Publications/alpha-iclp.ps
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   645 %%EndFont 
       
   646 %%BeginFont: CMR6
       
   647 %!PS-AdobeFont-1.1: CMR6 1.0
       
   648 %%CreationDate: 1991 Aug 20 16:39:02
       
   649 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
   650 11 dict begin
       
   651 /FontInfo 7 dict dup begin
       
   652 /version (1.0) readonly def
       
   653 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
   654 /FullName (CMR6) readonly def
       
   655 /FamilyName (Computer Modern) readonly def
       
   656 /Weight (Medium) readonly def
       
   657 /ItalicAngle 0 def
       
   658 /isFixedPitch false def
       
   659 end readonly def
       
   660 /FontName /CMR6 def
       
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   668 /FontBBox{-20 -250 1193 750}readonly def
       
   669 /UniqueID 5000789 def
       
   670 currentdict end
       
   671 currentfile eexec
       
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   673 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
       
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   714 %%EndFont 
       
   715 %%BeginFont: CMR7
       
   716 %!PS-AdobeFont-1.1: CMR7 1.0
       
   717 %%CreationDate: 1991 Aug 20 16:39:21
       
   718 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
   719 11 dict begin
       
   720 /FontInfo 7 dict dup begin
       
   721 /version (1.0) readonly def
       
   722 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
   723 /FullName (CMR7) readonly def
       
   724 /FamilyName (Computer Modern) readonly def
       
   725 /Weight (Medium) readonly def
       
   726 /ItalicAngle 0 def
       
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   728 end readonly def
       
   729 /FontName /CMR7 def
       
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   732 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
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   737 /FontBBox{-27 -250 1122 750}readonly def
       
   738 /UniqueID 5000790 def
       
   739 currentdict end
       
   740 currentfile eexec
       
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   769 985CC3604A2BE0A8235CC895B2B33CB7EE85FE4F2CD817BAC3D27ADD295D0A0E
       
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   783 %%EndFont 
       
   784 %%BeginFont: MSAM10
       
   785 %!PS-AdobeFont-1.1: MSAM10 2.1
       
   786 %%CreationDate: 1993 Sep 17 09:05:00
       
   787 % Math Symbol fonts were designed by the American Mathematical Society.
       
   788 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
   789 11 dict begin
       
   790 /FontInfo 7 dict dup begin
       
   791 /version (2.1) readonly def
       
   792 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
   793 /FullName (MSAM10) readonly def
       
   794 /FamilyName (Euler) readonly def
       
   795 /Weight (Medium) readonly def
       
   796 /ItalicAngle 0 def
       
   797 /isFixedPitch false def
       
   798 end readonly def
       
   799 /FontName /MSAM10 def
       
   800 /PaintType 0 def
       
   801 /FontType 1 def
       
   802 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
   803 /Encoding 256 array
       
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   805 dup 112 /rightanglenw put
       
   806 dup 113 /rightanglene put
       
   807 readonly def
       
   808 /FontBBox{8 -463 1331 1003}readonly def
       
   809 /UniqueID 5031981 def
       
   810 currentdict end
       
   811 currentfile eexec
       
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   813 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
       
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   842 FAFDB97FE4AF68181830374250C74EFD812447FFDAB011E6E6DBAF774770C7E8
       
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   856 %%EndFont 
       
   857 %%BeginFont: TeX-cmex9
       
   858 %!PS-AdobeFont-1.0: TeX-cmex9 001.001
       
   859 % Filtered by type1fix.pl 0.05
       
   860 %%EndComments
       
   861 13 dict dup begin
       
   862 /FontInfo 16 dict dup begin
       
   863 /Copyright (see\040copyright\040of\040original\040TeX\040font) def
       
   864 /FamilyName (TeX\040cmex9) def
       
   865 /FullName (TeX\040cmex9\040Regular) def
       
   866 /ItalicAngle 0 def
       
   867 /Notice (converted\040after\040April\0402001) def
       
   868 /UnderlinePosition -100 def
       
   869 /UnderlineThickness 50 def
       
   870 /Weight (Regular) def
       
   871 /isFixedPitch false def
       
   872 /version (001.001) def
       
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   882 /FontBBox {-26 -2961 1503 773} readonly def
       
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   884 currentdict end
       
   885 currentfile eexec
       
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   921 cleartomark
       
   922 %%EndFont 
       
   923 %%BeginFont: CMSS9
       
   924 %!PS-AdobeFont-1.1: CMSS9 1.0
       
   925 %%CreationDate: 1991 Aug 20 17:34:24
       
   926 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
   927 11 dict begin
       
   928 /FontInfo 7 dict dup begin
       
   929 /version (1.0) readonly def
       
   930 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
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   932 /FamilyName (Computer Modern) readonly def
       
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   935 /isFixedPitch false def
       
   936 end readonly def
       
   937 /FontName /CMSS9 def
       
   938 /PaintType 0 def
       
   939 /FontType 1 def
       
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   947 currentdict end
       
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   997 %%EndFont 
       
   998 %%BeginFont: CMBX10
       
   999 %!PS-AdobeFont-1.1: CMBX10 1.00B
       
  1000 %%CreationDate: 1992 Feb 19 19:54:06
       
  1001 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  1002 11 dict begin
       
  1003 /FontInfo 7 dict dup begin
       
  1004 /version (1.00B) readonly def
       
  1005 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  1006 /FullName (CMBX10) readonly def
       
  1007 /FamilyName (Computer Modern) readonly def
       
  1008 /Weight (Bold) readonly def
       
  1009 /ItalicAngle 0 def
       
  1010 /isFixedPitch false def
       
  1011 end readonly def
       
  1012 /FontName /CMBX10 def
       
  1013 /PaintType 0 def
       
  1014 /FontType 1 def
       
  1015 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
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  1020 /FontBBox{-301 -250 1164 946}readonly def
       
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  1313 cleartomark
       
  1314 %%EndFont 
       
  1315 %%BeginFont: CMSS10
       
  1316 %!PS-AdobeFont-1.1: CMSS10 1.0
       
  1317 %%CreationDate: 1991 Aug 20 17:33:34
       
  1318 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  1319 11 dict begin
       
  1320 /FontInfo 7 dict dup begin
       
  1321 /version (1.0) readonly def
       
  1322 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  1323 /FullName (CMSS10) readonly def
       
  1324 /FamilyName (Computer Modern) readonly def
       
  1325 /Weight (Medium) readonly def
       
  1326 /ItalicAngle 0 def
       
  1327 /isFixedPitch false def
       
  1328 end readonly def
       
  1329 /FontName /CMSS10 def
       
  1330 /PaintType 0 def
       
  1331 /FontType 1 def
       
  1332 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
  1333 /Encoding 256 array
       
  1334 0 1 255 {1 index exch /.notdef put} for
       
  1335 dup 0 /.notdef put
       
  1336 readonly def
       
  1337 /FontBBox{-61 -250 999 759}readonly def
       
  1338 /UniqueID 5000803 def
       
  1339 currentdict end
       
  1340 currentfile eexec
       
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  1423 cleartomark
       
  1424 %%EndFont 
       
  1425 %%BeginFont: CMTI10
       
  1426 %!PS-AdobeFont-1.1: CMTI10 1.00B
       
  1427 %%CreationDate: 1992 Feb 19 19:56:16
       
  1428 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  1429 11 dict begin
       
  1430 /FontInfo 7 dict dup begin
       
  1431 /version (1.00B) readonly def
       
  1432 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  1433 /FullName (CMTI10) readonly def
       
  1434 /FamilyName (Computer Modern) readonly def
       
  1435 /Weight (Medium) readonly def
       
  1436 /ItalicAngle -14.04 def
       
  1437 /isFixedPitch false def
       
  1438 end readonly def
       
  1439 /FontName /CMTI10 def
       
  1440 /PaintType 0 def
       
  1441 /FontType 1 def
       
  1442 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
  1443 /Encoding 256 array
       
  1444 0 1 255 {1 index exch /.notdef put} for
       
  1445 dup 0 /.notdef put
       
  1446 readonly def
       
  1447 /FontBBox{-163 -250 1146 969}readonly def
       
  1448 /UniqueID 5000828 def
       
  1449 currentdict end
       
  1450 currentfile eexec
       
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  1781 cleartomark
       
  1782 %%EndFont 
       
  1783 %%BeginFont: CMBX12
       
  1784 %!PS-AdobeFont-1.1: CMBX12 1.0
       
  1785 %%CreationDate: 1991 Aug 20 16:34:54
       
  1786 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  1787 11 dict begin
       
  1788 /FontInfo 7 dict dup begin
       
  1789 /version (1.0) readonly def
       
  1790 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  1791 /FullName (CMBX12) readonly def
       
  1792 /FamilyName (Computer Modern) readonly def
       
  1793 /Weight (Bold) readonly def
       
  1794 /ItalicAngle 0 def
       
  1795 /isFixedPitch false def
       
  1796 end readonly def
       
  1797 /FontName /CMBX12 def
       
  1798 /PaintType 0 def
       
  1799 /FontType 1 def
       
  1800 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
  1801 /Encoding 256 array
       
  1802 0 1 255 {1 index exch /.notdef put} for
       
  1803 dup 0 /.notdef put
       
  1804 readonly def
       
  1805 /FontBBox{-53 -251 1139 750}readonly def
       
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  1807 currentdict end
       
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  2042 cleartomark
       
  2043 %%EndFont 
       
  2044 %%BeginFont: CMBX9
       
  2045 %!PS-AdobeFont-1.1: CMBX9 1.0
       
  2046 %%CreationDate: 1991 Aug 20 16:36:25
       
  2047 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  2048 11 dict begin
       
  2049 /FontInfo 7 dict dup begin
       
  2050 /version (1.0) readonly def
       
  2051 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  2052 /FullName (CMBX9) readonly def
       
  2053 /FamilyName (Computer Modern) readonly def
       
  2054 /Weight (Bold) readonly def
       
  2055 /ItalicAngle 0 def
       
  2056 /isFixedPitch false def
       
  2057 end readonly def
       
  2058 /FontName /CMBX9 def
       
  2059 /PaintType 0 def
       
  2060 /FontType 1 def
       
  2061 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
  2062 /Encoding 256 array
       
  2063 0 1 255 {1 index exch /.notdef put} for
       
  2064 dup 0 /.notdef put
       
  2065 readonly def
       
  2066 /FontBBox{-58 -250 1195 750}readonly def
       
  2067 /UniqueID 5000767 def
       
  2068 currentdict end
       
  2069 currentfile eexec
       
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  2259 cleartomark
       
  2260 %%EndFont 
       
  2261 %%BeginFont: CMTT9
       
  2262 %!PS-AdobeFont-1.1: CMTT9 1.0
       
  2263 %%CreationDate: 1991 Aug 20 16:46:24
       
  2264 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  2265 11 dict begin
       
  2266 /FontInfo 7 dict dup begin
       
  2267 /version (1.0) readonly def
       
  2268 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  2269 /FullName (CMTT9) readonly def
       
  2270 /FamilyName (Computer Modern) readonly def
       
  2271 /Weight (Medium) readonly def
       
  2272 /ItalicAngle 0 def
       
  2273 /isFixedPitch true def
       
  2274 end readonly def
       
  2275 /FontName /CMTT9 def
       
  2276 /PaintType 0 def
       
  2277 /FontType 1 def
       
  2278 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
  2279 /Encoding 256 array
       
  2280 0 1 255 {1 index exch /.notdef put} for
       
  2281 dup 0 /.notdef put
       
  2282 readonly def
       
  2283 /FontBBox{-6 -233 542 698}readonly def
       
  2284 /UniqueID 5000831 def
       
  2285 currentdict end
       
  2286 currentfile eexec
       
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  2441 cleartomark
       
  2442 %%EndFont 
       
  2443 %%BeginFont: CMR9
       
  2444 %!PS-AdobeFont-1.1: CMR9 1.0
       
  2445 %%CreationDate: 1991 Aug 20 16:39:59
       
  2446 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  2447 11 dict begin
       
  2448 /FontInfo 7 dict dup begin
       
  2449 /version (1.0) readonly def
       
  2450 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  2451 /FullName (CMR9) readonly def
       
