(computer)n(-aided)e(reasoning.)166 4898 y(Ho)n(we)n(v)o(er)l(,)e(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2981
(ery)i(man)o(y)e(potential)h(applications)f(f)o(all)i(outside)e(the)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2982
(scope)f(of)h(\002rst-order)g(uni-)166 5019 y(\002cation,)39
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2983
b(because)h(the)o(y)e(in)l(v)n(olv)o(e)g(term)h(languages)g(with)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2984
(binding)f(operations)g(where)i(at)166 5139 y(the)d(v)o(ery)f(least)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2985
(we)g(do)g(not)f(wish)h(to)f(distinguish)f(terms)h(dif)n(fering)g(up)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2986
(to)g(the)f(renaming)166 5259 y(of)e(bound)e(names.)i(There)g(is)f(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2987
(lar)n(ge)g(body)f(of)g(w)o(ork)h(studying)e(languages)h(with)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2988
(binders)166 5380 y(through)h(the)g(use)g(of)h(v)n(arious)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2989
Fz(\025)p FA(-calculi)i(as)f(term)g(representation)g(languages,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2990
(leading)g(to)189 5712 y Fy(Accepted)25 b(for)e(publication)k(in)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2991
(Theoretical)h(Computer)g(Science.)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2992
%%Page: 2 2
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2993
TeXDict begin 2 1 bop 166 83 a Fx(higher)n(-or)l(der)34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2994
b(uni\002cation)g FA(algorithms)f(for)i(solving)f(equations)g(between)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2995
Fz(\025)p FA(-terms)f(mod-)166 203 y(ulo)23 b Fz(\013)q(\014)6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2996
b(\021)t FA(-equi)n(v)n(alence.)21 b(Ho)n(we)n(v)o(er)l(,)h(higher)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2997
(-order)i(uni\002cation)e(is)h(technically)g(complicated)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2998
324 y(without)k(being)h(completely)f(satisf)o(actory)g(from)h(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2999
(pragmatic)f(point)f(of)h(vie)n(w)-6 b(.)27 b(The)i(reason)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3000
444 y(lies)38 b(in)f(the)h(dif)n(ference)g(between)h(substitution)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3001
(for)j(\002rst-order)h(terms)e(and)h(for)g Fz(\025)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3002
FA(-terms.)166 565 y(The)31 b(former)h(is)f(a)h(simple)e(operation)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3003
(of)g(te)o(xtual)g(replacement)g(\(sometimes)f(called)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3004
Fx(gr)o(aft-)166 685 y(ing)g FA([1],)h(or)f Fx(conte)n(xt)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3005
(substitution)c FA([2,)k(Sect.)g(2.1]\),)f(whereas)h(the)g(latter)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3006
(also)g(in)l(v)n(olv)o(es)f(re-)166 805 y(namings)d(to)i(a)n(v)n(oid)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3007
(capture.)h(Capture-a)n(v)n(oidance)g(ensures)f(that)g(substitution)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3008
(respects)j Fz(\013)q FA(-)166 926 y(equi)n(v)n(alence,)c(b)n(ut)g(it)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3009
(complicates)f(higher)n(-order)h(uni\002cation)f(algorithms.)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3010
(Furthermore)i(it)166 1046 y(is)d(the)g(simple)f(te)o(xtual)g(form)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3011
(of)i(substitution)c(rather)j(than)g(the)g(more)g(complicated)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3012
(capture-)166 1166 y(a)n(v)n(oiding)j(form)i(which)f(occurs)g(in)g(man)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3013
o(y)g(informal)g(applications)f(of)h(\223uni\002cation)g(modulo)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3014
1287 y Fz(\013)q FA(-equi)n(v)n(alence\224.)k(F)o(or)h(e)o(xample,)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3015
(consider)h(the)g(follo)n(wing)e(schematic)h(rule)i(which)e(might)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3016
1407 y(form)j(part)g(of)g(the)g(inducti)n(v)o(e)e(de\002nition)h(of)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3017
(a)f(binary)g(e)n(v)n(aluation)e(relation)i Fw(+)g FA(for)g(the)g(e)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3018
(x-)166 1528 y(pressions)24 b(of)h(an)g(imaginary)e(functional)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3019
(programming)g(language:)1330 1758 y Fv(app)q Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3020
Fv(fn)h Fz(a:Y)5 b(;)17 b(X)8 b Fu(\))55 b Fw(+)g Fz(V)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3021
1304 1803 931 4 v 1304 1889 a Fv(let)26 b Fz(a)i Fu(=)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3022
Fz(X)k Fv(in)26 b Fz(Y)76 b Fw(+)56 b Fz(V)2290 1806
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3023
y FA(.)3338 1838 y(\(1\))166 2145 y(Here)27 b Fz(X)8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3024
b FA(,)25 b Fz(Y)47 b FA(and)26 b Fz(V)48 b FA(are)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3025
b(meta)n(v)n(ariables)f(standing)f(for)j(unkno)n(wn)d(programming)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3026
(language)166 2266 y(e)o(xpressions.)k(The)h(binders)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3027
Fv(fn)c Fz(a:)p Fu(\()p Fw(\000)p Fu(\))30 b FA(and)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3028
Fv(let)d Fz(a)36 b Fu(=)g Fz(X)d Fv(in)25 b Fu(\()p Fw(\000)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3029
Fu(\))30 b FA(may)f(v)o(ery)g(well)g(capture)166 2386
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3030
y(free)34 b(occurrences)g(of)g(the)f(v)n(ariable)g(named)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3031
Fz(a)g FA(when)g(we)h(instantiate)e(the)h(schematic)g(rule)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3032
2507 y(by)g(replacing)h(the)g(meta)n(v)n(ariable)e Fz(Y)56
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3033
b FA(with)32 b(an)i(e)o(xpression.)f(F)o(or)g(instance,)h(using)e(the)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3034
(rule)166 2627 y(scheme)25 b(in)f(a)h(bottom-up)e(search)j(for)f(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3035
(proof)g(of)1393 2873 y Fv(let)h Fz(a)i Fu(=)f(1)e Fv(in)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3036
Fz(a)56 b Fw(+)f Fu(1)1111 b FA(\(2\))166 3120 y(we)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3037
b(w)o(ould)f(use)h(a)g(substitution)d(that)i(does)h(in)l(v)n(olv)o(e)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3038
(capture,)i(namely)1304 3366 y Fu([)p Fz(X)36 b Fu(:=)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3039
b(1)o Fz(;)17 b(Y)49 b Fu(:=)28 b Fz(a;)17 b(V)49 b Fu(:=)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3040
b(1])166 3613 y FA(in)i(order)g(to)g(unify)f(the)h(goal)f(with)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3041
(conclusion)g(of)h(the)g(rule)g(\(1\)\227generating)f(the)h(ne)n(w)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3042
3733 y(goal)h Fv(app)q Fu(\()p Fv(fn)25 b Fz(a:a;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3043
b Fu(1\))38 b Fw(+)f Fu(1)30 b FA(from)g(the)g(hypothesis)e(of)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3044
(\(1\).)g(The)h(problem)e(with)g(this)h(is)f(that)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3045
3853 y(in)22 b(informal)g(practice)i(we)f(usually)e(identify)h(terms)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3046
(up)h(to)f Fz(\013)q FA(-equi)n(v)n(alence,)g(whereas)h(te)o(xtual)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3047
3974 y(substitution)f(does)j(not)f(respect)h Fz(\013)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3048
FA(-equi)n(v)n(alence.)f(F)o(or)h(e)o(xample,)f(up)h(to)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3049
Fz(\013)q FA(-equi)n(v)n(alence,)g(the)166 4094 y(goal)1403
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3050
4241 y Fv(let)h Fz(b)k Fu(=)e(1)e Fv(in)g Fz(b)56 b Fw(+)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3051
Fu(1)1121 b FA(\(3\))166 4417 y(is)34 b(the)f(same)h(as)g(\(2\).)g(W)-8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3052
b(e)34 b(might)f(think)g(\(erroneously!\))h(that)f(the)h(conclusion)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3053
(of)h(rule)g(\(1\))166 4537 y(is)i(the)f(same)h(as)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3054
Fv(let)26 b Fz(b)49 b Fu(=)f Fz(X)33 b Fv(in)25 b Fz(Y)70
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3055
b Fw(+)48 b Fz(V)58 b FA(without)35 b(changing)g(the)h(rule')-5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3056
b(s)35 b(hypothesis\227)166 4658 y(after)c(all,)f(if)g(we)h(are)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3057
(trying)e(to)h(mak)o(e)g Fz(\013)q FA(-equi)n(v)n(alence)f(disappear)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3058
(into)e(the)h(infrastructure,)166 4778 y(then)d(we)g(must)f(be)h(able)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3059
(to)f(replace)i(an)o(y)e Fx(part)i FA(of)f(what)g(we)g(ha)n(v)o(e)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3060
(with)f(an)h(equi)n(v)n(alent)e(part.)166 4898 y(So)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3061
b(we)g(might)e(be)h(tempted)g(to)g(unify)g(the)g(conclusion)f(with)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3062
(\(3\))h(via)f(the)g(te)o(xtual)g(substitu-)166 5019
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3063
y(tion)25 b Fu([)p Fz(X)35 b Fu(:=)28 b(1)p Fz(;)17 b(Y)49
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3064
b Fu(:=)27 b Fz(b)q(;)17 b(V)49 b Fu(:=)27 b(1])p FA(,)f(and)g(then)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3065
(apply)g(this)g(substitution)e(to)i(the)h(hypothesis)d(to)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3066
5139 y(obtain)28 b(a)h(wrong)f(goal,)h Fv(app)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3067
Fv(fn)d Fz(a:b;)17 b Fu(1\))35 b Fw(+)g Fu(1)p FA(.)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3068
b(Using)g Fz(\025)p FA(-calculus)g(and)h(higher)n(-order)g(uni\002-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3069
5259 y(cation)k(sa)n(v)o(es)f(us)g(from)h(such)g(slopp)o(y)f(thinking,)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3070
f(b)n(ut)h(at)h(the)g(e)o(xpense)f(of)h(ha)n(ving)f(to)h(mak)o(e)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3071
5380 y(e)o(xplicit)22 b(the)g(dependence)i(of)f(meta)n(v)n(ariables)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3072
(on)h(bindable)f(names)h(via)g(the)g(use)g(of)g(function)1773
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3073
5712 y(2)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3074
%%Page: 3 3
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3075
TeXDict begin 3 2 bop 166 83 a FA(v)n(ariables)24 b(and)h(application.)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3076
e(F)o(or)i(e)o(xample,)f(\(1\))h(w)o(ould)f(be)h(replaced)g(by)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3077
(something)e(lik)o(e)1310 289 y Fv(app)17 b Fu(\()p Fv(fn)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3078
Fz(\025a:F)31 b(a)p Fu(\))17 b Fz(X)62 b Fw(+)56 b Fz(V)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3079
1310 334 1001 4 v 1369 425 a Fv(let)18 b Fz(X)24 b Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3080
Fz(\025a:F)30 b(a)p Fu(\))56 b Fw(+)f Fz(V)1109 b FA(\(4\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3081
647 y(or)l(,)25 b(modulo)e Fz(\021)t FA(-equi)n(v)n(alence)1371
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3082
853 y Fv(app)17 b Fu(\()p Fv(fn)g Fz(F)d Fu(\))j Fz(X)63
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3083
b Fw(+)55 b Fz(V)p 1371 898 798 4 v 1468 984 a Fv(let)18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3084
b Fz(X)24 b(F)69 b Fw(+)56 b Fz(V)2224 901 y FA(.)3338
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3085
984 y(\(5\))166 1206 y(No)n(w)26 b(goal)h(\(3\))g(becomes)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3086
Fv(let)17 b Fu(1)g Fz(\025b:b)32 b Fw(+)g Fu(1)26 b FA(and)h(there)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3087
(is)g(no)g(problem)f(unifying)f(it)i(with)f(the)166 1326
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3088
y(conclusion)i(of)h(\(5\))h(via)f(a)g(capture-a)n(v)n(oiding)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3089
(substitution)d(of)j Fu(1)h FA(for)f Fz(X)8 b FA(,)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3090
b Fz(\025c:c)g FA(for)h Fz(F)43 b FA(and)29 b Fu(1)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3091
1447 y FA(for)c Fz(V)d FA(.)166 1668 y(This)36 b(is)h(all)f(v)o(ery)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3092
(\002ne,)g(b)n(ut)f(the)h(situation)e(is)i(not)f(as)h(pleasant)f(as)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3093
(for)g(\002rst-order)h(terms:)166 1788 y(higher)n(-order)43
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3094
b(uni\002cation)g(problems)f(can)h(be)h(undecidable,)e(decidable)h(b)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3095
(ut)g(lack)g(most)166 1909 y(general)h(uni\002ers,)f(or)g(ha)n(v)o(e)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3096
(such)g(uni\002ers)g(only)g(by)g(imposing)e(some)i(restrictions)f([3];)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3097
166 2029 y(see)36 b([4])g(for)g(a)g(surv)o(e)o(y)f(of)g(higher)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3098
(-order)h(uni\002cation.)f(W)-8 b(e)36 b(started)g(out)f(w)o(anting)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3099
(to)g(com-)166 2149 y(pute)42 b(with)g(binders)f(modulo)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3100
Fz(\013)q FA(-equi)n(v)n(alence,)g(and)h(someho)n(w)f(the)h(process)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3101
(of)h(making)166 2270 y(possibly-capturing)31 b(substitution)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3102
(respectable)k(has)f(led)g(to)f(function)h(v)n(ariables,)f(applica-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3103
2390 y(tion,)24 b(capture-a)n(v)n(oiding)g(substitution)e(and)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3104
Fz(\014)6 b(\021)t FA(-equi)n(v)n(alence.)23 b(Does)h(it)h(ha)n(v)o(e)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3105
(to)h(be)g(so?)f(No!)166 2611 y(F)o(or)43 b(one)g(thing,)f(se)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3106
(eral)g(authors)h(ha)n(v)o(e)g(already)g(noted)g(that)f(one)h(can)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3107
(mak)o(e)f(sense)g(of)166 2731 y(possibly-capturing)35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3108
b(substitution)f(modulo)i Fz(\013)q FA(-equi)n(v)n(alence)f(by)i(using)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3109
f Fx(e)n(xplicit)h(substitu-)166 2852 y(tions)21 b FA(in)h(the)h(term)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3110
(representation)g(language:)g(see)g([1,5\2269].)g(Compared)h(with)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3111
(those)h(w)o(orks,)166 2972 y(we)36 b(mak)o(e)g(a)h(number)f(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3112
(simpli\002cations.)e(First,)i(we)g(\002nd)g(that)g(we)g(do)g(not)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3113
(need)g(to)g(use)166 3093 y(function)24 b(v)n(ariables,)g(application)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3114
(or)i Fz(\014)6 b(\021)t FA(-equi)n(v)n(alence)23 b(in)h(our)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3115
(representation)g(language\227)166 3213 y(lea)n(ving)d(just)f(binders)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3116
(and)i Fz(\013)q FA(-equi)n(v)n(alence.)d(Secondly)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3117
b(,)21 b(instead)f(of)i(using)e(e)o(xplicit)g(substitu-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3118
3333 y(tions)26 b(of)h(names)g(for)h(names,)e(we)i(use)f(only)f(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3119
(special)g(case)h(of)f Fx(e)n(xplicit)g(permutations)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3120
FA(of)166 3454 y(names.)33 b(The)g(idea)g(of)g(using)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3121
(name-permutations,)f(and)i(in)f(particular)h(name-sw)o(appings,)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3122
3574 y(when)g(dealing)g(with)g Fz(\013)q FA(-con)l(v)o(ersion)f(w)o(as)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3123
i(described)f(in)g([10])h(and)f(there)h(is)f(gro)n(wing)f(e)n(vi-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3124
3694 y(dence)k(of)f(its)f(usefulness)g(\(see)i([11\22613],)f(for)g(e)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3125
(xample\).)f(When)i(a)f(name)g(substitution)d(is)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3126
3815 y(actually)f(a)g(permutation,)f(the)h(function)f(it)h(induces)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3127
(from)g(terms)g(to)f(terms)h(is)g(a)g(bijection;)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3128
3935 y(this)g(bijecti)n(vity)f(gi)n(v)o(es)g(the)i(operation)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3129
(permuting)e(names)i(v)o(ery)g(good)f(logical)h(proper)n(-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3130
4056 y(ties)21 b(compared)g(with)f(name)h(substitution.)d(Consider)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3131
(for)h(e)o(xample)e(the)h Fz(\013)q FA(-equi)n(v)n(alent)e(terms)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3132
4176 y Fv(fn)e Fz(a:b)j FA(and)g Fv(fn)d Fz(c:b)p FA(,)j(where)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3133
Fz(a)p FA(,)f Fz(b)h FA(and)g Fz(c)f FA(are)h(distinct.)e(If)i(we)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3134
(apply)g(the)h(substitution)c Fu([)p Fz(b)3141 4170 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3135
Ft(7!)3212 4176 y Fz(a)p Fu(])k FA(\(re-)166 4296 y(naming)f(all)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3136
(free)h(occurrences)f(of)h Fz(b)f FA(to)g(be)g Fz(a)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3137
FA(\))g(to)g(them)f(we)i(get)e Fv(fn)f Fz(a:a)i FA(and)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3138
Fv(fn)d Fz(c:a)p FA(,)j(which)g(are)166 4417 y(no)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3139
b(longer)g Fz(\013)q FA(-equi)n(v)n(alent.)f(Thus)g(renaming)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3140
(substitutions)d(do)k(not)e(respect)i Fz(\013)q FA(-equi)n(v)n(alence)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3141
166 4537 y(in)20 b(general,)h(and)g(an)o(y)f(uni\002cation)h(algorithm)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3142
e(using)h(them)g(needs)h(to)f(tak)o(e)h(e)o(xtra)f(precautions)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3143
4658 y(to)j(not)f(inadv)o(ertently)f(change)i(the)g(intended)f(meaning)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3144
h(of)g(terms.)f(The)h(traditional)f(solution)166 4778
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3145
y(for)27 b(this)f(problem)g(is)g(to)g(introduce)g(a)h(more)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3146
(complicated)e(form)i(of)g(renaming)f(substitution)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3147
4898 y(that)e(a)n(v)n(oids)f(capture)h(of)h(names)e(by)h(binders.)g(In)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3148
g(contrast,)f(the)h(simple)f(operation)h(of)g(name-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3149
5019 y(permutation)29 b(respects)h Fz(\013)q FA(-equi)n(v)n(alence;)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3150
(for)i(e)o(xample,)e(applying)g(the)h(name-permutation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3151
5139 y Fu(\()p Fz(a)17 b(b)p Fu(\))30 b FA(that)e(sw)o(aps)h(all)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3152
(occurrences)h(of)g Fz(a)f FA(and)g Fz(b)h FA(\(be)g(the)o(y)e(free,)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3153
(bound)f(or)g(binding\))f(to)h(the)166 5259 y(terms)f(abo)o(v)o(e)g(gi)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3154
n(v)o(es)f Fv(fn)17 b Fz(b:a)29 b FA(and)g Fv(fn)17 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3155
Fz(c:a)p FA(,)29 b(which)f(are)h(still)f Fz(\013)q FA(-equi)n(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3156
(alent.)e(W)-8 b(e)29 b(e)o(xploit)e(such)166 5380 y(good)38
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3157
b(properties)g(of)h(name-permutations)d(to)i(gi)n(v)o(e)g(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3158
(conceptually)e(simple)h(uni\002cation)1773 5712 y(3)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3159
eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3160
%%Page: 4 4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3161
TeXDict begin 4 3 bop 166 83 a FA(algorithm.)166 303
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3162
y(In)22 b(addition)e(to)h(the)g(use)g(of)h(e)o(xplicit)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3163
(name-permutations,)g(we)h(also)g(compute)g(symbolically)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3164
423 y(with)26 b(predicates)g(e)o(xpressing)f Fx(fr)l(eshness)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3165
FA(of)h(names)g(for)h(terms.)e(Such)i(predicates)f(certainly)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3166
544 y(feature)43 b(in)e(pre)n(vious)g(w)o(ork)h(on)f(binding)g(\(for)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3167
(e)o(xample,)f(Qu-Prolog')-5 b(s)41 b Fs(not)p 3030 544
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3168
30 4 v 35 w(free)p 3305 544 V 35 w(in)166 664 y FA(predicate)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3169
b([8],)g(the)f(notion)f(of)i(\223algebraic)g(independence\224)g(in)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3170
([14,)g(De\002nition)g(3],)g(and)h(the)166 785 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3171
(\223non-occurrence\224)31 b(predicates)f(of)g([15]\).)g(But)h(once)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3172
(again,)f(the)h(use)g(of)g(such)g(a)g(freshness)166 905
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3173
y(predicate)d(based)g(upon)f(name)h Fx(swapping)f FA(rather)h(than)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3174
(renaming,)g(which)h(arises)g(naturally)166 1025 y(from)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3175
b(the)g(w)o(ork)g(reported)g(in)g([10,16],)f(gi)n(v)o(es)g(us)h(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3176
(simpler)f(theory)h(with)f(good)h(algorith-)166 1146
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3177
y(mic)28 b(properties.)f(It)h(is)g(easy)g(to)f(see)i(why)e(there)h(is)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3178
(a)g(need)g(for)h(computing)d(with)h(freshness,)166 1266
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3179
y(gi)n(v)o(en)i(that)h(we)h(tak)o(e)g(a)g(\223nominal\224)f(approach)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3180
(to)f(binders.)g(\(In)h(other)f(w)o(ords)g(we)h(use)g(con-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3181
1386 y(crete)25 b(v)o(ersions)e(of)i(binding)e(and)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3182
Fz(\013)q FA(-equi)n(v)n(alence)g(in)g(which)g(bound)f(entities)h(are)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3183
(named)f(e)o(x-)166 1507 y(plicitly)-6 b(,)26 b(rather)i(than)g(using)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3184
(de)i(Bruijn-style)f(representations,)g(as)h(for)g(e)o(xample)f(in)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3185
([1,7].\))166 1627 y(A)i(basic)h(instance)e(of)i(our)f(generalised)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3186
(form)g(of)h Fz(\013)q FA(-equi)n(v)n(alence)e(identi\002es)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3187
Fv(fn)25 b Fz(a:X)39 b FA(with)166 1748 y Fv(fn)25 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3188
Fz(b:)p Fu(\()p Fz(a)17 b(b)p Fu(\))p Fr(\001)q Fz(X)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3189
b FA(pro)o(vided)25 b Fz(b)h Fx(is)e(fr)l(esh)i(for)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3190
Fz(X)8 b FA(,)25 b(where)h(the)f(subterm)f Fu(\()p Fz(a)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3191
b(b)p Fu(\))p Fr(\001)p Fz(X)34 b FA(indicates)24 b(an)i(e)o(x-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3192
1868 y(plicit)h(permutation\227namely)e(the)i(sw)o(apping)g(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3193
Fz(a)f FA(and)h Fz(b)p FA(\227w)o(aiting)f(to)g(be)h(applied)f(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3194
Fz(X)8 b FA(.)166 1988 y(W)-8 b(e)30 b(write)f(\223)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3195
Fz(b)g FA(is)g(fresh)g(for)h Fz(X)8 b FA(\224)29 b(symbolically)e(as)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3196
Fz(b)36 b Fu(#)g Fz(X)8 b FA(;)29 b(the)g(intended)f(meaning)h(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3197
(this)166 2109 y(relation)g(is)g(that)g Fz(b)h FA(does)f(not)g(occur)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3198
(free)i(in)e(an)o(y)f(\(ground\))h(term)g(that)g(may)g(be)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3199
(substituted)166 2229 y(for)23 b Fz(X)8 b FA(.)23 b(If)g(we)g(kno)n(w)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3200
(more)h(about)f Fz(X)31 b FA(we)23 b(may)f(be)h(able)g(to)f(eliminate)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3201
(the)h(e)o(xplicit)e(permuta-)166 2350 y(tion)26 b(in)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3202
Fu(\()p Fz(a)17 b(b)p Fu(\))p Fr(\001)p Fz(X)8 b FA(;)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3203
b(for)h(e)o(xample,)e(if)i(we)f(kne)n(w)g(that)g Fz(a)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3204
b Fu(#)g Fz(X)k FA(holds)25 b(as)i(well)f(as)h Fz(b)k
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3205
Fu(#)g Fz(X)8 b FA(,)26 b(then)166 2470 y Fu(\()p Fz(a)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3206
b(b)p Fu(\))p Fr(\001)p Fz(X)33 b FA(can)25 b(be)g(replaced)g(by)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3207
Fz(X)8 b FA(.)166 2690 y(It)24 b(should)e(already)i(be)g(clear)h(from)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3208
(these)h(simple)e(e)o(xamples)h(that)g(in)h(our)g(setting)e(the)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3209
(appro-)166 2810 y(priate)c(notion)f(of)h(term-equality)f(is)h(not)g(a)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3210
g(bare)h(equation,)e Fz(t)28 b Fw(\031)g Fz(t)2430 2774
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3211
y Ft(0)2454 2810 y FA(,)20 b(b)n(ut)g(rather)g(a)h(hypothetical)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3212
2931 y(judgement)j(of)g(the)h(form)1597 3051 y Fw(r)j(`)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3213
Fz(t)h Fw(\031)g Fz(t)1999 3010 y Ft(0)3338 3051 y FA(\(6\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3214
3200 y(where)37 b Fw(r)g FA(is)g(a)g Fx(fr)l(eshness)f(en)l(vir)l
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3215
(onment)r FA(\227a)f(\002nite)i(set)f Fw(f)p Fz(a)2317
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3216
3215 y FG(1)2407 3200 y Fu(#)50 b Fz(X)2619 3215 y FG(1)2658
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3217
3200 y Fz(;)17 b(:)g(:)g(:)f(;)h(a)2928 3215 y Fq(n)3025
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3218
3200 y Fu(#)50 b Fz(X)3237 3215 y Fq(n)3284 3200 y Fw(g)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3219
b FA(of)166 3320 y(freshness)25 b(assumptions.)d(F)o(or)j(e)o(xample)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3220
1055 3539 y Fw(f)p Fz(a)j Fu(#)g Fz(X)r(;)17 b(b)28 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3221
Fu(#)g Fz(X)8 b Fw(g)27 b(`)h Fv(fn)d Fz(a:X)36 b Fw(\031)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3222
b Fv(fn)d Fz(b:X)782 b FA(\(7\))166 3758 y(is)27 b(a)g(v)n(alid)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3223
(judgement)f(of)i(our)g Fx(nominal)f(equational)f(lo)o(gic)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3224
FA(.)h(Similarly)-6 b(,)26 b(judgements)f(about)166 3879
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3225
y(freshness)g(itself)f(will)g(tak)o(e)h(the)f(form)1571
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3226
4098 y Fw(r)k(`)g Fz(a)f Fu(#)h Fz(t)g(:)1290 b FA(\(8\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3227
4317 y(T)-8 b(w)o(o)34 b(e)o(xamples)f(of)i(v)n(alid)e(freshness)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3228
(judgements)f(are)i Fw(f)p Fz(a)46 b Fu(#)f Fz(X)8 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3229
Fw(g)45 b(`)h Fz(a)f Fu(#)h Fv(fn)25 b Fz(b:X)60 b FA(and)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3230
4438 y Fw(;)28 b(`)f Fz(a)h Fu(#)g Fv(fn)d Fz(a:X)8 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3231
FA(.)166 4658 y(The)20 b(freshness)f(en)l(vironment)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3232
Fw(r)i FA(in)f(judgements)f(of)i(the)f(form)g(\(6\))h(and)g(\(8\))f(e)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3233
(xpresses)g(fresh-)166 4778 y(ness)28 b(conditions)f(that)h(an)o(y)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3234
(te)o(xtual)f(substitution)f(of)j(terms)f(for)g(v)n(ariables)g(must)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3235
(respect)i(in)166 4898 y(order)k(for)f(the)g(right-hand)g(side)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3236
(the)g(judgement)f(to)h(be)g(v)n(alid)f(after)i(substitution.)d(This)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3237
166 5019 y(e)o(xplicit)37 b(use)h(of)g(freshness)f(mak)o(es)h(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3238
(operation)f(of)i(te)o(xtual)d(substitution)g(respect)i(our)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3239
5139 y(generalised)29 b(form)g(of)h Fz(\013)q FA(-equi)n(v)n(alence.)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3240
(F)o(or)h(e)o(xample,)g(if)g(we)h(were)g(na)m(\250)-30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3241
b(\021v)o(ely)28 b(to)h(re)o(gard)g(the)166 5259 y(terms)23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3242
b Fv(fn)i Fz(a:X)32 b FA(and)23 b Fv(fn)j Fz(b:X)32 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3243
FA(as)23 b Fz(\013)q FA(-equi)n(v)n(alent,)f(then)h(applying)f(for)i(e)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3244
o(xample)e(the)h(capturing)166 5380 y(substitution)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3245
Fu([)p Fz(X)44 b Fu(:=)35 b Fz(a)p Fu(])30 b FA(or)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3246
Fu([)p Fz(X)44 b Fu(:=)35 b Fz(b)p Fu(])30 b FA(results)e(into)h(tw)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3247
(o)f(terms)h(that)g(are)g Fx(not)i Fz(\013)q FA(-equi)n(v)n(alent)1773
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3248
5712 y(4)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3249
%%Page: 5 5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3250
TeXDict begin 5 4 bop 166 83 a FA(an)o(ymore.)22 b(\(A)h(similar)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3251
(observ)n(ation)g(partly)h(moti)n(v)n(ates)f(the)h(w)o(ork)h(in)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3252
([17].\))h(Ho)n(we)n(v)o(er)l(,)e(if)i(we)166 203 y(assume)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3253
Fz(a)27 b Fu(#)h Fz(X)h FA(and)22 b Fz(b)28 b Fu(#)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3254
Fz(X)h FA(as)21 b(in)g(\(7\),)g(then)g(all)g(problematic)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3255
(substitutions)e(are)k(ruled)e(out.)166 324 y(In)k(this)e(w)o(ay)i(we)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3256
(obtain)f(a)g(v)o(ersion)g(of)h Fz(\013)q FA(-equi)n(v)n(alence)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3257
(between)i(terms)f(with)f(v)n(ariables)h(that)166 444
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3258
y(is)g(respected)g(by)g(te)o(xtual)e(substitutions)f(\(see)k(Lemma)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3259
(2.14)h(belo)n(w\),)f(unlik)o(e)g(the)h(traditional)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3260
565 y(notion)h(of)g Fz(\013)q FA(-equi)n(v)n(alence.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3261
897 y Fx(Summary)166 1237 y FA(W)-8 b(e)26 b(will)f(represent)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3262
(languages)g(in)l(v)n(olving)e(binders)h(using)g(the)g(usual)h(notion)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3263
(of)i(\002rst-order)166 1357 y(terms)34 b(o)o(v)o(er)f(a)h(man)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3264
(y-sorted)f(signature,)g(b)n(ut)h(with)f(certain)h(distinguished)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3265
(constants)h(and)166 1478 y(function)26 b(symbols.)f(These)h(gi)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3266
(e)f(us)i(terms)f(with:)f(distinguished)f(constants)i(naming)f(bind-)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3267
166 1598 y(able)35 b(entities,)f(that)g(we)i(call)e Fx(atoms)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3268
FA(;)g(terms)h Fz(a:t)g FA(e)o(xpressing)f(a)h(generic)g(form)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3269
Fx(binding)166 1719 y FA(of)g(an)f(atom)g Fz(a)h FA(in)f(a)h(term)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3270
Fz(t)p FA(;)g(and)h(terms)f Fz(\031)t Fr(\001)o Fz(X)43
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3271
b FA(representing)34 b(an)g(e)o(xplicit)f Fx(permutation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3272
Fz(\031)166 1839 y FA(of)d(atoms)e(w)o(aiting)h(to)g(be)g(applied)g(to)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3273
h(whate)n(v)o(er)e(term)h(is)h(substituted)d(for)j(the)f(v)n(ariable)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3274
Fz(X)8 b FA(.)166 1959 y(Section)20 b(2)h(presents)e(this)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3275
(term-language)g(together)f(with)h(a)h(syntax-directed)e(inducti)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3276
(e)f(def-)166 2080 y(inition)25 b(of)i(the)g(pro)o(v)n(able)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3277
(judgements)h(of)h(the)f(form)h(\(6\))g(and)g(\(8\))g(which)f(for)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3278
Fx(gr)l(ound)h FA(terms)166 2200 y(\(i.e.)36 b(ones)g(with)f(no)g(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3279
(ariables\))h(agrees)g(with)g(the)f(usual)h(notions)e(of)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3280
Fz(\013)q FA(-equi)n(v)n(alence)f(and)166 2320 y(\223not)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3281
b(a)g(free)h(v)n(ariable)e(of)5 b(\224.)26 b(Ho)n(we)n(v)o(er)l(,)f(on)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3282
h(open)f(terms)h(our)f(judgements)g(dif)n(fer)g(from)h(these)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3283
2441 y(standard)h(notions.)f(Section)i(3)f(considers)g(uni\002cation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3284
(in)g(this)g(setting.)f(Solving)h(equalities)166 2561
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3285