  2452 /FamilyName (Computer Modern) readonly def
       
  2453 /Weight (Medium) readonly def
       
  2454 /ItalicAngle 0 def
       
  2455 /isFixedPitch false def
       
  2456 end readonly def
       
  2457 /FontName /CMR9 def
       
  2458 /PaintType 0 def
       
  2459 /FontType 1 def
       
  2460 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
  2461 /Encoding 256 array
       
  2462 0 1 255 {1 index exch /.notdef put} for
       
  2463 dup 0 /.notdef put
       
  2464 readonly def
       
  2465 /FontBBox{-39 -250 1036 750}readonly def
       
  2466 /UniqueID 5000792 def
       
  2467 currentdict end
       
  2468 currentfile eexec
       
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  2882 cleartomark
       
  2883 %%EndFont 
       
  2884 %%BeginFont: CMR10
       
  2885 %!PS-AdobeFont-1.1: CMR10 1.00B
       
  2886 %%CreationDate: 1992 Feb 19 19:54:52
       
  2887 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
       
  2888 11 dict begin
       
  2889 /FontInfo 7 dict dup begin
       
  2890 /version (1.00B) readonly def
       
  2891 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
       
  2892 /FullName (CMR10) readonly def
       
  2893 /FamilyName (Computer Modern) readonly def
       
  2894 /Weight (Medium) readonly def
       
  2895 /ItalicAngle 0 def
       
  2896 /isFixedPitch false def
       
  2897 end readonly def
       
  2898 /FontName /CMR10 def
       
  2899 /PaintType 0 def
       
  2900 /FontType 1 def
       
  2901 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
       
  2902 /Encoding 256 array
       
  2903 0 1 255 {1 index exch /.notdef put} for
       
  2904 dup 0 /.notdef put
       
  2905 readonly def
       
  2906 /FontBBox{-251 -250 1009 969}readonly def
       
  2907 /UniqueID 5000793 def
       
  2908 currentdict end
       
  2909 currentfile eexec
       
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  4017 %%EndProlog
       
  4018 %%BeginSetup
       
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  4020 TeXDict begin
       
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  4022  end
       
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  4024 %%Page: 1 1
       
  4025 TeXDict begin 1 0 bop 582 448 a FC(\013)p FB(Prolog)r(:)45
       
  4026 b(A)f(Logic)h(Programming)h(Language)g(with)932 598 y(Names,)h(Binding)
       
  4027 d(and)h FC(\013)p FB(-Equiv)-7 b(alence)1344 886 y FA(James)27
       
  4028 b(Cheney)1865 856 y Fz(1)1902 886 y FA(,)h(Christian)f(Urban)2547
       
  4029 856 y Fz(2)1147 1029 y Fy(1)1220 1060 y Fx(Cornell)g(Univ)n(ersit)n(y)d
       
  4030 (\()p Fw(jcheney@cs.cornell.edu)p Fx(\))1121 1120 y Fy(2)1194
       
  4031 1152 y Fx(Univ)n(ersit)n(y)g(of)j(Cam)n(bridge)f(\()p
       
  4032 Fw(cu200@cl.cam.ac.uk)p Fx(\))759 1470 y Fv(Abstract.)43
       
  4033 b Fx(There)25 b(are)h(t)n(w)n(o)g(w)n(ell-kno)n(wn)g(approac)n(hes)g
       
  4034 (to)g(programming)g(with)759 1562 y(names,)d(binding,)f(and)g(equiv)l
       
  4035 (alence)f(up)h(to)g(consisten)n(t)g(renaming:)h(represen)n(ting)759
       
  4036 1653 y(names)f(and)f(bindings)g(as)h(concrete)g(iden)n(ti\014ers)g(in)f
       
  4037 (a)g(\014rst-order)h(language)g(\(suc)n(h)759 1744 y(as)f(Prolog\),)h
       
  4038 (or)e(enco)r(ding)h(names)f(and)g(bindings)f(as)i(v)l(ariables)g(and)e
       
  4039 (abstractions)759 1836 y(in)24 b(a)g(higher-order)f(language)i(\(suc)n
       
  4040 (h)e(as)h Fu(\025)p Fx(Prolog\).)h(Ho)n(w)n(ev)n(er,)f(b)r(oth)f
       
  4041 (approac)n(hes)759 1927 y(ha)n(v)n(e)i(dra)n(wbac)n(ks:)h(the)f(former)
       
  4042 h(often)g(in)n(v)n(olv)n(es)f(stateful)h(name-generation)g(and)759
       
  4043 2018 y(requires)h(man)n(ual)g(de\014nitions)f(for)i Fu(\013)p
       
  4044 Fx(-equiv)l(alence)e(and)g(capture-a)n(v)n(oiding)g(sub-)759
       
  4045 2110 y(stitution,)31 b(and)f(the)g(latter)h(is)f(seman)n(tically)i(v)n
       
  4046 (ery)d(complicated,)j(so)e(reasoning)759 2201 y(ab)r(out)21
       
  4047 b(programs)h(written)f(using)g(either)f(approac)n(h)h(can)g(b)r(e)f(v)n
       
  4048 (ery)g(di\016cult.)h(Gab-)759 2292 y(ba)n(y)j(and)g(Pitts)h(ha)n(v)n(e)
       
  4049 f(dev)n(elop)r(ed)g(a)g(new)h(approac)n(h)f(to)h(enco)r(ding)g
       
  4050 (abstract)g(syn-)759 2384 y(tax)31 b(with)g(binding)g(based)g(on)g
       
  4051 (primitiv)n(e)g(op)r(erations)i(of)e(name-sw)n(apping)h(and)759
       
  4052 2475 y(freshness.)h(This)g(pap)r(er)e(presen)n(ts)h Fu(\013)p
       
  4053 Fx(Prolog)r(,)g(a)g(logic)h(programming)g(language)759
       
  4054 2566 y(that)20 b(uses)g(this)g(approac)n(h,)h(along)g(with)f(sev)n
       
  4055 (eral)h(illustrativ)n(e)f(example)g(programs)759 2658
       
  4056 y(and)26 b(an)f(op)r(erational)j(seman)n(tics.)523 2930
       
  4057 y Ft(1)112 b(In)m(tro)s(duction)523 3121 y FA(Names,)32
       
  4058 b(binding,)h Fs(\013)p FA(-equiv)-5 b(alence,)33 b(and)f(capture-a)n(v)
       
  4059 n(oiding)e(substitution)j(are)f(endemic)523 3221 y(phenomena)24
       
  4060 b(in)h(logics)f(and)h(programming)d(languages.)h(The)i(related)f
       
  4061 (concepts)g(of)h(name)523 3320 y(freshness,)f(fresh)g(name)h
       
  4062 (generation)e(and)h(equiv)-5 b(alence)24 b(up)h(to)g(consisten)n(t)f
       
  4063 (renaming)f(also)523 3420 y(app)r(ear)36 b(in)h(man)n(y)g(other)f
       
  4064 (domains,)h(including)g(state)g(iden)n(ti\014ers)f(in)h(\014nite)h
       
  4065 (automata,)523 3520 y(nonces)25 b(in)h(securit)n(y)e(proto)r(cols,)g
       
  4066 (and)h(c)n(hannel)g(names)g(in)h(pro)r(cess)e(calculi.)h(Dealing)g
       
  4067 (with)523 3619 y(names)33 b(is)g(therefore)f(an)h(imp)r(ortan)n(t)g
       
  4068 (practical)f(problem)g(in)i(meta-programming,)c(and)523
       
  4069 3719 y(there)f(are)g(a)g(v)-5 b(ariet)n(y)29 b(of)g(approac)n(hes)f(to)
       
  4070 h(doing)g(so,)g(in)n(v)n(olving)f(di\013eren)n(t)i(tradeo\013s)f([3,)13
       
  4071 b(4,)523 3819 y(9,)g(12,)g(15,)g(18,)g(21,)g(24])24 b(.)h(The)g(follo)n
       
  4072 (wing)e(are)h(imp)r(ortan)n(t)g(desiderata)g(for)g(suc)n(h)g(tec)n
       
  4073 (hniques:)581 3975 y Fr(\017)41 b Fq(Convenienc)l(e)6
       
  4074 b FA(:)43 b(Basic)d(op)r(erations)h(including)g(substitution,)h
       
  4075 Fs(\013)p FA(-equiv)-5 b(alence,)41 b(and)664 4075 y(fresh)28
       
  4076 b(name)f(generation)f(should)h(b)r(e)h(built-in.)581
       
  4077 4172 y Fr(\017)41 b Fq(Simplicity)7 b FA(:)29 b(The)f(seman)n(tics)e
       
  4078 (of)h(the)g(meta-language)e(should)i(b)r(e)h(as)e(simple)h(as)g(p)r
       
  4079 (os-)664 4272 y(sible)h(in)g(order)e(to)h(facilitate)h(reasoning)e(ab)r
       
  4080 (out)h(programs.)581 4370 y Fr(\017)41 b Fq(A)n(bstr)l(action)6
       
  4081 b FA(:)32 b(Lo)n(w-lev)n(el)e(implemen)n(tation)i(details)f(concerning)
       