y(between)h(abstractions)f Fz(a:t)34 b Fw(\031)q Fu(?)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3286
Fz(a)1385 2525 y Ft(0)1409 2561 y Fz(:t)1471 2525 y Ft(0)1522
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3287
2561 y FA(entails)28 b(solving)e(both)h(equalities)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3288
Fz(t)34 b Fw(\031)q Fu(?)f(\()p Fz(a)17 b(a)3130 2525
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3289
y Ft(0)3153 2561 y Fu(\))p Fr(\001)p Fz(t)3258 2525 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3290
Ft(0)3310 2561 y FA(and)166 2682 y(freshness)37 b(problems)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3291
Fz(a)51 b Fu(#?)g Fz(t)1297 2645 y Ft(0)1320 2682 y FA(.)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3292
b(Therefore)h(our)f(general)h(form)f(of)g Fx(nominal)f(uni\002cation)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3293
166 2802 y(pr)l(oblem)23 b FA(is)h(a)g(\002nite)h(collection)e(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3294
(indi)n(vidual)e(equality)i(and)g(freshness)g(problems.)f(Such)h(a)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3295
2922 y(problem)e Fz(P)37 b FA(is)23 b(solv)o(ed)f(by)h(pro)o(viding)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3296
(not)i(only)f(a)i(substitution)c Fz(\033)28 b FA(\(of)23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3297
b(terms)g(for)g(v)n(ariables\),)166 3043 y(b)n(ut)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3298
b(also)g(a)h(freshness)g(en)l(vironment)e Fw(r)i FA(\(as)g(abo)o(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3299
(e\),)f(which)g(together)g(ha)n(v)o(e)h(the)f(property)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3300
3163 y(that)25 b Fw(r)i(`)h Fz(\033)t Fu(\()p Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3301
Fu(\))g Fw(\031)h Fz(\033)t Fu(\()p Fz(t)976 3127 y Ft(0)999
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3302
3163 y Fu(\))c FA(and)g Fw(r)j(`)g Fz(a)g Fu(#)g Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3303
Fu(\()p Fz(t)1751 3127 y Ft(00)1794 3163 y Fu(\))d FA(hold)f(for)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3304
(each)h(indi)n(vidual)d(equality)h Fz(t)k Fw(\031)p Fu(?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3305
Fz(t)3430 3127 y Ft(0)166 3284 y FA(and)i(freshness)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3306
Fz(a)38 b Fu(#?)g Fz(t)1030 3247 y Ft(00)1102 3284 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3307
FA(in)30 b(the)g(problem)f Fz(P)14 b FA(.)30 b(Our)g(main)f(result)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3308
(with)f(respect)i(to)e(uni\002ca-)166 3404 y(tion)20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3309
b(is)h(that)g Fx(solvability)e(is)i(decidable)g(and)g(that)f(solvable)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3310
(pr)l(oblems)g(possess)g(most)h(g)o(ener)o(al)166 3524
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3311
y(solutions)30 b FA(\(for)i(a)g(reasonably)g(ob)o(vious)d(notion)i(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3312
(\223most)f(general\224\).)h(The)g(proof)g(is)f(via)g(a)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3313
3645 y(uni\002cation)i(algorithm)f(that)h(is)g(v)o(ery)g(similar)g(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3314
(the)h(\002rst-order)g(algorithm)e(gi)n(v)o(en)g(in)h(the)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3315
3765 y(no)n(w-common)23 b(transformational)g(style)h([18].)h(\(See)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3316
([19,)f(Sect.)g(2.6])g(or)g([20,)g(Sect.)g(4.6])g(for)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3317
3885 y(e)o(xpositions)k(of)j(this.\))f(Section)h(4)f(considers)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3318
(relationship)g(of)g(our)h(v)o(ersion)f(of)h(\223uni\002-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3319
4006 y(cation)26 b(modulo)f Fz(\013)q FA(-equi)n(v)n(alence\224)g(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3320
(e)o(xisting)g(approaches.)h(Section)g(5)g(assesses)g(what)g(has)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3321
4126 y(been)f(achie)n(v)o(ed)f(and)h(the)f(prospects)h(for)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3322
(applications.)166 4458 y Fx(Quiz)166 4799 y FA(T)-8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3323
b(o)29 b(appreciate)i(the)e(kind)g(of)h(problem)e(that)h(nominal)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3324
(uni\002cation)g(solv)o(es,)f(you)h(might)f(lik)o(e)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3325
4919 y(to)h(try)g(the)g(follo)n(wing)f(quiz)h(about)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3326
Fz(\025)p FA(-calculus)g([21])h(before)f(we)h(apply)f(our)g(algorithm)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3327
166 5039 y(to)24 b(solv)o(e)g(it)g(at)h(the)g(end)g(of)g(Section)f(3.)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3328
166 5259 y Fx(Assuming)i Fz(a)i Fx(and)g Fz(b)g Fx(ar)l(e)g(distinct)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3329
(variables)p FA(,)g(is)i(it)f(possible)f(to)i(\002nd)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3330
Fz(\025)p FA(-terms)h Fz(M)3062 5274 y FG(1)3101 5259
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3331
y Fz(;)17 b(:)g(:)g(:)f(;)h(M)3414 5274 y FG(7)166 5380
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3332
y FA(that)24 b(mak)o(e)h(the)g(follo)n(wing)e(pairs)h(of)h(terms)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3333
Fz(\013)q FA(-equi)n(v)n(alent?)1773 5712 y(5)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3334
%%Page: 6 6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3335
TeXDict begin 6 5 bop 206 83 a FA(\(1\))50 b Fz(\025a:\025b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3336
Fu(\()p Fz(M)764 98 y FG(1)821 83 y Fz(b)p Fu(\))125
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3337
b FA(and)f Fz(\025b:\025a:)p Fu(\()p Fz(a)17 b(M)1753
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3338
98 y FG(1)1794 83 y Fu(\))206 203 y FA(\(2\))50 b Fz(\025a:\025b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3339
Fu(\()p Fz(M)764 218 y FG(2)821 203 y Fz(b)p Fu(\))125
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3340
b FA(and)f Fz(\025b:\025a:)p Fu(\()p Fz(a)17 b(M)1753
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3341
218 y FG(3)1794 203 y Fu(\))206 324 y FA(\(3\))50 b Fz(\025a:\025b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3342
Fu(\()p Fz(b)17 b(M)822 339 y FG(4)862 324 y Fu(\))125
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3343
b FA(and)f Fz(\025b:\025a:)p Fu(\()p Fz(a)17 b(M)1753
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3344
339 y FG(5)1794 324 y Fu(\))206 444 y FA(\(4\))50 b Fz(\025a:\025b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3345
Fu(\()p Fz(b)17 b(M)822 459 y FG(6)862 444 y Fu(\))125
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3346
b FA(and)f Fz(\025a:\025a:)p Fu(\()p Fz(a)17 b(M)1763
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3347
459 y FG(7)1803 444 y Fu(\))166 679 y FA(If)28 b(it)g(is)f(possible)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3348
(to)g(\002nd)h(a)g(solution)e(for)j(an)o(y)e(of)h(these)f(four)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3349
(problems,)f(can)h(you)g(describe)166 800 y(what)36 b(all)g(possible)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3350
(solutions)h(for)h(that)f(problem)h(are)h(lik)o(e?)e(\(The)i(answers)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3351
(are)h(gi)n(v)o(en)d(in)166 920 y(Example)24 b(3.8.\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3352
1423 y FB(2)99 b(Nominal)25 b(equational)g(logic)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3353
1779 y FA(W)-8 b(e)31 b(tak)o(e)g(a)g(concrete)g(approach)g(to)f(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3354
(syntax)e(of)i(binders)f(in)g(which)h(bound)f(entities)f(are)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3355
1899 y(e)o(xplicitly)d(named.)i(Furthermore)h(we)g(do)f(not)g(assume)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3356
(that)f(the)i(names)f(of)g(bound)g(entities)166 2019
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3357
y(are)23 b(necessarily)f(v)n(ariables)f(\(things)g(that)h(may)f(be)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3358
(substituted)e(for\),)j(in)f(order)g(to)g(encompass)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3359
2140 y(e)o(xamples)29 b(lik)o(e)g(the)h Fz(\031)t FA(-calculus)f([22],)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3360
h(in)f(which)h(the)f(restriction)g(operator)h(binds)f(channel)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3361
2260 y(names)g(and)h(these)f(are)i(quite)e(dif)n(ferent)g(from)h(names)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3362
f(of)h(unkno)n(wn)e(processes.)h(Names)h(of)166 2380
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3363
y(bound)25 b(entities)g(will)g(be)h(called)g Fx(atoms)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3364
FA(.)f(This)h(is)f(partly)h(for)g(historical)f(reasons)h(\(stemming)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3365
2501 y(from)32 b(the)f(w)o(ork)h(by)f(the)h(second)g(tw)o(o)f(authors)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3366
([10]\))h(and)g(partly)f(to)h(indicate)f(that)g(the)h(in-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3367
2621 y(ternal)26 b(structure)h(of)f(such)g(names)g(is)g(irrele)n(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3368
(ant)g(to)g(us:)g(all)g(we)h(care)g(about)f(is)g(their)g(identity)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3369
2742 y(\(i.e.)i(whether)g(or)g(not)f(one)h(atom)g(is)f(the)h(same)g(as)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3370
g(another\))g(and)g(that)f(the)h(supply)f(of)h(atoms)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3371
2862 y(is)c(ine)o(xhaustible.)166 3097 y(Although)i(there)h(are)i(se)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3372
(v)o(eral)d(general)i(frame)n(w)o(orks)f(in)f(the)i(literature)f(for)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3373
(specifying)g(lan-)166 3217 y(guages)j(with)f(binders,)g(not)h(all)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3374
(of)h(them)g(meet)f(the)h(requirements)f(mentioned)g(in)h(the)f(pre-)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3375
166 3338 y(vious)g(paragraph.)h(Use)g(of)h(the)e(simply)g(typed)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3376
Fz(\025)p FA(-calculus)h(for)g(this)f(purpose)h(is)f(common;)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3377
3458 y(b)n(ut)35 b(as)g(discussed)f(in)h(the)g(Introduction,)f(it)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3378
(leads)g(to)f(a)i(problematic)e(uni\002cation)h(theory)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3379
b(.)166 3579 y(Among)29 b Fx(\002r)o(st-or)l(der)j FA(frame)n(w)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3380
(orks,)d(Plotkin')-5 b(s)29 b(notion)g(of)h Fx(binding)f(signatur)l(e)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3381
FA([23,24],)g(be-)166 3699 y(ing)f(unsorted,)h(equates)f(names)h(used)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3382
(in)f(binding)g(with)g(names)h(of)g(v)n(ariables)f(standing)g(for)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3383
3819 y(unkno)n(wn)22 b(terms;)h(so)h(it)f(is)g(not)g(suf)n(\002ciently)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3384
g(general)h(for)g(us.)g(A)g(\002rst-order)g(frame)n(w)o(ork)f(that)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3385
3940 y(does)h(meet)f(our)h(requirements)f(is)g(the)h(notion)e(of)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3386
Fx(nominal)e(alg)o(ebr)o(as)g FA(in)i([15].)f(The)h Fx(nominal)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3387
4060 y(signatur)l(es)19 b FA(that)i(we)g(use)g(in)f(this)g(paper)h(are)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3388
h(a)f(mild)e(\(b)n(ut)i(practically)f(useful\))h(generalisation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3389
4181 y(of)27 b(nominal)e(algebras)i(in)g(which)f(name-abstraction)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3390
(and)h(pairing)f(can)h(be)g(mix)o(ed)f(freely)h(in)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3391
4301 y(arities)h(\(rather)g(than)g(insisting)e(as)i(in)g([15])g(that)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3392
(the)g(ar)n(gument)g(sort)f(of)i(a)f(function)f(symbol)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3393
4421 y(be)e(normalised)f(to)g(a)h(tuple)f(of)h(abstractions\).)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3394
4656 y FB(De\002nition)f(2.1.)40 b FA(A)23 b Fx(nominal)f(signatur)l(e)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3395
h FA(is)g(speci\002ed)g(by:)g(a)h(set)g(of)f Fx(sorts)g(of)g(atoms)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3396
FA(\(typical)166 4777 y(symbol)28 b Fz(\027)6 b FA(\);)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3397
b(a)f(disjoint)e(set)i(of)g Fx(sorts)e(of)i(data)f FA(\(typical)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3398
(symbol)g Fz(\016)t FA(\);)g(and)h(a)h(set)e(of)h Fx(function)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3399
4897 y(symbols)25 b FA(\(typical)h(symbol)f Fz(f)11 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3400
FA(\),)26 b(each)h(of)g(which)f(has)g(an)g Fx(arity)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3401
FA(of)g(the)h(form)f Fz(\034)42 b Fw(!)30 b Fz(\016)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3402
FA(.)c(Here)h Fz(\034)166 5018 y FA(ranges)d(o)o(v)o(er)f(\(compound\))
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3403
g Fx(sorts)g FA(gi)n(v)o(en)g(by)g(the)h(grammar)g Fz(\034)39
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3404
b Fu(::=)28 b Fz(\027)34 b Fw(j)27 b Fz(\016)32 b Fw(j)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3405
b Fu(1)h Fw(j)f Fz(\034)k Fw(\002)19 b Fz(\034)39 b Fw(j)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3406
b(h)p Fz(\027)6 b Fw(i)p Fz(\034)39 b FA(.)166 5138 y(Sorts)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3407
b(of)g(the)h(form)f Fw(h)p Fz(\027)6 b Fw(i)p Fz(\034)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3408
b FA(classify)26 b(terms)g(that)f(are)i(binding)e(abstractions)g(of)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3409
(atoms)e(of)h(sort)166 5258 y Fz(\027)31 b FA(o)o(v)o(er)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3410
b(terms)g(of)g(sort)g Fz(\034)11 b FA(.)25 b(W)-8 b(e)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3411
b(will)e(e)o(xplain)h(the)g(syntax)g(and)g(properties)g(of)g(such)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3412
(terms)e(in)h(a)166 5379 y(moment.)1773 5712 y(6)p eop
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3413
end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3414
%%Page: 7 7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3415
TeXDict begin 7 6 bop 166 83 a FB(Example)31 b(2.2.)43
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3416
b FA(Here)31 b(is)f(a)g(nominal)f(signature)g(for)h(e)o(xpressions)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3417
(in)h(a)g(small)f(fragment)h(of)166 203 y(ML)24 b([25]:)638
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3418
416 y(sort)g(of)h(atoms:)267 b Fp(vid)638 530 y FA(sort)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3419
b(of)h(data:)340 b Fp(exp)638 645 y FA(function)24 b(symbols:)97
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3420
b Fv(vr)29 b Fu(:)e Fp(vid)38 b Fw(!)27 b Fp(exp)1454
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3421
759 y Fv(app)i Fu(:)f Fp(exp)f Fw(\002)c Fp(exp)33 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3422
Fw(!)27 b Fp(exp)1454 874 y Fv(fn)i Fu(:)e Fw(h)p Fp(vid)10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3423
b Fw(i)p Fp(exp)33 b Fw(!)27 b Fp(exp)1454 988 y Fv(lv)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3424
Fu(:)e Fp(exp)h Fw(\002)23 b(h)p Fp(vid)9 b Fw(i)p Fp(exp)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3425
b Fw(!)28 b Fp(exp)1454 1102 y Fv(lf)h Fu(:)e Fw(h)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3426
Fp(vid)10 b Fw(i)p Fu(\(\()p Fw(h)p Fp(vid)f Fw(i)p Fp(exp)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3427
Fu(\))23 b Fw(\002)f Fp(exp)6 b Fu(\))27 b Fw(!)h Fp(exp)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3428
b FA(.)166 1322 y(The)27 b(function)f(symbol)f Fv(vr)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3429
FA(constructs)e(terms)g(of)h(sort)g Fp(exp)32 b FA(representing)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3430
b(v)n(alue)f(identi\002ers)166 1442 y(\(named)e(by)g(atoms)f(of)h(sort)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3431
f Fp(vid)10 b FA(\);)24 b Fv(app)h FA(constructs)e(application)g(e)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3432
(xpressions)f(from)i(pairs)g(of)166 1562 y(e)o(xpressions;)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3433
b Fv(fn)p FA(,)h Fv(lv)h FA(and)g Fv(lf)g FA(construct)e(terms)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3434
(representing)g(respecti)n(v)o(ely)f(function)g(ab-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3435
1683 y(stractions)k(\()p Fv(fn)25 b(x)j Fu(=)p Fz(>)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3436
Fv(e)p FA(\),)34 b(local)f(v)n(alue)g(declarations)h(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3437
Fv(let)26 b(val)f(x)j Fu(=)g Fv(e1)d(in)h(e2)f(end)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3438
FA(\))34 b(and)166 1803 y(local)28 b(recursi)n(v)o(e)e(function)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3439
(declarations)g(\()p Fv(let)f(fun)g(f)f(x)j Fu(=)g Fv(e1)d(in)h(e2)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3440
(end)q FA(\).)j(The)f(arities)h(of)166 1924 y(the)f(function)g(symbols)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3441
e(specify)j(which)f(are)h(binders)f(and)g(in)g(which)g(w)o(ay)g(their)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3442
(ar)n(guments)166 2044 y(are)32 b(bound.)f(F)o(or)h(e)o(xample,)f(in)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3443
(the)h(e)o(xpression)e(\()p Fv(let)c(fun)g(f)f(x)j Fu(=)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3444
Fv(e1)f(in)f(e2)h(end)p FA(\))32 b(there)g(is)166 2164
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3445
y(a)h(binding)e(occurrence)i(of)g(the)f(v)n(alue)g(identi\002er)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3446
Fv(f)h FA(whose)f(scope)h(is)f(both)f(of)i Fv(e1)g FA(and)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3447
Fv(e2)q FA(;)166 2285 y(and)i(a)g(binding)e(occurrence)i(of)g(the)g(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3448
(alue)f(identi\002er)g Fv(x)h FA(whose)f(scope)h(is)f(just)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3449
Fv(e1)p FA(.)h(These)166 2405 y(binding)27 b(scopes)h(are)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3450
(re\003ected)f(by)g(the)f(ar)n(gument)g(sort)h(of)f(the)h(function)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3451
(symbol)g Fv(lf)q FA(.)i(This)166 2525 y(kind)i(of)h(speci\002cation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3452
(of)g(binding)e(scopes)i(is)f(of)h(course)g(a)g(feature)h(of)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3453
Fx(higher)n(-or)l(der)f(ab-)166 2646 y(str)o(act)24 b(syntax)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3454
FA([26],)g(using)g(function)f(types)h Fz(\027)6 b Fw(!)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3455
Fz(\034)37 b FA(in)25 b(simply)e(typed)i Fz(\025)p FA(-calculus)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3456
(where)h(we)166 2766 y(use)g(abstraction)g(sorts)g Fw(h)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3457
Fz(\027)6 b Fw(i)p Fz(\034)11 b FA(.)26 b(W)-8 b(e)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3458
b(shall)f(see)h(that)f(the)g(latter)g(ha)n(v)o(e)g(much)g(more)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3459
(elementary)166 2887 y(\(indeed,)f(\002rst-order\))g(properties)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3460
(compared)h(with)f(the)h(former)-5 b(.)166 3116 y FB(De\002nition)40
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3461
b(2.3.)49 b FA(Gi)n(v)o(en)38 b(a)i(nominal)e(signature,)h(we)g(assume)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3462
g(that)g(there)h(are)g(countably)166 3236 y(in\002nite)21
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3463
b(and)h(pairwise)f(disjoint)e(sets)j(of)f Fx(atoms)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3464
FA(\(typical)g(symbol)f Fz(a)p FA(\))i(for)g(each)g(sort)f(of)h(atoms)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3465
166 3357 y Fz(\027)6 b FA(,)27 b(and)f Fx(variables)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3466
FA(\(typical)g(symbol)f Fz(X)8 b FA(\))26 b(for)h(each)g(sort)f(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3467
(atoms)e Fz(\027)34 b FA(and)26 b(each)h(sort)f(of)h(data)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3468
3477 y Fz(\016)t FA(.)36 b(The)h Fx(terms)e FA(o)o(v)o(er)h(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3469
(nominal)f(signature)h(and)g(their)g(sorts)f(are)i(inducti)n(v)o(ely)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3470
(de\002ned)j(as)166 3597 y(follo)n(ws,)23 b(where)j(we)f(write)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3471
Fz(t)k Fu(:)g Fz(\034)36 b FA(to)25 b(indicate)f(that)g(a)i(term)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3472
Fz(t)h FA(has)g(sort)f Fz(\034)11 b FA(.)166 3826 y FB(Unit)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3473
b(v)o(alue)50 b Fw(hi)27 b Fu(:)h(1)p FA(.)166 3947 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3474
FB(P)o(airs)49 b Fw(h)p Fz(t)510 3962 y FG(1)550 3947
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3475
y Fz(;)17 b(t)629 3962 y FG(2)668 3947 y Fw(i)27 b Fu(:)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3476
Fz(\034)831 3962 y FG(1)893 3947 y Fw(\002)23 b Fz(\034)1035
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3477
3962 y FG(2)1075 3947 y FA(,)h(if)h Fz(t)1245 3962 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3478
FG(1)1312 3947 y Fu(:)j Fz(\034)1409 3962 y FG(1)1474
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3479
3947 y FA(and)d Fz(t)1678 3962 y FG(2)1745 3947 y Fu(:)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3480
Fz(\034)1842 3962 y FG(2)1882 3947 y FA(.)166 4067 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3481
FB(Data)50 b Fz(f)27 b(t)h Fu(:)g Fz(\016)t FA(,)c(if)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3482
Fz(f)36 b FA(is)24 b(a)h(function)f(symbol)f(of)i(arity)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3483
Fz(\034)39 b Fw(!)27 b Fz(\016)i FA(and)c Fz(t)j Fu(:)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3484
Fz(\034)11 b FA(.)166 4188 y FB(Atoms)50 b Fz(a)27 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3485
Fu(:)h Fz(\027)6 b FA(,)25 b(if)g Fz(a)g FA(is)g(an)g(atom)f(of)h(sort)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3486
f Fz(\027)6 b FA(.)166 4308 y FB(Atom-abstraction)50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3487
b Fz(a:t)29 b Fu(:)e Fw(h)p Fz(\027)6 b Fw(i)p Fz(\034)11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3488
b FA(,)26 b(if)e Fz(a)i FA(is)e(an)h(atom)f(of)h(sort)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3489
Fz(\027)32 b FA(and)24 b Fz(t)k Fu(:)g Fz(\034)11 b FA(.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3490
4428 y FB(Suspension)51 b Fz(\031)t Fr(\001)p Fz(X)35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3491
b Fu(:)28 b Fz(\034)11 b FA(,)21 b(if)g Fz(\031)32 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3492
Fu(=)27 b(\()p Fz(a)1414 4443 y FG(1)1471 4428 y Fz(b)1512
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3493
4443 y FG(1)1551 4428 y Fu(\)\()p Fz(a)1678 4443 y FG(2)1735
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3494
4428 y Fz(b)1776 4443 y FG(2)1815 4428 y Fu(\))17 b Fw(\001)g(\001)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3495
(\001)e Fu(\()p Fz(a)2092 4443 y Fq(n)2156 4428 y Fz(b)2197
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3496
4443 y Fq(n)2244 4428 y Fu(\))21 b FA(is)f(a)h(\002nite)g(list)f(whose)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3497
h(elements)266 4549 y Fu(\()p Fz(a)355 4564 y Fq(i)400
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3498
4549 y Fz(b)441 4564 y Fq(i)469 4549 y Fu(\))27 b FA(are)h(pairs)f(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3499
(atoms,)f(with)g Fz(a)1559 4564 y Fq(i)1614 4549 y FA(and)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3500
Fz(b)1826 4564 y Fq(i)1882 4549 y FA(of)g(the)g(same)f(sort,)h(and)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3501
Fz(X)35 b FA(is)26 b(a)h(v)n(ariable)g(of)266 4669 y(sort)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3502
Fz(\034)11 b FA(,)25 b(where)h Fz(\034)36 b FA(is)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3503
b(either)h(a)g(sort)g(of)f(data)h(or)g(a)g(sort)g(of)g(atoms)f(\(i.e.)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3504
Fz(\034)40 b Fu(::=)27 b Fz(\027)34 b Fw(j)28 b Fz(\016)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3505
FA(\).)166 4898 y(Recall)20 b(that)f(e)n(v)o(ery)g(\002nite)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3506
(permutation)f(can)i(be)f(e)o(xpressed)g(as)h(a)f(composition)f(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3507
(sw)o(appings)166 5019 y Fu(\()p Fz(a)255 5034 y Fq(i)300
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3508
5019 y Fz(b)341 5034 y Fq(i)370 5019 y Fu(\))p FA(;)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3509
b(the)g(list)f Fz(\031)33 b FA(of)28 b(pairs)h(of)f(atoms)g(occurring)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3510
(in)g(a)h(suspension)e(term)h Fz(\031)t Fr(\001)p Fz(X)36
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3511
b FA(speci\002es)28 b(a)166 5139 y(\002nite)34 b(permutation)f(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3512
(atoms)g(w)o(aiting)f(to)h(be)g(applied)g(once)g(we)h(kno)n(w)e(more)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3513
(about)g(the)166 5259 y(v)n(ariable)e Fz(X)40 b FA(\(by)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3514
b(substituting)d(for)k(it,)e(for)i(e)o(xample\).)e(W)-8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3515
b(e)33 b(represent)f(\002nite)g(permutations)166 5380
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3516
y(in)24 b(this)g(w)o(ay)h(because)g(it)f(is)g(really)g(the)h(operation)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3517
f(of)g(sw)o(apping)g(which)g(plays)g(a)h(fundamen-)1773
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3518
5712 y(7)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3519
%%Page: 8 8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3520
TeXDict begin 8 7 bop 166 83 a FA(tal)33 b(r)8 b(\210)-41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3521
b(ole)33 b(in)g(the)f(theory)-6 b(.)33 b(Since,)g(semantically)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3522
(speaking,)g(sw)o(apping)g(commutes)g(with)g(all)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3523
203 y(term-forming)f(operations,)h(we)h(can)g(normalise)e(terms)h(in)l
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3524
(v)n(olving)f(an)i(e)o(xplicit)e(sw)o(apping)166 324
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3525
y(operation)24 b(by)h(pushing)e(the)i(sw)o(ap)f(in)h(as)g(f)o(ar)g(as)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3526
(it)f(will)g(go,)h(until)e(it)h(reaches)i(a)f(v)n(ariable)f(\(ap-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3527
444 y(plying)g(the)h(sw)o(apping)g(to)f(atoms)h(that)g(it)g(meets)f(on)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3528
h(the)h(w)o(ay\);)f(the)g(terms)g(in)g(De\002nition)f(2.3)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3529
565 y(are)38 b(all)f(normalised)e(in)i(this)f(w)o(ay)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3530
b(,)37 b(with)f(e)o(xplicit)f(permutations)h(\223piled)g(up\224)h(in)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3531
(front)g(of)166 685 y(v)n(ariables)30 b(gi)n(ving)g(what)h(we)g(ha)n(v)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3532
o(e)g(called)g Fx(suspensions)p FA(.)f(In)h(case)h(the)f(permutation)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3533
Fz(\031)36 b FA(in)30 b(a)166 805 y(suspension)23 b(is)i(the)f(empty)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3534
(list,)g(we)h(just)f(write)g Fz(X)33 b FA(for)25 b Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3535
Fr(\001)p Fz(X)8 b FA(.)166 1038 y FB(De\002nition)38
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3536
b(2.4.)48 b FA(The)37 b Fx(permutation)e(action)p FA(,)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3537
Fz(\031)t Fr(\001)p Fz(t)p FA(,)h(of)g(a)h(\002nite)f(permutation)e(of)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3538
j(atoms)e Fz(\031)166 1159 y FA(on)31 b(a)h(term)f Fz(t)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3539
FA(is)f(de\002ned)h(as)f(in)g(Figure)h(1,)f(making)f(use)i(of)f(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3540
(follo)n(wing)d(notations.)h(The)166 1279 y(composition)36
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3541
b(of)i(a)h(permutation)d Fz(\031)42 b FA(follo)n(wed)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3542
b(by)h(a)h(sw)o(ap)f Fu(\()p Fz(a)17 b(b)p Fu(\))38 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3543
FA(is)g(gi)n(v)o(en)e(by)i(list-cons,)166 1399 y(written)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3544
b Fu(\()p Fz(a)17 b(b)p Fu(\))30 b(::)f Fz(\031)t FA(.)d(\(Note)f(that)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3545
h(we)g(apply)f(permutations)f(to)h(terms)g(on)h(the)f(left,)h(and)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3546
(hence)166 1520 y(the)20 b(order)g(of)g(the)g(composition)e(is)h(from)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3547
(right)f(to)h(left.\))g(The)g(composition)d(of)j Fz(\031)k
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3548
FA(follo)n(wed)19 b(by)166 1640 y(another)j(permutation)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3549
Fz(\031)1050 1604 y Ft(0)1096 1640 y FA(is)h(gi)n(v)o(en)f(by)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3550
(list-concatenation,)f(written)h(as)g Fz(\031)2772 1604
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3551
y Ft(0)2795 1640 y Fu(@)p Fz(\031)t FA(.)g(The)h Fx(identity)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3552
1761 y FA(permutation)j(is)g(gi)n(v)o(en)g(by)h(the)g(empty)f(list)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3553
Fu([])p FA(;)h(and)g(the)g Fx(in)l(ver)o(se)g FA(of)g(a)g(permutation)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3554
(is)g(gi)n(v)o(en)166 1881 y(by)f(list)e(re)n(v)o(ersal,)h(written)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3555
(as)g Fz(\031)1273 1845 y Ft(\000)p FG(1)1367 1881 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3556
FA(.)166 2114 y(Permutation)h(actions)g(ha)n(v)o(e)g(e)o(xcellent)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3557
(logical)g(properties)g(\(stemming)f(from)h(the)g(f)o(act)h(that)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3558
2234 y(the)o(y)f(are)i(bijections\).)e(W)-8 b(e)28 b(e)o(xploit)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3559
(these)i(properties)g(in)g(our)g(de\002nition)f(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3560
Fz(\013)q FA(-equi)n(v)n(alence)166 2355 y(for)g(terms)e(o)o(v)o(er)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3561
(a)h(nominal)e(signature,)g(which)h(is)g(respected)h(by)f(substitution)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3562
d(of)k(terms)f(for)166 2475 y(v)n(ariables)33 b(e)n(v)o(en)h(though)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3563
(the)h(latter)g(may)g(in)l(v)n(olv)o(e)f(capture)h(of)g(atoms)g(by)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3564
(binders.)f(T)-8 b(o)34 b(do)166 2595 y(so)e(we)h(will)f(need)h(to)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3565
(mak)o(e)h(use)g(of)f(an)h(auxiliary)f(relation)g(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3566
Fx(fr)l(eshness)f FA(between)h(atoms)166 2716 y(and)k(terms,)f(whose)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3567
(intended)g(meaning)g(is)g(that)g(the)g(atom)g(does)h(not)f(occur)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3568
(free)g(in)f(an)o(y)166 2836 y(substitution)23 b(instance)i(of)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3569
(term.)g(As)h(discussed)e(in)h(the)h(Introduction,)e(our)h(judgements)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3570
166 2957 y(about)j(term)f(equi)n(v)n(alence)g(\()p Fz(t)34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3571
b Fw(\031)h Fz(t)1374 2920 y Ft(0)1397 2957 y FA(\))29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3572
b(need)f(to)g(contain)f(hypotheses)f(about)i(the)g(freshness)g(of)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3573
3077 y(atoms)k(with)g(respect)h(to)f(v)n(ariables)g(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3574
Fz(a)43 b Fu(#)g Fz(X)8 b FA(\);)32 b(and)h(the)g(same)f(goes)h(for)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3575
(our)f(judgements)166 3197 y(about)25 b(freshness)g(itself)g(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3576
Fz(a)30 b Fu(#)f Fz(t)p FA(\).)d(Figure)f(2)h(gi)n(v)o(es)e(a)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3577
(syntax-directed)e(inducti)n(v)o(e)g(de\002nition)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3578
3318 y(of)h(equi)n(v)n(alence)f(and)g(freshness)h(using)f(judgements)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3579
(of)i(the)g(form)1115 3564 y Fw(r)i(`)h Fz(t)g Fw(\031)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3580
Fz(t)1517 3523 y Ft(0)1740 3564 y FA(and)199 b Fw(r)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3581
b(`)f Fz(a)h Fu(#)g Fz(t)166 3810 y FA(where)40 b Fz(t)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3582
FA(and)g Fz(t)743 3773 y Ft(0)806 3810 y FA(are)g(terms)f(of)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3583
(same)h(sort)f(o)o(v)o(er)f(a)i(gi)n(v)o(en)e(nominal)h(signature,)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3584
Fz(a)i FA(is)166 3930 y(an)34 b(atom,)g(and)g(the)g Fx(fr)l(eshness)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3585
(en)l(vir)l(onment)i Fw(r)f FA(is)f(a)i(\002nite)f(set)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3586
Fx(fr)l(eshness)f(constr)o(aints)166 4050 y Fz(a)c Fu(#)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3587
Fz(X)8 b FA(,)26 b(each)g(speci\002ed)g(by)f(an)g(atom)g(and)h(a)g(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3588
(ariable.)e(Rule)i(\()p Fw(\031)p FA(-suspension\))f(in)g(Figure)h(2)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3589
166 4171 y(mak)o(es)e(use)h(of)g(the)g(follo)n(wing)e(de\002nition.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3590
4404 y FB(De\002nition)36 b(2.5.)46 b FA(The)35 b Fx(disa)o(gr)l
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3591