  4082 g(names)g(should)h(b)r(e)664 4469 y(tak)n(en)27 b(care)g(of)g(b)n(y)h
       
  4083 (the)g(meta-language)d(and)i(hidden)i(from)e(the)h(programmer.)581
       
  4084 4567 y Fr(\017)41 b Fq(F)-6 b(aithfulness/A)l(de)l(quacy)7
       
  4085 b FA(:)32 b(Ob)5 b(ject)29 b(terms)g(should)g(b)r(e)h(in)f(bijectiv)n
       
  4086 (e)h(corresp)r(ondence)664 4666 y(with)e(the)g(v)-5 b(alues)27
       
  4087 b(of)h(some)f(meta-language)f(t)n(yp)r(e.)523 4825 y(In)h
       
  4088 Fq(\014rst-or)l(der)i(abstr)l(act)g(syntax)37 b FA(\(F)n(O)n(AS\),)27
       
  4089 b(ob)5 b(ject)26 b(languages)f(are)h(enco)r(ded)h(using)g(\014rst-)523
       
  4090 4924 y(order)32 b(terms)h(\(e.g.)h(Prolog)d(terms)i(or)g(ML)h(datat)n
       
  4091 (yp)r(es\).)f(Names)g(are)g(enco)r(ded)g(using)g(a)p
       
  4092 eop end
       
  4093 %%Page: 2 2
       
  4094 TeXDict begin 2 1 bop 523 448 a FA(concrete)25 b(datat)n(yp)r(e)g
       
  4095 Fs(v)s(ar)i FA(suc)n(h)e(as)g(strings,)g(and)g(binders)g(are)g(enco)r
       
  4096 (ded)g(using)g(\014rst-order)523 548 y(function)k(sym)n(b)r(ols)e(lik)n
       
  4097 (e)g Fs(lam)e Fp(:)f Fs(v)s(ar)d Fr(\002)d Fs(exp)23
       
  4098 b Fr(!)g Fs(exp)p FA(.)28 b(F)n(O)n(AS)f(has)h(sev)n(eral)e(disadv)-5
       
  4099 b(an)n(tages:)523 648 y(the)32 b(enco)r(ding)f(do)r(es)g(not)h(resp)r
       
  4100 (ect)f Fs(\013)p FA(-equiv)-5 b(alence,)31 b(damaging)f(adequacy;)g
       
  4101 (fresh)h(names)523 747 y(are)k(often)h(generated)f(using)g
       
  4102 (side-e\013ects,)h(complicating)f(the)h(seman)n(tics;)g(and)f(op)r
       
  4103 (era-)523 847 y(tions)e(lik)n(e)f Fs(\013)p FA(-equiv)-5
       
  4104 b(alence)32 b(and)h(substitution)g(m)n(ust)g(b)r(e)h(implemen)n(ted)f
       
  4105 (man)n(ually)f(\(and)523 946 y(painstakingly\).)g(Nameless)h(enco)r
       
  4106 (dings)g(lik)n(e)f(de)i(Bruijn)f(indices)g([3])g(ameliorate)f(some,)523
       
  4107 1046 y(but)c(not)g(all,)f(of)h(these)f(problems.)648
       
  4108 1169 y(In)32 b Fq(higher-or)l(der)k(abstr)l(act)e(syntax)41
       
  4109 b FA(\(HO)n(AS\))33 b([18],)e(ob)5 b(ject)32 b(languages)e(are)h(enco)r
       
  4110 (ded)523 1268 y(using)24 b(higher-order)d(terms)j(\(e.g.)g
       
  4111 Fs(\025)p FA(-terms)g(in)g Fs(\025)p FA(Prolog)f([16]\).)g(In)h(HO)n
       
  4112 (AS,)h(names)e(are)g(en-)523 1368 y(co)r(ded)30 b(as)e(meta-language)g
       
  4113 (v)-5 b(ariables)28 b(and)i(binders)f(are)f(enco)r(ded)i(with)g
       
  4114 (meta-language)523 1468 y Fs(\025)p FA(-abstraction)k(using)h
       
  4115 (higher-order)e(function)j(sym)n(b)r(ols)f(lik)n(e)g
       
  4116 Fs(lam)i Fp(:)f(\()p Fs(exp)g Fr(!)g Fs(exp)p Fp(\))g
       
  4117 Fr(!)523 1567 y Fs(exp)p FA(.)21 b(Capture-a)n(v)n(oiding)e
       
  4118 (substitution)j(and)f Fs(\013)p FA(-equiv)-5 b(alence)22
       
  4119 b(need)f(only)g(b)r(e)h(implemen)n(ted)523 1667 y(once,)27
       
  4120 b(in)i(the)f(meta-language,)e(and)h(can)h(b)r(e)g(inherited)g(b)n(y)g
       
  4121 (all)f(ob)5 b(ject)28 b(languages.)e(Ho)n(w-)523 1767
       
  4122 y(ev)n(er,)37 b(b)r(ecause)i(of)f(the)h(presence)e(of)i(t)n(yp)r(es)f
       
  4123 (lik)n(e)g Fs(exp)g FA(that)h(are)e(de\014ned)i(via)f(negativ)n(e)523
       
  4124 1866 y(recursion,)30 b(the)j(seman)n(tics)e(of)h(HO)n(AS)f(is)h
       
  4125 (complex)f([10])h(and)f(induction)h(principles)g(are)523
       
  4126 1966 y(di\016cult)d(to)g(dev)n(elop.)e(Moreo)n(v)n(er,)f(HO)n(AS)j
       
  4127 (cannot)f(deal)g(with)h(op)r(en)f(ob)5 b(ject)28 b(terms,)h(that)523
       
  4128 2065 y(is)34 b(terms)g(con)n(taining)f(free)h(v)-5 b(ariables.)33
       
  4129 b(In)h Fq(we)l(ak)j(HO)n(AS)43 b FA([4],)34 b(induction)g(principles)g
       
  4130 (are)523 2165 y(reco)n(v)n(ered)29 b(b)n(y)i(enco)r(ding)g(names)g
       
  4131 (using)g(a)g(concrete)f(t)n(yp)r(e)i Fs(v)s(ar)r FA(,)f(and)g(enco)r
       
  4132 (ding)g(binders)523 2265 y(enco)r(ded)e(as)f Fs(\025)p
       
  4133 FA(-abstractions)f(using)h(constructors)f(lik)n(e)h Fs(lam)e
       
  4134 Fp(:)f(\()p Fs(v)s(ar)i Fr(!)e Fs(exp)p Fp(\))f Fr(!)h
       
  4135 Fs(exp)p FA(.)j(In)523 2364 y(this)k(approac)n(h,)e Fs(\013)p
       
  4136 FA(-equiv)-5 b(alence)31 b(is)h(still)g(built-in,)g(but)g(substitution)
       
  4137 h(m)n(ust)e(b)r(e)i(de\014ned.)523 2464 y(Also,)h(w)n(eak)g(HO)n(AS)h
       
  4138 (enco)r(dings)f(ma)n(y)g(not)g(b)r(e)h(adequate)f(b)r(ecause)h(of)f
       
  4139 (the)h(presence)f(of)523 2564 y Fq(exotic)c FA(terms,)25
       
  4140 b(or)f(closed)g(terms)h(of)f(t)n(yp)r(e)i Fs(exp)e FA(whic)n(h)h(do)f
       
  4141 (not)h(corresp)r(ond)e(to)i(an)n(y)f(ob)5 b(ject)523
       
  4142 2663 y(term;)28 b(additional)f(w)n(ell-formedness)f(predicates)h(are)f
       
  4143 (needed)i(to)f(reco)n(v)n(er)f(adequacy)-7 b(.)648 2786
       
  4144 y(Recen)n(tly)g(,)29 b(Gabba)n(y)g(and)g(Pitts)h(dev)n(elop)r(ed)f(a)g
       
  4145 (no)n(v)n(el)g(approac)n(h)f(to)h(enco)r(ding)g(names)523
       
  4146 2886 y(and)36 b(binding)h([8],)f(based)f(on)h(taking)g
       
  4147 Fq(name-swapping)45 b FA(and)36 b Fq(fr)l(eshness)44
       
  4148 b FA(as)36 b(fundamen-)523 2985 y(tal)31 b(op)r(erations)e(on)h(names.)
       
  4149 g(This)h(approac)n(h)d(has)i(b)r(een)h(co)r(di\014ed)g(b)n(y)f(Pitts)h
       
  4150 (as)f(a)g(theory)523 3085 y(of)37 b(\014rst-order)f(logic)g(called)h
       
  4151 Fq(nominal)j(lo)l(gic)j FA([19],)37 b(in)g(whic)n(h)h(names)f(are)f(a)h
       
  4152 (\014rst-order)523 3184 y(abstract)c(data)h(t)n(yp)r(e)h(admitting)g
       
  4153 (only)f(sw)n(apping,)f(binding,)i(and)f(equalit)n(y)g(and)h(fresh-)523
       
  4154 3284 y(ness)29 b(testing)h(op)r(erations.)f(Ob)5 b(ject)29
       
  4155 b(language)f(v)-5 b(ariables)29 b(and)g(binding)h(can)g(b)r(e)g(enco)r
       
  4156 (ded)523 3384 y(using)35 b(names)f Fo(x)p Fs(;)14 b Fo(y)37
       
  4157 b FA(and)d Fq(name-abstr)l(actions)43 b Fo(x)p Fs(:t)p
       
  4158 FA(,)35 b(whic)n(h)g(are)f(considered)g(equal)g(up)h(to)523
       
  4159 3483 y Fs(\013)p FA(-equiv)-5 b(alence.)26 b(F)-7 b(or)25
       
  4160 b(example,)h(ob)5 b(ject)26 b(v)-5 b(ariables)24 b Fs(x)i
       
  4161 FA(and)g(binders)g Fs(\025x:t)g FA(can)g(b)r(e)g(enco)r(ded)523
       
  4162 3583 y(as)32 b(nominal)g(terms)g Fs(v)s(ar)r Fp(\()p
       
  4163 Fo(x)p Fp(\))i FA(and)e(abstractions)f Fs(lam)p Fp(\()p
       
  4164 Fo(x)p Fs(:t)p Fp(\))j FA(where)e Fs(v)s(ar)h Fp(:)e
       
  4165 Fs(id)g Fr(!)g Fs(exp)h FA(and)523 3683 y Fs(lam)24 b
       
  4166 Fp(:)f Fr(h)p Fs(id)p Fr(i)p Fs(exp)g Fr(!)g Fs(exp)p
       
  4167 FA(.)648 3805 y(W)-7 b(e)27 b(refer)f(to)i(this)f(approac)n(h)e(to)i
       
  4168 (programming)e(with)j(names)e(and)h(binding)h(as)e Fq(nom-)523
       
  4169 3905 y(inal)31 b(abstr)l(act)e(syntax)38 b FA(\(NAS\).)28
       
  4170 b(NAS)h(pro)n(vides)d Fs(\013)p FA(-equiv)-5 b(alence)27
       
  4171 b(and)h(fresh)f(name)g(gener-)523 4005 y(ation)32 b(for)g(free,)g
       
  4172 (while)h(remaining)f(seman)n(tically)f(simple,)i(requiring)e(neither)i
       
  4173 (recursiv)n(e)523 4104 y(t)n(yp)r(es)22 b(nor)g(stateful)g
       
  4174 (name-generation.)f(F)-7 b(urthermore,)21 b(names)h(are)f(su\016cien)n
       
  4175 (tly)h(abstract)523 4204 y(that)30 b(the)g(lo)n(w-lev)n(el)e(details)i
       
  4176 (of)f(name)h(generation)e(can)i(b)r(e)g(hidden)g(from)f(the)h(program-)
       
  4177 523 4303 y(mer,)g(and)h(exotic)f(terms)h(are)e(not)i(p)r(ossible)f(in)h
       
  4178 (NAS)h(enco)r(dings.)e(Ho)n(w)n(ev)n(er,)f(names)h(are)523
       
  4179 4403 y(still)40 b(su\016cien)n(tly)g(concrete)e(that)i(there)g(is)f(no)
       
  4180 g(problem)h(w)n(orking)d(with)k(op)r(en)e(terms.)523
       
  4181 4503 y(Therefore)26 b(NAS)j(mak)n(es)d(p)r(ossible)i(a)f(distinctiv)n
       
  4182 (e)g(new)h(st)n(yle)f(of)h(meta-programming.)648 4625
       
  4183 y(This)36 b(pap)r(er)g(presen)n(ts)g Fs(\013)p FA(Prolog)m(,)h(a)f
       
  4184 (logic)g(programming)e(language)h(based)g(on)i(the)523
       
  4185 4725 y(Horn)g(clause)g(fragmen)n(t)g(of)g(nominal)g(logic)g(whic)n(h)h
       
  4186 (supp)r(orts)f(nominal)g(abstract)g(syn-)523 4825 y(tax.)c(In)g(the)g
       
  4187 (rest)f(of)h(this)g(pap)r(er,)g(w)n(e)f(describ)r(e)h
       
  4188 Fs(\013)p FA(Prolog)n(,)g(and)g(discuss)f(its)h(uni\014cation)523
       
  4189 4924 y(and)i(constrain)n(t)f(solving)f(algorithm)h(\(due)i(to)e(Urban,)
       
  4190 h(Pitts,)g(and)g(Gabba)n(y)f([25]\))g(and)p eop end
       
  4191 %%Page: 3 3
       
  4192 TeXDict begin 3 2 bop 523 448 a FA(op)r(erational)24
       
  4193 b(seman)n(tics.)g(W)-7 b(e)25 b(also)f(discuss)h(an)f(imp)r(ortan)n(t)h
       
  4194 (op)r(en)g(issue:)g(our)f(curren)n(t)g(im-)523 548 y(plemen)n(tation)31
       
  4195 b(is)f(incomplete,)h(b)r(ecause)g(complete)f(pro)r(of)g(searc)n(h)g(in)
       
  4196 h Fs(\013)p FA(Prolog)d(requires)523 648 y(solving)d
       
  4197 Fq(e)l(quivariant)30 b(uni\014c)l(ation)j FA(problems,)26
       
  4198 b(whic)n(h)g(are)f Fn(NP)p FA(-complete)h(in)h(general)e([2].)523
       
  4199 747 y(Ho)n(w)n(ev)n(er,)33 b(this)i(problem)f(can)h(often)g(b)r(e)g(a)n
       
  4200 (v)n(oided,)f(and)g(w)n(e)h(giv)n(e)f(sev)n(eral)f(examples)h(of)523
       
  4201 847 y(in)n(teresting)27 b(languages)f(and)i(relations)f(that)h(can)f(b)
       
  4202 r(e)i(enco)r(ded)f(using)f(NAS)i(in)f Fs(\013)p FA(Prolog)n(.)523
       
  4203 946 y(W)-7 b(e)28 b(conclude)f(with)h(a)g(discussion)e(of)i(related)f
       
  4204 (languages)f(and)h(future)h(w)n(ork.)523 1203 y Ft(2)112
       
  4205 b(Syn)m(tax)523 1394 y FA(The)19 b(term)g(language)f(of)h
       
  4206 Fs(\013)p FA(Prolog)e(consists)h(of)h Fq(\(nominal\))j(terms)p
       
  4207 FA(,)d(constructed)g(according)523 1494 y(to)28 b(the)f(grammar)1408
       
  4208 1593 y Fs(t)c Fp(::=)g Fs(X)29 b Fr(j)23 b Fo(n)g Fr(j)g
       
  4209 Fo(n)p Fs(:t)g Fr(j)h Fp(\()p Fo(n)j(m)p Fp(\))19 b Fr(\001)g
       
  4210 Fs(t)k Fr(j)g Fs(f)8 b Fp(\()p 2457 1529 30 4 v Fs(t)q
       
  4211 Fp(\))523 1736 y FA(where)40 b Fs(X)48 b FA(is)41 b(a)f
       
  4212 Fq(\(lo)l(gic\))j(variable)p FA(,)g Fs(f)50 b FA(is)41
       
  4213 b(a)f Fq(function)i(symb)l(ol)51 b FA(\(w)n(e)41 b(write)p
       
  4214 2979 1672 V 40 w Fs(t)g FA(to)g(denote)523 1836 y(a)33
       
  4215 b(\(p)r(ossibly)h(empt)n(y\))g(sequence)f Fp(\()p Fs(t)1660
       
  4216 1848 y Fz(1)1698 1836 y Fs(;)14 b(:)g(:)g(:)g(;)g(t)1913
       
  4217 1848 y Fm(n)1958 1836 y Fp(\))p FA(\),)35 b(and)f Fo(n)p
       
  4218 Fs(;)14 b Fo(m)33 b FA(are)g Fq(names)p FA(.)h(By)f(con)n(v)n(en)n
       
  4219 (tion,)523 1936 y(function)f(sym)n(b)r(ols)f(are)g(lo)n(w)n(er)f(case,)
       
  4220 h(logic)f(v)-5 b(ariables)31 b(are)f(capitalized,)h(and)h(names)f(are)
       
  4221 523 2035 y(prin)n(ted)25 b(using)f(the)h Fo(sans-serif)30
       
  4222 b FA(t)n(yp)r(eface.)24 b(W)-7 b(e)25 b(shall)f(refer)g(to)g(a)h(term)f
       
  4223 (of)h(the)g(form)f Fs(f)8 b Fp(\()p 3243 1971 V Fs(t)q
       
  4224 Fp(\))25 b FA(as)523 2135 y(an)j(atomic)f(term.)i(T)-7
       
  4225 b(erms)27 b(of)h(the)h(form)e Fo(n)p Fs(:t)h FA(are)f(called)h
       
  4226 Fq(abstr)l(actions)p FA(,)h(and)f(terms)g(of)g(the)523
       
  4227 2234 y(form)22 b Fp(\()p Fo(n)g(m)p Fp(\))7 b Fr(\001)g
       
  4228 Fs(t)23 b FA(are)e(called)g Fq(swapping)p FA(,)j(whic)n(h)e(in)n
       
  4229 (tuitiv)n(ely)g(denote)g(the)g(result)g(of)g(sw)n(apping)523
       
  4230 2334 y(names)34 b Fo(n)p Fs(;)14 b Fo(m)35 b FA(within)h
       
  4231 Fs(t)p FA(.)f(Sw)n(apping)f(tak)n(es)g(higher)g(precedence)g(than)h
       
  4232 (abstraction,)f(i.e.,)523 2434 y Fp(\()p Fo(a)39 b(b)p
       
  4233 Fp(\))25 b Fr(\001)h Fo(c)p Fs(:t)41 b Fp(=)g(\(\()p
       
  4234 Fo(a)e(b)p Fp(\))25 b Fr(\001)h Fo(c)p Fp(\))p Fs(:t)p
       
  4235 FA(.)39 b(V)-7 b(ariables)37 b(cannot)h(b)r(e)h(used)f(to)g(form)g
       
  4236 (abstractions)f(and)523 2533 y(transp)r(ositions,)26
       
  4237 b(i.e.,)i Fs(X)r(:t)g FA(and)f Fp(\()p Fs(X)35 b(Y)18
       
  4238 b Fp(\))h Fr(\001)f Fs(t)28 b FA(are)f(not)g(legal)g(terms.)648
       
  4239 2633 y Fs(\013)p FA(Prolog)33 b(has)h(a)h(ML-lik)n(e)f(p)r(olymorphic)h
       
  4240 (t)n(yp)r(e)g(system.)g(T)n(yp)r(es)g(are)f(classi\014ed)g(in)n(to)523
       
  4241 2733 y(t)n(w)n(o)23 b Fq(kinds)7 b FA(:)24 b Fn(t)m(yp)s(e)p
       
  4242 FA(,)f(the)h(kind)f(of)h(all)f(t)n(yp)r(es,)g(and)g Fn(name)p
       
  4243 2292 2733 25 4 v 30 w(t)m(yp)s(e)p FA(,)h(the)f(kind)h(of)f(t)n(yp)r
       
  4244 (es)g(inhab-)523 2832 y(ited)31 b(only)g(b)n(y)f(names.)g(T)n(yp)r(es)h
       
  4245 (classify)f(terms,)g(and)h(include)g(atomic)g(t)n(yp)r(e)g(constructor)
       
  4246 523 2932 y(applications)25 b Fs(c)p Fp(\()p Fs(\033)1099
       
  4247 2944 y Fz(1)1136 2932 y Fs(;)14 b(:)g(:)g(:)g(;)g(\033)1369
       
  4248 2944 y Fm(n)1414 2932 y Fp(\))27 b FA(as)e(w)n(ell)h(as)g(t)n(yp)r(e)g
       
  4249 (v)-5 b(ariables)25 b Fs(\013)i FA(and)f(abstraction)f(t)n(yp)r(es)h
       
  4250 Fs(:\027)5 b(\033)s FA(.)523 3031 y(In)37 b(an)g(abstraction,)f(the)h
       
  4251 (kind)g(of)g Fs(\027)42 b FA(m)n(ust)37 b(b)r(e)h Fn(name)p
       
  4252 2330 3031 V 29 w(t)m(yp)s(e)q FA(.)f(T)n(yp)r(e)g(constructor)e(and)523
       
  4253 3131 y(unin)n(terpreted)30 b(function)g(sym)n(b)r(ol)f(declarations)f
       
  4254 (are)h(of)h(the)g(form)f(as)g Fs(c)e Fp(:)g(\()p 2952
       
  4255 3083 50 4 v Fs(\024)p Fp(\))g Fr(!)g Fs(\024)3219 3101
       
  4256 y Fl(0)3271 3131 y FA(and)523 3231 y Fs(f)49 b Fp(:)41
       
  4257 b(\()p 709 3183 51 4 v Fs(\033)s Fp(\))g Fr(!)g Fs(\033)1008
       
  4258 3201 y Fl(0)1030 3231 y FA(,)d(where)g Fs(\024)g FA(and)h
       
  4259 Fs(\033)h FA(indicate)f(kinds)f(and)g(t)n(yp)r(es)g(resp)r(ectiv)n(ely)
       
  4260 -7 b(.)38 b(The)g(re-)523 3330 y(sult)32 b(t)n(yp)r(e)g(of)g(an)g(unin)
       
  4261 n(terpreted)f(function)i(sym)n(b)r(ol)e(ma)n(y)g(not)h(b)r(e)g(a)g
       
  4262 (built-in)g(t)n(yp)r(e)g(or)f(a)523 3430 y Fn(name)p
       
  4263 751 3430 25 4 v 30 w(t)m(yp)s(e)p FA(.)d(Relation)g(sym)n(b)r(ols)f
       
  4264 (are)f(declared)h(as)h Fn(pred)g Fs(p)p Fp(\()p 2523
       
  4265 3382 51 4 v Fs(\033)r Fp(\))h FA(and)e(in)n(terpreted)h(func-)523
       
  4266 3530 y(tion)39 b(sym)n(b)r(ols)g(as)g Fn(func)h Fs(f)8
       
  4267 b Fp(\()p 1446 3482 V Fs(\033)s Fp(\))43 b(=)f Fs(\033)1730
       
  4268 3499 y Fl(0)1752 3530 y FA(.)d(T)n(yp)r(e)g(abbreviations)f(can)h(b)r
       
  4269 (e)h(made)f(with)h(the)523 3629 y(declaration)25 b Fn(t)m(yp)s(e)j
       
  4270 Fs(c)p Fp(\()p 1231 3581 55 4 v Fs(\013)p Fp(\))23 b(=)g
       
  4271 Fs(\033)s FA(.)k(The)f(latter)h(three)f(declaration)g(forms)g(are)g(lo)
       
  4272 r(osely)g(based)523 3729 y(on)f(Mercury)e(syn)n(tax)h([23].)g(W)-7
       
  4273 b(e)25 b(assume)f(built-in)i(and)e(self-explanatory)f(t)n(yp)r(e)i(and)
       
  4274 g(func-)523 3828 y(tion)j(sym)n(b)r(ols)f(for)g(pairs)f(\()p
       
  4275 Fp(\()p Fs(x;)14 b(y)s Fp(\))24 b(:)f Fs(\033)e Fr(\002)d
       
  4276 Fs(\033)1840 3798 y Fl(0)1862 3828 y FA(\))28 b(and)f(lists)h(\()p
       
  4277 Fp([])p Fs(;)14 b(x)23 b Fp(::)g Fs(y)s(;)14 b Fp([)p
       
  4278 Fs(x)p Fr(j)p Fs(y)s Fp(])24 b(:)f([)p Fs(\033)s Fp(])p
       
  4279 FA(\).)648 3928 y(A)n(tomic)28 b(form)n(ulas)g Fs(A)h
       
  4280 FA(are)e(terms)h(of)h(the)g(form)f Fs(p)p Fp(\()p Fs(t)2281
       
  4281 3940 y Fz(1)2318 3928 y Fs(;)14 b(:)g(:)g(:)g(;)g(t)2533
       
  4282 3940 y Fm(n)2579 3928 y Fp(\))p FA(,)29 b(where)f Fs(p)h
       
  4283 FA(is)f(a)g Fq(r)l(elation)523 4028 y(symb)l(ol)p FA(.)k
       
  4284 Fq(Constr)l(aints)38 b Fs(C)f FA(include)31 b(freshness)f(form)n(ulas)g
       
  4285 Fs(t)e Fp(#)h Fs(u)p FA(,)i(and)g(equalit)n(y)f(form)n(ulas)523
       
  4286 4127 y Fs(t)45 b Fp(=)f Fs(u)p FA(.)d(In)g Fs(t)j Fp(#)h
       
  4287 Fs(u)p FA(,)c(the)g(term)f Fs(t)h FA(m)n(ust)g(b)r(e)g(of)f(some)g
       
  4288 (name)h(t)n(yp)r(e)f Fs(\027)50 b Fp(:)45 b Fn(name)p
       
  4289 3173 4127 25 4 v 30 w(t)m(yp)s(e)p FA(,)523 4227 y(whereas)35
       
  4290 b Fs(u)h FA(ma)n(y)f(b)r(e)h(of)g(an)n(y)f(t)n(yp)r(e;)h(in)g
       
  4291 Fs(t)h Fp(=)f Fs(u)p FA(,)g(b)r(oth)h Fs(t)f FA(and)f
       
  4292 Fs(u)h FA(m)n(ust)g(b)r(e)h(of)e(the)i(same)523 4327
       
  4293 y(t)n(yp)r(e.)26 b Fq(Go)l(als)34 b Fs(G)27 b FA(consist)f(of)g
       
  4294 (sequences)f(of)h(constrain)n(ts)f(and)h(atomic)f(form)n(ulas.)g
       
  4295 Fq(Pr)l(o)l(gr)l(am)523 4426 y(clauses)34 b FA(include)28
       
  4296 b(Horn)e(clauses)g(of)h(the)h(form)e Fs(A)e Fp(:)p Fr(\000)e
       
  4297 Fs(G)28 b FA(and)e(function-de\014nition)i(clauses)523
       
  4298 4526 y(of)j(the)g(form)g Fs(f)8 b Fp(\()p 1048 4462 30
       
  4299 4 v Fs(t)q Fp(\))29 b(=)f Fs(t)1263 4496 y Fl(0)1314
       
  4300 4526 y Fp(:)p Fr(\000)g Fs(G)p FA(,)j(whic)n(h)g(in)n(tro)r(duce)g(a)f
       
  4301 (\(conditional\))h(rewrite)f(rule)h(for)f(an)523 4625
       
  4302 y(atomic)d(term)h(with)g(an)f(in)n(terpreted)g(head)h(sym)n(b)r(ol)f
       
  4303 Fs(f)8 b FA(.)648 4725 y(By)38 b(con)n(v)n(en)n(tion,)f(constan)n(t)g
       
  4304 (sym)n(b)r(ols)h(are)f(function)i(sym)n(b)r(ols)f(applied)g(the)h(empt)
       