(eement)f(set)i FA(of)f(tw)o(o)f(permutations)f Fz(\031)39
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3592
b FA(and)34 b Fz(\031)2909 4368 y Ft(0)2967 4404 y FA(is)h(the)f(set)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3593
(of)166 4540 y(atoms)24 b Fp(ds)8 b Fu(\()p Fz(\031)t(;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3594
b(\031)727 4504 y Ft(0)750 4540 y Fu(\))815 4487 y Fo(def)820
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3595
4540 y Fu(=)32 b Fw(f)p Fz(a)27 b Fw(j)h Fz(\031)t Fr(\001)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3596
Fz(a)g Fw(6)p Fu(=)g Fz(\031)1444 4504 y Ft(0)1467 4540
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3597
y Fr(\001)p Fz(a)p Fw(g)p FA(.)166 4773 y(Note)38 b(that)f(e)n(v)o(ery)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3598
g(disagreement)g(set)h Fp(ds)8 b Fu(\()p Fz(\031)t(;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3599
b(\031)1856 4737 y Ft(0)1879 4773 y Fu(\))38 b FA(is)f(a)h(subset)f(of)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3600
h(the)g Fx(\002nite)f FA(set)h(of)g(atoms)166 4893 y(occurring)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3601
b(in)f(either)h(of)g(the)g(lists)f Fz(\031)33 b FA(and)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3602
Fz(\031)1712 4857 y Ft(0)1735 4893 y FA(,)g(because)h(if)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3603
Fz(a)i FA(does)e(not)h(occur)g(in)g(those)f(lists,)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3604
5014 y(then)i(from)g(Figure)h(1)f(we)h(get)g Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3605
Fr(\001)o Fz(a)39 b Fu(=)f Fz(a)g Fu(=)g Fz(\031)1819
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3606
4977 y Ft(0)1842 5014 y Fr(\001)p Fz(a)p FA(.)31 b(T)-8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3607
b(o)30 b(illustrate)f(the)i(use)f(of)h(disagreement)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3608
5134 y(sets,)24 b(consider)h(the)f(judgement)909 5380
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3609
y Fw(f)p Fz(a)k Fu(#)g Fz(X)8 b(;)17 b(c)27 b Fu(#)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3610
Fz(X)8 b Fw(g)27 b(`)h Fu(\()p Fz(a)17 b(c)p Fu(\)\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3611
Fz(a)g(b)p Fu(\))p Fr(\001)o Fz(X)36 b Fw(\031)28 b Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3612
Fz(b)17 b(c)p Fu(\))p Fr(\001)p Fz(X)57 b(:)1773 5712
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3613
y FA(8)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3614
%%Page: 9 9
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3615
TeXDict begin 9 8 bop 166 3 3288 4 v 166 1022 4 1020
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3616
v 791 332 a Fu([])p Fr(\001)p Fz(a)1028 280 y Fo(def)1032
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3617
332 y Fu(=)104 b Fz(a)327 628 y Fu(\(\()p Fz(a)454 643
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3618
y FG(1)510 628 y Fz(a)561 643 y FG(2)601 628 y Fu(\))27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3619
b(::)h Fz(\031)t Fu(\))p Fr(\001)p Fz(a)1028 576 y Fo(def)1032
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3620
628 y Fu(=)1212 404 y Fn(8)1212 479 y(>)1212 504 y(>)1212
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3621
528 y(<)1212 678 y(>)1212 703 y(>)1212 728 y(:)1286 488
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3622
y Fz(a)1337 503 y FG(1)1528 488 y FA(if)c Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3623
Fz(a)k Fu(=)g Fz(a)1938 503 y FG(2)1286 632 y Fz(a)1337
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3624
647 y FG(2)1528 632 y FA(if)c Fz(\031)t Fr(\001)p Fz(a)k
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3625
Fu(=)g Fz(a)1938 647 y FG(1)1286 777 y Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3626
Fz(a)100 b FA(otherwise)2430 188 y Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3627
Fw(hi)2698 135 y Fo(def)2702 188 y Fu(=)k Fw(hi)2237
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3628
368 y Fz(\031)t Fr(\001)o Fw(h)p Fz(t)2401 383 y FG(1)2441
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3629
368 y Fz(;)17 b(t)2520 383 y FG(2)2559 368 y Fw(i)2698
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3630
316 y Fo(def)2702 368 y Fu(=)104 b Fw(h)p Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3631
Fz(t)3047 383 y FG(1)3086 368 y Fz(;)17 b(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3632
Fz(t)3256 383 y FG(2)3295 368 y Fw(i)2321 549 y Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3633
Fr(\001)p Fu(\()p Fz(f)27 b(t)p Fu(\))2698 496 y Fo(def)2702
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3634
549 y Fu(=)104 b Fz(f)27 b Fu(\()p Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3635
Fz(t)p Fu(\))2318 730 y Fz(\031)t Fr(\001)p Fu(\()p Fz(a:t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3636
Fu(\))2698 677 y Fo(def)2702 730 y Fu(=)104 b(\()p Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3637
Fr(\001)p Fz(a)p Fu(\))p Fz(:)p Fu(\()p Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3638
Fz(t)p Fu(\))2229 910 y Fz(\031)t Fr(\001)o Fu(\()p Fz(\031)2416
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3639
874 y Ft(0)2439 910 y Fr(\001)p Fz(X)8 b Fu(\))2698 858
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3640
y Fo(def)2702 910 y Fu(=)104 b(\()p Fz(\031)t Fu(@)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3641
Fz(\031)3114 874 y Ft(0)3137 910 y Fu(\))p Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3642
Fz(X)p 3450 1022 V 166 1025 3288 4 v 1075 1162 a FD(Fig.)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3643
b(1.)h(Permutation)i(action)g(on)f(terms,)f FC(\031)s
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3644
Fm(\001)q FC(t)p FD(.)p 166 1267 V 166 3748 4 2482 v
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3645
637 1441 445 4 v 637 1525 a Fl(r)i(`)f(hi)i(\031)f(hi)1123
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3646
1464 y FD(\()p Fl(\031)p FD(-unit\))1653 1395 y Fl(r)g(`)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3647
FC(t)1868 1409 y FG(1)1932 1395 y Fl(\031)g FC(t)2061
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3648
1362 y Ft(0)2061 1419 y FG(1)2191 1395 y Fl(r)g(`)g FC(t)2406
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3649
1409 y FG(2)2471 1395 y Fl(\031)g FC(t)2600 1362 y Ft(0)2600
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3650
1419 y FG(2)p 1653 1439 987 4 v 1739 1525 a Fl(r)g(`)f(h)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3651
FC(t)1988 1539 y FG(1)2028 1525 y FC(;)15 b(t)2101 1539
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3652
y FG(2)2141 1525 y Fl(i)25 b(\031)g(h)p FC(t)2365 1492
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3653
y Ft(0)2365 1550 y FG(1)2405 1525 y FC(;)15 b(t)2478
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3654
1492 y Ft(0)2478 1550 y FG(2)2518 1525 y Fl(i)2680 1460
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3655
y FD(\()p Fl(\031)p FD(-pair\))494 1693 y Fl(r)25 b(`)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3656
FC(t)g Fl(\031)g FC(t)863 1660 y Ft(0)p 424 1713 531
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3657
4 v 424 1800 a Fl(r)g(`)g FC(f)g(t)g Fl(\031)g FC(f)f(t)932
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3658
1767 y Ft(0)997 1734 y FD(\()p Fl(\031)p FD(-function)i(symbol\))2052
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3659
1693 y Fl(r)f(`)g FC(t)g Fl(\031)g FC(t)2421 1660 y Ft(0)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3660
1979 1713 539 4 v 1979 1800 a Fl(r)g(`)g FC(a:t)g Fl(\031)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3661
FC(a:t)2494 1767 y Ft(0)2559 1736 y FD(\()p Fl(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3662
FD(-abstraction-1\))741 1968 y FC(a)g Fl(6)p Fk(=)g FC(a)958
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3663
1935 y Ft(0)1072 1968 y Fl(r)g(`)g FC(t)g Fl(\031)g Fk(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3664
FC(a)15 b(a)1554 1935 y Ft(0)1578 1968 y Fk(\))p Fm(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3665
FC(t)1675 1935 y Ft(0)1789 1968 y Fl(r)25 b(`)g FC(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3666
Fk(#)g FC(t)2178 1935 y Ft(0)p 741 2010 1461 4 v 1190
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3667
2097 a Fl(r)g(`)g FC(a:t)g Fl(\031)g FC(a)1647 2064 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3668
Ft(0)1671 2097 y FC(:t)1729 2064 y Ft(0)2243 2033 y FD(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3669
Fl(\031)p FD(-abstraction-2\))p 338 2314 400 4 v 338
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3670
2394 a Fl(r)g(`)g FC(a)g Fl(\031)g FC(a)779 2337 y FD(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3671
Fl(\031)p FD(-atom\))1350 2265 y Fk(\()p FC(a)g Fk(#)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3672
FC(X)7 b Fk(\))26 b Fl(2)f(r)50 b FD(for)24 b(all)52
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3673
b FC(a)25 b Fl(2)g Fj(ds)8 b Fk(\()p FC(\031)s(;)15 b(\031)2620
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3674
2232 y Ft(0)2644 2265 y Fk(\))p 1350 2307 1330 4 v 1685
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3675
2394 a Fl(r)25 b(`)g FC(\031)s Fm(\001)p FC(X)32 b Fl(\031)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3676
b FC(\031)2209 2361 y Ft(0)2233 2394 y Fm(\001)p FC(X)2721
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3677
2329 y FD(\()p Fl(\031)p FD(-suspension\))p 659 2687
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3678
427 4 v 659 2772 a Fl(r)g(`)g FC(a)h Fk(#)f Fl(hi)1128
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3679
2710 y FD(\()p Fk(#)p FD(-unit\))1663 2650 y Fl(r)g(`)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3680
FC(a)g Fk(#)g FC(t)2052 2664 y FG(1)2182 2650 y Fl(r)g(`)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3681
FC(a)h Fk(#)f FC(t)2572 2664 y FG(2)p 1663 2687 948 4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3682
v 1831 2772 a Fl(r)g(`)g FC(a)g Fk(#)g Fl(h)p FC(t)2255
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3683
2786 y FG(1)2295 2772 y FC(;)15 b(t)2368 2786 y FG(2)2408
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3684
2772 y Fl(i)2652 2709 y FD(\()p Fk(#)p FD(-pair\))1215
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3685
2933 y Fl(r)25 b(`)f FC(a)i Fk(#)f FC(t)p 1180 2971 459
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3686
4 v 1180 3050 a Fl(r)g(`)g FC(a)g Fk(#)g FC(f)f(t)1680
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3687
2992 y FD(\()p Fk(#)p FD(-function)i(symbol\))p 422 3263
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3688
463 4 v 422 3343 a Fl(r)f(`)g FC(a)g Fk(#)g FC(a:t)926
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3689
3286 y FD(\()p Fk(#)p FD(-abstraction-1\))1794 3218 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3690
FC(a)h Fl(6)p Fk(=)f FC(a)2012 3185 y Ft(0)2126 3218
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3691
y Fl(r)g(`)g FC(a)g Fk(#)g FC(t)p 1794 3256 721 4 v 1912
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3692
3343 a Fl(r)g(`)g FC(a)g Fk(#)g FC(a)2316 3310 y Ft(0)2339
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3693
3343 y FC(:t)2556 3279 y FD(\()p Fk(#)p FD(-abstraction-2\))731
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3694
3515 y FC(a)g Fl(6)p Fk(=)g FC(a)948 3482 y Ft(0)p 638
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3695
3552 428 4 v 638 3639 a Fl(r)g(`)f FC(a)i Fk(#)f FC(a)1042
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3696
3606 y Ft(0)1107 3575 y FD(\()p Fk(#)p FD(-atom\))1682
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3697
3516 y Fk(\()p FC(\031)1772 3483 y Ft(\000)p FG(1)1867
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3698
3516 y Fm(\001)p FC(a)g Fk(#)g FC(X)7 b Fk(\))26 b Fl(2)f(r)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3699
1682 3559 693 4 v 1767 3639 a(r)g(`)g FC(a)g Fk(#)g FC(\031)s
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3700
Fm(\001)q FC(X)2417 3581 y FD(\()p Fk(#)p FD(-suspension\))p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3701
3450 3748 4 2482 v 166 3751 3288 4 v 1092 3889 a(Fig.)e(2.)g(Inducti)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3702
(v)o(e)i(de\002nition)g(of)f Fl(\031)e FD(and)i Fk(#)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3703
FD(.)166 4073 y FA(This)g(holds)f(by)i(applying)e(rule)i(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3704
Fw(\031)p FA(-suspension\))f(in)g(Figure)h(2,)f(since)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3705
(disagreement)g(set)166 4193 y(of)h(the)g(permutations)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3706
Fu(\()p Fz(a)17 b(c)p Fu(\)\()p Fz(a)g(b)p Fu(\))24 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3707
FA(and)h Fu(\()p Fz(b)17 b(c)p Fu(\))25 b FA(is)f Fw(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3708
Fz(a;)17 b(c)p Fw(g)p FA(.)166 4417 y FB(Remark)32 b(2.6)f(\(Fr)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3709
(eshness)h(en)l(vir)n(onments\).)46 b FA(Note)31 b(that)g(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3710
(freshness)h(en)l(vironment)f(on)166 4537 y(the)d(left-hand)f(side)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3711
(of)g(judgements)e(in)i(the)g(rules)f(in)h(Figure)g(2)g(does)f(not)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3712
(change)g(from)f(hy-)166 4658 y(potheses)d(to)f(conclusion.)g(So)i(in)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3713
(the)g(same)g(w)o(ay)g(that)g(we)h(assume)e(v)n(ariables)h(ha)n(v)o(e)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3714
(attached)166 4778 y(sorting)i(information,)f(we)i(could)f(dispense)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3715
(with)g(the)g(use)h(of)g(freshness)f(en)l(vironments)f(en-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3716
4898 y(tirely)d(by)g(attaching)f(the)h(freshness)g(information)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3717
(directly)h(to)g(v)n(ariables.)f(Ho)n(we)n(v)o(er)l(,)g(we)i(\002nd)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3718
5019 y(the)31 b(use)g(of)g(freshness)g(en)l(vironments)f(more)h(ele)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3719
(gant)f(\(for)i(one)f(thing,)f(without)g(them)g(tw)o(o)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3720
5139 y(v)n(ariables)24 b(with)g(the)h(same)g(name)g(b)n(ut)f(dif)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3721
(ferent)g(freshness)h(information)f(w)o(ould)g(ha)n(v)o(e)g(to)h(be)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3722
5259 y(re)o(garded)30 b(as)h(dif)n(ferent\).)f(The)o(y)g(also)g(mak)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3723
(e)g(life)h(simpler)e(when)i(we)f(come)h(on)f(to)g(nominal)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3724
5380 y(uni\002cation)24 b(problems)g(and)h(their)f(solutions)f(in)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3725
(the)h(ne)o(xt)f(section.)1773 5712 y(9)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3726
%%Page: 10 10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3727
TeXDict begin 10 9 bop 166 83 a FA(Belo)n(w)27 b(we)g(sk)o(etch)f(a)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3728
(proof)e(that)h Fw(\031)g FA(is)g(an)g(equi)n(v)n(alence)e(relation.)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3729
(At)f(\002rst)h(sight)f(this)g(prop-)166 203 y(erty)k(might)e(be)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3730
(surprising)e(considering)g(the)i(\223unsymmetric\224)e(de\002nition)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3731
(of)h(the)f(rule)h(\()p Fw(\031)p FA(-)166 324 y(abstraction-2\).)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3732
b(Ho)n(we)n(v)o(er)e(it)i(holds)f(because)i(of)f(the)g(good)g(logical)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3733
(properties)h(of)g(the)g(rela-)166 444 y(tion)30 b Fw(\031)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3734
FA(with)f(respect)h(to)f(permutation)f(actions.)h(Although)f(reasoning)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3735
h(about)g Fw(\031)h FA(is)f(rather)166 565 y(pleasant)k(once)h(equi)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3736
(v)n(alence)e(is)h(pro)o(v)o(ed,)f(establishing)f(it)i(\002rst)h(is)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3737
(rather)g(trick)o(y\227mainly)166 685 y(because)29 b(of)f(the)h(lar)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3738
(ge)g(number)f(of)g(cases,)h(b)n(ut)f(also)g(because)h(se)n(v)o(eral)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3739
(f)o(acts)g(needed)h(in)f(the)166 805 y(proof)21 b(are)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3740
(interdependent.)1180 769 y FG(1)1258 805 y FA(W)-8 b(e)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3741
b(\002rst)g(sho)n(w)e(that)h(permutations)f(can)i(be)g(mo)o(v)o(ed)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3742
(from)h(one)166 926 y(side)28 b(of)g(the)g(freshness)g(relation)g(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3743
(the)g(other)g(by)g(forming)f(the)i(in)l(v)o(erse)e(permutation,)g(and)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3744
166 1046 y(that)d(the)h(freshness)g(relation)f(is)g(preserv)o(ed)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3745
(under)g(permutation)e(actions.)166 1266 y FB(Lemma)i(2.7.)206
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3746
1486 y Fx(\(1\))50 b(If)41 b Fw(r)28 b(`)g Fz(a)f Fu(#)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3747
Fz(\031)t Fr(\001)p Fz(t)42 b Fx(then)f Fw(r)28 b(`)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3748
Fz(\031)1500 1450 y Ft(\000)p FG(1)1594 1486 y Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3749
Fz(a)h Fu(#)g Fz(t)g Fx(.)206 1606 y(\(2\))50 b(If)41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3750
b Fw(r)28 b(`)g Fz(\031)t Fr(\001)o Fz(a)g Fu(#)g Fz(t)42
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3751
b Fx(then)f Fw(r)28 b(`)f Fz(a)h Fu(#)g Fz(\031)1688
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3752
1570 y Ft(\000)p FG(1)1782 1606 y Fr(\001)p Fz(t)g Fx(.)206
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3753
1727 y(\(3\))50 b(If)41 b Fw(r)28 b(`)g Fz(a)f Fu(#)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3754
Fz(t)42 b Fx(then)f Fw(r)28 b(`)g Fz(\031)t Fr(\001)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3755
Fz(a)g Fu(#)g Fz(\031)t Fr(\001)p Fz(t)g Fx(.)166 2059
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3756
y FB(PR)m(OOF)-11 b(.)49 b FA(\(1\))27 b(and)g(\(2\))h(are)g(by)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3757
(routine)g(inductions)f(on)h(the)g(structure)g(of)g Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3758
FA(,)h(using)e(the)h(f)o(act)166 2179 y(that)g Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3759
Fr(\001)p Fz(a)33 b Fu(=)g Fz(b)28 b FA(if)n(f)f Fz(a)34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3760
b Fu(=)e Fz(\031)1067 2143 y Ft(\000)p FG(1)1162 2179
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3761
y Fr(\001)o Fz(b)d FA(;)e(\(3\))h(is)f(a)h(consequence)g(of)g(\(2\))g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3762
(and)f(the)h(f)o(act)g(that)f(permuta-)166 2300 y(tions)d(are)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3763
(bijections)f(on)g(atoms.)p 3382 2300 4 68 v 3386 2236
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3764
60 4 v 3386 2300 V 3445 2300 4 68 v 166 2632 a(According)h(to)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3765
(de\002nition)g(of)h(the)f(permutation)g(action)g(gi)n(v)o(en)f(in)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3766
(Figure)h(1,)g(if)g(we)g(push)166 2752 y(a)38 b(permutation)f(inside)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3767
(a)i(term,)e(we)i(need)f(to)g(apply)f(the)h(permutation)f(to)h(all)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3768
(atoms)h(we)166 2873 y(meet)e(on)g(the)g(w)o(ay)-6 b(.)35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3769
b(Suppose)h(we)h(apply)e(tw)o(o)h(distinct)e(permutations,)h(say)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3770
Fz(\031)k FA(and)c Fz(\031)3292 2836 y Ft(0)3315 2873
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3771
y FA(,)g(to)166 2993 y(a)d(term)f Fz(t)p FA(,)g(then)g(in)g(general)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3772
Fz(\031)t Fr(\001)o Fz(t)g FA(and)f Fz(\031)1583 2957
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3773
y Ft(0)1607 2993 y Fr(\001)o Fz(t)h FA(are)g(not)f Fz(\013)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3774
FA(-equi)n(v)n(alent\227the)d(disagreement)j(set)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3775
3113 y Fz(ds)p Fu(\()p Fz(\031)t(;)17 b(\031)463 3077
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3776
y Ft(0)485 3113 y Fu(\))36 b FA(characterises)g(all)f(atoms)g(which)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3777
(potentially)f(lead)h(to)h(dif)n(ferences.)f(Ho)n(we)n(v)o(er)l(,)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3778
3234 y(if)30 b(we)g(assume)g(that)g(all)f(atoms)h(in)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3779
Fz(ds)p Fu(\()p Fz(\031)t(;)17 b(\031)1709 3198 y Ft(0)1732
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3780
3234 y Fu(\))30 b FA(are)h(fresh)f(for)g Fz(t)p FA(,)h(then)e(we)i(can)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3781
f(infer)g(that)g(the)166 3354 y(permutation)19 b(actions)g(produce)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3782
(equi)n(v)n(alent)e(terms.)h(This)h(is)f(made)h(precise)g(in)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3783
(follo)n(wing)166 3474 y(lemma.)166 3694 y FB(Lemma)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3784
b(2.8.)44 b Fx(Given)30 b(any)h Fz(\031)j Fx(and)c Fz(\031)1488
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3785
3658 y Ft(0)1511 3694 y Fx(,)h(if)f Fw(r)38 b(`)g Fz(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3786
Fu(#)g Fz(t)31 b Fx(holds)e(for)h(all)g Fz(a)38 b Fw(2)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3787
Fz(ds)p Fu(\()p Fz(\031)t(;)17 b(\031)3166 3658 y Ft(0)3189
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3788
3694 y Fu(\))p Fx(,)30 b(then)166 3815 y Fw(r)e(`)f Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3789
Fr(\001)p Fz(t)h Fw(\031)g Fz(\031)683 3779 y Ft(0)706
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3790
3815 y Fr(\001)p Fz(t)p Fx(.)166 4147 y FB(PR)m(OOF)-11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3791
b(.)49 b FA(By)25 b(induction)g(on)g(the)g(structure)h(of)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3792
Fz(t)p FA(,)h(for)g(all)f Fz(\031)30 b FA(and)25 b Fz(\031)2541
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3793
4111 y Ft(0)2590 4147 y FA(simultaneously)-6 b(,)23 b(using)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3794
4267 y(the)e(f)o(act)h(about)f(disagreement)g(sets)g(that)g(for)h(all)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3795
(atoms)f Fz(a;)d(b)p FA(,)22 b(if)f Fz(a)28 b Fw(2)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3796
Fz(ds)p Fu(\()p Fz(\031)t(;)17 b Fu(\()p Fz(\031)t Fr(\001)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3797
Fz(b)51 b(\031)3090 4231 y Ft(0)3113 4267 y Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3798
Fz(b)p Fu(\))28 b(::)g Fz(\031)3393 4231 y Ft(0)3416
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3799
4267 y Fu(\))166 4388 y FA(then)d Fz(a)i Fw(2)h Fz(ds)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3800
Fu(\()p Fz(\031)t(;)17 b(\031)832 4352 y Ft(0)855 4388
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3801
y Fu(\))p FA(.)p 3382 4388 V 3386 4324 60 4 v 3386 4388
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3802
V 3445 4388 4 68 v 166 4720 a(An)27 b(e)o(xample)g(of)g(this)g(lemma)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3803
(is)h(that)g Fw(r)33 b(`)f Fz(\031)t Fr(\001)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3804
Fz(a)17 b(b)p Fu(\))p Fr(\001)p Fz(t)32 b Fw(\031)h Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3805
Fz(\031)t Fr(\001)p Fz(a)50 b(\031)t Fr(\001)p Fz(b)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3806
Fu(\))p Fr(\001)p Fz(\031)t Fr(\001)p Fz(t)27 b FA(is)g(a)h(v)n(alid)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3807
(judge-)166 4840 y(ment,)e(because)h(the)g(disagreement)f(set)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3808
Fz(ds)p Fu(\()p Fz(\031)t Fu(@\()p Fz(a)17 b(b)p Fu(\))g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3809
Fz(;)32 b Fu(\()p Fz(\031)t Fr(\001)p Fz(a)50 b(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3810
Fr(\001)p Fz(b)p Fu(\))28 b(::)f Fz(\031)t Fu(\))e FA(is)g(empty)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3811
b(.)p 166 4943 299 4 v 166 5007 a FG(1)257 5040 y FD(In)107
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3812
b(addition)j(some)d(further)i(simple)g(properties)h(of)d(permutations)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3813
(and)e(dis-)166 5153 y(agreement)j(sets)g(need)f(to)f(be)h(established)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3814
j(\002rst.)c(A)f(machine-check)o(ed)114 b(proof)166 5266
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3815
y(of)i FF(all)g FD(results)h(using)g(the)g(theorem)f(pro)o(v)o(er)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3816
(Isabelle)h(can)e(be)g(found)h(at)166 5379 y Fi(http://www.cl.c)o(am)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3817
(.a)o(c.)o(uk/)o(us)o(er)o(s/)o(cu)o(200)o(/U)o(ni)o(fi)o(ca)o(tio)o(n)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3818
p FD(.)1748 5712 y FA(10)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3819
%%Page: 11 11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3820
TeXDict begin 11 10 bop 166 83 a FA(The)25 b(ne)o(xt)f(lemma)g(sho)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3821
(ws)f(that)i Fw(\031)g FA(respects)g(the)g(freshness)f(relation.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3822
317 y FB(Lemma)h(2.9.)41 b Fx(If)25 b Fw(r)j(`)f Fz(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3823
Fu(#)g Fz(t)d Fx(and)g Fw(r)i(`)h Fz(t)g Fw(\031)g Fz(t)1818
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3824
281 y Ft(0)1842 317 y Fx(,)c(then)h Fw(r)j(`)f Fz(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3825
Fu(#)g Fz(t)2510 281 y Ft(0)2533 317 y Fx(.)166 770 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3826
FB(PR)m(OOF)-11 b(.)49 b FA(Routine)24 b(induction)f(on)i(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3827
(de\002nition)g(of)h Fw(\031)h FA(using)d(Lemma)i(2.7.)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3828
3382 770 4 68 v 3386 706 60 4 v 3386 770 V 3445 770 4
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3829
68 v 166 1224 a(F)o(or)j(sho)n(wing)d(transiti)n(vity)g(of)j(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3830
(relation)g Fw(\031)p FA(,)h(it)f(will)f(be)i(necessary)g(to)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3831
(de\002ne)h(a)g(measure)166 1344 y(that)c(counts)g(all)h(term)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3832
(constructors)g(occurring)h(in)f(a)i(term.)166 1578 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3833
FB(De\002nition)g(2.10.)40 b FA(The)25 b Fx(size)g FA(of)f(a)i(term)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3834
Fz(t)h FA(is)g(the)f(natural)h(number)f Fw(j)p Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3835
Fw(j)h FA(de\002ned)g(by:)1184 1844 y Fw(j)p Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3836
Fr(\001)p Fz(X)8 b Fw(j)p Fz(;)17 b Fw(j)p Fz(a)p Fw(j)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3837
Fz(;)g Fw(jhij)1774 1792 y Fo(def)1778 1844 y Fu(=)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3838
b(1)1368 2012 y Fw(j)p Fz(a:t)p Fw(j)p Fz(;)17 b Fw(j)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3839
Fz(f)26 b(t)p Fw(j)1774 1959 y Fo(def)1778 2012 y Fu(=)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3840
b(1)22 b(+)g Fw(j)p Fz(t)p Fw(j)1420 2179 y(jh)p Fz(t)1522
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3841
2194 y FG(1)1561 2179 y Fz(;)17 b(t)1640 2194 y FG(2)1680
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3842
2179 y Fw(ij)1774 2126 y Fo(def)1778 2179 y Fu(=)32 b(1)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3843
b(+)g Fw(j)p Fz(t)2118 2194 y FG(1)2158 2179 y Fw(j)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3844
Fu(+)h Fw(j)p Fz(t)2368 2194 y FG(2)2408 2179 y Fw(j)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3845
2539 y FA(Notice)d(that)g(the)g(size)g(of)h(a)f(term)g(is)g(preserv)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3846
(ed)g(under)h(permutation)d(actions)i(\(i.e.)g Fw(j)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3847
Fz(\031)t Fr(\001)p Fz(t)p Fw(j)27 b Fu(=)h Fw(j)p Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3848
Fw(j)p FA(\))166 2660 y(and)d(respected)g(by)f(the)h(relation)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3849
Fw(\031)i FA(in)e(the)h(sense)f(that)h(if)g Fw(r)i(`)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3850
Fz(t)g Fw(\031)g Fz(t)2591 2624 y Ft(0)2639 2660 y FA(then)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3851
Fw(j)p Fz(t)p Fw(j)i Fu(=)h Fw(j)p Fz(t)3121 2624 y Ft(0)3144
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3852
2660 y Fw(j)p FA(.)166 2894 y FB(Theor)n(em)f(2.11)d(\(Equi)o(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3853
(alence\).)43 b Fw(r)28 b(`)f(\000)h(\031)g(\000)e Fx(is)e(an)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3854
(equivalence)f(r)l(elation.)166 3347 y FB(PR)m(OOF)-11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3855
b(.)49 b FA(Re\003e)o(xi)n(vity)19 b(is)h(by)h(a)g(simple)e(induction)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3856
(on)g(the)h(structure)f(of)h(terms.)f(T)m(ransiti)n(vity)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3857
3467 y(is)k(by)h(an)g(induction)e(on)h(the)h(size)g(of)g(terms:)e(a)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3858
(slight)f(complication)f(is)h(that)g(man)o(y)g(subcases)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3859
3588 y(need)e(to)f(be)h(analysed)f(\(for)h(e)o(xample)f(\002)n(v)o(e)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3860
(subcases)h(when)f(dealing)g(with)g(abstractions\))g(and)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3861
3708 y(also)26 b(that)g(transiti)n(vity)e(needs)j(to)f(be)g(sho)n(wn)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3862
(by)g(mutual)f(induction)g(with)h(the)g(f)o(act)h(that)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3863
Fw(\031)h FA(is)166 3829 y(preserv)o(ed)e(under)f(permutation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3864
(actions,)g(that)g(is)837 4076 y(gi)n(v)o(en)f(an)o(y)k
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3865
Fz(\031)t(;)45 b FA(if)27 b Fw(r)h(`)f Fz(t)h Fw(\031)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3866
Fz(t)1870 4035 y Ft(0)1922 4076 y FA(then)f Fw(r)g(`)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3867
Fz(\031)t Fr(\001)p Fz(t)g Fw(\031)g Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3868
Fz(t)2705 4035 y Ft(0)2756 4076 y Fz(:)555 b FA(\(9\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3869
4323 y(W)-8 b(e)36 b(illustrate)e(the)i(proof)f(of)h(transiti)n(vity)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3870
(for)j(the)f(case)i(when)e Fw(r)48 b(`)f Fz(a)2767 4338
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3871
y FG(1)2807 4323 y Fz(:t)2869 4338 y FG(1)2957 4323 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3872
Fw(\031)h Fz(a)3133 4338 y FG(2)3172 4323 y Fz(:t)3234
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3873
4338 y FG(2)3310 4323 y FA(and)166 4444 y Fw(r)28 b(`)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3874
Fz(a)416 4459 y FG(2)456 4444 y Fz(:t)518 4459 y FG(2)585
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3875
4444 y Fw(\031)i Fz(a)742 4459 y FG(3)781 4444 y Fz(:t)843
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3876
4459 y FG(3)908 4444 y FA(hold,)24 b(with)g Fz(a)1388
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3877
4459 y FG(1)1428 4444 y FA(,)g Fz(a)1528 4459 y FG(2)1593
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3878
4444 y FA(and)h Fz(a)1813 4459 y FG(3)1877 4444 y FA(all)g(distinct)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3879
(atoms,)h(and)h(we)g(ha)n(v)o(e)f(to)h(pro)o(v)o(e)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3880
4564 y Fw(r)j(`)f Fz(a)416 4579 y FG(1)456 4564 y Fz(:t)518
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3881
4579 y FG(1)585 4564 y Fw(\031)i Fz(a)742 4579 y FG(3)781
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3882
4564 y Fz(:t)843 4579 y FG(3)883 4564 y FA(.)20 b(By)h(the)f(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3883
Fw(\031)p FA(-abstraction-2\))h(rule)g(we)f(can)h(infer)g(from)f(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3884
(assumptions)166 4685 y(the)25 b(follo)n(wing)e(f)o(acts:)803
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3885
4954 y(\(i\))155 b Fw(r)27 b(`)h Fz(t)1286 4969 y FG(1)1353
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3886
4954 y Fw(\031)g Fu(\()p Fz(a)1547 4969 y FG(1)1604 4954
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3887
y Fz(a)1655 4969 y FG(2)1694 4954 y Fu(\))p Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3888
Fz(t)1799 4969 y FG(2)2075 4954 y FA(\(ii\))119 b Fw(r)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3889
b(`)f Fz(a)2566 4969 y FG(1)2633 4954 y Fu(#)h Fz(t)2777
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3890
4969 y FG(2)803 5135 y FA(\(iii\))99 b Fw(r)27 b(`)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3891
Fz(t)1286 5150 y FG(2)1353 5135 y Fw(\031)g Fu(\()p Fz(a)1547
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3892
5150 y FG(2)1604 5135 y Fz(a)1655 5150 y FG(3)1694 5135
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3893
y Fu(\))p Fr(\001)p Fz(t)1799 5150 y FG(3)2075 5135 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3894
FA(\(i)n(v\))99 b Fw(r)28 b(`)f Fz(a)2566 5150 y FG(2)2633
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3895
5135 y Fu(#)h Fz(t)2777 5150 y FG(3)166 5380 y FA(Belo)n(w)d(we)g(gi)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3896
(v)o(e)e(the)i(steps)f(that)g(pro)o(v)o(e)g Fw(r)k(`)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3897
Fz(a)1826 5395 y FG(1)1866 5380 y Fz(:t)1928 5395 y FG(1)1995
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3898
5380 y Fw(\031)i Fz(a)2152 5395 y FG(3)2191 5380 y Fz(:t)2253
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3899
5395 y FG(3)2293 5380 y FA(.)1748 5712 y(11)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3900
%%Page: 12 12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3901
TeXDict begin 12 11 bop 166 126 a FA(\(a\))106 b Fw(r)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3902
b(`)f Fu(\()p Fz(a)670 141 y FG(1)726 126 y Fz(a)777
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3903
141 y FG(2)817 126 y Fu(\))p Fr(\001)p Fz(t)922 141 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3904
FG(2)989 126 y Fw(\031)h Fu(\()p Fz(a)1183 141 y FG(1)1239