  4305 n(y)523 4825 y(argumen)n(t)24 b(list;)i(w)n(e)f(write)h
       
  4306 Fs(c)f FA(instead)g(of)h Fs(c)p Fp(\(\))p FA(,)g(and)f
       
  4307 Fs(c)e Fp(:)g Fs(\034)36 b FA(instead)25 b(of)h Fs(c)d
       
  4308 Fp(:)g(\(\))g Fr(!)h Fs(\034)10 b FA(.)26 b(This)f(also)523
       
  4309 4924 y(applies)j(to)h(prop)r(ositional)e(and)h(t)n(yp)r(e)h(constan)n
       
  4310 (ts.)f(W)-7 b(e)29 b(abbreviate)e(clauses)h Fs(A)d Fp(:)p
       
  4311 Fr(\000)f Fp(\(\))29 b FA(and)p eop end
       
  4312 %%Page: 4 4
       
  4313 TeXDict begin 4 3 bop 523 448 a Fs(f)8 b Fp(\()p 604
       
  4314 384 30 4 v Fs(t)q Fp(\))32 b(=)e Fs(t)824 418 y Fl(0)878
       
  4315 448 y Fp(:)p Fr(\000)h Fp(\(\))p FA(,)i(where)f Fp(\(\))h
       
  4316 FA(denotes)g(the)f(empt)n(y)h(sequence,)f(as)g Fs(A)h
       
  4317 FA(and)g Fs(f)8 b Fp(\()p 2992 384 V Fs(t)p Fp(\))32
       
  4318 b(=)f Fs(t)3212 418 y Fl(0)3234 448 y FA(.)i(W)-7 b(e)523
       
  4319 548 y(write)33 b Fs(V)18 b Fp(\()p Fr(\001)p Fp(\))35
       
  4320 b FA(and)e Fs(N)9 b Fp(\()p Fr(\001)p Fp(\))34 b FA(for)f(the)i(v)-5
       
  4321 b(ariables)32 b(or)h(names)g(of)g(a)h(term)f(or)g(form)n(ula.)g(Observ)
       
  4322 n(e)523 648 y(that)j Fs(N)9 b Fp(\()p Fr(\001)p Fp(\))37
       
  4323 b FA(includes)f(all)f(o)r(ccurrences)g(of)h(names)f(in)h
       
  4324 Fs(t)p FA(,)g(ev)n(en)g(abstracted)f(ones,)g(hence)523
       
  4325 747 y Fs(N)9 b Fp(\()p Fo(x)p Fs(:)p Fo(x)p Fp(\))29
       
  4326 b(=)f Fr(f)p Fo(x)p Fr(g)p FA(.)j(W)-7 b(e)31 b(sa)n(y)e(a)i(nominal)f
       
  4327 (term)h Fs(e)g FA(is)g Fq(gr)l(ound)39 b FA(when)31 b
       
  4328 Fs(V)18 b Fp(\()p Fs(e)p Fp(\))29 b(=)f Fr(;)p FA(;)i(names)h(ma)n(y)
       
  4329 523 847 y(app)r(ear)22 b(in)i(ground)e(terms,)i(so)e
       
  4330 Fs(f)8 b Fp(\()p Fs(X)r(;)14 b(Y)20 b Fp(\))j FA(is)h(not)f(ground)f
       
  4331 (but)i Fs(f)8 b Fp(\()p Fo(x)p Fs(;)14 b Fo(y)q Fp(\))25
       
  4332 b FA(is.)f(W)-7 b(e)23 b(write)h Fs(V)18 b(N)9 b Fp(\()p
       
  4333 Fs(t)p Fp(\))523 946 y FA(for)27 b Fs(V)18 b Fp(\()p
       
  4334 Fs(t)p Fp(\))h Fr([)g Fs(N)9 b Fp(\()p Fs(t)p Fp(\))p
       
  4335 FA(.)523 1199 y Ft(3)112 b(Seman)m(tics)523 1386 y FA(In)32
       
  4336 b(this)h(section)f(w)n(e)f(presen)n(t)h(an)g(op)r(erational)f(seman)n
       
  4337 (tics)g(for)h Fs(\013)p FA(Prolog)e(programs.)g(W)-7
       
  4338 b(e)523 1485 y(describ)r(e)25 b(the)g(equalit)n(y)g(and)g(freshness)f
       
  4339 (theory)h(of)g(nominal)g(logic,)f(nominal)h(uni\014cation,)523
       
  4340 1585 y(and)32 b Fs(\013)p FA(Prolog)n('s)g(execution)h(algorithm,)e
       
  4341 (emphasizing)h(the)g(main)h(no)n(v)n(elties)e(relativ)n(e)g(to)523
       
  4342 1685 y(standard)c(uni\014cation)g(and)h(logic)e(programming)g
       
  4343 (execution.)523 1921 y Fn(3.1)95 b(Equalit)m(y)-8 b(,)31
       
  4344 b(freshness,)g(and)h(uni\014cation)523 2074 y FA(Figure)e(1)g(sho)n(ws)
       
  4345 g(the)h(axioms)f(of)g(equalit)n(y)h(and)f(freshness)g(for)g(ground)g
       
  4346 (nominal)g(terms)523 2173 y(\(based)39 b(on)f([19,)13
       
  4347 b(25]\).)39 b(The)g(sw)n(apping)f(axioms)g Fp(\()p Fs(S)2198
       
  4348 2185 y Fz(1)2235 2173 y Fp(\))p FA({)p Fp(\()p Fs(S)2392
       
  4349 2185 y Fz(5)2429 2173 y Fp(\))i FA(describ)r(e)e(the)h(b)r(eha)n(vior)f
       
  4350 (of)523 2273 y(sw)n(apping.)28 b(F)-7 b(rom)30 b(no)n(w)e(on,)i(w)n(e)f
       
  4351 (assume)f(that)i(all)f(terms)g(are)g(normalized)f(with)i(resp)r(ect)523
       
  4352 2373 y(to)21 b(these)g(axioms)g(\(read)f(righ)n(t-to-left)h(as)f
       
  4353 (rewrite)h(rules\),)g(so)f(that)i(sw)n(aps)e(are)g(not)i(presen)n(t)523
       
  4354 2472 y(in)f(ground)f(terms)h(and)g(are)f(presen)n(t)g(only)h
       
  4355 (surrounding)f(v)-5 b(ariables)19 b(in)j(non-ground)d(terms.)648
       
  4356 2572 y(The)34 b(next)g(t)n(w)n(o)f(axioms)g Fp(\()p Fs(A)1560
       
  4357 2584 y Fz(1)1598 2572 y Fp(\))p FA(,)i Fp(\()p Fs(A)1781
       
  4358 2584 y Fz(2)1819 2572 y Fp(\))f FA(de\014ne)g(equalit)n(y)g(for)g
       
  4359 (abstractions.)e(The)i(\014rst)523 2672 y(axiom)24 b(is)g(a)g(simple)g
       
  4360 (congruence)f(prop)r(ert)n(y)-7 b(.)24 b(The)g(second)g(guaran)n(tees)e
       
  4361 (that)j(abstractions)523 2771 y(are)19 b(equal)g(\\up)g(to)g
       
  4362 (renaming".)g(Tw)n(o)f(abstractions)g(of)i(di\013eren)n(t)f(names)h
       
  4363 Fo(x)p Fs(:t;)14 b Fo(y)q Fs(:u)20 b FA(are)f(equal)523
       
  4364 2871 y(just)h(in)g(case)e(their)i(b)r(o)r(dies)f(are)g(equal)g(up)h(to)
       
  4365 f(sw)n(apping)f(the)i(names)f(\(i.e.,)h Fs(t)j Fp(=)g(\()p
       
  4366 Fo(x)d(y)q Fp(\))r Fr(\001)r Fs(u)p Fp(\))h FA(and)523
       
  4367 2970 y Fo(x)i FA(do)r(es)g(not)g(app)r(ear)e(free)i(in)g
       
  4368 Fs(u)g FA(\(i..e.,)g Fo(x)h Fp(#)f Fs(u)p FA(\))g(Symmetrically)-7
       
  4369 b(,)23 b(it)g(su\016ces)g(to)f(c)n(hec)n(k)g Fo(y)j Fp(#)e
       
  4370 Fs(t)p FA(;)523 3070 y(the)32 b(t)n(w)n(o)g(conditions)f(are)g(equiv)-5
       
  4371 b(alen)n(t)32 b(if)g Fs(t)f Fp(=)f(\()p Fo(x)i(y)q Fp(\))23
       
  4372 b Fr(\001)e Fs(u)p FA(.)32 b(F)-7 b(or)32 b(example,)f
       
  4373 Fo(x)p Fs(:g)s Fp(\()p Fo(x)p Fp(\))h(=)e Fo(y)q Fs(:g)s
       
  4374 Fp(\()p Fo(y)q Fp(\))523 3170 y FA(and)d Fo(x)p Fs(:f)8
       
  4375 b Fp(\()p Fo(x)p Fs(;)14 b Fo(y)q Fp(\))26 b(=)c Fo(z)p
       
  4376 Fs(:f)8 b Fp(\()p Fo(z)p Fs(;)14 b Fo(y)q Fp(\))p FA(,)30
       
  4377 b(but)e Fo(x)p Fs(:f)8 b Fp(\()p Fo(x)p Fs(;)14 b Fo(y)q
       
  4378 Fp(\))25 b Fr(6)p Fp(=)e Fo(y)q Fs(:f)8 b Fp(\()p Fo(y)q
       
  4379 Fs(;)14 b Fo(x)p Fp(\))30 b FA(b)r(ecause)d Fo(x)c Fp(#)g
       
  4380 Fs(f)8 b Fp(\()p Fo(y)q Fs(;)14 b Fo(x)p Fp(\))30 b FA(fails.)648
       
  4381 3269 y(The)j(freshness)f(axioms)g Fp(\()p Fs(F)1549 3281
       
  4382 y Fz(1)1587 3269 y Fp(\))p FA({\()p Fs(F)1746 3281 y
       
  4383 Fz(5)1783 3269 y Fp(\))i FA(describ)r(e)f(the)g(freshness)g(relation.)f
       
  4384 (In)n(tuitiv)n(ely)-7 b(,)523 3369 y Fo(x)29 b Fp(#)f
       
  4385 Fs(t)j FA(means)f(\\name)h Fo(x)g FA(do)r(es)f(not)h(app)r(ear)f(un)n
       
  4386 (b)r(ound)h(in)g Fs(t)p FA(".)f(F)-7 b(or)31 b(example,)f(it)h(is)g
       
  4387 (nev)n(er)523 3469 y(the)e(case)e(that)i Fo(x)c Fp(#)f
       
  4388 Fo(x)p FA(,)29 b(whereas)e(an)n(y)h(t)n(w)n(o)g(distinct)h(names)f(are)
       
  4389 f(fresh)h(\()p Fo(x)d Fr(6)p Fp(=)f Fo(y)i Fr(\))f Fo(x)g
       
  4390 Fp(#)f Fo(y)q FA(\).)523 3568 y(Moreo)n(v)n(er,)31 b(freshness)h
       
  4391 (passes)g(through)h(function)h(sym)n(b)r(ols)f(\(in)h(particular,)e(an)
       
  4392 n(y)g(name)523 3668 y(is)d(fresh)g(for)g(an)n(y)f(constan)n(t\).)h(The)
       