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3905
126 y Fz(a)1290 141 y FG(2)1330 126 y Fu(\)\()p Fz(a)1457
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3906
141 y FG(2)1513 126 y Fz(a)1564 141 y FG(3)1604 126 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3907
Fu(\))p Fr(\001)p Fz(t)1709 141 y FG(3)2740 126 y FA(by)c(\(iii\))h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3908
(and)g(IH)g(\(9\))166 307 y(\(b\))100 b Fw(r)28 b(`)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3909
Fz(t)616 322 y FG(1)683 307 y Fw(\031)i Fu(\()p Fz(a)878
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3910
322 y FG(1)934 307 y Fz(a)985 322 y FG(2)1024 307 y Fu(\)\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3911
Fz(a)1151 322 y FG(2)1208 307 y Fz(a)1259 322 y FG(3)1298
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3912
307 y Fu(\))p Fr(\001)p Fz(t)1403 322 y FG(3)2255 307
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3913
y FA(by)c(\(i\),)g(\(a\))g(and)g(IH)g(\(transiti)n(vity\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3914
488 y(\(c\))106 b Fz(ds)p Fu(\(\()p Fz(a)606 503 y FG(1)662
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3915
488 y Fz(a)713 503 y FG(2)752 488 y Fu(\)\()p Fz(a)879
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3916
503 y FG(2)935 488 y Fz(a)986 503 y FG(3)1026 488 y Fu(\))17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3917
b Fz(;)33 b Fu(\()p Fz(a)1230 503 y FG(1)1286 488 y Fz(a)1337
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3918
503 y FG(3)1377 488 y Fu(\)\))27 b(=)h Fw(f)p Fz(a)1685
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3919
503 y FG(1)1724 488 y Fz(;)17 b(a)1819 503 y FG(2)1859
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3920
488 y Fw(g)1038 b FA(by)25 b(de\002nition)166 668 y(\(d\))100
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3921
b Fw(r)28 b(`)f Fz(a)632 683 y FG(1)699 668 y Fu(#)h(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3922
Fz(a)897 683 y FG(2)954 668 y Fz(a)1005 683 y FG(3)1044
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3923
668 y Fu(\))p Fr(\001)p Fz(t)1149 683 y FG(3)2361 668
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3924
y FA(by)c(\(ii\),)h(\(iii\))f(and)h(Lemma)f(2.9)166 849
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3925
y(\(e\))106 b Fw(r)28 b(`)f Fz(a)632 864 y FG(1)699 849
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3926
y Fu(#)h Fz(t)843 864 y FG(3)1804 849 y FA(by)c Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3927
Fz(a)2017 864 y FG(2)2073 849 y Fz(a)2124 864 y FG(3)2164
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3928
849 y Fu(\))p Fr(\001)p Fz(a)2285 864 y FG(1)2352 849
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3929
y Fu(=)k Fz(a)2507 864 y FG(1)2546 849 y FA(,)d(\(d\))g(and)g(Lemma)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3930
(2.7\(i\))166 1029 y(\(f\))117 b Fw(r)28 b(`)f Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3931
Fz(a)670 1044 y FG(1)726 1029 y Fz(a)777 1044 y FG(2)817
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3932
1029 y Fu(\)\()p Fz(a)944 1044 y FG(2)1000 1029 y Fz(a)1051
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3933
1044 y FG(3)1091 1029 y Fu(\))p Fr(\001)o Fz(t)1195 1044
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3934
y FG(3)1263 1029 y Fw(\031)h Fu(\()p Fz(a)1457 1044 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3935
FG(1)1513 1029 y Fz(a)1564 1044 y FG(3)1604 1029 y Fu(\))p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3936
Fr(\001)p Fz(t)1709 1044 y FG(3)2220 1029 y FA(by)c(\(c\),)h(\(i)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3937
(v\),)g(\(e\))g(and)g(Lemma)f(2.8)166 1210 y(\(g\))100
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3938
b Fw(r)28 b(`)f Fz(t)616 1225 y FG(1)683 1210 y Fw(\031)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3939
Fu(\()p Fz(a)878 1225 y FG(1)934 1210 y Fz(a)985 1225
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3940
y FG(3)1024 1210 y Fu(\))p Fr(\001)p Fz(t)1129 1225 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3941
FG(3)2244 1210 y FA(by)c(\(b\),)g(\(f\))g(and)g(IH)g(\(transiti)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3942
(vity\))166 1390 y(\(h\))100 b Fw(r)28 b(`)f Fz(a)632
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3943
1405 y FG(1)672 1390 y Fz(:t)734 1405 y FG(1)801 1390
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3944
y Fw(\031)h Fz(a)957 1405 y FG(3)997 1390 y Fz(:t)1059
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3945
1405 y FG(3)2162 1390 y FA(by)c(\(e\),)i(\(g\))f(and)g(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3946
Fw(\031)p FA(-abstraction-2\))166 1621 y(The)g(other)g(cases)g(are)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3947
(by)f(similar)e(ar)n(guments.)i(Symmetry)f(is)g(then)h(by)g(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3948
(routine)f(induction)166 1741 y(on)h(the)f(de\002nition)g(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3949
Fw(\031)g FA(using)f(Lemma)g(2.8)h(and)g(transiti)n(vity)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3950
b(.)p 3382 1741 4 68 v 3386 1677 60 4 v 3386 1741 V 3445
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3951
1741 4 68 v 166 2082 a(No)n(w)23 b(it)h(is)f(relati)n(v)o(ely)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3952
(straightforw)o(ard)g(to)h(obtain)f(the)h(follo)n(wing)e(properties)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3953
(of)g(our)g(equi)n(v-)166 2202 y(alence)h(relation)g(with)f(respect)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3954
(to)f(permutation)g(actions.)166 2422 y FB(Cor)n(ollary)g(2.12.)206
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3955
2643 y Fx(\(1\))50 b Fw(r)28 b(`)f Fz(t)h Fw(\031)g Fz(\031)798
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3956
2606 y Ft(\000)p FG(1)893 2643 y Fr(\001)o Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3957
Fr(\001)p Fz(t)1050 2606 y Ft(0)1126 2643 y Fx(if)c(and)h(only)f(if)52
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3958
b Fw(r)28 b(`)g Fz(t)f Fw(\031)i Fz(t)2088 2606 y Ft(0)2139
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3959
2643 y Fx(.)206 2763 y(\(2\))50 b Fw(r)28 b(`)f Fz(t)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3960
Fw(\031)g Fz(\031)t Fr(\001)p Fz(t)865 2727 y Ft(0)941
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3961
2763 y Fx(if)c(and)h(only)f(if)52 b Fw(r)28 b(`)f Fz(\031)1758
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3962
2727 y Ft(\000)p FG(1)1853 2763 y Fr(\001)p Fz(t)g Fw(\031)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3963
Fz(t)2088 2727 y Ft(0)2139 2763 y Fx(.)206 2883 y(\(3\))50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3964
b(Given)32 b(any)h Fz(\031)j Fx(and)c Fz(\031)1151 2847
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3965
y Ft(0)1174 2883 y Fx(,)h(if)48 b Fw(r)42 b(`)f Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3966
Fr(\001)p Fz(t)h Fw(\031)g Fz(\031)1909 2847 y Ft(0)1932
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3967
2883 y Fr(\001)p Fz(t)50 b Fx(then)32 b(for)f(all)h Fz(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3968
Fx(in)f Fz(ds)p Fu(\()p Fz(\031)t(;)17 b(\031)3030 2847
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3969
y Ft(0)3052 2883 y Fu(\))32 b Fx(we)i(have)372 3004 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3970
Fw(r)28 b(`)f Fz(a)h Fu(#)g Fz(t)p Fx(.)166 3345 y FB(PR)m(OOF)-11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3971
b(.)49 b FA(\(i\))38 b(follo)n(ws)f(immediately)g(from)h(Lemma)g(2.8)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3972
(and)f(transiti)n(vity;)e(\(ii\))i(follo)n(ws)166 3465
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3973
y(from)i(\(9\))h(and)f(\(i\);)g(and)g(\(iii\))g(is)g(by)g(a)g(routine)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3974
(induction)f(on)h(the)g(structure)g(of)g Fz(t)h FA(using)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3975
3585 y(Lemma)24 b(2.9.)p 3382 3585 V 3386 3522 60 4 v
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3976
3386 3585 V 3445 3585 4 68 v 166 3927 a(The)33 b(main)f(reason)h(for)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3977
(using)f(suspensions)f(in)h(the)h(syntax)f(of)g(terms)h(is)f(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3978
(enable)h(a)g(def-)166 4047 y(inition)d(of)j Fx(substitution)c(of)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3979
(terms)h(for)f(variables)g FA(that)h(allo)n(ws)f(capture)h(of)g(free)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3980
(atoms)e(by)166 4167 y(atom-abstractions)i(while)i(still)e(respecting)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3981
Fz(\013)q FA(-equi)n(v)n(alence.)e(The)i(follo)n(wing)e(lemma)i(es-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3982
4288 y(tablishes)24 b(this.)f(First)i(we)g(gi)n(v)o(e)f(some)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3983
(terminology)f(and)i(notation)e(for)i(term-substitution.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3984
4508 y FB(De\002nition)37 b(2.13.)47 b FA(A)36 b Fx(substitution)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3985
Fz(\033)40 b FA(is)c(a)g(sort-respecting)f(function)g(from)h(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3986
(ariables)f(to)166 4628 y(terms)28 b(with)h(the)f(property)h(that)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3987
Fz(\033)t Fu(\()p Fz(X)8 b Fu(\))35 b(=)g Fz(X)i FA(for)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3988
b(all)g(b)n(ut)f(\002nitely)h(man)o(y)f(v)n(ariables)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3989
Fz(X)8 b FA(.)28 b(W)-8 b(e)166 4749 y(write)20 b Fp(dom)6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3990
b Fu(\()p Fz(\033)t Fu(\))20 b FA(for)g(the)g(\002nite)f(set)h(of)g(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3991
(ariables)f Fz(X)27 b FA(satisfying)19 b Fz(\033)t Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3992
Fz(X)8 b Fu(\))27 b Fw(6)p Fu(=)g Fz(X)8 b FA(.)20 b(If)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3993
Fp(dom)7 b Fu(\()p Fz(\033)t Fu(\))20 b FA(con-)166 4869
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3994
y(sists)28 b(of)h(distinct)f(v)n(ariables)g Fz(X)1269
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3995
4884 y FG(1)1308 4869 y Fz(;)17 b(:)g(:)g(:)f(;)h(X)1608
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3996
4884 y Fq(n)1684 4869 y FA(and)29 b Fz(\033)t Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3997
Fz(X)2035 4884 y Fq(i)2063 4869 y Fu(\))36 b(=)f Fz(t)2283
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3998
4884 y Fq(i)2341 4869 y FA(for)29 b Fz(i)36 b Fu(=)g(1)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3999
Fz(::n)p FA(,)29 b(we)h(sometimes)166 4989 y(write)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4000
b Fz(\033)k FA(as)1204 5110 y Fz(\033)j Fu(=)27 b([)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4001
Fz(X)1502 5125 y FG(1)1569 5110 y Fu(:=)h Fz(t)1735 5125
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4002
y FG(1)1775 5110 y Fz(;)17 b(:)g(:)g(:)e(;)i(X)2074 5125
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4003
y Fq(n)2149 5110 y Fu(:=)27 b Fz(t)2314 5125 y Fq(n)2362
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4004
5110 y Fu(])p Fz(:)872 b FA(\(10\))166 5259 y(W)-8 b(e)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4005
b(write)f Fz(\033)t Fu(\()p Fz(t)p Fu(\))g FA(for)h(the)f(result)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4006
Fx(applying)f(a)h(substitution)e Fz(\033)40 b FA(to)c(a)h(term)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4007
Fz(t)p FA(;)g(this)f(is)h(the)166 5380 y(term)g(obtained)g(from)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4008
Fz(t)h FA(by)f(replacing)g(each)h(suspension)e Fz(\031)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4009
Fr(\001)p Fz(X)44 b FA(in)36 b Fz(t)h FA(\(as)g Fz(X)44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4010
b FA(ranges)37 b(o)o(v)o(er)1748 5712 y(12)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4011
%%Page: 13 13
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4012
TeXDict begin 13 12 bop 166 83 a Fp(dom)7 b Fu(\()p Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4013
Fu(\))p FA(\))39 b(by)h(the)f(term)g Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4014
Fz(\033)t Fu(\()p Fz(X)8 b Fu(\))39 b FA(got)g(by)g(letting)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4015
Fz(\031)43 b FA(act)d(on)f(the)g(term)g Fz(\033)t Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4016
Fz(X)8 b Fu(\))40 b FA(using)e(the)166 203 y(de\002nition)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4017
b(in)g(Figure)h(1.)g(F)o(or)g(e)o(xample,)e(if)i Fz(\033)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4018
b Fu(=)c([)p Fz(X)41 b Fu(:=)33 b Fw(h)p Fz(b;)17 b(Y)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4019
b Fw(i)p Fu(])27 b FA(and)h Fz(t)33 b Fu(=)g Fz(a:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4020
Fu(\()p Fz(a)17 b(b)p Fu(\))p Fr(\001)q Fz(X)8 b FA(,)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4021
b(then)166 324 y Fz(\033)t Fu(\()p Fz(t)p Fu(\))h(=)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4022
Fz(a:)p Fw(h)p Fz(a;)17 b Fu(\()p Fz(a)g(b)p Fu(\))p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4023
Fr(\001)p Fz(Y)k Fw(i)p FA(.)k(Gi)n(v)o(en)e(substitutions)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4024
Fz(\033)29 b FA(and)c Fz(\033)2169 288 y Ft(0)2193 324
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4025
y FA(,)g(and)f(freshness)h(en)l(vironments)f Fw(r)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4026
444 y FA(and)h Fw(r)418 408 y Ft(0)441 444 y FA(,)g(we)g(write)869
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4027
747 y(\(a\))100 b Fw(r)1162 705 y Ft(0)1213 747 y Fw(`)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4028
b Fz(\033)t Fu(\()p Fw(r)p Fu(\))199 b FA(and)g(\(b\))100
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4029
b Fw(r)27 b(`)h Fz(\033)k Fw(\031)c Fz(\033)2728 705
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4030
y Ft(0)3288 747 y FA(\(11\))166 1049 y(to)i(mean,)f(for)i(\(a\),)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4031
(that)g Fw(r)1119 1013 y Ft(0)1179 1049 y Fw(`)37 b Fz(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4032
Fu(#)h Fz(\033)t Fu(\()p Fz(X)8 b Fu(\))30 b FA(holds)f(for)h(each)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4033
Fu(\()p Fz(a)38 b Fu(#)f Fz(X)8 b Fu(\))37 b Fw(2)h(r)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4034
b FA(and,)f(for)i(\(b\),)166 1169 y(that)24 b Fw(r)k(`)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4035
Fz(\033)t Fu(\()p Fz(X)8 b Fu(\))27 b Fw(\031)h Fz(\033)955
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4036
1133 y Ft(0)978 1169 y Fu(\()p Fz(X)8 b Fu(\))25 b FA(holds)f(for)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4037
(all)f Fz(X)36 b Fw(2)28 b Fp(dom)7 b Fu(\()p Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4038
Fu(\))22 b Fw([)g Fp(dom)7 b Fu(\()p Fz(\033)2601 1133
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4039
y Ft(0)2624 1169 y Fu(\))p FA(.)166 1430 y FB(Lemma)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4040
b(2.14)g(\(Substitution\).)44 b Fx(Substitution)25 b(commutes)j(with)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4041
(the)h(permutation)d(action:)166 1551 y Fz(\033)t Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4042
Fz(\031)t Fr(\001)p Fz(t)p Fu(\))j(=)f Fz(\031)t Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4043
Fu(\()p Fz(\033)t Fu(\()p Fz(t)p Fu(\)\))p Fx(.)e(Substitution)d(also)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4044
(pr)l(eserves)h Fw(\031)g Fx(and)f Fu(#)i Fx(in)e(the)h(following)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4045
(sense:)206 1812 y(\(1\))50 b(if)24 b Fw(r)535 1776 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4046
Ft(0)586 1812 y Fw(`)k Fz(\033)t Fu(\()p Fw(r)p Fu(\))d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4047
Fx(and)f Fw(r)k(`)f Fz(t)h Fw(\031)g Fz(t)1494 1776 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4048
Ft(0)1518 1812 y Fx(,)d(then)f Fw(r)1847 1776 y Ft(0)1898
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4049
1812 y Fw(`)k Fz(\033)t Fu(\()p Fz(t)p Fu(\))f Fw(\031)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4050
Fz(\033)t Fu(\()p Fz(t)2422 1776 y Ft(0)2445 1812 y Fu(\))p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4051
Fx(;)206 1932 y(\(2\))50 b(if)24 b Fw(r)535 1896 y Ft(0)586
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4052
1932 y Fw(`)k Fz(\033)t Fu(\()p Fw(r)p Fu(\))d Fx(and)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4053
Fw(r)k(`)f Fz(a)h Fu(#)g Fz(t)p Fx(,)d(then)g Fw(r)1844
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4054
1896 y Ft(0)1895 1932 y Fw(`)i Fz(a)h Fu(#)g Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4055
Fu(\()p Fz(t)p Fu(\))p Fx(.)166 2612 y FB(PR)m(OOF)-11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4056
b(.)49 b FA(The)19 b(\002rst)h(sentence)g(follo)n(ws)e(by)i(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4057
(routine)f(induction)f(on)i(the)f(structure)h(of)g Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4058
FA(.)g(The)166 2733 y(second)25 b(follo)n(ws)e(by)h(induction)g(on)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4059
(the)h(de\002nition)f(of)h Fw(\031)g FA(and)g Fu(#)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4060
FA(using)f(Lemma)g(2.8.)p 3382 2733 4 68 v 3386 2669
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4061
60 4 v 3386 2733 V 3445 2733 4 68 v 166 3413 a(W)-8 b(e)38
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4062
b(claim)f(that)g(the)g(relation)g Fw(\031)h FA(de\002ned)g(in)f(Figure)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4063
h(2)g(gi)n(v)o(es)d(the)j(correct)g(notion)e(of)i Fz(\013)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4064
FA(-)166 3533 y(equi)n(v)n(alence)d(for)h(terms)f(o)o(v)o(er)g(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4065
(nominal)e(signature.)h(This)g(is)h(reasonable,)g(gi)n(v)o(en)e(Theo-)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4066
166 3654 y(rem)24 b(2.11)g(and)g(the)g(f)o(act)g(that,)g(by)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4067
(de\002nition,)g(it)h(satis\002es)g(rules)g(\()p Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4068
FA(-abstraction-1\))g(and)g(\()p Fw(\031)p FA(-)166 3774
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4069
y(abstraction-2\).)34 b(Further)i(e)n(vidence)f(is)f(pro)o(vided)g(by)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4070
(the)g(follo)n(wing)e(proposition,)g(which)166 3894 y(sho)n(ws)d(that)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4071
(for)g(ground)f(terms)g Fw(\031)h FA(agrees)g(with)f(the)h(follo)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4072
(wing)e(more)h(traditional)g(de\002ni-)166 4015 y(tion)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4073
b(of)h Fz(\013)q FA(-equi)n(v)n(alence.)166 4276 y FB(De\002nition)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4074
(2.15)f(\(Na)954 4275 y(\250)957 4276 y(\021v)o(e)h Fh(\013)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4075
FB(-equi)o(v)o(alence\).)37 b FA(De\002ne)21 b(the)f(binary)h(relation)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4076
f Fz(t)28 b Fu(=)2966 4291 y Fq(\013)3043 4276 y Fz(t)3078
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4077
4240 y Ft(0)3122 4276 y FA(between)166 4396 y(terms)h(o)o(v)o(er)f(a)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4078
(nominal)e(signature)h(to)g(be)h(the)f(least)g(sort-respecting)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4079
(congruence)g(relation)166 4517 y(satisfying)i Fz(a:t)43
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4080
b Fu(=)818 4532 y Fq(\013)909 4517 y Fz(b:)p Fu([)p Fz(a)1055
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4081
4511 y Ft(7!)1127 4517 y Fz(b)p Fu(])p Fz(t)33 b FA(whene)n(v)o(er)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4082
Fz(b)h FA(is)f(an)h(atom)f(\(of)h(the)f(same)h(sort)f(as)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4083
Fz(a)p FA(\))h(not)f(oc-)166 4637 y(curring)j(at)h(all)f(in)g(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4084
(term)f Fz(t)p FA(.)h(Here)g Fu([)p Fz(a)1624 4631 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4085
Ft(7!)1695 4637 y Fz(b)p Fu(])p Fz(t)g FA(indicates)f(the)h(result)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4086
(of)g(replacing)h(all)f(free)166 4757 y(occurrences)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4087
b(of)f Fz(a)g FA(with)f Fz(b)h FA(in)g Fz(t)p FA(.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4088
5019 y FB(Pr)n(oposition)39 b(2.16)f(\(Adequacy\).)50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4089
b Fx(If)39 b Fz(t)g Fx(and)f Fz(t)1872 4983 y Ft(0)1934
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4090
5019 y Fx(ar)l(e)h(gr)l(ound)e(terms)h FA(\(i.e.)h(terms)f(with)g(no)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4091
166 5139 y(v)n(ariables)d(and)g(hence)h(no)f(suspensions\))f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4092
Fx(o)o(ver)i(a)f(nominal)f(signatur)l(e)o(,)g(then)i(the)f(r)l(elation)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4093
166 5259 y Fz(t)d Fu(=)309 5274 y Fq(\013)390 5259 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4094
Fz(t)425 5223 y Ft(0)476 5259 y Fx(of)26 b(De\002nition)g(2.15)g(holds)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4095
g(if)g(and)h(only)g(if)f Fw(;)31 b(`)h Fz(t)g Fw(\031)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4096
Fz(t)2375 5223 y Ft(0)2426 5259 y Fx(is)26 b(pr)l(o)o(vable)g(fr)l(om)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4097
(the)g(rules)166 5380 y(in)31 b(F)l(igur)l(e)f(2.)h(Furthermor)l(e)o(,)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4098
f Fw(;)39 b(`)h Fz(a)f Fu(#)h Fz(t)31 b Fx(is)g(pr)l(o)o(vable)f(if)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4099
(and)f(only)h(if)g Fz(a)g Fx(is)g(not)f(in)h(the)g(set)1748
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4100
5712 y FA(13)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4101
%%Page: 14 14
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4102
TeXDict begin 14 13 bop 166 83 a Fp(F)-10 b(A)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4103
Fz(t)p Fu(\))25 b Fx(of)g(fr)l(ee)g(atoms)f(of)g Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4104
Fx(,)h(de\002ned)g(by:)1366 325 y Fp(F)-10 b(A)q Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4105
Fw(hi)p Fu(\))1674 266 y Fg(def)1676 325 y Fu(=)30 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4106
Fw(;)1173 498 y Fp(F)-10 b(A)q Fu(\()p Fw(h)p Fz(t)1412
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4107
513 y FG(1)1451 498 y Fz(;)17 b(t)1530 513 y FG(2)1569
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4108
498 y Fw(i)p Fu(\))1674 439 y Fg(def)1676 498 y Fu(=)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4109
b Fp(F)-10 b(A)p Fu(\()p Fz(t)1981 513 y FG(1)2021 498
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4110
y Fu(\))22 b Fw([)h Fp(F)-10 b(A)p Fu(\()p Fz(t)2369
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4111
513 y FG(2)2408 498 y Fu(\))1333 672 y Fp(F)g(A)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4112
Fz(f)28 b(t)p Fu(\))1674 613 y Fg(def)1676 672 y Fu(=)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4113
Fp(F)-10 b(A)p Fu(\()p Fz(t)p Fu(\))1393 846 y Fp(F)g(A)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4114
Fu(\()p Fz(a)p Fu(\))1674 787 y Fg(def)1676 846 y Fu(=)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4115
b Fw(f)p Fz(a)p Fw(g)1330 1019 y Fp(F)-10 b(A)q Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4116
Fz(a:t)p Fu(\))1674 960 y Fg(def)1676 1019 y Fu(=)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4117
b Fp(F)-10 b(A)p Fu(\()p Fz(t)p Fu(\))23 b Fw(\000)f(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4118
Fz(a)p Fw(g)p Fz(:)166 1357 y FB(PR)m(OOF)-11 b(.)49
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4119
b FA(The)24 b(proof)h(is)f(similar)g(to)g(the)h(proof)g(of)g([10,)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4120
(Proposition)g(2.2].)p 3382 1357 4 68 v 3386 1293 60
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4121
4 v 3386 1357 V 3445 1357 4 68 v 166 1694 a(F)o(or)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4122
b(non-ground)f(terms,)h(the)g(relations)g Fu(=)1722 1709
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4123
y Fq(\013)1804 1694 y FA(and)h Fw(\031)f FA(dif)n(fer!)h(F)o(or)f(e)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4124
(xample)f Fz(a:X)52 b Fu(=)3204 1709 y Fq(\013)3296 1694
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4125
y Fz(b:X)166 1815 y FA(al)o(w)o(ays)24 b(holds,)f(whereas)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4126
Fw(;)j(`)f Fz(a:X)36 b Fw(\031)28 b Fz(b:X)33 b FA(is)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4127
b(not)f(pro)o(v)n(able)g(unless)h Fz(a)k Fu(=)f Fz(b)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4128
FA(.)e(This)f(disagree-)166 1935 y(ment)h(is)g(to)g(be)g(e)o(xpected,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4129
(since)h(we)f(noted)g(in)g(the)g(Introduction)g(that)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4130
Fu(=)2746 1950 y Fq(\013)2821 1935 y FA(is)h Fx(not)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4131
FA(preserv)o(ed)166 2056 y(by)e(substitution,)c(whereas)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4132
b(from)e(Lemma)h(2.14)f(we)h(kno)n(w)f(that)g Fw(\031)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4133
FA(is.)166 2453 y FB(3)99 b(Uni\002cation)166 2794 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4134
FA(Gi)n(v)o(en)37 b(terms)h Fz(t)h FA(and)g Fz(t)996
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4135
2758 y Ft(0)1058 2794 y FA(of)g(the)f(same)h(sort)f(o)o(v)o(er)g(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4136
(nominal)e(signature,)h(can)h(we)g(decide)166 2914 y(whether)21
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4137
b(or)h(not)e(there)i(is)f(a)h(substitution)c(of)j(terms)g(for)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4138
(v)n(ariables)g(in)f Fz(t)i FA(and)f Fz(t)2984 2878 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4139
Ft(0)3029 2914 y FA(that)g(mak)o(es)166 3034 y(them)k(equal)g(in)g(the)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4140
g(sense)h(of)f(the)g(relation)g Fw(\031)h FA(introduced)f(in)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4141
(pre)n(vious)f(section?)h(Since)166 3155 y(instances)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4142
b(of)g Fw(\031)h FA(are)h(established)d(modulo)g(freshness)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4143
(constraints,)g(it)f(mak)o(es)i(more)f(sense)166 3275
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4144
y(to)c(ask)g(whether)g(or)g(not)g(there)g(is)g(both)f(a)i(substitution)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4145
c Fz(\033)30 b FA(and)c(a)h(freshness)f(en)l(vironment)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4146
Fw(r)166 3396 y FA(for)k(which)f Fw(r)34 b(`)h Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4147
Fu(\()p Fz(t)p Fu(\))f Fw(\031)h Fz(\033)t Fu(\()p Fz(t)1244
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4148
3359 y Ft(0)1268 3396 y Fu(\))28 b FA(holds.)g(As)g(for)h(ordinary)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4149
(\002rst-order)h(uni\002cation,)e(solving)166 3516 y(such)h(an)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4150
(equational)g(problem)g(may)h(thro)n(w)f(up)g Fx(se)o(ver)o(al)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4151
FA(equational)g(subproblems;)e(b)n(ut)j(an)166 3636 y(added)21
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4152
b(complication)f(here)i(is)f(that)g(because)h(of)f(rule)h(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4153
Fw(\031)p FA(-abstraction-2\))g(in)f(Figure)g(2,)g(equa-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4154
3757 y(tional)30 b(problems)g(may)h(generate)g Fx(fr)l(eshness)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4155
FA(problems,)f(i.e.)h(ones)f(in)l(v)n(olving)f(the)i(relation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4156
3877 y Fu(#)p FA(.)c(W)-8 b(e)28 b(are)g(thus)e(led)h(to)f(the)h(follo)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4157
n(wing)e(de\002nition)h(of)i(uni\002cation)e(problems)g(for)h(nominal)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4158
166 3998 y(equational)d(logic.)166 4218 y FB(De\002nition)k(3.1.)42
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4159
b FA(A)27 b Fx(uni\002cation)f(pr)l(oblem)f Fz(P)41 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4160
FA(o)o(v)o(er)26 b(a)i(nominal)d(signature)i(is)f(a)i(\002nite)f(set)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4161
(of)166 4338 y(atomic)32 b(problems,)f(each)i(of)g(which)f(is)g(either)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4162
g(an)h Fx(equational)e(pr)l(oblem)g Fz(t)42 b Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4163
Fu(?)g Fz(t)3086 4302 y Ft(0)3143 4338 y FA(where)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4164
b Fz(t)166 4458 y FA(and)27 b Fz(t)372 4422 y Ft(0)422
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4165
4458 y FA(are)g(terms)f(of)h(the)f(same)h(sort)f(o)o(v)o(er)f(the)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4166
(signature,)f(or)g(a)h Fx(fr)l(eshness)f(pr)l(oblem)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4167
Fz(a)31 b Fu(#?)g Fz(t)166 4579 y FA(where)e Fz(a)g FA(is)f(an)g(atom)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4168
(and)g Fz(t)h FA(a)g(term)f(o)o(v)o(er)f(the)i(signature.)e(A)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4169
Fx(solution)d FA(for)j Fz(P)42 b FA(consists)27 b(of)h(a)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4170
4699 y(pair)d Fu(\()p Fw(r)p Fz(;)17 b(\033)t Fu(\))24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4171
b FA(where)i Fw(r)f FA(is)f(a)h(freshness)g(en)l(vironment)e(and)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4172
Fz(\033)k FA(is)24 b(a)h(substitution)d(satisfying)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4173
4919 y Fw(\017)50 b(r)27 b(`)h Fz(a)g Fu(#)g Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4174
Fu(\()p Fz(t)p Fu(\))52 b FA(for)26 b(each)53 b Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4175
Fz(a)27 b Fu(#?)h Fz(t)p Fu(\))g Fw(2)g Fz(P)66 b FA(and)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4176
5039 y Fw(\017)50 b(r)27 b(`)h Fz(\033)t Fu(\()p Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4177
Fu(\))g Fw(\031)g Fz(\033)t Fu(\()p Fz(t)900 5003 y Ft(0)923
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4178
5039 y Fu(\))53 b FA(for)25 b(each)53 b Fu(\()p Fz(t)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4179
b Fw(\031)p Fu(?)g Fz(t)1677 5003 y Ft(0)1701 5039 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4180
Fu(\))f Fw(2)h Fz(P)14 b FA(.)166 5259 y(W)-8 b(e)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4181
b(write)f Ff(U)p Fu(\()p Fz(P)14 b Fu(\))22 b FA(for)i(the)f(set)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4182
(all)g(solutions)e(of)i(a)g(problem)g Fz(P)14 b FA(.)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4183
b Fu(\()p Fw(r)p Fz(;)17 b(\033)t Fu(\))28 b Fw(2)g Ff(U)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4184
Fu(\()p Fz(P)14 b Fu(\))22 b FA(is)h(a)h Fx(most)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4185
5380 y(g)o(ener)o(al)i FA(solution)g(for)i Fz(P)40 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4186
FA(if)28 b(gi)n(v)o(en)e(an)o(y)g(other)h(solution)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4187
Fu(\()p Fw(r)2296 5344 y Ft(0)2319 5380 y Fz(;)17 b(\033)2422
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4188
5344 y Ft(0)2445 5380 y Fu(\))33 b Fw(2)f Ff(U)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4189
Fz(P)14 b Fu(\))p FA(,)27 b(then)g(there)h(is)e(a)1748
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4190
5712 y(14)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4191
%%Page: 15 15
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4192
TeXDict begin 15 14 bop 166 83 a FA(substitution)18 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4193
Fz(\033)711 47 y Ft(00)775 83 y FA(satisfying)i Fw(r)1267
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4194
47 y Ft(0)1318 83 y Fw(`)28 b Fz(\033)1466 47 y Ft(00)1508
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4195
83 y Fu(\()p Fw(r)p Fu(\))21 b FA(and)h Fw(r)1937 47
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4196
y Ft(0)1988 83 y Fw(`)27 b Fz(\033)2135 47 y Ft(00)2187
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4197
83 y Fw(\016)9 b Fz(\033)31 b Fw(\031)d Fz(\033)2496
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4198
47 y Ft(0)2520 83 y FA(.)21 b(\(Here)h(we)g(are)g(using)e(the)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4199
203 y(notation)25 b(of)h(\(11\);)f(and)h Fz(\033)1076
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4200
167 y Ft(00)1142 203 y Fw(\016)d Fz(\033)30 b FA(denotes)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4201
b(the)h Fx(substitution)d(composition)h FA(of)i Fz(\033)k
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4202
FA(follo)n(wed)25 b(by)166 339 y Fz(\033)225 303 y Ft(00)267
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4203
339 y FA(,)j(gi)n(v)o(en)e(by)h Fu(\()p Fz(\033)789 303
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4204
y Ft(00)855 339 y Fw(\016)d Fz(\033)t Fu(\)\()p Fz(X)8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4205
b Fu(\))1223 287 y Fo(def)1227 339 y Fu(=)37 b Fz(\033)1399
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4206
303 y Ft(00)1441 339 y Fu(\()p Fz(\033)t Fu(\()p Fz(X)8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4207
b Fu(\)\))p FA(.\))27 b(A)g(solution)f Fu(\()p Fw(r)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4208
Fz(;)17 b(\033)t Fu(\))32 b Fw(2)g Ff(U)p Fu(\()p Fz(P)14
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4209
b Fu(\))27 b FA(is)g Fx(idempotent)166 460 y FA(pro)o(vided)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4210
Fw(r)j(`)h Fz(\033)e Fw(\016)c Fz(\033)32 b Fw(\031)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4211
Fz(\033)t FA(.)166 683 y(W)-8 b(e)31 b(describe)g(an)g(algorithm)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4212
(which,)h(gi)n(v)o(en)f(an)o(y)h(nominal)f(uni\002cation)h(problem,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4213
(decides)166 803 y(whether)i(or)h(not)e(it)h(has)g(a)h(solution)d(and)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4214
(if)f(it)g(does,)g(returns)g(a)g(most)f(general)i(\(and)f(idem-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4215
923 y(potent\))23 b(solution.)e(The)j(algorithm)e(uses)h(labelled)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4216
(transformations,)f(directly)h(generalising)166 1044
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4217
y(the)31 b(presentation)f(of)i(\002rst-order)f(uni\002cation)g(in)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4218
([19,)g(Sect.)h(2.6])f(which)f(in)h(turn)g(is)g(based)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4219
1164 y(upon)g(the)g(approach)h(in)g([18].)f(\(See)i(also)e([20,)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4220
(Sect.)g(4.6])f(for)h(a)g(detailed)f(e)o(xposition,)e(b)n(ut)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4221
1284 y(not)d(using)f(labels.\))h(W)-8 b(e)26 b(use)g(tw)o(o)g(types)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4222
(of)i(labelled)e(transformation)g(between)i(uni\002cation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4223
1405 y(problems,)d(namely)1248 1547 y Fz(P)1410 1494
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4224
y Fq(\033)1352 1547 y Fu(=)-17 b Fw(\))28 b Fz(P)1616
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4225
1506 y Ft(0)1738 1547 y FA(and)99 b Fz(P)2136 1494 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4226
Ft(r)2086 1547 y Fu(=)-17 b Fw(\))27 b Fz(P)2349 1506
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4227
y Ft(0)166 1702 y FA(where)i(the)g(substitution)d Fz(\033)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4228
b FA(is)c(either)g(the)f(identity)g Fz(")p FA(,)g(or)h(a)g(single)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4229
(replacement)h Fu([)p Fz(X)43 b Fu(:=)36 b Fz(t)p Fu(])p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4230
FA(;)166 1822 y(and)24 b(where)h(the)f(freshness)g(en)l(vironment)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4231
Fw(r)j FA(is)e(either)h(empty)f Fw(;)p FA(,)h(or)h(a)f(singleton)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4232
Fw(f)p Fz(a)k Fu(#)h Fz(X)8 b Fw(g)p FA(.)166 1943 y(The)21
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4233
b(le)o(gal)f(transformations)g(are)h(gi)n(v)o(en)f(in)h(Figure)g(3.)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4234
(This)f(\002gure)i(uses)f(the)g(notation)e Fz(P)j Fw(])8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4235
b Fz(P)3430 1906 y Ft(0)166 2063 y FA(to)26 b(indicate)f(the)h(union)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4236
(of)g(problems)f Fz(P)40 b FA(and)26 b Fz(P)1869 2027
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4237
y Ft(0)1918 2063 y FA(that)g(are)g(disjoint)f(\()p Fz(P)36
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4238
b Fw(\\)24 b Fz(P)2866 2027 y Ft(0)2919 2063 y Fu(=)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4239
b Fw(;)p FA(\);)c(and)g(the)166 2183 y(notation)j Fz(\033)t(P)44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4240
b FA(to)30 b(indicate)g(the)g(problem)f(resulting)g(from)h(applying)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4241
(the)h(substitution)e Fz(\033)34 b FA(to)166 2304 y(all)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4242
b(the)f(terms)g(occurring)h(in)g(the)f(problem)g Fz(P)14
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4243
b FA(.)166 2526 y FB(Algorithm.)33 b FA(Gi)n(v)o(en)18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4244
b(a)h(uni\002cation)f(problem)g Fz(P)c FA(,)19 b(the)g(algorithm)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4245
(proceeds)i(in)g(tw)o(o)g(phases.)3398 2490 y FG(2)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4246
2647 y FA(In)j(the)g(\002rst)g(phase)g(it)f(applies)g(as)h(man)o(y)1627
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4247
2594 y Fq(\033)1569 2647 y Fu(=)-17 b Fw(\))22 b FA(transformations)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4248
(as)i(possible)f(\(non-determin-)166 2767 y(istically\).)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4249
b(If)i(this)f(results)g(in)g(a)h(problem)f(containing)f(no)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4250
(equational)e(subproblems,)g(then)166 2888 y(it)d(proceeds)h(to)f(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4251
(second)g(phase;)g(otherwise)g(it)g(halts)g(signalling)f(f)o(ailure.)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4252
(In)h(the)f(second)166 3024 y(phase)22 b(it)f(applies)g(as)g(man)o(y)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4253
1192 2971 y Ft(r)1142 3024 y Fu(=)-17 b Fw(\))21 b FA(transformations)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4254
(as)i(possible)e(\(non-deterministically\).)f(If)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4255
3145 y(this)24 b(does)h(not)f(result)g(in)h(the)g(empty)f(problem,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4256
(then)g(it)g(halts)h(signalling)e(f)o(ailure;)h(otherwise)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4257
3265 y(o)o(v)o(erall)g(it)g(has)h(constructed)f(a)h(transformation)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4258
(sequence)i(of)g(the)g(form)1152 3509 y Fz(P)1298 3454
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4259
y Fq(\033)1338 3463 y Fe(1)1256 3509 y Fu(=)-17 b Fw(\))28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4260
b(\001)17 b(\001)g(\001)1625 3455 y Fq(\033)1665 3463
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4261
y Fd(n)1587 3509 y Fu(=)-17 b Fw(\))27 b Fz(P)1850 3468
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4262
y Ft(0)1933 3454 y(r)1992 3463 y Fe(1)1901 3509 y Fu(=)-17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4263
b Fw(\))27 b(\001)17 b(\001)g(\001)2252 3455 y Ft(r)2311
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4264
3463 y Fd(m)2231 3509 y Fu(=)-17 b Fw(\))28 b(;)820 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4265
FA(\(12\))166 3734 y(\(where)26 b Fz(P)545 3698 y Ft(0)593
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4266
3734 y FA(does)f(not)g(contain)f(an)o(y)h(equational)f(subproblems\))g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4267
(and)h(the)g(algorithm)f(returns)166 3854 y(the)h(solution)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4268
Fu(\()p Fw(r)780 3869 y FG(1)841 3854 y Fw([)g(\001)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4269
b(\001)g(\001)j([)j(r)1240 3869 y Fq(m)1306 3854 y Fz(;)34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4270
b(\033)1422 3869 y Fq(n)1491 3854 y Fw(\016)22 b(\001)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4271
b(\001)g(\001)j(\016)i Fz(\033)1828 3869 y FG(1)1868
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4272
3854 y Fu(\))p FA(.)166 4077 y(T)-8 b(o)31 b(sho)n(w)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4273
(correctness)h(of)g(this)f(algorithm,)f(we)i(\002rst)f(establish)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4274
(that)g(all)g(sequences)h(of)166 4198 y(uni\002cation)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4275
b(transitions)f(must)h(terminate.)166 4420 y FB(Lemma)h(3.2.)41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4276
b Fx(Ther)l(e)26 b(is)e(no)h(in\002nite)f(series)g(of)g(uni\002cation)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4277
(tr)o(ansitions.)166 4783 y FB(PR)m(OOF)-11 b(.)49 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4278
FA(Since)28 b(e)n(v)o(ery)f(reduction)f(sequence)i(consists)e(of)i(tw)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4279
(o)f(\(possibly)f(empty\))h(subse-)166 4920 y(quences,)j(namely)g(one)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4280
(containing)e(only)1757 4867 y Fq(\033)1699 4920 y Fu(=)-17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4281
b Fw(\))p FA(-steps)30 b(and)h(the)f(other)g(only)2941
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4282
4867 y Ft(r)2891 4920 y Fu(=)-17 b Fw(\))p FA(-steps,)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4283
b(we)166 5040 y(can)23 b(sho)n(w)f(termination)f(for)i(both)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4284
(subsequences)g(separately)-6 b(.)22 b(F)o(or)h(e)n(v)o(ery)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4285
(uni\002cation)g(prob-)166 5161 y(lem)g Fz(P)36 b FA(we)23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4286
b(de\002ne)h(a)f(measure)f(of)h(the)g(size)f(of)h Fz(P)36
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4287
b FA(to)22 b(be)h(the)g(le)o(xicographically)e(ordered)i(pair)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4288
166 5282 299 4 v 166 5346 a FG(2)257 5379 y FD(See)g(Remark)g(3.9)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4289
(for)g(discussion)i(of)e(this)g(use)g(of)f(tw)o(o)g(phases.)1748
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4290
5712 y FA(15)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4291
%%Page: 16 16
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4292
TeXDict begin 16 15 bop 166 3 3288 4 v 166 3123 4 3121
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4293
v 204 154 a FD(\()p Fl(\031)p Fk(?)p FD(-unit\))798 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4294
Fw(fhi)27 b(\031)p Fu(?)h Fw(hig)21 b(])i Fz(P)2063 101
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4295
y Fq(")1999 154 y Fu(=)-17 b Fw(\))34 b Fz(P)204 335
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4296
y FD(\()p Fl(\031)p Fk(?)p FD(-pair\))412 b Fw(fh)p Fz(t)1084
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4297
350 y FG(1)1123 335 y Fz(;)17 b(t)1202 350 y FG(2)1241
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4298
335 y Fw(i)28 b(\031)p Fu(?)g Fw(h)p Fz(t)1533 298 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4299
Ft(0)1533 359 y FG(1)1572 335 y Fz(;)17 b(t)1651 298
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4300
y Ft(0)1651 359 y FG(2)1691 335 y Fw(ig)k(])i Fz(P)2063
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4301
281 y Fq(")1999 335 y Fu(=)-17 b Fw(\))34 b(f)p Fz(t)2277
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4302
350 y FG(1)2344 335 y Fw(\031)p Fu(?)28 b Fz(t)2530 298
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4303
y Ft(0)2530 359 y FG(1)2570 335 y Fz(;)17 b(t)2649 350
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4304
y FG(2)2716 335 y Fw(\031)p Fu(?)28 b Fz(t)2902 298 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4305
Ft(0)2902 359 y FG(2)2942 335 y Fw(g)21 b([)i Fz(P)204
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4306
515 y FD(\()p Fl(\031)p Fk(?)p FD(-function)j(symbol\))256
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4307
b Fw(f)p Fz(f)27 b(t)h Fw(\031)q Fu(?)f Fz(f)h(t)1706
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4308
479 y Ft(0)1729 515 y Fw(g)22 b(])h Fz(P)2063 462 y Fq(")1999
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4309
515 y Fu(=)-17 b Fw(\))34 b(f)p Fz(t)27 b Fw(\031)q Fu(?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4310
Fz(t)2490 479 y Ft(0)2514 515 y Fw(g)22 b([)h Fz(P)204
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4311
696 y FD(\()p Fl(\031)p Fk(?)p FD(-abstraction-1\))372
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4312
b Fw(f)p Fz(a:t)28 b Fw(\031)q Fu(?)f Fz(a:t)1705 660
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4313
y Ft(0)1729 696 y Fw(g)22 b(])h Fz(P)2063 643 y Fq(")1999
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4314
696 y Fu(=)-17 b Fw(\))34 b(f)p Fz(t)27 b Fw(\031)q Fu(?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4315
Fz(t)2490 660 y Ft(0)2514 696 y Fw(g)22 b([)h Fz(P)204
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4316
876 y FD(\()p Fl(\031)p Fk(?)p FD(-abstraction-2\))349
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4317
b Fw(f)p Fz(a:t)28 b Fw(\031)p Fu(?)g Fz(a)1620 840 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4318
Ft(0)1644 876 y Fz(:t)1706 840 y Ft(0)1729 876 y Fw(g)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4319
b(])h Fz(P)2063 823 y Fq(")1999 876 y Fu(=)-17 b Fw(\))34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4320
b(f)p Fz(t)27 b Fw(\031)q Fu(?)g(\()p Fz(a)17 b(a)2612
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4321
840 y Ft(0)2636 876 y Fu(\))p Fr(\001)p Fz(t)2741 840
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4322
y Ft(0)2764 876 y Fz(;)g(a)28 b Fu(#?)g Fz(t)3077 840
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4323
y Ft(0)3100 876 y Fw(g)22 b([)h Fz(P)2781 1010 y FA(pro)o(vided)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4324
Fz(a)k Fw(6)p Fu(=)f Fz(a)3392 973 y Ft(0)204 1143 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4325
FD(\()p Fl(\031)p Fk(?)p FD(-atom\))809 b Fw(f)p Fz(a)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4326
b Fw(\031)p Fu(?)g Fz(a)p Fw(g)22 b(])h Fz(P)2063 1090
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4327
y Fq(")1999 1143 y Fu(=)-17 b Fw(\))34 b Fz(P)204 1324
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4328
y FD(\()p Fl(\031)p Fk(?)p FD(-suspension\))315 b Fw(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4329
Fz(\031)t Fr(\001)p Fz(X)35 b Fw(\031)q Fu(?)27 b Fz(\031)1585
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4330
1287 y Ft(0)1609 1324 y Fr(\001)p Fz(X)8 b Fw(g)21 b(])i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4331
Fz(P)2063 1270 y Fq(")1999 1324 y Fu(=)-17 b Fw(\))34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4332
b(f)p Fz(a)27 b Fu(#?)h Fz(X)36 b Fw(j)27 b Fz(a)h Fw(2)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4333
Fp(ds)8 b Fu(\()p Fz(\031)t(;)17 b(\031)3118 1287 y Ft(0)3141
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4334
1324 y Fu(\))p Fw(g)22 b([)g Fz(P)204 1583 y FD(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4335
Fl(\031)p Fk(?)p FD(-v)n(ariable\))1259 1504 y Fw(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4336
Fz(t)27 b Fw(\031)q Fu(?)g Fz(\031)t Fr(\001)p Fz(X)8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4337
b Fw(g)22 b(])h Fz(P)1259 1685 y Fw(f)p Fz(\031)t Fr(\001)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4338
Fz(X)36 b Fw(\031)p Fu(?)28 b Fz(t)p Fw(g)22 b(])h Fz(P)1939
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4339
1384 y Fn(9)1939 1459 y(>)1939 1484 y(=)1939 1633 y(>)1939
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4340
1658 y(;)2058 1530 y Fq(\033)1999 1583 y Fu(=)-17 b Fw(\))34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4341
b Fz(\033)t(P)160 b FA(with)52 b Fz(\033)31 b Fu(=)d([)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4342
Fz(X)36 b Fu(:=)27 b Fz(\031)3227 1547 y Ft(\000)p FG(1)3321
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4343
1583 y Fr(\001)p Fz(t)p Fu(])2181 1724 y FA(pro)o(vided)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4344
Fz(X)33 b FA(does)25 b(not)f(occur)h(in)f Fz(t)204 1928
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4345
y FD(\()p Fk(#?)p FD(-unit\))815 b Fw(f)p Fz(a)28 b Fu(#?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4346
Fw(hig)21 b(])i Fz(P)2061 1875 y Ft(;)1999 1928 y Fu(=)-17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4347
b Fw(\))34 b Fz(P)204 2108 y FD(\()p Fk(#?)p FD(-pair\))622
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4348
b Fw(f)p Fz(a)28 b Fu(#?)g Fw(h)p Fz(t)1533 2123 y FG(1)1572
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4349
2108 y Fz(;)17 b(t)1651 2123 y FG(2)1691 2108 y Fw(ig)k(])i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4350
Fz(P)2061 2055 y Ft(;)1999 2108 y Fu(=)-17 b Fw(\))34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4351
b(f)p Fz(a)27 b Fu(#?)h Fz(t)2510 2123 y FG(1)2550 2108
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4352
y Fz(;)17 b(a)28 b Fu(#?)g Fz(t)2863 2123 y FG(2)2902
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4353
2108 y Fw(g)22 b([)h Fz(P)204 2289 y FD(\()p Fk(#?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4354
FD(-function)j(symbol\))330 b Fw(f)p Fz(a)28 b Fu(#?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4355
Fz(f)f(t)p Fw(g)22 b(])h Fz(P)2061 2236 y Ft(;)1999 2289
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4356
y Fu(=)-17 b Fw(\))34 b(f)p Fz(a)27 b Fu(#?)h Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4357
Fw(g)22 b([)h Fz(P)204 2469 y FD(\()p Fk(#?)p FD(-abstraction-1\))449
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4358
b Fw(f)p Fz(a)28 b Fu(#?)g Fz(a:t)p Fw(g)22 b(])h Fz(P)2061
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4359
2416 y Ft(;)1999 2469 y Fu(=)-17 b Fw(\))34 b Fz(P)204
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4360
2650 y FD(\()p Fk(#?)p FD(-abstraction-2\))426 b Fw(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4361
Fz(a)27 b Fu(#?)h Fz(a)1643 2614 y Ft(0)1667 2650 y Fz(:t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4362
Fw(g)22 b(])h Fz(P)2061 2597 y Ft(;)1999 2650 y Fu(=)-17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4363
b Fw(\))34 b(f)p Fz(a)27 b Fu(#?)h Fz(t)p Fw(g)22 b([)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4364
Fz(P)47 b FA(pro)o(vided)24 b Fz(a)k Fw(6)p Fu(=)f Fz(a)3392
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4365
2614 y Ft(0)204 2831 y FD(\()p Fk(#?)p FD(-atom\))777
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4366
b Fw(f)p Fz(a)28 b Fu(#?)g Fz(a)1706 2794 y Ft(0)1729
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4367
2831 y Fw(g)22 b(])h Fz(P)2061 2777 y Ft(;)1999 2831
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4368
y Fu(=)-17 b Fw(\))34 b Fz(P)526 b FA(pro)o(vided)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4369
b Fz(a)k Fw(6)p Fu(=)f Fz(a)3392 2794 y Ft(0)204 3011
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4370
y FD(\()p Fk(#?)p FD(-suspension\))458 b Fw(f)p Fz(a)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4371
b Fu(#?)g Fz(\031)t Fr(\001)p Fz(X)8 b Fw(g)21 b(])i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4372
Fz(P)2049 2958 y Ft(r)1999 3011 y Fu(=)-17 b Fw(\))34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4373
b Fz(P)113 b FA(with)24 b Fw(r)j Fu(=)h Fw(f)p Fz(\031)2893
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4374
2975 y Ft(\000)p FG(1)2987 3011 y Fr(\001)p Fz(a)g Fu(#)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4375
Fz(X)8 b Fw(g)p 3450 3123 V 166 3126 3288 4 v 1214 3263
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4376
a FD(Fig.)23 b(3.)g(Labelled)h(transformations.)166 3422
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4377
y FA(of)29 b(natural)f(numbers)f Fu(\()p Fz(n)1050 3437
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4378
y FG(1)1090 3422 y Fz(;)17 b(n)1192 3437 y FG(2)1231
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4379
3422 y Fu(\))p FA(,)29 b(where)g Fz(n)1653 3437 y FG(1)1721
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4380
3422 y FA(is)f(the)g(number)g(of)g(dif)n(ferent)g(v)n(ariables)g(used)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4381
(in)166 3542 y Fz(P)14 b FA(,)24 b(and)h Fz(n)519 3557
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4382
y FG(2)584 3542 y FA(is)f(the)h(size)f(\(see)i(De\002nition)e(2.10\))g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4383
(of)h(all)g(equational)f(problems)f(in)i Fz(P)14 b FA(,)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4384
b(that)g(is)1334 3767 y Fz(n)1392 3782 y FG(2)1459 3714
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4385
y Fo(def)1464 3767 y Fu(=)1671 3684 y Fn(X)1572 3872
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4386
y FG(\()p Fq(t)p Ft(\031)q FG(?)p Fq(t)1738 3853 y Fc(0)1761
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4387
3872 y FG(\))p Ft(2)p Fq(P)1906 3767 y Fw(j)p Fz(t)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4388
Fw(j)e Fu(+)g Fw(j)p Fz(t)2180 3726 y Ft(0)2203 3767
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4389
y Fw(j)28 b Fz(:)166 4084 y FA(In)34 b(e)n(v)o(ery)592
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4390
4031 y Fq(\033)533 4084 y Fu(=)-17 b Fw(\))p FA(-step)34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4391
b(this)e(measure)i(decreases:)g(the)f(\()p Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4392
FA(?-v)n(ariable\))h(transition)e(eliminates)166 4205
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4393
y(\(completely\))20 b(one)g(v)n(ariable)h(from)f(the)g(uni\002cation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4394
(problem,)g(and)h(therefore)g Fz(n)2984 4220 y FG(1)3044
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4395
4205 y FA(decreases;)166 4325 y(the)j(\()p Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4396
FA(?-suspension\))f(transition)g(may)g(eliminate)g(a)h(v)n(ariable)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4397
(and)h(also)g(decreases)g(the)g(size)166 4445 y Fz(n)224
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4398
4460 y FG(2)264 4445 y FA(;)i(all)h(other)f(transitions)f(lea)n(v)o(e)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4399
(the)g(number)f(of)h(v)n(ariables)f(unchanged,)g(b)n(ut)g(decrease)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4400
Fz(n)3389 4460 y FG(2)3429 4445 y FA(.)166 4582 y(F)o(or)d(the)525
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4401
4529 y Ft(r)474 4582 y Fu(=)-17 b Fw(\))p FA(-steps)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4402
b(the)f(size)1696 4619 y Fn(X)1601 4808 y FG(\()p Fq(a)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4403
FG(#?)q Fq(t)p FG(\))p Ft(2)p Fq(P)1929 4702 y Fw(j)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4404
Fz(t)p Fw(j)166 4927 y FA(decreases)30 b(in)e(e)n(v)o(ery)g(step.)h(T)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4405
-8 b(aking)28 b(both)g(f)o(acts)h(together)f(means)h(that)f(e)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4406
(ery)g(reduction)h(se-)166 5047 y(quence)c(must)f(terminate.)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4407
3382 5047 4 68 v 3386 4983 60 4 v 3386 5047 V 3445 5047
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4408
4 68 v 166 5380 a(The)e(follo)n(wing)f(lemmas)g(help)h(us)g(to)g(sho)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4409
(w)f(that)h(the)g(algorithm)f(gi)n(v)o(es)g(correct)i(results)e(upon)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4410
1748 5712 y(16)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4411
%%Page: 17 17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4412
TeXDict begin 17 16 bop 166 83 a FA(termination.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4413
306 y FB(Lemma)25 b(3.3.)41 b Fx(If)25 b Fw(r)j(`)f Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4414
Fu(\()p Fz(\031)t Fr(\001)p Fz(X)8 b Fu(\))27 b Fw(\031)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4415
Fz(\033)t Fu(\()p Fz(t)p Fu(\))c Fx(then)f Fw(r)k(`)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4416
Fz(\033)g Fw(\016)22 b Fu([)p Fz(X)35 b Fu(:=)28 b Fz(\031)2518
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4417
270 y Ft(\000)p FG(1)2612 306 y Fr(\001)p Fz(t)p Fu(])g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4418
Fw(\031)g Fz(\033)t Fx(.)166 669 y FB(PR)m(OOF)-11 b(.)49
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4419
b FA(W)-8 b(e)32 b(ha)n(v)o(e)f(to)h(pro)o(v)o(e)e(that)i(both)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4420
(substitutions)d(agree)33 b(\(modulo)e Fw(\031)p FA(\))h(on)g(all)f(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4421
(ari-)166 790 y(ables)f(in)f Fz(dom)p Fu(\()p Fz(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4422
Fu(\))d Fw([)g(f)p Fz(X)8 b Fw(g)p FA(.)30 b(The)g(only)f(interesting)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4423
(case)h(is)g(for)g(the)g(substitutions)c(applied)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4424
910 y(to)35 b Fz(X)8 b FA(,)34 b(when)h(we)g(need)g(to)g(sho)n(w)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4425
(that)g Fw(r)46 b(`)h Fz(\033)t Fu(\()p Fz(\031)1985
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4426
874 y Ft(\000)p FG(1)2079 910 y Fr(\001)p Fz(t)p Fu(\))f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4427
Fw(\031)h Fz(\033)t Fu(\()p Fz(X)8 b Fu(\))p FA(.)35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4428
b(By)g(Lemma)f(2.14)h(we)166 1030 y(can)i(commute)e(the)h(permutation)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4429
(to)h(the)g(outside)f(and)h(mo)o(v)o(e)f(it)h(to)g(the)g(other)g(side)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4430
(of)g Fw(\031)166 1151 y FA(by)h(Lemma)g(2.12\227this)e(gi)n(v)o(es)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4431
Fw(r)51 b(`)g Fz(\033)t Fu(\()p Fz(t)p Fu(\))g Fw(\031)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4432
Fz(\031)t Fr(\001)p Fz(\033)t Fu(\()p Fz(X)8 b Fu(\))p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4433
FA(.)37 b(The)g(case)h(then)f(follo)n(ws)f(from)166 1271
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4434
y(the)27 b(assumptions)e(by)h(symmetry)g(and)h(commuting)e(the)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4435
(permutation)f(inside)g(the)h(substitu-)166 1392 y(tion.)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4436
3382 1392 4 68 v 3386 1328 60 4 v 3386 1392 V 3445 1392
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4437
4 68 v 166 1653 a FB(Lemma)g(3.4.)41 b Fx(Given)26 b(a)g(uni\002cation)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4438
e(pr)l(oblem)h Fz(P)14 b Fx(,)25 b Fu(\()p Fw(r)p Fz(;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4439
b(\033)t Fu(\))29 b Fw(2)h Ff(U)p Fu(\()p Fz(\033)2538
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4440
1616 y Ft(0)2562 1653 y Fz(P)14 b Fu(\))25 b Fx(holds)g(if)g(and)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4441
(only)f(if)166 1773 y Fu(\()p Fw(r)p Fz(;)17 b(\033)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4442
b Fw(\016)c Fz(\033)543 1737 y Ft(0)566 1773 y Fu(\))28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4443
b Fw(2)g Ff(U)p Fu(\()p Fz(P)14 b Fu(\))p Fx(.)166 2136
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4444
y FB(PR)m(OOF)-11 b(.)49 b FA(Simple)24 b(calculation)g(using)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4445
(f)o(act)i(that)e Fz(\033)t Fu(\()p Fz(\033)2236 2100
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4446
y Ft(0)2259 2136 y Fu(\()p Fz(t)p Fu(\)\))k(=)f(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4447
Fz(\033)f Fw(\016)c Fz(\033)2789 2100 y Ft(0)2813 2136
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4448
y Fu(\)\()p Fz(t)p Fu(\))p FA(.)p 3382 2136 V 3386 2073
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4449
60 4 v 3386 2136 V 3445 2136 4 68 v 166 2500 a(The)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4450
b(follo)n(wing)e(tw)o(o)i(lemmas)f(sho)n(w)g(that)h(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4451
(uni\002cation)g(transformations)e(can)j(be)f(used)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4452
2620 y(to)d(determine)g(whether)h(or)f(not)g(solutions)f(e)o(xists)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4453
(and)h(to)h(describe)f(all)g(of)h(them)f(if)g(the)o(y)g(do)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4454
2741 y(e)o(xist.)166 2964 y FB(Lemma)d(3.5.)228 3186
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4455
y Fx(\(i\))50 b(If)25 b Fu(\()p Fw(r)579 3150 y Ft(0)602
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4456
3186 y Fz(;)17 b(\033)705 3150 y Ft(0)728 3186 y Fu(\))37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4457
b Fw(2)g Ff(U)p Fu(\()p Fz(P)14 b Fu(\))24 b Fx(and)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4458
Fz(P)1500 3133 y Fq(\033)1442 3186 y Fu(=)-17 b Fw(\))37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4459
b Fz(P)1715 3150 y Ft(0)1738 3186 y Fz(;)17 b Fx(then)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4460
b Fu(\()p Fw(r)2099 3150 y Ft(0)2122 3186 y Fz(;)17 b(\033)2225
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4461
3150 y Ft(0)2248 3186 y Fu(\))37 b Fw(2)g Ff(U)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4462
Fz(P)2612 3150 y Ft(0)2635 3186 y Fu(\))25 b Fx(and)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4463
Fw(r)2955 3150 y Ft(0)3015 3186 y Fw(`)37 b Fz(\033)3172
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4464
3150 y Ft(0)3205 3186 y Fw(\016)25 b Fz(\033)41 b Fw(\031)372
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4465
3307 y Fz(\033)431 3271 y Ft(0)454 3307 y Fz(:)200 3427
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4466
y Fx(\(ii\))50 b(If)25 b Fu(\()p Fw(r)579 3391 y Ft(0)602
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4467
3427 y Fz(;)17 b(\033)705 3391 y Ft(0)728 3427 y Fu(\))28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4468
b Fw(2)g Ff(U)p Fu(\()p Fz(P)14 b Fu(\))24 b Fx(and)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4469
Fz(P)1465 3374 y Ft(r)1415 3427 y Fu(=)-17 b Fw(\))27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4470
b Fz(P)1678 3391 y Ft(0)1701 3427 y Fz(;)17 b Fx(then)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4471
b Fu(\()p Fw(r)2062 3391 y Ft(0)2085 3427 y Fz(;)17 b(\033)2188
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4472
3391 y Ft(0)2211 3427 y Fu(\))28 b Fw(2)g Ff(U)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4473
Fz(P)2557 3391 y Ft(0)2580 3427 y Fu(\))d Fx(and)f Fw(r)2900
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4474
3391 y Ft(0)2951 3427 y Fw(`)j Fz(\033)3098 3391 y Ft(0)3122
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4475
3427 y Fu(\()p Fw(r)p Fu(\))p Fz(:)166 3791 y FB(PR)m(OOF)-11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4476
b(.)49 b FA(W)-8 b(e)27 b(just)e(gi)n(v)o(e)h(the)g(details)g(for)h(tw)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4477
o(o)f(uni\002cation)g(transitions:)f(the)i(case)g(for)g(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4478
Fw(\031)p Fu(?)p FA(-)166 3911 y(suspension\))h(follo)n(ws)f(from)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4479
(Lemma)g(2.12\(iii\);)f(and)h(the)g(\()p Fw(\031)p Fu(?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4480
FA(-v)n(ariable\))h(case)f(is)g(a)h(conse-)166 4031 y(quence)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4481
b(of)g(Lemmas)f(3.3)g(and)h(3.4.)p 3382 4031 V 3386 3967
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4482
60 4 v 3386 4031 V 3445 4031 4 68 v 166 4292 a FB(Lemma)g(3.6.)228
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4483
4515 y Fx(\(i\))50 b(If)25 b Fu(\()p Fw(r)579 4479 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4484
Ft(0)602 4515 y Fz(;)17 b(\033)705 4479 y Ft(0)728 4515
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4485
y Fu(\))28 b Fw(2)g Ff(U)p Fu(\()p Fz(P)1074 4479 y Ft(0)1097
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4486
4515 y Fu(\))c Fx(and)h Fz(P)1496 4462 y Fq(\033)1438
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4487
4515 y Fu(=)-17 b Fw(\))27 b Fz(P)1701 4479 y Ft(0)1724
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4488
4515 y Fz(;)17 b Fx(then)24 b Fu(\()p Fw(r)2085 4479
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4489
y Ft(0)2109 4515 y Fz(;)17 b(\033)2212 4479 y Ft(0)2257
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4490
4515 y Fw(\016)22 b Fz(\033)t Fu(\))27 b Fw(2)h Ff(U)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4491
Fu(\()p Fz(P)14 b Fu(\))p Fz(:)200 4655 y Fx(\(ii\))50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4492
b(If)25 b Fu(\()p Fw(r)579 4619 y Ft(0)602 4655 y Fz(;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4493
b(\033)705 4619 y Ft(0)728 4655 y Fu(\))28 b Fw(2)g Ff(U)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4494
Fu(\()p Fz(P)1074 4619 y Ft(0)1097 4655 y Fu(\))p Fz(;)44
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4495
b(P)1360 4602 y Ft(r)1310 4655 y Fu(=)-17 b Fw(\))27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4496
b Fz(P)1573 4619 y Ft(0)1621 4655 y Fx(and)d Fw(r)1878
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4497
4619 y Ft(00)1949 4655 y Fw(`)j Fz(\033)2096 4619 y Ft(0)2119
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4498
4655 y Fu(\()p Fw(r)p Fu(\))p Fz(;)17 b Fx(then)25 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4499
Fu(\()p Fw(r)2640 4619 y Ft(0)2685 4655 y Fw([)d(r)2856
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4500
4619 y Ft(00)2899 4655 y Fz(;)17 b(\033)3002 4619 y Ft(0)3025
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4501
4655 y Fu(\))28 b Fw(2)g Ff(U)p Fu(\()p Fz(P)14 b Fu(\))p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4502
Fz(:)166 5019 y FB(PR)m(OOF)-11 b(.)49 b FA(Once)33 b(again,)f(we)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4503
(just)f(gi)n(v)o(e)g(the)g(details)g(for)i(tw)o(o)e(uni\002cation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4504
(transitions:)f(the)166 5139 y(\()p Fw(\031)p Fu(?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4505
FA(-suspension\))23 b(case)h(follo)n(ws)e(from)h(Lemma)f(2.8;)h(and)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4506
(the)h(\()p Fw(\031)p Fu(?)p FA(-v)n(ariable\))f(case)h(follo)n(ws)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4507
5259 y(from)34 b(Lemma)f(3.4)h(and)g(the)g(f)o(act)h(that)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4508
Fz(t)p Fu([)p Fz(X)53 b Fu(:=)45 b Fz(\031)1994 5223
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4509
y Ft(\000)p FG(1)2088 5259 y Fr(\001)p Fz(t)p Fu(])g(=)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4510
Fz(t)p FA(,)35 b(which)e(holds)g(by)h(the)g(side-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4511
5380 y(condition)23 b(on)i(the)g(\()p Fw(\031)p Fu(?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4512
FA(-v)n(ariable\))g(transition)e(about)h(the)h(non-occurrence)h(of)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4513
Fz(X)33 b FA(in)25 b Fz(t)p FA(.)p 3382 5380 V 3386 5316
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4514
60 4 v 3386 5380 V 3445 5380 4 68 v 1748 5712 a(17)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4515
eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4516
%%Page: 18 18
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4517
TeXDict begin 18 17 bop 166 83 a FA(The)26 b(follo)n(wing)d(theorem)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4518
(establishes)e(the)i(correctness)f(of)h(the)g(nominal)e(uni\002cation)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4519
(algo-)166 203 y(rithm)f(and)h(is)f(the)h(central)g(result)f(of)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4520
(paper)-5 b(.)166 432 y FB(Theor)n(em)27 b(3.7)d(\(Corr)n(ectness\).)43
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4521
b Fx(Given)25 b(a)f(uni\002cation)g(pr)l(oblem)f Fz(P)228
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4522
660 y Fx(\(i\))50 b(if)24 b(the)h(algorithm)e(fails)g(on)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4523
Fz(P)14 b Fx(,)24 b(then)h Fz(P)38 b Fx(has)24 b(no)h(solution;)e(and)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4524
200 780 y(\(ii\))50 b(if)31 b(the)h(algorithm)e(succeeds)i(on)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4525
Fz(P)14 b Fx(,)32 b(then)f(the)h(r)l(esult)f(it)g(pr)l(oduces)g(is)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4526
(an)h(idempotent)372 900 y(most)24 b(g)o(ener)o(al)g(solution.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4527
1308 y FB(PR)m(OOF)-11 b(.)49 b FA(When)37 b(f)o(ailure)g(happens)g(it)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4528
f(is)h(because)h(of)f(certain)g(subproblems)f(that)g(mani-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4529
1428 y(festly)41 b(ha)n(v)o(e)g(no)g(solution)f(\(namely)h(in)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4530