  4393 h(abstraction)e(freshness)g(rules)h(are)f(more)h(in)n(teresting:)523
       
  4394 3768 y Fo(x)23 b Fp(#)h Fo(x)p Fs(:t)i FA(is)h(unconditionally)e(v)-5
       
  4395 b(alid)27 b(b)r(ecause)f(an)n(y)f(name)h(is)h(fresh)f(for)f(a)h(term)h
       
  4396 (in)f(whic)n(h)h(it)523 3867 y(is)j(immediately)g(abstracted,)e
       
  4397 (whereas)h(if)h Fo(x)g FA(and)g Fo(y)h FA(are)d(di\013eren)n(t)i
       
  4398 (names,)g(then)g Fo(x)d Fp(#)f Fo(y)q Fs(:t)523 3967
       
  4399 y FA(just)i(in)g(case)f Fo(x)c Fp(#)g Fs(t)p FA(.)608
       
  4400 4302 y Fk(\()p Fu(S)685 4310 y Fy(1)719 4302 y Fk(\))j(\()p
       
  4401 Fj(n)f(m)p Fk(\))17 b Fi(\001)g Fj(n)k Fk(=)g Fj(m)77
       
  4402 b Fk(\()p Fu(S)1373 4310 y Fy(2)1407 4302 y Fk(\))26
       
  4403 b(\()p Fj(n)f(m)p Fk(\))17 b Fi(\001)g Fj(m)22 b Fk(=)f
       
  4404 Fj(n)100 b Fk(\()p Fu(S)2085 4310 y Fy(3)2119 4302 y
       
  4405 Fk(\))25 b Fj(x)d Fk(#)f Fj(n)p Fu(;)13 b Fj(x)22 b Fk(#)f
       
  4406 Fj(m)h Fi(\))f Fk(\()p Fj(n)k(m)p Fk(\))17 b Fi(\001)g
       
  4407 Fj(x)22 b Fk(=)f Fj(x)608 4394 y Fk(\()p Fu(S)685 4402
       
  4408 y Fy(4)719 4394 y Fk(\))26 b(\()p Fj(n)f(m)p Fk(\))17
       
  4409 b Fi(\001)g Fu(f)8 b Fk(\()p 1092 4336 28 4 v Fu(t)o
       
  4410 Fk(\))21 b(=)h Fu(f)8 b Fk(\(\()p Fj(n)24 b(m)p Fk(\))17
       
  4411 b Fi(\001)p 1568 4336 V 17 w Fu(t)p Fk(\))382 b(\()p
       
  4412 Fu(S)2085 4402 y Fy(5)2119 4394 y Fk(\))25 b(\()p Fj(n)g(m)p
       
  4413 Fk(\))17 b Fi(\001)h Fk(\()p Fj(x)p Fu(:t)p Fk(\))j(=)g(\()p
       
  4414 Fj(n)26 b(m)p Fk(\))16 b Fi(\001)i Fj(x)p Fu(:)p Fk(\()p
       
  4415 Fj(n)26 b(m)p Fk(\))17 b Fi(\001)g Fu(t)608 4485 y Fk(\()p
       
  4416 Fu(A)695 4493 y Fy(1)729 4485 y Fk(\))26 b Fu(t)21 b
       
  4417 Fk(=)g Fu(u)g Fi(\))g Fj(n)p Fu(:t)g Fk(=)g Fj(n)p Fu(:u)628
       
  4418 b Fk(\()p Fu(A)2095 4493 y Fy(2)2129 4485 y Fk(\))25
       
  4419 b Fu(t)c Fk(=)g(\()p Fj(n)k(m)p Fk(\))17 b Fi(\001)h
       
  4420 Fu(u)e Fi(^)i Fj(n)j Fk(#)g Fu(u)g Fi(\))g Fj(n)p Fu(:t)g
       
  4421 Fk(=)g Fj(m)p Fu(:u)608 4577 y Fk(\()p Fu(F)687 4585
       
  4422 y Fy(1)721 4577 y Fk(\))26 b Fj(n)21 b Fi(6)p Fk(=)g
       
  4423 Fj(m)g Fi(\))g Fj(n)g Fk(#)g Fj(m)77 b Fk(\()p Fu(F)1462
       
  4424 4585 y Fy(2)1496 4577 y Fk(\))26 b Fi(:)p Fk(\()p Fj(n)21
       
  4425 b Fk(#)g Fj(n)p Fk(\))159 b(\()p Fu(F)2087 4585 y Fy(3)2121
       
  4426 4577 y Fk(\))2189 4521 y Fh(V)2253 4542 y Fg(n)2253 4600
       
  4427 y(i)p Fy(=1)2369 4577 y Fj(n)21 b Fk(#)g Fu(t)2543 4585
       
  4428 y Fg(i)2591 4577 y Fi(\))g Fj(n)g Fk(#)g Fu(f)8 b Fk(\()p
       
  4429 2911 4519 V Fu(t)o Fk(\))608 4669 y(\()p Fu(F)687 4677
       
  4430 y Fy(4)721 4669 y Fk(\))26 b Fj(n)21 b Fk(#)g Fj(n)p
       
  4431 Fu(:t)996 b Fk(\()p Fu(F)2087 4677 y Fy(5)2121 4669 y
       
  4432 Fk(\))25 b Fj(n)c Fk(#)g Fj(m)c Fi(^)h Fj(n)j Fk(#)g
       
  4433 Fu(t)g Fi(\))g Fj(n)g Fk(#)h Fj(m)p Fu(:t)1163 4910 y
       
  4434 Fv(Fig.)14 b(1.)25 b Fx(Ground)g(equational)h(and)g(freshness)g(theory)
       
  4435 p eop end
       
  4436 %%Page: 5 5
       
  4437 TeXDict begin 5 4 bop 648 448 a Fq(Nominal)32 b(uni\014c)l(ation)j
       
  4438 FA(is)30 b(uni\014cation)f(of)g(nominal)g(terms)h(up)f(to)g
       
  4439 Fs(\013)p FA(-equiv)-5 b(alence)29 b(\(as)523 548 y(formalized)34
       
  4440 b(b)n(y)f(the)i(axioms)e(of)h(Figure)g(1\).)g(F)-7 b(or)34
       
  4441 b(ground)f(terms,)h(nominal)g(uni\014cation)523 648 y(coincides)19
       
  4442 b(with)i Fs(\013)p FA(-equiv)-5 b(alence:)19 b(for)h(example,)f(the)h
       
  4443 (term)g Fo(n)p Fs(:)p Fo(n)g FA(uni\014es)g(with)h Fo(m)p
       
  4444 Fs(:)p Fo(m)p FA(,)f(but)g Fo(n)p Fs(:)p Fo(m)523 747
       
  4445 y FA(and)f Fo(n)p Fs(:)p Fo(n)g FA(do)h(not)f(unify)-7
       
  4446 b(.)20 b(Ho)n(w)n(ev)n(er,)d(non-ground)h(terms)h(suc)n(h)g(as)g
       
  4447 Fo(n)p Fs(:X)26 b FA(and)19 b Fo(m)p Fs(:X)26 b FA(unify)19
       
  4448 b(only)523 847 y(sub)5 b(ject)30 b(to)g(the)g Fq(fr)l(eshness)j(c)l
       
  4449 (onstr)l(aints)j Fo(n)27 b Fp(#)g Fs(X)36 b FA(and)30
       
  4450 b Fo(m)d Fp(#)g Fs(X)7 b FA(.)30 b(A)g(freshness)f(constrain)n(t)523
       
  4451 946 y(of)23 b(the)h(form)e Fo(n)h Fp(#)h Fs(X)29 b FA(states)23
       
  4452 b(that)g Fs(X)30 b FA(ma)n(y)22 b(not)h(b)r(e)h(instan)n(tiated)f(with)
       
  4453 g(a)g(term)g(con)n(taining)523 1046 y(a)40 b(free)g(o)r(ccurrence)f(of)
       
  4454 h Fo(n)p FA(.)g(The)g(problem)g Fo(n)p Fs(:X)50 b Fr(\031)p
       
  4455 Fp(?)44 b Fo(m)p Fs(:Y)59 b FA(is)40 b(uni\014ed)h(b)n(y)e
       
  4456 (substitution)523 1146 y Fs(X)31 b Fp(=)24 b(\()p Fo(n)29
       
  4457 b(m)p Fp(\))19 b Fr(\001)h Fs(Y)47 b FA(sub)5 b(ject)29
       
  4458 b(to)f(the)h(constrain)n(t)e Fo(n)e Fp(#)g Fs(X)7 b FA(;)28
       
  4459 b(that)h(is,)f Fs(X)35 b FA(m)n(ust)29 b(b)r(e)g(iden)n(tical)f(to)523
       
  4460 1245 y Fs(Y)49 b FA(with)31 b Fo(n)f FA(and)g Fo(m)g
       
  4461 FA(sw)n(app)r(ed,)f(and)h Fo(n)g FA(m)n(ust)h(b)r(e)f(fresh)g(for)g
       
  4462 Fs(X)7 b FA(.)29 b(The)h(nominal)g(uni\014cation)523
       
  4463 1345 y(algorithm)c(therefore)h(also)f(m)n(ust)h(solv)n(e)f(freshness)h
       
  4464 (\(or)g Fq(disuni\014c)l(ation)6 b FA(\))28 b(subproblems)f(of)523
       
  4465 1445 y(the)h(form)f Fs(t)c Fp(#?)h Fs(u)p FA(,)k(where)f
       
  4466 Fs(t)g FA(is)h(of)f(name)h(t)n(yp)r(e.)648 1546 y(Urban,)40
       
  4467 b(Pitts,)g(and)h(Gabba)n(y)e([25])h(dev)n(elop)r(ed)g(an)g(algorithm)g
       
  4468 (for)g(solving)f(nomi-)523 1646 y(nal)f(uni\014cation)h(and)f
       
  4469 (freshness)g(constrain)n(t)f(problems)h(of)g(the)h(form)f(encoun)n
       
  4470 (tered)g(in)523 1745 y Fs(\013)p FA(Prolog)n(.)30 b(A)g(mo)r(di\014ed)g
       
  4471 (form)f(of)g(this)h(algorithm)f(is)g(used)h(in)g(our)e(curren)n(t)h
       
  4472 (implemen)n(ta-)523 1845 y(tion.)21 b(F)-7 b(or)20 b(space)g(reasons,)e
       
  4473 (w)n(e)i(omit)h(a)f(fuller)h(discussion)f(of)g(the)h(details)g(of)f
       
  4474 (the)h(algorithm,)523 1944 y(and)30 b(note)h(that)f(an)n(y)g(other)g
       
  4475 (constrain)n(t)f(solving)h(pro)r(cedure)f(for)h(nominal)g(equalit)n(y)g
       
  4476 (and)523 2044 y(freshness)d(constrain)n(ts)f(could)h(b)r(e)h(used)g
       
  4477 (instead.)523 2302 y Fn(3.2)95 b(Op)s(erational)31 b(seman)m(tics)523
       
  4478 2476 y FA(W)-7 b(e)26 b(no)n(w)f(presen)n(t)g(the)h(op)r(erational)e
       
  4479 (seman)n(tics)h(of)h Fs(\013)p FA(Prolog)e(programs.)f(This)j(seman)n
       
  4480 (tics)523 2576 y(is)32 b(based)g(lo)r(osely)f(on)h(that)h(of)f
       
  4481 Fq(c)l(onstr)l(aint)h(lo)l(gic)i(pr)l(o)l(gr)l(amming)41
       
  4482 b FA([11],)31 b(o)n(v)n(er)g(the)h(domain)523 2676 y(of)e(nominal)f
       
  4483 (terms)h(as)f(axiomatized)f(in)j(Figure)e(1.)g(A)h Fq(pr)l(o)l(gr)l(am)
       