(\002rst)h(phase,)f Fz(a)58 b Fw(\031)q Fu(?)g Fz(a)2641
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4531
1392 y Ft(0)2706 1428 y FA(with)41 b Fz(a)59 b Fw(6)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4532
Fu(=)f Fz(a)3220 1392 y Ft(0)3243 1428 y FA(,)42 b(and)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4533
1548 y Fz(\031)t Fr(\001)p Fz(X)i Fw(\031)p Fu(?)37 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4534
Fz(f)27 b(t)j FA(or)g Fz(f)d(t)37 b Fw(\031)p Fu(?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4535
Fz(\031)t Fr(\001)o Fz(X)h FA(with)28 b Fz(X)38 b FA(occurring)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4536
b(in)g Fz(t)p FA(;)h(in)f(the)g(second)h(phase,)f Fz(a)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4537
b Fu(#?)f Fz(a)p FA(\).)166 1669 y(Therefore)30 b(part)e(\(i\))h(is)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4538
(a)g(consequence)g(of)f(Lemma)h(3.5.)f(F)o(or)h(part)f(\(ii\))h(one)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4539
(gets)f(that)g(a)i(se-)166 1789 y(quence)22 b(lik)o(e)g(\(12\))g(e)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4540
(xists,)f(and)h(thus)g Fu(\()p Fw(r)p Fz(;)17 b(\033)t
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4541
Fu(\))27 b(=)g(\()p Fw(r)1970 1804 y FG(1)2022 1789 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4542
Fw([)12 b(\001)17 b(\001)g(\001)12 b([)g(r)2391 1804
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4543
y Fq(m)2458 1789 y Fz(;)34 b(\033)2574 1804 y Fq(n)2633
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4544
1789 y Fw(\016)12 b(\001)17 b(\001)g(\001)11 b(\016)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4545
Fz(\033)2941 1804 y FG(1)2982 1789 y Fu(\))22 b FA(is)f(in)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4546
Ff(U)p Fu(\()p Fz(P)14 b Fu(\))166 1910 y FA(by)19 b(Lemma)g(3.6)g(and)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4547
h(the)f(f)o(act)h(that)f Fu(\()p Fw(;)p Fz(;)e(")p Fu(\))26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4548
b Fw(2)i Ff(U)p Fu(\()p Fw(;)p Fu(\))p FA(.)20 b(Furthermore)f(from)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4549
(Lemma)g(3.5,)g(we)h(get)166 2030 y(that)k(an)o(y)g(other)h(solution)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4550
Fu(\()p Fw(r)1203 1994 y Ft(0)1227 2030 y Fz(;)17 b(\033)1330
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4551
1994 y Ft(0)1353 2030 y Fu(\))27 b Fw(2)h Ff(U)p Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4552
Fz(P)14 b Fu(\))24 b FA(satis\002es)h Fw(r)2184 1994
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4553
y Ft(0)2235 2030 y Fw(`)i Fz(\033)2382 1994 y Ft(0)2405
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4554
2030 y Fu(\()p Fw(r)p Fu(\))e FA(and)f Fw(r)2840 1994
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4555
y Ft(0)2891 2030 y Fw(`)k Fz(\033)3039 1994 y Ft(0)3084
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4556
2030 y Fw(\016)21 b Fz(\033)31 b Fw(\031)d Fz(\033)3405
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4557
1994 y Ft(0)3429 2030 y FA(,)166 2150 y(so)c(that)h Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4558
Fw(r)p Fz(;)17 b(\033)t Fu(\))24 b FA(is)g(indeed)h(a)g(most)e(general)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4559
i(solution.)e(Since)i(one)g(of)g(those)f(solutions)f(is)h(the)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4560
2271 y(most)31 b(general)h(solution)f Fu(\()p Fw(r)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4561
Fz(;)17 b(\033)t Fu(\))p FA(,)31 b(we)i(also)f(kno)n(w)f(that)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4562
Fw(r)42 b(`)f Fz(\033)31 b Fw(\016)d Fz(\033)45 b Fw(\031)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4563
Fz(\033)c FA(and)32 b(hence)g(that)166 2391 y Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4564
Fw(r)p Fz(;)17 b(\033)t Fu(\))25 b FA(is)f(idempotent.)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4565
3382 2391 4 68 v 3386 2327 60 4 v 3386 2391 V 3445 2391
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4566
4 68 v 166 2798 a(W)-8 b(e)30 b(no)n(w)f(apply)g(the)g(nominal)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4567
(uni\002cation)h(algorithm)f(to)h(solv)o(e)g(the)g(quiz)g(questions)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4568
(from)166 2919 y(the)d(Introduction.)166 3147 y FB(Example)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4569
b(3.8.)45 b FA(Using)32 b(the)g(\002rst)h(three)f(function)g(symbols)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4570
(of)h(the)h(nominal)e(signature)h(of)166 3267 y(Example)23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4571
b(2.2)f(to)h(represent)h Fz(\025)p FA(-terms,)e(the)i(Quiz)f(at)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4572
(end)g(of)g(the)h(Introduction)d(translates)166 3388
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4573
y(into)26 b(the)g(follo)n(wing)f(four)i(uni\002cation)f(problems)f(o)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4574
(v)o(er)h(that)g(signature,)g(where)h Fz(a)g FA(and)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4575
Fz(b)g FA(are)166 3508 y(distinct)c(atoms)h(of)h(sort)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4576
Fp(vid)35 b FA(and)25 b Fz(X)1439 3523 y FG(1)1478 3508
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4577
y Fz(;)17 b(:)g(:)g(:)f(;)h(X)1778 3523 y FG(7)1842 3508
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4578
y FA(are)26 b(distinct)d(v)n(ariables)h(of)h(sort)f Fp(exp)6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4579
b FA(:)587 3770 y Fz(P)650 3785 y FG(1)717 3717 y Fo(def)722
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4580
3770 y Fu(=)29 b Fw(f)p Fv(fn)17 b Fz(a:)p Fv(fn)h Fz(b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4581
Fv(app)q Fw(h)p Fz(X)1536 3785 y FG(1)1575 3770 y Fz(;)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4582
Fv(vr)g Fz(b)p Fw(i)28 b(\031)p Fu(?)g Fv(fn)17 b Fz(b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4583
Fv(fn)h Fz(a:)p Fv(app)q Fw(h)p Fv(vr)f Fz(a;)g(X)2870
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4584
3785 y FG(1)2909 3770 y Fw(ig)p FA(,)587 3950 y Fz(P)650
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4585
3965 y FG(2)717 3898 y Fo(def)722 3950 y Fu(=)29 b Fw(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4586
Fv(fn)17 b Fz(a:)p Fv(fn)h Fz(b:)p Fv(app)q Fw(h)p Fz(X)1536
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4587
3965 y FG(2)1575 3950 y Fz(;)f Fv(vr)g Fz(b)p Fw(i)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4588
b(\031)p Fu(?)g Fv(fn)17 b Fz(b:)p Fv(fn)h Fz(a:)p Fv(app)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4589
Fw(h)p Fv(vr)f Fz(a;)g(X)2870 3965 y FG(3)2909 3950 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4590
Fw(ig)p FA(,)587 4131 y Fz(P)650 4146 y FG(3)717 4079
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4591
y Fo(def)722 4131 y Fu(=)29 b Fw(f)p Fv(fn)17 b Fz(a:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4592
Fv(fn)h Fz(b:)p Fv(app)q Fw(h)p Fv(vr)f Fz(b;)g(X)1740
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4593
4146 y FG(4)1779 4131 y Fw(i)28 b(\031)p Fu(?)g Fv(fn)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4594
b Fz(b:)p Fv(fn)h Fz(a:)p Fv(app)q Fw(h)p Fv(vr)f Fz(a;)g(X)2870
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4595
4146 y FG(5)2909 4131 y Fw(ig)p FA(,)587 4312 y Fz(P)650
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4596
4327 y FG(4)717 4259 y Fo(def)722 4312 y Fu(=)29 b Fw(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4597
Fv(fn)17 b Fz(a:)p Fv(fn)h Fz(b:)p Fv(app)q Fw(h)p Fv(vr)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4598
Fz(b;)g(X)1740 4327 y FG(6)1779 4312 y Fw(i)28 b(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4599
Fu(?)g Fv(fn)17 b Fz(a:)p Fv(fn)h Fz(a:)p Fv(app)q Fw(h)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4600
Fv(vr)f Fz(a;)g(X)2880 4327 y FG(7)2919 4312 y Fw(ig)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4601
FA(.)166 4550 y(Applying)23 b(the)i(nominal)e(uni\002cation)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4602
(algorithm)e(described)i(abo)o(v)o(e,)e(we)i(\002nd)g(that)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4603
4778 y Fw(\017)50 b Fz(P)329 4793 y FG(1)393 4778 y FA(has)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4604
b(no)f(solution;)166 4898 y Fw(\017)50 b Fz(P)329 4913
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4605
y FG(2)397 4898 y FA(has)29 b(a)h(most)e(general)h(solution)f(gi)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4606
(en)f(by)i Fw(r)1987 4913 y FG(2)2062 4898 y Fu(=)36
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4607
b Fw(;)29 b FA(and)g Fz(\033)2481 4913 y FG(2)2557 4898
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4608
y Fu(=)35 b([)p Fz(X)2776 4913 y FG(2)2852 4898 y Fu(:=)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4609
Fv(vr)17 b Fz(b;)g(X)3275 4913 y FG(3)3351 4898 y Fu(:=)266
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4610
5019 y Fv(vr)g Fz(a)p Fu(])p FA(;)166 5139 y Fw(\017)50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4611
b Fz(P)329 5154 y FG(3)393 5139 y FA(has)25 b(a)g(most)e(general)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4612
(solution)d(gi)n(v)o(en)g(by)h Fw(r)1952 5154 y FG(3)2019
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4613
5139 y Fu(=)k Fw(;)d FA(and)g Fz(\033)2422 5154 y FG(3)2489
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4614
5139 y Fu(=)j([)p Fz(X)2701 5154 y FG(4)2768 5139 y Fu(:=)f(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4615
Fz(a)17 b(b)p Fu(\))p Fr(\001)p Fz(X)3196 5154 y FG(5)3236
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4616
5139 y Fu(])p FA(;)166 5259 y Fw(\017)50 b Fz(P)329 5274
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4617
y FG(4)403 5259 y FA(has)35 b(a)g(most)f(general)i(solution)d(gi)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4618
(en)g(by)i Fw(r)2034 5274 y FG(4)2120 5259 y Fu(=)47
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4619
b Fw(f)p Fz(b)f Fu(#)h Fz(X)2589 5274 y FG(7)2629 5259
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4620
y Fw(g)35 b FA(and)g Fz(\033)2948 5274 y FG(3)3034 5259
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4621
y Fu(=)47 b([)p Fz(X)3265 5274 y FG(6)3351 5259 y Fu(:=)266
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4622
5380 y(\()p Fz(b)17 b(a)p Fu(\))p Fr(\001)p Fz(X)564
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4623
5395 y FG(7)603 5380 y Fu(])p FA(.)1748 5712 y(18)p eop
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4624
end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4625
%%Page: 19 19
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4626
TeXDict begin 19 18 bop 166 3 3288 4 v 166 2372 4 2369
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4627
v 283 252 a Fq(P)328 261 y Fe(1)438 210 y Fd(")395 252
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4628
y FG(=)-12 b Ft(\))33 b(f)p Fb(fn)13 b Fq(b:)p Fb(app)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4629
Ft(h)p Fq(X)900 261 y Fe(1)936 252 y Fq(;)e Fb(vr)h Fq(b)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4630
Ft(i)20 b(\031)p FG(?)g Fb(fn)13 b Fq(b:)p Fb(app)p Ft(h)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4631
Fb(vr)g Fq(b;)f FG(\()p Fq(a)g(b)p FG(\))p Fa(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4632
Fq(X)1858 261 y Fe(1)1893 252 y Ft(i)p Fq(;)24 b(a)c
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4633
FG(#?)g Fb(fn)12 b Fq(a:)p Fb(app)q Ft(h)p Fb(vr)h Fq(a;)e(X)2614
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4634
261 y Fe(1)2649 252 y Ft(ig)34 b Fo(\()p Ft(\031)p FG(?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4635
Fo(-abstraction-2\))438 329 y Fd(")395 370 y FG(=)-12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4636
b Ft(\))33 b(f)p Fb(app)q Ft(h)p Fq(X)768 379 y Fe(1)803
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4637
370 y Fq(;)12 b Fb(vr)g Fq(b)p Ft(i)20 b(\031)p FG(?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4638
Fb(app)q Ft(h)p Fb(vr)13 b Fq(b;)e FG(\()p Fq(a)i(b)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4639
FG(\))p Fa(\001)p Fq(X)1594 379 y Fe(1)1629 370 y Ft(i)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4640
Fq(;)31 b(a)20 b FG(#?)g Fb(fn)12 b Fq(a:)p Fb(app)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4641
Ft(h)p Fb(vr)h Fq(a;)f(X)2358 379 y Fe(1)2393 370 y Ft(ig)290
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4642
b Fo(\()p Ft(\031)p FG(?)p Fo(-abstraction-1\))405 489
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4643
y Ft(\001)11 b(\001)h(\001)54 b(\001)12 b(\001)f(\001)2120
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4644
b(\001)11 b(\001)h(\001)438 542 y Fd(")395 583 y FG(=)-12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4645
b Ft(\))33 b(f)p Fq(X)635 592 y Fe(1)690 583 y Ft(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4646
FG(?)20 b Fb(vr)12 b Fq(b;)31 b Fb(vr)12 b Fq(b)20 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4647
Ft(\031)p FG(?)g(\()p Fq(a)13 b(b)p FG(\))p Fa(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4648
Fq(X)1416 592 y Fe(1)1450 583 y Fq(;)31 b(a)21 b FG(#?)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4649
Fb(fn)13 b Fq(a:)p Fb(app)q Ft(h)p Fb(vr)f Fq(a;)g(X)2152
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4650
592 y Fe(1)2187 583 y Ft(ig)496 b Fo(\()p Ft(\031)p FG(?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4651
Fo(-pair\))433 660 y Fd(\033)395 702 y FG(=)-12 b Ft(\))33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4652
b(f)p Fb(vr)13 b Fq(b)20 b Ft(\031)o FG(?)g Fb(vr)13
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4653
b Fq(a;)31 b(a)20 b FG(#?)g Fb(fn)12 b Fq(a:)p Fb(app)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4654
Ft(h)p Fb(vr)h Fq(a;)f Fb(vr)g Fq(b)p Ft(ig)40 b Fo(with)21
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4655
b Fq(\033)h FG(=)e([)p Fq(X)2148 711 y Fe(1)2202 702
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4656
y FG(:=)f Fb(vr)12 b Fq(b)p FG(])317 b Fo(\()p Ft(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4657
FG(?)p Fo(-v)n(ariable\))438 778 y Fd(")395 820 y FG(=)-12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4658
b Ft(\))33 b(f)p Fq(b)20 b Ft(\031)p FG(?)g Fq(a;)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4659
b(a)20 b FG(#?)f Fb(fn)13 b Fq(a:)p Fb(app)q Ft(h)p Fb(vr)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4660
Fq(a;)g Fb(vr)h Fq(b)p Ft(ig)1154 b Fo(\()p Ft(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4661
FG(?)p Fo(-function)19 b(symbol\))542 938 y FG(F)-8 b(AIL)283
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4662
1128 y Fq(P)328 1137 y Fe(4)438 1086 y Fd(")395 1128
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4663
y FG(=)c Ft(\))33 b(f)p Fb(fn)13 b Fq(b:)p Fb(app)p Ft(h)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4664
Fb(vr)g Fq(b;)f(X)1045 1137 y Fe(6)1079 1128 y Ft(i)20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4665
b(\031)p FG(?)g Fb(fn)13 b Fq(a:)p Fb(app)q Ft(h)p Fb(vr)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4666
Fq(a;)g(X)1716 1137 y Fe(7)1751 1128 y Ft(ig)932 b Fo(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4667
Ft(\031)p FG(?)p Fo(-abstraction-1\))438 1204 y Fd(")395
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4668
1246 y FG(=)-12 b Ft(\))33 b(f)p Fb(app)q Ft(h)p Fb(vr)13
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4669
b Fq(b;)f(X)913 1255 y Fe(6)947 1246 y Ft(i)20 b(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4670
FG(?)g Fb(app)q Ft(h)p Fb(vr)13 b Fq(b;)e FG(\()p Fq(b)i(a)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4671
FG(\))p Fa(\001)p Fq(X)1594 1255 y Fe(7)1629 1246 y Ft(i)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4672
Fq(;)31 b(b)20 b FG(#?)g Fb(app)q Ft(h)p Fb(vr)12 b Fq(a;)g(X)2211
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4673
1255 y Fe(7)2246 1246 y Ft(ig)437 b Fo(\()p Ft(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4674
FG(?)p Fo(-abstraction-2\))405 1364 y Ft(\001)11 b(\001)h(\001)54
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4675
b(\001)12 b(\001)f(\001)2120 b(\001)11 b(\001)h(\001)438
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4676
1417 y Fd(")395 1459 y FG(=)-12 b Ft(\))33 b(f)p Fq(b)20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4677
b Ft(\031)p FG(?)g Fq(b;)31 b(X)874 1468 y Fe(6)928 1459
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4678
y Ft(\031)p FG(?)20 b(\()p Fq(b)13 b(a)p FG(\))p Fa(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4679
Fq(X)1251 1468 y Fe(7)1286 1459 y Fq(;)31 b(b)20 b FG(#?)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4680
Fb(app)q Ft(h)p Fb(vr)13 b Fq(a;)f(X)1841 1468 y Fe(7)1875
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4681
1459 y Ft(ig)808 b Fo(\()p Ft(\031)p FG(?)p Fo(-function)19
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4682
b(symbol\))438 1535 y Fd(")395 1577 y FG(=)-12 b Ft(\))33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4683
b(f)p Fq(X)635 1586 y Fe(6)690 1577 y Ft(\031)p FG(?)20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4684
b(\()p Fq(b)12 b(a)p FG(\))p Fa(\001)p Fq(X)1012 1586
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4685
y Fe(7)1047 1577 y Fq(;)31 b(b)20 b FG(#?)g Fb(app)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4686
Ft(h)p Fb(vr)13 b Fq(a;)f(X)1602 1586 y Fe(7)1637 1577
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4687
y Ft(ig)1046 b Fo(\()p Ft(\031)p FG(?)p Fo(-atom\))433
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4688
1654 y Fd(\033)395 1695 y FG(=)-12 b Ft(\))33 b(f)p Fq(b)20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4689
b FG(#?)g Fb(app)q Ft(h)p Fb(vr)13 b Fq(a;)e(X)1081 1704
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4690
y Fe(7)1116 1695 y Ft(ig)67 b Fo(with)21 b Fq(\033)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4691
FG(=)e([)p Fq(X)1598 1704 y Fe(6)1652 1695 y FG(:=)f(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4692
Fq(b)12 b(a)p FG(\))p Fa(\001)q Fq(X)1961 1704 y Fe(7)1995
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4693
1695 y FG(])730 b Fo(\()p Ft(\031)p FG(?)p Fo(-v)n(ariable\))436
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4694
1777 y Fc(;)395 1818 y FG(=)-12 b Ft(\))33 b(f)p Fq(b)20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4695
b FG(#?)g Ft(h)p Fb(vr)13 b Fq(a;)f(X)976 1827 y Fe(7)1010
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4696
1818 y Ft(ig)1673 b Fo(\()p FG(#?)p Fo(-function)19 b(symbol\))405
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4697
1937 y Ft(\001)11 b(\001)h(\001)54 b(\001)12 b(\001)f(\001)2120
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4698
b(\001)11 b(\001)h(\001)436 1994 y Fc(;)395 2036 y FG(=)-12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4699
b Ft(\))33 b(f)p Fq(b)20 b FG(#?)g Fq(a;)31 b(b)20 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4700
FG(#?)g Fq(X)1047 2045 y Fe(7)1082 2036 y Ft(g)1628 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4701
Fo(\()p FG(#?)p Fo(-function)19 b(symbol\))436 2117 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4702
Fc(;)395 2159 y FG(=)-12 b Ft(\))33 b(f)p Fq(b)20 b FG(#?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4703
Fq(X)797 2168 y Fe(7)832 2159 y Ft(g)1878 b Fo(\()p FG(#?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4704
Fo(-atom\))427 2237 y Fc(r)395 2278 y FG(=)-12 b Ft(\))33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4705
b(;)67 b Fo(with)21 b Ft(r)e FG(=)g Ft(f)p Fq(b)i FG(#)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4706
Fq(X)1156 2287 y Fe(7)1191 2278 y Ft(g)1519 b Fo(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4707
FG(#?)p Fo(-suspension\))p 3450 2372 V 166 2375 3288
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4708
4 v 1308 2512 a FD(Fig.)23 b(4.)g(Example)h(deri)n(v)n(ations)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4709
2705 y FA(Deri)n(v)n(ations)j(for)j Fz(P)864 2720 y FG(1)933
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4710
2705 y FA(and)f Fz(P)1169 2720 y FG(4)1237 2705 y FA(are)h(sk)o(etched)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4711
f(in)g(Figure)h(4.)f(Using)f(the)h(Adequac)o(y)g(property)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4712
2826 y(of)j(Proposition)e(2.16,)i(one)f(can)i(interpret)e(these)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4713
(solutions)e(as)i(the)f(follo)n(wing)f(statements)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4714
2946 y(about)24 b(the)h Fz(\025)p FA(-terms)f(mentioned)g(in)g(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4715
(quiz.)p 166 3085 V 166 4368 4 1284 v 227 3212 a FB(Quiz)g(answers)267
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4716
3332 y FA(\(1\))50 b(There)26 b(is)e(no)h Fz(\025)p FA(-term)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4717
Fz(M)1298 3347 y FG(1)1363 3332 y FA(making)g(the)g(\002rst)h(pair)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4718
(of)g(terms)f Fz(\013)q FA(-equi)n(v)n(alent.)267 3453
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4719
y(\(2\))50 b(The)25 b(only)f(solution)f(for)i(the)g(second)g(problem)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4720
(is)g(to)g(tak)o(e)h Fz(M)2585 3468 y FG(2)2653 3453
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4721
y Fu(=)i Fz(b)f FA(and)e Fz(M)3085 3468 y FG(3)3153 3453
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4722
y Fu(=)j Fz(a)p FA(.)267 3573 y(\(3\))50 b(F)o(or)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4723
b(the)g(third)g(problem)f(we)h(can)g(tak)o(e)g Fz(M)1894
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4724
3588 y FG(5)1958 3573 y FA(to)g(be)g(an)o(y)f Fz(\025)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4725
FA(-term,)h(so)g(long)f(as)h(we)g(tak)o(e)433 3693 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4726
Fz(M)527 3708 y FG(4)592 3693 y FA(to)h(be)g(the)f(result)g(of)h(sw)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4727
(apping)f(all)h(occurrences)g(of)g Fz(a)g FA(and)g Fz(b)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4728
FA(throughout)f Fz(M)3321 3708 y FG(5)3360 3693 y FA(.)267
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4729
3814 y(\(4\))50 b(F)o(or)21 b(the)f(last)g(problem,)f(we)i(can)g(tak)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4730
(e)f Fz(M)1844 3829 y FG(7)1904 3814 y FA(to)g(be)h(an)o(y)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4731
Fz(\025)p FA(-term)g(that)g Fx(does)g(not)f(contain)433
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4732
3934 y(fr)l(ee)30 b(occurr)l(ences)f(of)g Fz(b)p FA(,)h(so)e(long)h(as)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4733
g(we)g(tak)o(e)h Fz(M)2199 3949 y FG(6)2268 3934 y FA(to)e(be)i(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4734
(result)f(of)h(sw)o(apping)433 4055 y(all)k(occurrences)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4735
Fz(b)g FA(and)f Fz(a)h FA(throughout)e Fz(M)2088 4070
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4736
y FG(7)2128 4055 y FA(,)h(or)h(equi)n(v)n(alently)d(\(since)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4737
Fz(b)g FA(is)f(not)433 4175 y(free)c(in)e Fz(M)813 4190
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4738
y FG(7)852 4175 y FA(\),)h(taking)e Fz(M)1306 4190 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4739
FG(6)1373 4175 y FA(to)h(be)g(the)g(result)g(of)h(replacing)f(all)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4740
(free)h(occurrences)g(of)433 4295 y Fz(a)f FA(in)e Fz(M)706
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4741
4310 y FG(7)771 4295 y FA(with)g Fz(b)p FA(.)p 3450 4368
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4742
V 166 4371 3288 4 v 166 4554 a FB(Remark)34 b(3.9)f(\(Separation)i(of)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4743
(the)g(algorithm)f(into)h(tw)o(o)g(phases\).)46 b FA(W)-8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4744
b(e)34 b(or)n(ganised)f(the)166 4675 y(algorithm)f(into)g(tw)o(o)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4745
(phases:)g(equation-solving)e(follo)n(wed)h(by)h(freshness-solving.)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4746
(Note)166 4795 y(that)22 b(the)f(second)h(phase)g(is)g(crucial)g(for)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4747
(the)g(soundness)f(of)h(the)f(algorithm.)g(Consider)h(for)g(e)o(x-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4748
4915 y(ample)i(the)h(uni\002cation)f(problem)g(consisting)f(of)i(tw)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4749
(o)f(terms)h(which)f(are)i Fx(not)g Fz(\013)q FA(-equi)n(v)n(alent:)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4750
1551 5148 y Fw(f)p Fz(a:b)i Fw(\031)q Fu(?)f Fz(b:a)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4751
Fw(g)1220 b FA(\(13\))166 5380 y(After)29 b(applying)d(the)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4752
(transformation)f(\()p Fw(\031)q Fu(?)p FA(-abstraction-2\))h(one)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4753
(needs)g(to)g(solv)o(e)f(the)h(prob-)1748 5712 y(19)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4754
eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4755
%%Page: 20 20
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4756
TeXDict begin 20 19 bop 166 83 a FA(lem)29 b Fw(f)p Fz(a)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4757
b Fw(\031)p Fu(?)g Fz(a;)17 b(a)36 b Fu(#?)h Fz(a)p Fw(g)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4758
FA(,)30 b(whose)f(\002rst)h(component)e(is)h(solv)o(ed)g(by)g(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4759
Fw(\031)q Fu(?)p FA(-atom\).)g(F)o(ailure)g(is)166 203
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4760
y(only)g(signalled)g(by)g(the)h(algorithm)e(in)i(the)g(second)f(phase)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4761
(when)g(attempting)e(to)h(solv)o(e)g(the)166 324 y(unsolv)n(able)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4762
(freshness)h(problem)g Fw(f)p Fz(a)33 b Fu(#?)g Fz(a)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4763
Fw(g)p FA(.)28 b(The)g(second)f(phase,)h(i.)f(e.)h(solving)e(all)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4764
(fresh-)166 444 y(ness)e(problems,)f(ensures)h(that)f(the)h(uni\002ers)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4765
g(calculated)g(by)g(the)g(algorithm)f(are)h(sound)g(with)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4766
565 y(respect)g(to)g(our)f(notion)g(of)h Fz(\013)q FA(-equi)n(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4767
(alence.)166 955 y(W)-8 b(e)27 b(used)f(this)g(separation)g(of)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4768
(algorithm)f(into)h(tw)o(o)g(phases)g(in)g(order)h(to)f(mak)o(e)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4769
(cor)n(-)166 1075 y(rectness)c(proof)f(easier)-5 b(.)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4770
b(More)f(ef)n(\002cient)h(algorithms)e(w)o(ould)h(seek)g(to)h(minimise)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4771
d(the)j(amount)166 1196 y(of)29 b(redundant)g(calculations)f(before)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4772
(f)o(ailures)f(are)h(signalled,)d(by)i(solving)f(freshness)h(prob-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4773
1316 y(lems)g(more)g(eagerly)-6 b(.)29 b(Ho)n(we)n(v)o(er)l(,)f(care)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4774
(needs)f(then)g(to)g(be)g(tak)o(en)g(to)g(not)g(remo)o(v)o(e)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4775
(freshness)166 1436 y(constraints)h(from)g(problems)g(too)h(early)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4776
b(.)29 b(F)o(or)h(e)o(xample,)f(consider)h(the)f(follo)n(wing)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4777
(uni\002ca-)166 1557 y(tion)c(problem,)g(which)g(has)h(no)f(solution.)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4778
1420 2117 y Fw(f)p Fz(a)k Fu(#?)g Fz(X)r(;)17 b(a)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4779
b Fw(\031)p Fu(?)g Fz(X)8 b Fw(g)1088 b FA(\(14\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4780
2677 y(If)40 b(one)g(applies)f(\002rst)h(\()p Fu(#?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4781
FA(-suspension\))f(follo)n(wed)f(by)i(\()p Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4782
Fu(?)q FA(-v)n(ariable\),)f(then)g(one)h(gets)f(a)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4783
2798 y Fx(wr)l(ong)31 b FA(result,)g(namely)g Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4784
Fw(f)p Fz(a)40 b Fu(#)g Fz(X)8 b Fw(g)p Fz(;)17 b Fu([)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4785
Fz(X)48 b Fu(:=)40 b Fz(a)p Fu(]\))p FA(.)32 b(The)f(problem)g(is)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4786
(that)g(the)h(substitution)166 2918 y Fu([)p Fz(X)46
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4787
b Fu(:=)38 b Fz(a)p Fu(])31 b FA(has)f(not)g(been)g(properly)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4788
(propagated)g(to)g(the)g(freshness)g(constraint)g Fz(a)38
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4789
b Fu(#)g Fz(X)8 b FA(.)30 b(If)166 3039 y(freshness)h(problems)g(are)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4790
(solv)o(ed)e(more)i(eagerly)-6 b(,)31 b(then)g(proper)h(propagation)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4791
(of)i(substitu-)166 3159 y(tions)24 b(into)g(freshness)g(constraints)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4792
(needs)h(to)f(be)h(tak)o(en)g(into)f(account.)166 3549
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4793
y FB(Remark)34 b(3.10)f(\(Atoms)g(ar)n(e)h(not)f(v)o(ariables\).)46
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4794
b FA(Nominal)32 b(uni\002cation)h(uni\002es)g(v)n(ariables,)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4795
3670 y(b)n(ut)e(it)f(does)h(not)g(unify)f(atoms.)h(Indeed)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4796
(operation)f(of)i(identifying)d(tw)o(o)i(atoms)f(by)h(re-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4797
3790 y(naming)h(one)i(of)f(them)g(to)g(be)h(the)f(other)g(does)g(not)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4798
(necessarily)g(preserv)o(e)h(the)f(v)n(alidity)f(of)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4799
3910 y(the)k(judgements)f(in)h(Figure)g(2.)g(F)o(or)h(e)o(xample,)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4800
Fw(;)49 b(`)g Fz(a:b)g Fw(\031)h Fz(c:b)37 b FA(holds)e(if)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4801
Fz(b)50 b Fw(6)p Fu(=)e Fz(a;)17 b(c)p FA(;)36 b(b)n(ut)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4802
4031 y(renaming)30 b Fz(b)g FA(to)g(be)g Fz(a)h FA(in)f(this)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4803
(judgement)g(we)h(get)g Fw(;)37 b(`)h Fz(a:a)g Fw(\031)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4804
Fz(c:a)p FA(,)30 b(which)g(does)g(not)g(hold)166 4151
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4805
y(so)g(long)f(as)i Fz(a)38 b Fw(6)p Fu(=)f Fz(c)p FA(.)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4806
b(Referring)g(to)f(De\002nition)f(2.3,)h(you)g(will)f(see)i(that)e(we)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4807
(do)f(allo)n(w)f(v)n(ari-)166 4271 y(ables)e(ranging)f(o)o(v)o(er)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4808
(sorts)h(of)g(atoms;)f(and)h(such)f(v)n(ariables)h(can)g(be)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4809
(uni\002ed)g(lik)o(e)g(an)o(y)f(other)166 4392 y(v)n(ariables.)e(Ho)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4810
(we)n(v)o(er)l(,)g(if)h Fz(A)g FA(is)f(such)h(a)g(v)n(ariable,)f(then)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4811
(it)f(cannot)h(appear)g(in)g(abstraction)f(po-)166 4512
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4812
y(sition,)19 b(i.e.)h(as)h Fz(A:t)p FA(.)g(This)e(is)h(because)h(we)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4813
(speci\002cally)f(restricted)g(abstraction)g(to)g(range)h(o)o(v)o(er)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4814
166 4633 y(atoms,)27 b(rather)h(than)g(o)o(v)o(er)f(arbitrary)h(terms)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4815
(of)h(atom)f(sort.)g(Such)i(a)f(restriction)f(seems)g(nec-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4816
4753 y(essary)35 b(to)g(obtain)f(single,)g(most)g(general,)h(solutions)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4817
e(to)i(nominal)f(uni\002cation)g(problems.)166 4873 y(F)o(or)i(without)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4818
f(such)h(a)h(restriction,)e(because)i(of)f(rule)g(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4819
Fw(\031)p FA(-abstraction-2\))h(in)f(Figure)g(2)h(we)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4820
4994 y(w)o(ould)27 b(also)h(ha)n(v)o(e)f(to)h(allo)n(w)f(v)n(ariables)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4821
(to)g(appear)i(on)e(the)h(left-hand)g(side)f(of)h(freshness)g(re-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4822
5114 y(lations)c(and)i(in)f(suspended)f(permutations.)g(So)i(then)f(we)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4823
g(w)o(ould)g(get)g(uni\002cation)g(problems)166 5235
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4824
y(lik)o(e)i Fw(f)p Fu(\()p Fz(A)17 b(B)5 b Fu(\))p Fr(\001)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4825
Fz(C)40 b Fw(\031)p Fu(?)33 b Fz(C)7 b Fw(g)p FA(,)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4826
b(where)g Fz(A)p FA(,)g Fz(B)33 b FA(and)28 b Fz(C)34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4827
b FA(are)29 b(v)n(ariables)e(of)h(atom)f(sort;)g(this)g(has)g(tw)o(o)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4828
166 5355 y(incomparable)d(solutions,)f(namely)h Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4829
Fw(;)p Fz(;)17 b Fu([)p Fz(A)27 b Fu(:=)h Fz(B)5 b Fu(]\))25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4830
b FA(and)g Fu(\()p Fw(f)p Fz(A)i Fu(#)h Fz(C)r(;)17 b(B)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4831
b Fu(#)c Fz(C)7 b Fw(g)p Fz(;)17 b(")p Fu(\))p FA(.)1748
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4832
5712 y(20)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4833
%%Page: 21 21
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4834
TeXDict begin 21 20 bop 166 83 a FB(4)99 b(Related)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4835
b(w)o(ork)166 424 y Fx(Higher)n(-or)l(der)e(pattern)g(uni\002cation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4836
765 y FA(Most)32 b(pre)n(vious)h(w)o(ork)g(on)g(uni\002cation)g(for)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4837
(languages)g(with)g(binders)g(is)g(based)g(on)g(forms)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4838
885 y(of)h(higher)n(-order)g(uni\002cation,)f(i.e.)g(solving)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4839
(equations)h(between)h Fz(\025)p FA(-terms)f(modulo)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4840
Fz(\013)q(\014)6 b(\021)t FA(-)166 1005 y(equi)n(v)n(alence)40
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4841
b(\()p Fu(=)787 1020 y Fq(\013\014)s(\021)917 1005 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4842
FA(\))i(by)e(capture-a)n(v)n(oiding)h(substitution)d(of)j(terms)g(for)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4843
(function)f(v)n(ari-)166 1126 y(ables.)33 b(Notable)f(among)g(that)h(w)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4844
o(ork)g(is)f(Miller')-5 b(s)32 b Fx(higher)n(-or)l(der)g(pattern)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4845
(uni\002cation)f FA(used)166 1246 y(in)22 b(his)f Fz(L)470
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4846
1261 y Fq(\025)538 1246 y FA(logic)h(programming)f(language)h([3].)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4847
(This)f(kind)h(of)g(uni\002cation)g(retains)f(the)h(good)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4848
1367 y(properties)j(of)h(\002rst-order)g(uni\002cation:)e(a)i(linear)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4849
(-time)f(decision)g(procedure)h(and)g(e)o(xistence)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4850
1487 y(of)34 b(most)f(general)h(uni\002ers.)g(This)f(good)g(beha)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4851
(viour)g(of)h(higher)n(-order)g(pattern)g(uni\002cation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4852
1607 y(is)c(the)h(result)f(of)h(equations)f(being)g(solv)o(ed)f(only)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4853
(modulo)g Fu(=)2356 1622 y Fq(\013\014)2441 1631 y Fe(0)2475
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4854
1622 y Fq(\021)2548 1607 y FA(\(where)h Fz(\014)2910
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4855
1622 y FG(0)2950 1607 y FA(-equi)n(v)n(alence)166 1728
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4856
y(is)26 b(the)g(restricted)g(form)g(of)g Fz(\014)6 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4857
FA(-equi)n(v)n(alence)25 b(that)g(identi\002es)h Fu(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4858
Fz(\025x:M)10 b Fu(\))p Fz(y)30 b FA(and)d Fz(M)10 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4859
Fu([)p Fz(y)t(=x)p Fu(])26 b FA(with)g Fz(y)166 1848
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4860
y FA(being)i(a)i(v)n(ariable\))e(and)h(of)g Fz(\025)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4861
FA(-terms)f(being)g(restricted)h(such)g(that)f(function)g(v)n(ariables)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4862
g(may)166 1969 y(only)f(be)h(applied)f(to)g(distinct)f(bound)h(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4863
(ariables.)g(An)h(empirical)f(study)f(by)i(Michaylo)o(v)e(and)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4864
2089 y(Pfenning)31 b([27])g(suggests)e(that)i(most)f(uni\002cations)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4865
(arising)g(dynamically)f(in)i(higher)n(-order)166 2209
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4866
y(logic)k(programming)g(satisfy)g(Miller')-5 b(s)35 b(restrictions,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4867
(b)n(ut)g(that)h(it)f(rules)h(out)g(some)f(useful)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4868
2330 y(programming)23 b(idioms.)166 2550 y(The)i(main)g(dif)n(ference)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4869
(between)g(higher)n(-order)g(pattern)g(uni\002cation)g(and)g(nominal)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4870
(uni\002ca-)166 2671 y(tion)29 b(is)h(that)g(the)g(former)g(solv)o(es)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4871
(a)h(set)g(of)g(equations)f(by)h(calculating)g(a)g Fx(captur)l
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4872
(e-avoiding)166 2791 y FA(substitution,)23 b(while)j(the)g(latter)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4873
(calculates)f(a)h Fx(possibly-capturing)c FA(substitution)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4874
Fx(and)k FA(some)166 2911 y(freshness)33 b(constraints.)f(Moreo)o(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4875
(er)l(,)g(uni\002ers)h(in)f(higher)n(-order)i(pattern)e(uni\002cation)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4876
(solv)o(e)166 3032 y(equations)40 b(with)h(respect)h(to)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4877
Fu(=)1327 3047 y Fq(\013\014)1412 3056 y Fe(0)1446 3047
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4878
y Fq(\021)1488 3032 y FA(;)g(whereas)h(in)f(nominal)f(uni\002cation,)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4879
(uni\002ers)g(solv)o(e)166 3152 y(equations)f(with)h(respect)g(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4880
(the)g(equi)n(v)n(alence)f Fw(\031)i FA(de\002ned)f(in)g(Figure)h(2,)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4881
(which)f(agrees)166 3272 y(with)29 b Fz(\013)q FA(-equi)n(v)n(alence)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4882
(on)i(ground)f(terms)g(\(see)h(Proposition)e(2.16\),)h(b)n(ut)g(dif)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4883
(fers)h(from)f(it)g(on)166 3393 y(open)g(terms,)f(since)h(unlik)o(e)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4884
Fz(\013)q FA(-equi)n(v)n(alence,)f(it)g(is)h(respected)g(by)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4885
(possibly-capturing)e(sub-)166 3513 y(stitutions)c(\(see)j(Lemma)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4886
(2.14\).)g(F)o(or)g(us,)g(the)g(main)g(disadv)n(antage)f(of)i(higher)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4887
(-order)f(pattern)166 3634 y(uni\002cation)k(is)h(the)f(one)h(common)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4888
(to)g(most)g(approaches)h(based)f(on)h(higher)n(-order)g(abstract)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4889
3754 y(syntax)23 b(that)h(w)o(as)g(discussed)f(in)g(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4890
(Introduction:)e(one)i(cannot)g Fx(dir)l(ectly)g FA(e)o(xpress)f(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4891
(com-)166 3874 y(mon)33 b(idiom)g(of)h(possibly-capturing)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4892
(substitution)h(of)i(terms)f(for)h(meta)n(v)n(ariables.)f(Instead)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4893
3995 y(one)26 b(has)f(to)g(encode)h(meta)n(v)n(ariables)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4894
Fz(X)33 b FA(as)26 b(function)e(v)n(ariables)h(applied)g(to)g(distinct)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4895
f(lists)h(of)166 4115 y(\(bound\))d(v)n(ariables,)g Fz(X)i(x)1069
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4896
4130 y FG(1)1126 4115 y Fz(:)17 b(:)g(:)f(x)1312 4130
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4897
y Fq(n)1359 4115 y FA(,)23 b(and)f(use)h(capture-a)n(v)n(oiding)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4898
(substitution.)f(At)i(\002rst)h(sight,)166 4236 y(there)e(seems)f(to)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4899
(be)g(a)g(simple)f(encoding)g(for)h(doing)f(that.)g(Consider)h(for)g(e)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4900
o(xample)f(the)g(purely)166 4356 y(equational)k(nominal)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4901
(uni\002cation)i(problem)1582 4577 y Fz(a:X)36 b Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4902
Fu(?)28 b Fz(b:b)1251 b FA(\(15\))166 4798 y(which)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4903
b(is)g(solv)o(ed)f(by)i Fu(\()p Fw(;)p Fz(;)17 b Fu([)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4904
Fz(X)43 b Fu(:=)37 b Fz(a)p Fu(]\))p FA(.)29 b(The)h(literal)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4905
(encoding)g(as)g(the)h(higher)n(-order)f(pattern)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4906
4918 y(uni\002cation)23 b(problem)h Fz(\025a:X)35 b Fu(=)1300
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4907
4933 y Fq(\013\014)1385 4942 y Fe(0)1420 4933 y Fq(\021)1462
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4908
4918 y Fu(?)p Fz(\025b:b)25 b FA(does)e(not)h(w)o(ork)g(of)g(course,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4909
(because)g(there)h(is)e(no)166 5039 y(capture-a)n(v)n(oiding)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4910
b(substitution)e(that)i(solv)o(es)f(this)h(problem.)f(Ho)n(we)n(v)o(er)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4911
l(,)h Fz(X)41 b FA(can)34 b(be)g(made)166 5159 y(dependent)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4912
b(on)h Fz(a)g FA(yielding)f(the)g(uni\002cation)g(problem)1381
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4913
5380 y Fz(\025a:)p Fu(\()p Fz(X)8 b(a)p Fu(\))28 b(=)1836
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4914
5395 y Fq(\013\014)1921 5404 y Fe(0)1956 5395 y Fq(\021)1998
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4915
5380 y Fu(?)f Fz(\025b:b)1051 b FA(\(16\))1748 5712 y(21)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4916
eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4917
%%Page: 22 22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4918
TeXDict begin 22 21 bop 166 83 a FA(which)30 b(is)g(solv)o(ed)g(by)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4919
(the)h(capture-a)n(v)n(oiding)e(substitution)f(of)j Fz(\025c:c)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4920
FA(for)g Fz(X)8 b FA(.)30 b(If)h(one)g(further)166 203
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4921
y(applies)d(to)h Fz(\025c:c)g FA(the)g(atom)f Fz(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4922
FA(used)g(by)g(the)f(encoding,)h(then)f(one)h(can)h(read)f(back)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4923
(orig-)166 324 y(inal)f(solution)f Fu([)p Fz(X)43 b Fu(:=)35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4924
b Fz(a)p Fu(])29 b FA(by)g(applying)f(some)g Fz(\014)6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4925
b FA(-reductions.)27 b(There)j(are)f(ho)n(we)n(v)o(er)f(se)n(v)o(eral)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4926
166 444 y(problems)j(with)h(this)f(encoding.)g(First,)h(the)g(encoding)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4927
g(in)g(general)g(results)g(in)f(a)i(quadratic)166 565
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4928
y(blo)n(w-up)24 b(in)g(the)h(size)f(of)h(terms.)f(F)o(or)h(e)o(xample)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4929
(the)h(nominal)e(uni\002cation)h(problem)1325 861 y Fz(a:b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4930
Fw(h)p Fz(X)r(;)17 b(Y)22 b Fw(i)28 b(\031)p Fu(?)g Fz(a:b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4931
Fw(h)p Fz(a;)17 b(b)p Fw(i)994 b FA(\(17\))166 1158 y(solv)o(ed)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4932
b(by)g(the)h(uni\002er)g Fu(\()p Fw(;)p Fz(;)17 b Fu([)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4933
Fz(X)44 b Fu(:=)37 b Fz(a;)17 b(Y)58 b Fu(:=)36 b Fz(b)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4934
Fu(]\))31 b FA(needs)e(to)h(be)g(encoded)f(so)h(that)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4935
Fz(X)38 b FA(and)29 b Fz(Y)166 1278 y FA(depend)c(on)f(both)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4936
Fz(a)h FA(and)g Fz(b)p FA(.)g(This)f(gi)n(v)o(es)g(the)g(higher)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4937
(-order)h(pattern)g(problem)975 1575 y Fz(\025a:\025b:)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4938
Fw(h)p Fz(X)g(a)17 b(b;)g(Y)38 b(a)17 b(b)p Fw(i)28 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4939
Fu(=)1880 1590 y Fq(\013\014)1965 1599 y Fe(0)1999 1590
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4940
y Fq(\021)2041 1575 y Fu(?)g Fz(\025a:\025b:)p Fw(h)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4941
Fz(a;)17 b(b)p Fw(i)28 b Fz(:)644 b FA(\(18\))166 1871
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4942
y(In)35 b(the)g(general)h(case,)g(the)f(encoding)f(needs)i(to)e(mak)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4943
(e)i(meta)n(v)n(ariables)e(dependent)h(on)g Fx(all)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4944
1992 y FA(atoms)23 b(occurring)g(in)h(a)g(nominal)e(uni\002cation)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4945
(problem,)g(re)o(gardless)f(of)i(whether)g(the)o(y)f(actu-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4946
2112 y(ally)f(occur)g(in)g(an)h(indi)n(vidual)d(equational)h(problem.)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4947
(F)o(or)g(e)o(xample,)f(if)h Fz(X)31 b FA(occurs)22 b(else)n(where)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4948
2232 y(within)31 b(the)i(scope)f(of)h(abstractions)e(of)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4949
Fz(c)p FA(,)f Fz(d)p FA(,)g Fz(e)h FA(and)f Fz(f)11 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4950
FA(,)33 b(then)f Fz(X)40 b FA(needs)33 b(to)f(be)g(encoded)h(as)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4951
2353 y Fu(\()p Fz(X)24 b(a)17 b(b)g(c)g(d)g(e)g(f)11
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4952
b Fu(\))26 b FA(e)n(v)o(en)h(though)f(an)i(indi)n(vidual)d(equational)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4953
(problem)g(might)f(contain)h(only)g Fz(a)166 2473 y FA(and)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4954
Fz(b)p FA(.)h(Secondly)-6 b(,)23 b(and)h(more)g(importantly)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4955
b(,)22 b(we)i(cannot)g(see)h(ho)n(w)e(to)h(encode)g(our)g(freshness)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4956
2594 y(constraints)35 b(using)h(this)g(kind)f(of)i(higher)n(-order)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4957
(patterns.)f(\(Note)g(that)g(in)h(nominal)e(uni\002-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4958
2714 y(cation,)28 b(freshness)g(constraints)f(do)h(not)g(necessarily)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4959
(come)g(from)g(analysing)f(abstractions,)166 2834 y(rather)e(the)o(y)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4960
(can)h(be)g(chosen)g(arbitrarily)-6 b(.\))166 3093 y(A)34
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4961
b(more)g(promising)e(tar)n(get)j(for)f(a)h(reduction)e(of)h(nominal)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4962
(uni\002cation)h(to)f(some)h(form)g(of)166 3213 y(higher)n(-order)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4963
b(pattern)g(uni\002cation)f(is)h Fz(\025\033)t FA(,)g(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4964
Fz(\025)p FA(-calculus)g(with)f(de-Bruijn)i(indices)e(and)h(e)o(x-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4965
3333 y(plicit)d(substitutions.)e(Do)n(wek)i Fx(et)h(al)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4966
FA([28])g(present)g(a)g(v)o(ersion)f(of)h(higher)n(-order)g(pattern)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4967
(uni-)166 3454 y(\002cation)f(for)f Fz(\025\033)29 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4968
FA(in)24 b(which)g(uni\002cation)g(problems)f(are)j(solv)o(ed,)d(as)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4969
(in)g(nominal)g(uni\002cation,)166 3574 y(by)i(te)o(xtual)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4970
(replacements)i(of)g(terms)g(for)g(v)n(ariables;)f(ho)n(we)n(v)o(er)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4971
(a)j(\223pre-cooking\224)e(operation)166 3694 y(ensures)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4972
b(that)f(the)h(te)o(xtual)f(replacements)h(can)g(be)g(f)o(aithfully)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4973
(related)h(to)g(capture-a)n(v)n(oiding)166 3815 y(substitutions.)24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4974
b(It)k(seems)f(possible)f(that)g(the)i(freshness)f(\(as)h(well)f(as)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4975
(the)g(equational\))g(prob-)166 3935 y(lems)34 b(of)g(nominal)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4976
(uni\002cation)h(can)h(be)g(encoded)f(into)g(higher)n(-order)g(pattern)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4977
h(uni\002cation)166 4056 y(problems)21 b(o)o(v)o(er)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4978
Fz(\025\033)t FA(,)i(using)f(a)h(non-tri)n(vial)d(translation)i(in)l(v)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4979
n(olving)e(the)j(use)f(of)h(the)g(shift)e(oper)n(-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4980
4176 y(ator)k(and)f(the)g(introduction)f(of)h(fresh)h(uni\002cation)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4981
(v)n(ariables.)f(The)i(details)e(of)i(this)e(encoding)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4982
4296 y(still)32 b(remain)i(to)f(be)h(in)l(v)o(estigated.)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4983
(Furthermore,)j(it)f(is)h(not)f(clear)h(to)g(us)f(ho)n(w)g(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4984
(translate)166 4417 y(solutions)k(obtained)i(via)g(the)g(encoding)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4985
(back)h(into)g(solutions)e(of)i(the)g(original)f(nominal)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4986
4537 y(uni\002cation)33 b(problem.)f(But)h(e)n(v)o(en)f(if)i(it)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4987
(turns)h(out)f(that)h(it)g(is)g(possible)f(to)g(reduce)i(nominal)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4988
4658 y(uni\002cation)24 b(to)g(the)g(algorithm)f(of)i(Do)n(wek)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4989
Fx(et)g(al)p FA(,)g(the)h(calculations)e(in)l(v)n(olv)o(ed)g(in)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4990
(translating)166 4778 y(our)h(terms)g(into)f Fz(\025\033)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4991
b FA(patterns)c(and)g(then)g(using)f(higher)n(-order)h(pattern)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4992
(uni\002cation)f(seem)h(f)o(ar)166 4898 y(more)j(intricate)f(than)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4993
(our)h(simple)e(algorithm)h(that)g(solv)o(es)f(nominal)h(uni\002cation)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4994
g(problems)166 5019 y(directly)-6 b(.)27 b(The)h(conclusion)f(we)h(dra)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4995
o(w)g(is)g(that)f(an)h(encoding)g(of)g(nominal)f(uni\002cation)g(prob-)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4996
166 5139 y(lems)34 b(into)g(higher)n(-order)h(pattern)g(uni\002cation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4997
(problems)e(\(using)i(de)g(Bruijn)g(indices)f(and)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4998
5259 y(e)o(xplicit)c(substitutions\))f(might)i(be)g(possible,)g(b)n(ut)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4999
g(such)h(an)f(encoding)h(is)f(no)g(substitute)f(in)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5000
5380 y(practice)25 b(for)g(ha)n(ving)f(the)h(simple,)f(direct)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5001
(algorithm)g(we)h(presented)f(here.)1748 5712 y(22)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5002
eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5003
%%Page: 23 23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5004
TeXDict begin 23 22 bop 166 83 a Fx(Hamana')l(s)24 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5005
Fz(\014)657 98 y FG(0)697 83 y Fx(-uni\002cation)f(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5006
Fz(\025)p Fx(-terms)h(with)f(\223holes\224)166 433 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5007
FA(Hamana)31 b([5,29])f(manages)h(to)f(add)h(possibly-capturing)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5008
(substitution)g(to)j(a)g(language)f(lik)o(e)166 554 y(Miller')-5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5009
b(s)20 b Fz(L)569 569 y Fq(\025)615 554 y FA(.)i(This)f(is)g(achie)n(v)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5010
o(ed)g(by)h(adding)f(syntax)g(for)h(e)o(xplicit)e(renaming)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5011
(operations)g(and)166 674 y(by)31 b(recording)g(implicit)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5012
(dependencies)h(of)g(v)n(ariables)g(upon)g(bindable)f(names)h(in)g(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5013
(typing)166 795 y(conte)o(xt.)20 b(The)h(mathematical)f(foundation)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5014
(for)j(Hamana')-5 b(s)20 b(system)g(is)g(the)h(model)f(of)h(binding)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5015
915 y(syntax)29 b(of)h(Fiore)g Fx(et)f(al)h FA([24].)f(The)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5016
(mathematical)e(foundation)h(for)h(our)f(w)o(ork)h(appeared)g(at)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5017
1035 y(the)25 b(same)f(time)g(\(see)i([10]\))f(and)g(is)f(in)g(a)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5018
(sense)e(complementary)-6 b(.)23 b(F)o(or)i(in)g(Hamana')-5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5019
b(s)24 b(system)166 1156 y(the)g(typing)e(conte)o(xt)h(restricts)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5020
(which)h(terms)f(may)h(be)g(substituted)d(for)j(a)h(v)n(ariable)e(by)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5021
(gi)n(ving)166 1276 y(a)39 b(\002nite)f(set)g(of)g(names)g(that)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5022
Fx(must)g(contain)f FA(the)h(free)i(names)e(of)g(such)g(a)h(term;)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5023
(whereas)166 1396 y(we)29 b(gi)n(v)o(e)e(a)i(\002nite)f(set)g(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5024
(names)f(which)g(the)h(term')-5 b(s)27 b(free)j(v)n(ariables)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5025
Fx(must)h(avoid)p FA(.)g(Since)h Fz(\013)q FA(-)166 1517
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5026
y(con)l(v)o(ersion)c(is)i(phrased)f(in)g(terms)g(of)h(a)n(v)n(oidance,)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5027
f(i.e.)h(freshness)f(of)h(names,)f(our)h(approach)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5028
1637 y(seems)g(more)h(natural)g(if)g(one)f(w)o(ants)h(to)f(compute)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5029
Fz(\013)q FA(-equi)n(v)n(alences)g(concretely)-6 b(.)27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5030
b(On)g(top)h(of)166 1758 y(that,)d(our)g(use)g(of)h(name)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5031
(permutations,)f(rather)i(than)f(arbitrary)g(renaming)g(functions,)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5032
(leads)166 1878 y(to)31 b(technical)f(simpli\002cations.)f(In)i(an)o(y)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5033
f(case,)i(the)f(bottom)e(line)i(is)f(that)h(Hamana')-5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5034
b(s)30 b(system)166 1998 y(seems)k(more)h(complicated)e(than)h(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5035
(one)f(presented)h(here)g(and)f(does)g(not)g(possess)g(most)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5036
2119 y(general)25 b(uni\002ers.)166 2512 y Fx(Qu-Pr)l(olo)o(g)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5037
2863 y FA(The)h(w)o(ork)g([8,9])g(on)g(uni\002cation)g(in)g(Qu-Prolog)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5038
(is)f(most)g(closely)h(related)g(to)g(that)g(reported)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5039
2983 y(here.)32 b(Qu-Prolog)g(is)g(a)g(mature)g(logic)f(programming)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5040
(language)i(addressing)f(man)o(y)g(prob-)166 3103 y(lems)g(we)i(set)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5041
(out)f(in)h(the)g(Introduction.)e(T)-8 b(o)32 b(be)o(gin)f(with,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5042
(Qu-Prolog')-5 b(s)32 b(uni\002cation)f(algo-)166 3224
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5043
y(rithm)j(uni\002es)g(terms)g(modulo)g Fz(\013)q FA(-equi)n(v)n(alence)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5044
f(and)i(may)f(produce)h(solutions)d(that,)i(as)h(in)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5045
3344 y(nominal)18 b(uni\002cation,)h(depend)g(on)g(freshness)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5046
(constraints)f(\(in)h(Qu-Prolog)g(such)g(constraints)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5047
3465 y(are)28 b(represented)g(by)f(a)h(predicate)g(called)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5048
Fs(not)p 1845 3465 30 4 v 35 w(free)p 2120 3465 V 35
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5049
w(in)p FA(\).)g(Furthermore,)h(meta)n(v)n(ariables)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5050
3585 y(are)k(substituted)d(in)i(a)g(possibly-capturing)e(manner)-5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5051
b(.)30 b(Ho)n(we)n(v)o(er)l(,)g(there)h(are)h(also)f(a)g(number)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5052
3705 y(of)24 b(dif)n(ferences)g(between)f(nominal)g(uni\002cation)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5053
(and)h(uni\002cation)f(in)g(Qu-Prolog.)g(The)h(most)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5054
3826 y(ob)o(vious)29 b(dif)n(ference)j(is)f(that)g(the)g(term)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5055
(language)g(in)g(Qu-Prolog)g(is)g(richer)h(than)f(our)g(term)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5056
3946 y(language)22 b(o)o(v)o(er)f(nominal)f(signatures;)h(for)h(e)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5057
(xample)f(Qu-Prolog)h(allo)n(ws)f(v)n(ariables)g(in)g(bind-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5058
4066 y(ing)26 b(position)e(and)i(permits)f(e)o(xplicit)g(substitutions)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5059
e(of)j(terms)g(for)g(v)n(ariables.)g(This)f(richness)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5060
4187 y(of)19 b(the)h(term)f(language)g(leads)g(to)g(a)g(number)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5061
(dif)n(\002culties.)f(First,)h(the)g(uni\002cation)g(problems)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5062
4307 y(in)31 b(Qu-Prolog)g(are)h(only)f(semi-decidable)f(\(whereas)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5063
(the)f(nominal)f(uni\002cation)h(problems)166 4428 y(are)j(decidable\))
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5064
f(and)g(as)g(a)h(result)e(the)h(algorithm)f(emplo)o(yed)g(in)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5065
(Qu-Prolog)f(can)i(lea)n(v)o(e)f(as)166 4548 y(unsolv)o(ed)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5066
b(some)h(uni\002cation)g(problems)g(that)g(are)i(\223too)e(dif)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5067
(\002cult\224.)g(This)g(means)g(the)h(uni\002-)166 4668
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5068
y(cation)g(transformations)g(in)g(Qu-Prolog,)g(while)g(sho)n(wn)g(not)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5069
(to)g(delete)h(an)o(y)f(solutions)f(nor)166 4789 y(to)d(introduce)h(an)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5070
o(y)f(ne)n(w)g(ones,)h(do)f(not)g(al)o(w)o(ays)h(lead)g(to)f(problems)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5071
(from)g(which)g(an)h(e)o(xplicit)166 4909 y(solution)e(can)i(be)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5072
(obtained.)f(Secondly)-6 b(,)26 b(as)h(we)g(illustrated)e(in)i(Remark)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5073
(3.10,)f(the)h(possibil-)166 5029 y(ity)d(of)h(forming)e(terms)h(with)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5074
(uni\002cation)g(v)n(ariables)g(in)g(binding)f(position)g(means)h(that)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5075
g(most)166 5150 y(general)h(solutions)e(may)h(not)h(e)o(xist.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5076
5380 y(Another)j(dif)n(ference)h(arises)f(from)g(the)h(f)o(act)f(that)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5077
(in)g(Qu-Prolog)h(binders)e(are)i(renamed)g(via)1748
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5078
5712 y(23)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5079
%%Page: 24 24
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5080
TeXDict begin 24 23 bop 166 83 a FA(capture-a)n(v)n(oiding)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5081
b(substitutions.)d(This)j(means)g(that)h(fresh)f(names)h(need)g(to)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5082
(be)h(introduced)166 203 y(during)c(uni\002cation)g(in)h(order)g(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5083
(respect)g Fz(\013)q FA(-equi)n(v)n(alence.)f(This)g(is)g(not)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5084
(necessary)g(in)g(nomi-)166 324 y(nal)j(uni\002cation,)e(because)j(the)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5085
e(permutation)f(operation)h(already)h(respects)g Fz(\013)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5086
FA(-equi)n(v)n(alence.)166 444 y(In)k(f)o(act)g(the)f(introduction)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5087
(of)i(fresh)g(atoms)f(during)g(uni\002cation)g(leads)g(to)g(a)h(more)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5088
(compli-)166 565 y(cated)g(notion)f(of)h(most)f(general)h(solution.)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5089
(Consider)h(the)h(follo)n(wing)e(v)n(ariant)h(of)h(the)g(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5090
Fw(\031)p Fu(?)p FA(-)166 685 y(abstraction-2\))24 b(transformation:)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5091
166 921 y Fu(\()p Fw(\031)p Fu(?)p FA(-abstraction-2)881
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5092
878 y Ft(0)904 921 y Fu(\))k Fw(f)p Fz(a:t)g Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5093
Fu(?)g Fz(a)1363 880 y Ft(0)1386 921 y Fz(:t)1448 880
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5094
y Ft(0)1472 921 y Fw(g])p Fz(P)1756 868 y Fq(")1692 921
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5095
y Fu(=)-17 b Fw(\))28 b(f)p Fu(\()p Fz(a)17 b(b)p Fu(\))p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5096
Fr(\001)p Fz(t)28 b Fw(\031)p Fu(?)g(\()p Fz(a)2449 880
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5097
y Ft(0)2489 921 y Fz(b)p Fu(\))p Fr(\001)p Fz(t)2635
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5098
880 y Ft(0)2659 921 y Fz(;)17 b(b)28 b Fu(#?)g Fz(t;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5099
b(b)28 b Fu(#?)g Fz(t)3265 880 y Ft(0)3288 921 y Fw(g[)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5100
Fz(P)166 1157 y FA(which)d(is)g(applicable)g(pro)o(vided)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5101
Fz(a)29 b Fw(6)p Fu(=)g Fz(a)1576 1121 y Ft(0)1625 1157
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5102
y FA(and)d Fz(b)g FA(is)f(a)g(fresh)h(atom,)f(not)g(occurring)g(else)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5103
(where)166 1277 y(in)39 b(the)g(problem.)g(This)f(rule)i(is)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5104
(essentially)f(the)h(re\002nement)h(step)e(that)h(uni\002es)h(tw)o(o)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5105
(ab-)166 1398 y(stracted)24 b(terms)f(in)g(Qu-Prolog)h(\(see)g([8,)g(P)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5106
o(age)g(105]\).)g(If)g(we)g(were)g(to)g(use)f(\()p Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5107
Fu(?)p FA(-abstraction-)166 1518 y(2)216 1482 y Ft(0)239
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5108
1518 y FA(\))31 b(instead)g(of)g(\()p Fw(\031)p Fu(?)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5109
FA(-abstraction-2\))g(in)f(our)h(nominal)f(uni\002cation)g(algorithm,)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5110
(then)i(when)166 1639 y(applied)24 b(to)h(the)f(problem)1486
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5111
1775 y Fw(f)j Fz(a:X)36 b Fw(\031)q Fu(?)27 b Fz(b:Y)50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5112
b Fw(g)1154 b FA(\(19\))166 1941 y(it)29 b(w)o(ould)g(produce)h(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5113
(solution)e Fu(\()p Fw(f)p Fz(a)37 b Fu(#)g Fz(Y)5 b(;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5114
b(c)37 b Fu(#)g Fz(Y)21 b Fw(g)p Fz(;)c Fu([)p Fz(X)45
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5115
b Fu(:=)37 b(\()p Fz(a)17 b(c)p Fu(\)\()p Fz(b)g(c)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5116
Fu(\))p Fr(\001)o Fz(Y)k Fu(]\))p FA(.)30 b(While)g(this)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5117
2061 y(solution)e(solv)o(es)g(the)i(problem,)e(it)h(is)h(not)f(a)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5118
(most)e(general)i(solution)e(according)h(to)g(De\002ni-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5119
2181 y(tion)h(3.1\227we)h(lost)g(the)g(information)f(that)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5120
Fz(c)i FA(is)f(a)g(completely)g(fresh)g(atom.)g(On)g(the)g(other)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5121
2302 y(hand,)21 b(applying)f(transformation)g(\()p Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5122
Fu(?)p FA(-abstraction-2\))i(to)e(\(19\))i(leads)f(to)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5123
Fu(\()p Fw(f)p Fz(a)27 b Fu(#)h Fz(Y)22 b Fw(g)p Fz(;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5124
b Fu([)p Fz(X)35 b Fu(:=)166 2422 y(\()p Fz(a)17 b(b)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5125
Fu(\))p Fr(\001)p Fz(Y)k Fu(]\))p FA(\227a)k(most)f(general)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5126
(solution.)166 2650 y(Ov)o(erall,)i(the)h(theory)g(of)g(Qu-Prolog')-5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5127
b(s)27 b(uni\002cation)h(is)f(more)h(comple)o(x)f(than)h(that)g(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5128
(nomi-)166 2770 y(nal)22 b(uni\002cation:)g(in)g(nominal)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5129
(uni\002cation)h(we)g(do)h(not)e(need)i(to)f(resort)h(to)f(a)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5130
(semantic)g(notion)166 2891 y(of)28 b Fz(\013)q FA(-equi)n(v)n(alence)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5131
(in)h(order)h(to)g(sho)n(w)e(the)i(correctness)g(of)f(the)h(nominal)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5132
(uni\002cation)h(algo-)166 3011 y(rithm;)h(and)i(the)g(use)f(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5133
(permutations)e(mak)o(es)i(our)f Fw(\031)p FA(-relation)h(much)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5134
(simpler)g(compared)166 3132 y(with)f(Qu-Prolog')-5 b(s)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5135
b(use)g(of)h(the)f(traditional)f(notion)g(of)i Fz(\013)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5136
FA(-equi)n(v)n(alence)e(e)o(xtended)h(to)g(terms)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5137
3252 y(with)c(meta)n(v)n(ariables.)166 3707 y FB(5)99
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5138
b(Conclusion)25 b(and)h(Futur)n(e)g(W)-7 b(ork)166 4056
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5139
y FA(In)19 b(this)f(paper)h(we)g(ha)n(v)o(e)g(proposed)f(a)h(ne)n(w)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5140
(solution)f(to)i(the)g(problem)f(of)g(computing)g(possibly-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5141
4176 y(capturing)i(substitutions)d(that)j(unify)g(terms)g(in)l(v)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5142
(olving)e(binders)i(up)g(to)g Fz(\013)q FA(-con)l(v)o(ersion.)f(T)-8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5143
b(o)20 b(do)166 4296 y(so)30 b(we)h(considered)f(a)h(man)o(y-sorted)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5144
(\002rst-order)i(term)g(language)f(with)g(distinguished)e(col-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5145
4417 y(lections)h(of)h(constants)f(called)h Fx(atoms)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5146