  4484 37 b FA(is)30 b(a)f(set)h Fr(P)36 b FA(of)30 b(program)523
       
  4485 2775 y(clauses,)e(closed)g(under)h(p)r(erm)n(utativ)n(e)f(renaming)g
       
  4486 (of)h(names)f(and)h(v)-5 b(ariables.)27 b(A)i Fq(pr)l(o)l(gr)l(am)523
       
  4487 2875 y(state)f FA(consists)22 b(a)g(goal)f Fs(G)i FA(and)f(a)g(set)g
       
  4488 Fr(r)h FA(of)f(equalit)n(y)g(and)g(freshness)f(constrain)n(ts;)g(w)n(e)
       
  4489 h(shall)523 2975 y(write)31 b Fr(h)p Fs(G)g Fr(j)e(ri)k
       
  4490 FA(for)e(suc)n(h)g(a)g(state.)g(An)i Fq(answer)41 b FA(to)31
       
  4491 b(this)h(query)f(is)g(a)g(set)h(of)f(constrain)n(ts)523
       
  4492 3074 y Fr(r)592 3044 y Fl(0)614 3074 y FA(.)h(W)-7 b(e)31
       
  4493 b(de\014ne)h(the)g(op)r(erational)d(seman)n(tics)i(of)g(an)g
       
  4494 Fs(\013)p FA(Prolog)e(query)i(using)g(transitions)523
       
  4495 3174 y(of)g(the)g(form)g Fr(h)p Fs(G)e Fr(j)g(ri)g(\000)-14
       
  4496 b(!)29 b(h)p Fs(G)1535 3144 y Fl(0)1586 3174 y Fr(j)g(r)1707
       
  4497 3144 y Fl(0)1729 3174 y Fr(i)i FA(and)g(write)g Fs(G)e
       
  4498 Fr(\000)-15 b(!)2400 3144 y Fl(\003)2466 3174 y Fr(r)32
       
  4499 b FA(if)f Fr(h)p Fs(G)e Fr(j)g(;i)f(\000)-14 b(!)3060
       
  4500 3144 y Fl(\003)3126 3174 y Fr(h;)29 b(j)f(ri)p FA(.)523
       
  4501 3273 y(The)g(rules)f(for)g(the)h(transitions)e(are)h(as)g(follo)n(ws:)
       
  4502 562 3438 y Fr(h)p Fs(C)q(;)14 b(G)24 b Fr(j)f(ri)100
       
  4503 b(\000)-14 b(!)23 b(h)p Fs(G)h Fr(j)f(f)p Fs(C)6 b Fr(g)18
       
  4504 b([)h(ri)135 b FA(if)28 b Fr(f)p Fs(C)6 b Fr(g)18 b([)g(r)28
       
  4505 b FA(satis\014able)562 3539 y Fr(h)p Fs(p)p Fp(\()p 669
       
  4506 3474 30 4 v Fs(t)p Fp(\))p Fs(;)14 b(G)23 b Fr(j)h(ri)f(\000)-14
       
  4507 b(!)23 b(h)p 1216 3474 V Fs(t)h Fp(=)p 1357 3491 51 4
       
  4508 v 22 w Fs(u;)14 b(G)1509 3509 y Fl(0)1532 3539 y Fs(;)g(G)23
       
  4509 b Fr(j)g(ri)h FA(if)k Fp(\()p Fs(p)p Fp(\()p 2011 3491
       
  4510 V Fs(u)p Fp(\))c(:)p Fr(\000)e Fs(G)2292 3509 y Fl(0)2315
       
  4511 3539 y Fp(\))h Fr(2)g(P)1828 3640 y FA(and)k Fs(V)18
       
  4512 b(N)9 b Fp(\()p Fs(p)p Fp(\()p 2236 3592 V Fs(u)p Fp(\))24
       
  4513 b(:)p Fr(\000)e Fs(G)2517 3610 y Fl(0)2540 3640 y Fp(\))c
       
  4514 Fr(\\)h Fs(V)f(N)9 b Fp(\()p Fs(p)p Fp(\()p 2911 3575
       
  4515 30 4 v Fs(t)p Fp(\))p Fs(;)14 b(G;)g Fr(r)p Fp(\))24
       
  4516 b(=)f Fr(;)562 3739 y(h)p Fs(G)g Fr(j)g(ri)198 b(\000)-14
       
  4517 b(!)23 b(h)p Fs(G)h Fr(j)f(r)1420 3709 y Fl(0)1442 3739
       
  4518 y Fr(i)354 b FA(if)28 b Fr(r)1973 3709 y Fl(0)2018 3739
       
  4519 y Fr(`)23 b(r)523 3926 y FA(In)30 b(the)g(last)f(rule,)h
       
  4520 Fr(r)1194 3896 y Fl(0)1242 3926 y Fr(`)d(r)i FA(is)h(constrain)n(t)e
       
  4521 (en)n(tailmen)n(t)i(in)g(the)g(theory)f(of)g(Figure)g(1;)h(this)523
       
  4522 4026 y(rule)38 b(p)r(ermits)g(constrain)n(t)g(simpli\014cation)g(via)f
       
  4523 (uni\014cation.)i(In)f Fs(\013)p FA(Prolog)n(,)g(as)g(usual)g(in)523
       
  4524 4126 y(logic)26 b(programming,)g(v)-5 b(ariables)26 b(in)h(program)f
       
  4525 (clauses)g(or)g(rewriting)h(rules)f(are)h(renamed)523
       
  4526 4225 y(to)k(new)f(v)-5 b(ariables)30 b(during)g(bac)n(k)n(c)n(haining;)
       
  4527 f(in)h(addition,)h(names)f(are)g(freshened)g(to)h(new)523
       
  4528 4325 y(names.)e(Rewriting)h(rules)f Fs(f)8 b Fp(\()p
       
  4529 1471 4261 V Fs(t)q Fp(\))26 b(=)g Fs(u)h Fp(:)p Fr(\000)f
       
  4530 Fs(G)k FA(de\014ning)g(function)g(sym)n(b)r(ols)f(are)g(translated)523
       
  4531 4424 y(to)f(a)f(clausal)f(form)i Fs(p)1206 4436 y Fm(f)1247
       
  4532 4424 y Fp(\()p 1279 4360 V Fs(t)q(;)14 b(u)p Fp(\))23
       
  4533 b(:)p Fr(\000)g Fs(G)1628 4394 y Fl(0)1678 4424 y FA(via)k
       
  4534 Fq(\015attening)p FA(,)g(as)g(in)h(man)n(y)f(Prolog)e(systems.)648
       
  4535 4526 y(It)34 b(is)f(straigh)n(tforw)n(ard)e(to)i(sho)n(w)g(that)h(our)f
       
  4536 (op)r(erational)f(seman)n(tics)h(is)g(sound)g(with)523
       
  4537 4625 y(resp)r(ect)d(to)f(an)h(appropriate)e(v)-5 b(arian)n(t)29
       
  4538 b(of)g(nominal)h(logic.)f(The)h(pro)r(of)f(of)h(this)g(fact)g(relies)
       
  4539 523 4725 y(on)41 b(the)h(soundness)e(of)i(nominal)f(uni\014cation)g
       
  4540 (for)g(nominal)g(equational)f(satis\014abilit)n(y)523
       
  4541 4825 y(\([25,)f(Thm.)h(2]\).)f(Ho)n(w)n(ev)n(er,)f(completeness)h
       
  4542 (fails,)g(b)r(ecause)g(w)n(e)h(ha)n(v)n(e)e(not)h(tak)n(en)g(in)n(to)
       
  4543 523 4924 y(accoun)n(t)33 b Fq(e)l(quivarianc)l(e)p FA(,)j(an)f(imp)r
       
  4544 (ortan)n(t)f(prop)r(ert)n(y)f(of)h(nominal)g(logic)f(that)i(guaran)n
       
  4545 (tees)p eop end
       
  4546 %%Page: 6 6
       
  4547 TeXDict begin 6 5 bop 523 448 a FA(that)41 b(v)-5 b(alidit)n(y)40
       
  4548 b(is)g(preserv)n(ed)f(b)n(y)h(name-sw)n(apping)f([19].)h(F)-7
       
  4549 b(ormally)g(,)39 b(the)i(equiv)-5 b(ariance)523 548 y(axiom)31
       
  4550 b(asserts)g(that)h Fs(p)p Fp(\()p 1307 484 30 4 v Fs(t)p
       
  4551 Fp(\))e Fr(\))h Fs(p)p Fp(\(\()p Fo(n)h(m)p Fp(\))22
       
  4552 b Fr(\001)p 1859 484 V 21 w Fs(t)p Fp(\))32 b FA(is)g(v)-5
       
  4553 b(alid)32 b(in)g(nominal)g(logic)f(for)g(an)n(y)g(atomic)523
       
  4554 648 y(form)n(ula)c Fs(p)p Fp(\()p 903 583 V Fs(t)p Fp(\))h
       
  4555 FA(and)g(names)f Fo(n)p Fs(;)14 b Fo(m)p FA(.)28 b(F)-7
       
  4556 b(or)27 b(example,)h(for)f(an)n(y)g(binary)g(relation)g
       
  4557 Fn(pred)h Fs(p)p Fp(\()p Fs(\027)q(;)14 b(\027)5 b Fp(\))523
       
  4558 747 y FA(for)24 b Fs(\027)k Fp(:)23 b Fn(name)p 991 747
       
  4559 25 4 v 30 w(t)m(yp)s(e)p FA(,)i(w)n(e)f(ha)n(v)n(e)f
       
  4560 Fs(p)p Fp(\()p Fo(x)p Fs(;)14 b Fo(y)q Fp(\))47 b Fr(\()-14
       
  4561 b(\))46 b Fs(p)p Fp(\()p Fo(y)q Fs(;)14 b Fo(z)p Fp(\))26
       
  4562 b FA(v)-5 b(alid)24 b(in)h(b)r(oth)g(directions)e(b)r(ecause)523
       
  4563 847 y(the)34 b(sw)n(apping)f Fp(\()p Fo(x)h(y)q Fp(\)\()p
       
  4564 Fo(y)j(z)p Fp(\))d FA(translates)e(b)r(et)n(w)n(een)i(them.)g(But)g
       
  4565 (man)n(y-to-one)e(renamings)523 946 y(ma)n(y)27 b(not)h(preserv)n(e)d
       
  4566 (v)-5 b(alidit)n(y:)28 b(for)f(example,)g Fo(x)d Fp(#)f
       
  4567 Fo(y)h Fr(\))f Fo(z)g Fp(#)h Fo(z)j FA(is)h(not)g(v)-5
       
  4568 b(alid.)648 1046 y(Because)21 b(of)h(equiv)-5 b(ariance,)20
       
  4569 b(bac)n(k)n(c)n(haining)g(based)i(on)g(nominal)g(uni\014cation)g(is)f
       
  4570 (incom-)523 1146 y(plete.)29 b(F)-7 b(or)27 b(example,)h(giv)n(en)g
       
  4571 (program)e(clause)i Fs(p)p Fp(\()p Fo(n)p Fp(\))h FA(where)e
       
  4572 Fo(n)i FA(is)f(a)g(name,)g(the)h(goal)e Fs(p)p Fp(\()p
       
  4573 Fo(n)p Fp(\))523 1245 y FA(cannot)f(b)r(e)h(solv)n(ed.)e(Ev)n(en)h
       
  4574 (though)g Fs(p)p Fp(\()p Fo(n)p Fp(\))e Fr(\))f Fs(p)p
       
  4575 Fp(\()p Fo(n)p Fp(\))j FA(is)h(ob)n(viously)e(v)-5 b(alid,)26
       
  4576 b(pro)r(of)g(searc)n(h)f(fails)523 1345 y(b)r(ecause)i(the)g(program)e
       
  4577 (clause)h Fs(p)p Fp(\()p Fo(n)p Fp(\))i FA(m)n(ust)f(b)r(e)g(freshened)
       