FA(and)h(with)f Fx(atom-abstr)o(action)e FA(operations)i(for)h(bind-)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5147
166 4537 y(ing)35 b(atoms)f(in)i(terms.)e(This)h(pro)o(vides)f(a)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5148
(simple,)e(b)n(ut)h(\003e)o(xible,)g(frame)n(w)o(ork)g(for)h(specify-)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5149
166 4658 y(ing)28 b(binding)g(operations)g(and)h(their)f(scopes,)h(in)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5150
(which)h(the)f(bound)g(entities)g(are)i(e)o(xplicitly)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5151
4778 y(named.)37 b(By)i(using)d(v)n(ariables)h(pre\002x)o(ed)h(with)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5152
(suspended)g(permutations,)f(one)i(can)g(ha)n(v)o(e)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5153
4898 y(substitution)27 b(of)j(terms)f(for)h(v)n(ariables)f(both)g(allo)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5154
n(w)f(capture)i(of)g(atoms)f(by)g(binders)g(and)h(re-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5155
5019 y(spect)i Fz(\013)q FA(-equi)n(v)n(alence)f(\(renaming)h(of)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5156
(bound)e(atoms\).)h(The)g(de\002nition)g(of)g Fz(\013)q
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5157
FA(-equi)n(v)n(alence)166 5139 y(for)d(the)g(term)g(language)f(mak)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5158
(es)h(use)g(of)g(an)g(auxiliary)f Fx(fr)l(eshness)g FA(relation)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5159
(between)g(atoms)166 5259 y(and)i(terms)g(which)g(generalises)h(the)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5160
(\223not)g(a)h(free)g(atom)f(of)5 b(\224)32 b(relation)f(from)h(ground)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5161
e(terms)166 5380 y(to)h(terms)f(with)h(v)n(ariables;)f(furthermore,)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5162
(because)g(v)n(ariables)g(stand)f(for)i(unkno)n(wn)d(terms,)1748
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5163
5712 y(24)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5164
%%Page: 25 25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5165
TeXDict begin 25 24 bop 166 3 3288 4 v 166 1030 4 1027
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5166
v 227 127 a Fs(type)59 b(Gamma)g(\(var)g(X\))g(A)h(:-)f(mem)g(\(pair)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5167
(X)g(A\))h(Gamma.)227 248 y(type)f(Gamma)g(\(app)g(M)g(N\))h(B)f(:-)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5168
(type)f(Gamma)f(M)i(\(arrow)e(A)i(B\),)1782 368 y(type)f(Gamma)f(N)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5169
(A.)227 489 y(type)f(Gamma)g(\(lam)g(x.M\))g(\(arrow)f(A)i(B\))f(/)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5170
(x#Gamma)e(:-)1782 609 y(type)h(\(pair)f(x)i(A\)::Gamma)d(M)j(B.)227
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5171
850 y(mem)g(A)f(A::Tail.)227 970 y(mem)h(A)f(B::Tail)f(:-)i(mem)f(A)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5172
(Tail.)p 3450 1030 V 166 1033 3288 4 v 1134 1170 a FD(Fig.)22
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5173
b(5.)h(An)g(e)o(xample)h FC(\013)p FD(Prolog)h(program)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5174
1431 y FA(hence)c(with)g(unkno)n(wn)e(free)j(atoms,)e(it)g(is)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5175
(necessary)i(to)e(mak)o(e)h(hypotheses)e(about)i(the)f(fresh-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5176
1551 y(ness)33 b(of)h(atoms)f(for)h(v)n(ariables)e(in)i(judgements)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5177
(about)h(term)g(equi)n(v)n(alence)g(and)g(freshness.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5178
1671 y(This)e(reliance)h(on)f(\223freshness\224,)g(coupled)g(with)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5179
(name-sw)o(apping)g(rather)g(than)h(renaming,)166 1792
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5180
y(lead)39 b(to)f(a)g(ne)n(w)g(notion)f(of)i(uni\002cation)f(problem)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5181
(in)h(which)g(instances)g(of)g(both)g(equi)n(v)n(a-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5182
1912 y(lence)31 b(and)f(freshness)g(ha)n(v)o(e)g(to)g(be)g(solv)o(ed)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5183
(by)h(gi)n(ving)f(term-substitutions)e(and)j(\(possibly\))166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5184
2032 y(freshness)h(conditions)f(on)h(v)n(ariables)g(in)g(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5185
(solution.)d(W)-8 b(e)32 b(sho)n(wed)f(that)g(this)g(uni\002cation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5186
2153 y(problem)24 b(is)g(decidable)h(and)g(unitary)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5187
b(.)166 2396 y(Chene)o(y)g(,)29 b(Gabbay)h(and)g(Urban)h([30,31])e(are)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5188
i(in)l(v)o(estigating)c(the)j(e)o(xtent)f(to)h(which)f(nominal)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5189
2516 y(uni\002cation)k(can)h(be)g(used)f(in)g(resolution-based)g(proof)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5190
g(search)h(for)g(a)g(form)g(of)f(\002rst-order)166 2637
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5191
y(logic)38 b(programming)f(for)i(languages)f(with)g(binders)f(\(with)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5192
(a)h(vie)n(w)f(to)g(pro)o(viding)f(better)166 2757 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5193
(machine-assistance)h(for)i(structural)e(operational)h(semantics\).)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5194
(Such)h(a)h(logic)e(program-)166 2877 y(ming)28 b(language)g(should)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5195
(permit)g(a)h(concrete,)h(\223nominal\224)e(approach)h(to)f(bound)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5196
(entities)g(in)166 2998 y(programs)j(while)f(ensuring)g(that)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5197
(computation)e(\(which)i(in)g(this)f(case)i(is)f(the)g(computation)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5198
3118 y(of)38 b(answers)f(to)h(queries\))f(respects)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5199
Fz(\013)q FA(-equi)n(v)n(alence)e(between)i(terms.)f(This)g(is)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5200
(illustrated)166 3238 y(with)25 b(the)h(Prolog-lik)o(e)g(program)f(in)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5201
(Figure)g(5,)g(which)g(implements)e(a)i(simple)f(typing)g(algo-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5202
3359 y(rithm)d(for)i Fz(\025)p FA(-terms.)f(The)g(third)f(clause)i(is)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5203
(the)i(interesting)e(one.)h(First,)g(note)g(the)g(term)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5204
Fs(\(lam)166 3479 y(x.M\))p FA(,)29 b(which)g(uni\002es)g(with)g(an)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5205
(y)g Fz(\025)p FA(-abstraction.)g(The)h(binder)f Fs(x)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5206
FA(,)g(roughly)g(speaking,)g(has)166 3600 y(in)24 b(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5207
(\223nominal\224)f(approach)h(a)g(v)n(alue)g(which)f(can)h(be)g(used)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5208
(in)f(the)h(body)f(of)h(the)g(clause,)g(for)166 3720
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5209
y(e)o(xample)h(for)h(adding)f Fs(\(pair)59 b(x)h(A\))26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5210
b FA(to)h(the)f(conte)o(xt)g Fs(Gamma)p FA(.)g(Secondly)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5211
b(,)26 b(the)h(freshness)166 3840 y(constraint)h Fs(x)16
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5212
b(#)h(Gamma)27 b FA(ensures)i(that)f Fs(Gamma)g FA(cannot)g(be)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5213
(replaced)g(by)g(a)g(term)f(that)h(con-)166 3961 y(tains)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5214
Fs(x)h FA(freely)-6 b(.)28 b(Since)h(this)f(clause)h(is)f(intended)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5215
(to)h(implement)e(the)h(usual)g(rule)h(for)g(typing)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5216
4081 y Fz(\025)p FA(-abstractions)1361 4211 y Fw(f)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5217
Fz(x)f Fu(:)g Fz(A)p Fw(g)22 b([)h Fu(\000)49 b Fz(.)h(M)38
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5218
b Fu(:)28 b Fz(B)p 1361 4256 898 4 v 1399 4342 a Fu(\000)50
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5219
b Fz(.)g(\025x:M)39 b Fu(:)27 b Fz(A)h Fw(\033)g Fz(B)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5220
4537 y FA(its)f(operational)h(beha)n(viour)f(is)h(gi)n(v)o(en)f(by:)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5221
(choose)h(fresh)g(names)g(for)g Fs(Gamma)p FA(,)f Fs(x)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5222
FA(,)h Fs(M)p FA(,)g Fs(A)g FA(and)166 4658 y Fs(B)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5223
FA(\(this)f(is)h(standard)f(in)h(Prolog-lik)o(e)f(languages\),)h(unify)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5224
f(the)h(head)g(of)g(the)g(clause)g(with)f(the)166 4778
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5225
y(goal)19 b(formula,)h(apply)f(the)g(resulting)g(uni\002er)h(to)f(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5226
(body)f(of)h(the)f(clause)h(and)g(mak)o(e)f(sure)h(that)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5227
4898 y Fs(Gamma)f FA(is)h(not)f(replaced)i(by)f(a)g(term)g(that)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5228
(contains)f(freely)i(the)e(fresh)i(name)f(we)g(ha)n(v)o(e)g(chosen)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5229
5019 y(for)31 b Fs(x)p FA(.)g(Similar)f(f)o(acilities)g(for)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5230
Fx(functional)e(pr)l(o)o(gr)o(amming)f FA(already)j(e)o(xist)f(in)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5231
(the)h(FreshML)166 5139 y(language,)38 b(b)n(uilt)f(upon)h(the)h(same)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5232
(foundations:)f(see)h([13])h(and)f Fv(www)p Fz(:)p Fv(freshml)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5233
Fz(:)p Fv(org)t FA(.)g(W)-8 b(e)166 5259 y(are)27 b(also)f(interested)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5234
(in)g(the)g(special)g(case)h(of)f(\223nominal)g(matching\224)f(and)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5235
(its)g(application)f(to)166 5380 y(term-re)n(writing)e(modulo)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5236
Fz(\013)q FA(-equi)n(v)n(alence.)1748 5712 y(25)p eop
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5237
end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5238
%%Page: 26 26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5239
TeXDict begin 26 25 bop 166 83 a Fx(A)25 b(note)f(on)h(comple)n(xity)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5240
166 459 y FA(If)i(these)f(applications)f(sho)n(w)g(that)g(nominal)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5241
(uni\002cation)h(is)f(practically)h(useful,)g(then)g(it)f(be-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5242
579 y(comes)33 b(important)e(to)i(study)f(its)h(comple)o(xity)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5243
b(.)30 b(The)j(presentations)f(of)h(the)g(term)g(language)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5244
700 y(in)26 b(Section)g(2)g(and)h(of)f(the)g(algorithm)f(in)h(Section)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5245
(3)g(were)h(chosen)f(for)h(clarity)f(and)g(to)g(mak)o(e)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5246
820 y(the)d(proof)g(of)h(correctness)1121 784 y FG(3)1201
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5247
820 y FA(easier)l(,)g(rather)f(than)g(for)h(ef)n(\002cienc)o(y)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5248
b(.)22 b(One)i(source)f(of)h(increased)166 940 y(ef)n(\002cienc)o(y)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5249
(is)g(to)h(delay)f(the)g(application)g(of)g(permutations:)f(instead)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5250
(of)i(pushing)e(permuta-)166 1061 y(tion)k(inside)g(terms)g(until)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5251
(the)o(y)h(reach)h(suspension)f(as)g(we)h(do)g(here,)g(one)f(should)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5252
(just)g(push)166 1181 y(them)38 b(under)h(the)f(\002rst)h(constructor)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5253
(\(pairing,)g(function)g(symbol)f(application,)h(or)g(atom-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5254
1301 y(abstraction\))25 b(in)h(order)g(to)f(proceed)i(with)e(the)g(ne)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5255
(xt)g(step)h(of)g(decomposition.)d(Ho)n(we)n(v)o(er)l(,)i(the)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5256
1422 y(main)30 b(inef)n(\002cienc)o(y)h(of)g(the)f(algorithm)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5257
(presented)h(in)f(Section)h(3)g(comes)f(from)h(the)g(lack)g(of)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5258
1542 y(sharing)24 b(in)h(terms)f(and)h(substitutions.)c(Thus)j(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5259
(uni\002cation)f(problem)g(tak)o(en)h(from)f([32])450
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5260
1833 y Fw(f)p Fz(f)11 b Fu(\()p Fz(X)678 1848 y FG(1)717
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5261
1833 y Fz(;)17 b(X)842 1848 y FG(1)881 1833 y Fu(\))27
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5262
b Fw(\031)q Fu(?)h Fz(X)1179 1848 y FG(2)1218 1833 y
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5263
Fz(;)17 b(f)11 b Fu(\()p Fz(X)1440 1848 y FG(2)1479 1833
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5264
y Fz(;)17 b(X)1604 1848 y FG(2)1643 1833 y Fu(\))28 b
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5265
Fw(\031)p Fu(?)g Fz(X)1941 1848 y FG(3)1980 1833 y Fz(;)17
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5266
b(:)g(:)g(:)f(;)h(f)11 b Fu(\()p Fz(X)2377 1848 y Fq(n)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5267
Ft(\000)p FG(1)2513 1833 y Fz(;)17 b(X)2638 1848 y Fq(n)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5268
Ft(\000)p FG(1)2775 1833 y Fu(\))28 b Fw(\031)p Fu(?)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5269
Fz(X)3073 1848 y Fq(n)3120 1833 y Fw(g)166 2124 y FA(which)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5270
b(illustrates)f(that)g(the)h(na)m(\250)-30 b(\021v)o(e)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5271
b(algorithm)f(for)h(classical)g(\002rst-order)g(uni\002cation)g(has)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5272
2244 y(e)o(xponential)27 b(time)g(comple)o(xity)-6 b(,)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5273
b(also)i(applies)f(to)h(the)g(algorithm)f(for)i(nominal)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5274
(uni\002cation)166 2364 y(gi)n(v)o(en)36 b(here.)i(If)g(one)g(adapts)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5275
(a)h(representation)g(for)g(terms)f(using)f(techniques)h(de)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5276
(eloped)166 2485 y(in)26 b([32])h(or)f([33],)h(which)f(are)h(based)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5277
(on)g(directed)h(ac)o(yclic)f(graphs,)g(then)g(one)h(easily)f(arri)n(v)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5278
o(es)166 2605 y(at)c(an)g(algorithm)e(with)h(quadratic)h(time)f(comple)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5279
o(xity)-6 b(.)19 b(The)j(reason)g(for)g(the)g(quadratic,)f(rather)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5280
2725 y(than)j(linear)l(,)h(time-comple)o(xity)d(is)i(that)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5281
(permutations)f(need)i(to)f(be)h(applied)f(to)g(some)g(atoms)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5282
2846 y(when)30 b(deciding)g(whether)g(the)g(rules)h(\()p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5283
Fw(\031)p Fu(?)p FA(-abstraction-1\))f(or)h(\()p Fw(\031)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5284
Fu(?)p FA(-abstraction-2\))f(are)h(ap-)166 2966 y(plicable,)37
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5285
b(and)g(these)g(permutations)e(\(represented)j(as)f(lists)f(of)h(sw)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5286
(appings\))f(might)f(gro)n(w)166 3087 y(linearly)27 b(with)g(the)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5287
(number)f(of)h(nodes.)g(Using)f(a)h(representation)f(of)h(permutations)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5288
e(that)i(al-)166 3207 y(lo)n(ws)36 b(for)i(a)g(more)g(ef)n(\002cient)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5289
(calculation)g(of)h(their)f(action)g(on)h(atoms)e(does)i(not)f(impro)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5290
(v)o(e)166 3327 y(the)c(quadratic)f(time)g(comple)o(xity)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5291
b(,)30 b(because)k(it)e(mak)o(es)g(the)h(operation)f(of)h(composing)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5292
(tw)o(o)166 3448 y(permutations)h(become)h(linear)l(,)g(while)g(this)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5293
(can)i(be)f(done)g(in)g(constant)f(time)h(when)g(using)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5294
3568 y(the)i(list-of-sw)o(appings)e(representation.)i(F)o(or)g(higher)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5295
(-order)g(patterns,)f(Qian)h(managed)g(to)166 3689 y(de)n(v)o(eloped)30
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5296
b(a)i(uni\002cation)g(algorithm)e(with)h(linear)g(time-comple)o(xity)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5297
([34].)j(It)g(seems)f(that)166 3809 y(adapting)22 b(Qian')-5
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5298
b(s)23 b(algorithm)e(to)i(nominal)f(uni\002cation)g(via)h(an)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5299
(encoding)f(of)i(nominal)d(terms)166 3929 y(into)h(higher)n(-order)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5300
(patterns)g(as)g(discussed)f(in)h(Section)g(4)g(will)f(not)h(solv)o(e)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5301
(this)g(problem.)g(F)o(or)166 4050 y(the)35 b(encoding)g(mak)o(es)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5302
(the)g(resulting)f(higher)n(-order)i(patterns)f(quadratically)f(longer)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5303
h(than)166 4170 y(the)30 b(original)g(nominal)f(terms,)h(so)h(this)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5304
(method)h(w)o(ould)f(only)h(pro)o(vide)g(another)g(algorithm)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5305
4290 y(with)24 b(quadratic)h(time)f(comple)o(xity)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5306
b(.)166 4546 y(T)e(o)20 b(sum)g(up,)g(there)h(is)f(a)g(v)o(ersion)g(of)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5307
g(nominal)f(uni\002cation)h(with)g(quadratic)g(time)f(comple)o(xity)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5308
b(,)166 4666 y(b)n(ut)19 b(is)g(it)f(is)h(still)f(an)h(open)g(question)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5309
f(whether)i(a)f(v)o(ersion)g(can)g(be)h(de)n(v)o(eloped)d(with)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5310
Fx(linear)i FA(time)166 4787 y(comple)o(xity)-6 b(.)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5311
166 5169 299 4 v 166 5233 a FG(3)257 5266 y FD(See)47
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5312
b Fi(http://www.cl.ca)o(m.)o(ac)o(.u)o(k/u)o(se)o(rs)o(/c)o(u2)o(00/)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5313
(Un)o(if)o(ic)o(at)o(ion)40 b FD(for)49 b(the)f(Is-)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5314
5379 y(abelle)25 b(proof)f(scripts.)1748 5712 y FA(26)p
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5318
423 y FA(A)38 b(preliminary)g(v)o(ersion)f(of)h(this)g(paper)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5319
(appeared)h(as)g([35].)f(W)-8 b(e)39 b(thank)f(James)f(Chene)o(y)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5320
b(,)166 544 y(Gilles)33 b(Do)n(wek,)h(Ro)o(y)g(Dyckhof)n(f,)f(Dale)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5321
(Miller)l(,)e(Frank)i(Pfenning,)f(Francois)g(Pottier)g(and)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5322
664 y(Helmut)28 b(Schwichtenber)n(g)i(for)g(comments)e(on)h(this)f(w)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5323
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5324
y(by)25 b(UK)f(EPSRC)j(grants)d(GR/R29697)h(\(Urban\))g(and)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5325
(GR/R07615)f(\(Pitts)g(and)h(Gabbay\).)166 1168 y FB(Refer)n(ences)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5326
1501 y FD([1])71 b(G.)24 b(Do)n(wek,)g(T)-7 b(.)24 b(Hardin,)h(C.)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5327
(Kirchner)l(,)k(Higher)n(-order)h(uni\002cation)f(via)e(e)o(xplicit)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5328
(substitutions,)342 1614 y(in:)g(10th)h(Annual)g(Symposium)f(on)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5329
(Logic)g(in)g(Computer)h(Science,)f(IEEE)e(Computer)j(Society)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5330
1727 y(Press,)d(W)-7 b(ashington,)25 b(1995,)g(pp.)e(366\226374.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5331
1911 y([2])71 b(C.)40 b(A.)g(Gunter)l(,)i(Semantics)g(of)f(Programming)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5332
i(Languages:)g(Structures)h(and)d(T)-6 b(echniques,)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5333
2024 y(F)o(oundations)26 b(of)e(Computing,)g(MIT)f(Press,)g(1992.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5334
2209 y([3])71 b(D.)19 b(Miller)l(,)i(A)e(logic)i(programming)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5335
(language)g(with)e(lambda-abstraction,)25 b(function)d(v)n(ariables,)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5336
342 2322 y(and)i(simple)h(uni\002cation,)g(Journal)g(of)f(Logic)g(and)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5337
(Computation)h(1)e(\(1991\))i(497\226536.)166 2506 y([4])71
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5338
b(G.)39 b(Do)n(wek,)f(Higher)n(-order)43 b(uni\002cation)e(and)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5339
(matching,)h(in:)f(A.)e(Robinson,)j(A.)d(V)-12 b(oronk)o(o)o(v)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5340
2619 y(\(Eds.\),)23 b(Handbook)j(of)d(Automated)i(Reasoning,)g(Else)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5341
(vier)l(,)g(2001,)f(Ch.)f(16,)g(pp.)g(1009\2261062.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5342
2804 y([5])71 b(M.)61 b(Hamana,)h(A)f(logic)j(programming)g(language)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5343
(based)e(on)f(binding)j(algebras,)f(in:)342 2917 y(N.)48
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5344
b(K)m(obayashi,)k(B.)c(C.)g(Pierce)i(\(Eds.\),)f(Theoretical)i(Aspects)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5345
g(of)e(Computer)i(Softw)o(are,)342 3030 y(4th)d(International)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5346
(Symposium,)c(T)-8 b(A)l(CS)45 b(2001,)j(Sendai,)f(Japan,)h(October)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5347
(29-31,)g(2001,)342 3143 y(Proceedings,)h(V)-12 b(ol.)46
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5348
b(2215)h(of)f(Lecture)h(Notes)f(in)g(Computer)h(Science,)g(Springer)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5349
(-V)-10 b(erlag,)342 3256 y(Berlin,)24 b(2001,)g(pp.)g(243\226262.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5350
3440 y([6])71 b(M.)19 b(Hashimoto,)i(A.)e(Ohori,)h(A)f(typed)i(conte)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5351
(xt)g(calculus,)h(Theoretical)h(Computer)d(Science)h(266)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5352
3553 y(\(2001\))k(249\226271.)166 3738 y([7])71 b(M.)29
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5353
b(Sato,)h(T)-7 b(.)28 b(Sakurai,)j(Y)-12 b(.)29 b(Kame)o(yama,)g(A)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5354
(simply)i(typed)g(conte)o(xt)g(calculus)h(with)e(\002rst-class)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5355
3851 y(en)l(vironments,)d(Journal)e(of)f(Functional)i(and)e(Logic)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5356
(Programming)i(2002)g(\(4\).)166 4035 y([8])71 b(P)-10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5357
b(.)28 b(Nick)o(olas,)i(P)-10 b(.)28 b(J.)g(Robinson,)i(The)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(Qu-Prolog)h(uni\002cation)h(algorithm:)g(F)o(ormalisation)g(and)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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4148 y(correctness,)c(Theoretical)e(computer)h(Science)e(169)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(\(1996\))h(81\226112.)166 4333 y([9])71 b(R.)19 b(P)o(aterson,)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(Uni\002cation)h(of)e(schemes)i(of)e(quanti\002ed)i(terms,)f(in:)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(Proc.)g(of)g(UNIF)f(1990,)i(1990,)342 4446 y(unpublished)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(proceedings.)166 4631 y([10])e(M.)h(J.)h(Gabbay)-6
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(,)28 b(A.)f(M.)g(Pitts,)h(A)f(ne)n(w)g(approach)k(to)d(abstract)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(syntax)f(with)f(v)n(ariable)i(binding,)342 4744 y(F)o(ormal)23
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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4928 y([11])h(L.)e(Caires,)h(L.)e(Cardelli,)j(A)e(spatial)i(logic)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(for)f(concurrenc)o(y)j(\(part)e(II\),)f(in:)g(L.)e(Brim,)h(P)-10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(.)23 b(Jan)5 b(\013)-35 b(car)l(,)342 5041 y(M.)52
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(K\013)-30 b(ret)m(\264)j(\021nsk)8 b(\264)-38 b(y,)54
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(A.)d(K)o(u)5 b(\013)-35 b(cera)53 b(\(Eds.\),)g(CONCUR)c(2002)54
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(August)f(20-23,)g(2002.)h(Proceedings,)342 5267 y(V)-12
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(Springer)n(-V)-10 b(erlag,)32 b(Berlin,)d(2002,)g(pp.)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5380 y(209\226225.)1748 5712 y FA(27)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(\(Ed.\),)e(F)o(oundations)k(of)d(Softw)o(are)g(Science)h(and)f
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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422 y(of)24 b(Lecture)g(Notes)g(in)f(Computer)i(Science,)f(Springer)n
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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612 y([13])i(M.)37 b(R.)g(Shinwell,)h(A.)f(M.)g(Pitts,)h(M.)f(J.)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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725 y(made)j(simple,)h(in:)f(Eighth)g(A)l(CM)e(SIGPLAN)f(International)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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45 b(Conference)e(on)e(Functional)342 838 y(Programming)25
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(pp.)f(263\226274.)166 1028 y([14])j(A.)18 b(Salibra,)h(On)g(the)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(algebraic)i(models)f(of)f(lambda)h(calculus,)h(Theoretical)g(Computer)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(.)36 b(Orejas,)i(P)-10 b(.)37 b(G.)f(Spirakis,)j(J.)e(Leeuwen)i
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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1783 y(Science,)25 b(Springer)n(-V)-10 b(erlag,)26 b(Heidelber)n(g,)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(Nominal)h(logic,)g(a)f(\002rst)g(order)h(theory)h(of)e(names)h(and)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(of)f(meta-v)n(ariables,)i(in:)e(M.)f(Baaz)342 2390 y(\(Ed.\),)32
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(&)g(KGC\),)342 2502 y(V)-5 b(ienna,)45 b(Austria.)h(Proccedings,)h(V)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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-12 b(ol.)44 b(2803)i(of)e(Lecture)i(Notes)f(in)g(Computer)g(Science,)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5416
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(An)d(ef)n(\002cient)i(uni\002cation)i(algorithm,)e(A)l(CM)e(T)m(rans.)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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342 2919 y(Programming)25 b(Languages)h(and)e(Systems)f(4)h(\(2\))f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(Abramsk)o(y)-6 b(,)21 b(D.)d(M.)h(Gabbay)-6 b(,)21 b(T)-7
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5422
b(.)19 b(S.)g(E.)f(Maibaum)342 3222 y(\(Eds.\),)27 b(Handbook)i(of)f
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(Logic)f(in)g(Computer)i(Science,)e(V)-12 b(olume)28
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5424
b(2,)f(Oxford)h(Uni)n(v)o(erity)g(Press,)342 3335 y(1992,)d(pp.)e
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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3638 y(1998.)166 3828 y([21])26 b(H.)33 b(P)-10 b(.)31
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5430
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5435
y([23])h(G.)k(D.)f(Plotkin,)j(An)e(illati)n(v)o(e)i(theory)h(of)d
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(relations,)j(in:)f(R.)d(Cooper)l(,)j(Mukai,)f(J.)f(Perry)h(\(Eds.\),)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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4660 y(Uni)n(v)o(ersity)-6 b(,)25 b(1990,)f(pp.)g(133\226146.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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4851 y([24])i(M.)34 b(P)-10 b(.)34 b(Fiore,)g(G.)g(D.)g(Plotkin,)h(D.)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(T)l(uri,)g(Abstract)i(syntax)h(and)e(v)n(ariable)i(binding,)g(in:)e
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5443
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5267 y([25])i(R.)44 b(Milner)l(,)j(M.)d(T)-7 b(ofte,)45
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(R.)f(Harper)l(,)i(D.)e(MacQueen,)i(The)f(De\002nition)h(of)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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1020 y([28])i(G.)i(Do)n(wek,)g(T)-7 b(.)27 b(Hardin,)i(C.)e(Kirchner)l
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5464
(e)o(xplicit)342 1133 y(substitutions:)36 b(the)31 b(case)h(of)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5465
(higher)n(-order)k(patterns,)d(in:)g(Proc.)e(of)h(JICSLP)-10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5466
b(,)29 b(1996,)j(pp.)f(259\226)342 1246 y(273.)166 1433
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5467
y([29])26 b(M.)33 b(Hamana,)h(Simple)f FC(\014)1179 1447
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5468
y FG(0)1219 1433 y FD(-uni\002cation)j(for)e(terms)g(with)g(conte)o(xt)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5469
h(holes,)g(in:)f(C.)e(Ringeissen,)342 1545 y(C.)d(T)m(inelli,)i(R.)e(T)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5470
m(reinen,)h(R.)f(M.)g(V)-10 b(erma)30 b(\(Eds.\),)g(Proc.)f(of)i(UNIF)d
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5471
(2002,)j(2002,)g(unpublished)342 1658 y(proceedings.)166
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5472
1845 y([30])26 b(J.)37 b(Chene)o(y)-6 b(,)37 b(C.)e(Urban,)j
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5473
FC(\013)p FD(Prolog,)f(a)g(fresh)h(approach)h(to)e(logic)h(programming)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5474
h(modulo)f FC(\013)p FD(-)342 1958 y(equi)n(v)n(alence,)32
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5475
b(in:)d(J.)g(Le)n(vy)-6 b(,)28 b(M.)g(K)m(ohlhase,)j(J.)d(Niehren,)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5476
(M.)e(V)-5 b(illaret)29 b(\(Eds.\),)g(Proc.)g(of)g(UNIF)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5477
2071 y(2003,)j(no.)e(DSIC-II/12/03)i(in)f(Departamento)i(de)d(Sistemas)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5478
h(Inform)5 b(\264)-35 b(aticos)34 b(y)c(Computaci)8 b(\264)-38
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5479
b(on)342 2183 y(T)-6 b(echnical)25 b(Report)f(Series,)g(Uni)n(v)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5480
(ersidad)h(Polit)5 b(\264)-35 b(ecnica)26 b(de)e(V)-10
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5481
b(alencia,)24 b(2003,)g(pp.)g(15\22619.)166 2370 y([31])i(M.)41
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5482
b(Gabbay)-6 b(,)42 b(J.)f(Chene)o(y)-6 b(,)42 b(A)f(proof)i(theory)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5483
(for)f(nominal)h(logic,)f(in:)g(Nineteenth)i(Annual)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5484
2483 y(IEEE)38 b(Symposium)j(on)e(Logic)h(in)g(Computer)h(Science,)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5485
(IEEE)e(Computer)i(Society)h(Press,)342 2596 y(W)-7 b(ashington,)26
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5486
b(2004.)166 2782 y([32])g(M.)40 b(S.)g(P)o(aterson,)h(M.)f(N.)g(W)-7
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5487
b(e)o(gman,)40 b(Linear)i(uni\002cation,)g(Journal)h(of)e(Computer)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5488
(System)342 2895 y(Sciences)25 b(16)f(\(2\))g(\(1978\))h(158\226167.)
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5489
166 3081 y([33])h(A.)j(Martelli,)h(U.)f(Montanari,)i(An)e(ef)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5490
(\002cient)i(uni\002cation)h(algorithm,)f(A)l(CM)d(T)m(ransactions)33
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5491
b(on)342 3194 y(Programming)25 b(Languages)h(and)e(Systems)f(4)h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5492
(\(2\).)166 3381 y([34])i(Z.)20 b(Qian,)g(Uni\002cation)i(of)e(higher)n
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5493
(-order)25 b(patterns)d(in)f(linear)h(time)e(and)h(space,)h(Journal)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5494
(of)f(Logic)342 3494 y(and)j(Computation)i(6)d(\(3\))h(\(1996\))h
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5495
(315\226341.)166 3680 y([35])h(C.)18 b(Urban,)i(A.)d(M.)i(Pitts,)f(M.)g
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5496
(J.)h(Gabbay)-6 b(,)20 b(Nominal)g(uni\002cation,)h(in:)e(M.)f(Baaz)i
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5497
(\(Ed.\),)e(Computer)342 3793 y(Science)34 b(Logic)f(and)g(8th)g(K)o
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5498
(urt)g(G)8 b(\250)-38 b(odel)33 b(Colloquium)h(\(CSL)-8
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5499
b('03)32 b(&)g(KGC\),)f(V)-5 b(ienna,)32 b(Austria.)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5500
3906 y(Proceedings,)49 b(V)-12 b(ol.)46 b(2803)h(of)f(Lecture)h(Notes)f
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5501
(in)g(Computer)h(Science,)g(Springer)n(-V)-10 b(erlag,)342
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5502
4019 y(Berlin,)24 b(2003,)g(pp.)g(513\226527.)1748 5712
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5503
y FA(29)p eop end
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5504
%%Trailer
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5505
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5506
userdict /end-hook known{end-hook}if
5c816239deaa added Unification subdirectory
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5507
%%EOF