  4578 g(to)g Fs(p)p Fp(\()p Fo(n)2629 1315 y Fl(0)2651 1345
       
  4579 y Fp(\))p FA(,)h(and)e Fs(p)p Fp(\()p Fo(n)3012 1315
       
  4580 y Fl(0)3034 1345 y Fp(\))i FA(and)f Fs(p)p Fp(\()p Fo(n)p
       
  4581 Fp(\))523 1445 y FA(do)e(not)g(unify)-7 b(.)26 b(Ho)n(w)n(ev)n(er,)d(b)
       
  4582 n(y)i(equiv)-5 b(ariance)23 b(these)i(form)n(ulas)f(are)g(equiv)-5
       
  4583 b(alen)n(t)25 b(in)g(nominal)523 1544 y(logic,)i(since)g
       
  4584 Fs(p)p Fp(\()p Fo(n)1061 1514 y Fl(0)1083 1544 y Fp(\))d
       
  4585 Fr(\))f Fs(p)p Fp(\(\()p Fo(n)28 b(n)1466 1514 y Fl(0)1487
       
  4586 1544 y Fp(\))19 b Fr(\001)g Fo(n)1623 1514 y Fl(0)1645
       
  4587 1544 y Fp(\))k Fr(\))g Fs(p)p Fp(\()p Fo(n)p Fp(\))g
       
  4588 Fr(\))g Fs(p)p Fp(\(\()p Fo(n)28 b(n)2306 1514 y Fl(0)2328
       
  4589 1544 y Fp(\))19 b Fr(\001)g Fo(n)p Fp(\))k Fr(\))g Fs(p)p
       
  4590 Fp(\()p Fo(n)2743 1514 y Fl(0)2765 1544 y Fp(\))p FA(.)648
       
  4591 1644 y(This)k(can)g(b)r(e)h(\014xed)g(b)n(y)f(adding)g(a)h(transition)f
       
  4592 (rule)1291 1806 y Fr(h)p Fs(p)p Fp(\()p 1398 1741 30
       
  4593 4 v Fs(t)p Fp(\))p Fs(;)14 b(G)24 b Fr(j)f(ri)h(\000)-15
       
  4594 b(!)23 b(h)p Fs(p)p Fp(\(\()p Fo(a)29 b(b)p Fp(\))18
       
  4595 b Fr(\001)p 2256 1741 V 19 w Fs(t)p Fp(\))p Fs(;)c(G)23
       
  4596 b Fr(j)g(ri)h Fs(:)523 1967 y FA(Ho)n(w)n(ev)n(er,)31
       
  4597 b(this)i(rule)g(in)n(tro)r(duces)f(nondeterminism.)h(T)-7
       
  4598 b(o)32 b(p)r(erform)h(goal-directed)e(pro)r(of)523 2067
       
  4599 y(searc)n(h,)22 b(it)i(seems)f(preferable)f(to)i(replace)e(the)i(naiv)n
       
  4600 (e)f(bac)n(k)n(c)n(haining)e(rule)i(ab)r(o)n(v)n(e)f(with)i(one)523
       
  4601 2167 y(based)j(on)g(unifying)h(up)g(to)g(nominal)f(equalit)n(y)g(mo)r
       
  4602 (dulo)g(a)h(p)r(erm)n(utation:)755 2324 y Fr(h)p Fs(p)p
       
  4603 Fp(\()p 862 2260 V Fs(t)q Fp(\))p Fs(;)14 b(G)23 b Fr(j)g(ri)h(\000)-14
       
  4604 b(!)23 b(h)p Fs(\031)f Fr(\001)p 1522 2260 V 18 w Fs(t)h
       
  4605 Fp(=)p 1663 2276 51 4 v 23 w Fs(u;)14 b(G)1815 2294 y
       
  4606 Fl(0)1837 2324 y Fs(;)g(G)23 b Fr(j)g(ri)921 2425 y FA(if)28
       
  4607 b Fp(\()p Fs(p)p Fp(\()p 1104 2377 V Fs(u)q Fp(\))23
       
  4608 b(:)p Fr(\000)g Fs(G)1386 2395 y Fl(0)1408 2425 y Fp(\))g
       
  4609 Fr(2)h(P)34 b FA(and)28 b Fs(V)18 b(N)9 b Fp(\()p Fs(p)p
       
  4610 Fp(\()p 2043 2377 V Fs(u)p Fp(\))23 b(:)p Fr(\000)g Fs(G)2324
       
  4611 2395 y Fl(0)2346 2425 y Fp(\))c Fr(\\)g Fs(V)f(N)9 b
       
  4612 Fp(\()p Fs(p)p Fp(\()p 2718 2361 30 4 v Fs(t)p Fp(\))p
       
  4613 Fs(;)14 b(G;)g Fr(r)p Fp(\))24 b(=)e Fr(;)523 2588 y
       
  4614 FA(where)e Fs(\031)k FA(is)d(a)g(sequence)f(of)h(transp)r(ositions)f
       
  4615 Fp(\()p Fo(a)1994 2600 y Fz(1)2052 2588 y Fo(b)2095 2600
       
  4616 y Fz(1)2132 2588 y Fp(\))14 b Fr(\001)g(\001)g(\001)g
       
  4617 Fp(\()p Fo(a)2361 2600 y Fm(n)2428 2588 y Fo(b)2471 2600
       
  4618 y Fm(n)2517 2588 y Fp(\))p FA(.)22 b(W)-7 b(e)21 b(use)g(the)g(term)g
       
  4619 Fq(e)l(quiv-)523 2687 y(ariant)31 b(uni\014c)l(ation)k
       
  4620 FA(for)28 b(the)h(problem)f(of)h(unifying)g(up)f(to)h(nominal)f
       
  4621 (equalit)n(y)g(mo)r(dulo)g(a)523 2787 y(p)r(erm)n(utation.)20
       
  4622 b(Ho)n(w)n(ev)n(er,)e(ev)n(en)h(deciding)h(whether)f(an)h(equiv)-5
       
  4623 b(arian)n(t)19 b(uni\014cation)h(problem)523 2886 y(has)31
       
  4624 b(a)h(solution)f(is)g Fn(NP)p FA(-complete)h([2].)f(This)h(do)r(es)f
       
  4625 (not)h(necessarily)e(mean)i(that)g(equiv-)523 2986 y(arian)n(t)25
       
  4626 b(uni\014cation)h(is)g(impractical.)g(Dev)n(eloping)f(a)h(practical)f
       
  4627 (approac)n(h)f(to)i(equiv)-5 b(arian)n(t)523 3086 y(uni\014cation)26
       
  4628 b(or)f(constrain)n(t)g(solving)f(is)i(the)h(sub)5 b(ject)26
       
  4629 b(of)f(curren)n(t)g(researc)n(h,)f(ho)n(w)n(ev)n(er,)g(and)523
       
  4630 3185 y(the)36 b(curren)n(t)e(v)n(ersion)g(of)h Fs(\013)p
       
  4631 FA(Prolog)e(opts)i(for)f(e\016ciency)i(o)n(v)n(er)d(completeness.)i(W)
       
  4632 -7 b(e)35 b(ha)n(v)n(e)523 3285 y(exp)r(erimen)n(ted)30
       
  4633 b(with)g(brute-force)e(searc)n(h)g(and)h(more)g(adv)-5
       
  4634 b(anced)29 b(tec)n(hniques)h(for)f(equiv-)523 3385 y(arian)n(t)d
       
  4635 (uni\014cation)i(but)g(ha)n(v)n(e)f(y)n(et)g(to)g(\014nd)h(a)g
       
  4636 (satisfactory)e(solution.)648 3484 y(Nev)n(ertheless,)19
       
  4637 b(our)h(incomplete)g(implemen)n(tation)g(of)h Fs(\013)p
       
  4638 FA(Prolog)d(is)i(still)h(useful.)g(Equiv-)523 3584 y(arian)n(t)36
       
  4639 b(uni\014cation)h(do)r(es)g(not)g(seem)f(necessary)g(for)g(man)n(y)h
       
  4640 (in)n(teresting)f Fs(\013)p FA(Prolog)f(pro-)523 3684
       
  4641 y(grams,)22 b(including)h(all)f(purely)h(\014rst-order)e(programs)g
       
  4642 (and)h(all)h(the)h(example)e(programs)f(in)523 3783 y(this)h(pap)r(er)f
       
  4643 (\(capture-a)n(v)n(oiding)f(substitution,)i(t)n(yping,)f(etc.\).)i(In)e
       
  4644 (fact,)h(the)g(seman)n(tics)f(w)n(e)523 3883 y(ha)n(v)n(e)29
       
  4645 b(presen)n(ted)g(is)h(complete)g(for)f(suc)n(h)h(programs.)d(In)j(a)g
       
  4646 (separate)e(pap)r(er,)i(w)n(e)f(iden)n(tify)523 3982
       
  4647 y(\(and)k(pro)n(v)n(e)d(correct\))i(a)g(condition)g(on)g(program)f
       
  4648 (clauses)g(that)i(ensures)f(that)g(nominal)523 4082 y
       
  4649 (uni\014cation-based)27 b(bac)n(k)n(c)n(haining)e(is)j(complete)55
       
  4650 b([26].)523 4331 y Ft(4)112 b(Example:)39 b(the)e Ff(\025)p
       
  4651 Ft(-calculus)523 4514 y FA(The)27 b(protot)n(ypical)f(example)h(of)h(a)
       
  4652 f(language)e(with)j(v)-5 b(ariable)27 b(binding)g(is)h(the)f
       
  4653 Fs(\025)p FA(-calculus.)523 4613 y(In)e Fs(\013)p FA(Prolog)n(,)g(the)g
       
  4654 (syn)n(tax)f(of)g Fs(\025)p FA(-terms)h(ma)n(y)f(b)r(e)h(describ)r(ed)f
       
  4655 (with)i(the)f(follo)n(wing)e(t)n(yp)r(e)i(and)523 4713
       
  4656 y(constructor)h(declarations:)676 4836 y Fs(id)d Fp(:)g
       
  4657 Fn(name)p 1046 4836 25 4 v 30 w(t)m(yp)s(e)p Fs(:)189
       
  4658 b(exp)23 b Fp(:)g Fn(t)m(yp)s(e)p Fs(:)676 4936 y(v)s(ar)i
       
  4659 Fp(:)e Fs(id)g Fr(!)g Fs(exp:)235 b(app)23 b Fp(:)g(\()p
       
  4660 Fs(exp;)14 b(exp)p Fp(\))22 b Fr(!)h Fs(exp:)189 b(lam)24
       
  4661 b Fp(:)f Fr(h)p Fs(id)p Fr(i)p Fs(exp)g Fr(!)g Fs(exp:)p
       
  4662 eop end
       
  4663 %%Page: 7 7
       
  4664 TeXDict begin 7 6 bop 523 448 a FA(W)-7 b(e)36 b(mak)n(e)e(the)i
       
  4665 (simplifying)f(assumption)g(that)g(the)h(v)-5 b(ariables)34
       
  4666 b(of)h(ob)5 b(ject)35 b Fs(\025)p FA(-terms)g(are)523
       
  4667 548 y(constan)n(ts)27 b(of)g(t)n(yp)r(e)h Fs(id)p FA(.)g(Then)f(w)n(e)h
       
  4668 (can)f(translate)f Fs(\025)p FA(-terms)i(as)f(follo)n(ws:)731
       
  4669 704 y Fe(p)p Fo(x)p Fe(q)22 b Fp(=)h Fs(v)s(ar)r Fp(\()p
       
  4670 Fo(x)p Fp(\))167 b Fe(p)p Fs(e)1445 716 y Fz(1)1510 704
       
  4671 y Fs(e)1550 716 y Fz(2)1587 704 y Fe(q)22 b Fp(=)h Fs(app)p
       
  4672 Fp(\()p Fe(p)p Fs(e)1984 716 y Fz(1)2021 704 y Fe(q)p
       
  4673 Fs(;)14 b Fe(p)p Fs(e)2182 716 y Fz(2)2218 704 y Fe(q)p
       
  4674 Fp(\))165 b Fe(p)p Fs(\025)p Fo(x)p Fs(:e)q Fe(q)22 b
       
  4675 Fp(=)h Fs(lam)p Fp(\()p Fo(x)p Fs(:)p Fe(p)p Fs(e)p Fe(q)p
       
  4676 Fp(\))523 859 y FA(It)g(is)g(not)g(di\016cult)h(to)f(v)n(erify)f(that)h
       
  4677 Fs(e)g FA(is)g(a)f Fs(\025)p FA(-term)h(if)h(and)e(only)h(if)g
       
  4678 Fe(p)p Fs(e)p Fe(q)f FA(is)h(a)g Fq(close)l(d)32 b FA(nominal)523
       
  4679 959 y(term,)c(i.e.)f Fs(F)12 b(V)18 b Fp(\()p Fe(p)p
       
  4680 Fs(e)p Fe(q)p Fp(\))k(=)h Fr(;)p FA(,)k(and)h(w)n(e)f(ha)n(v)n(e)f
       
  4681 (that)i Fs(e)23 b Fr(\021)2182 971 y Fm(\013)2252 959
       
  4682 y Fs(e)2292 929 y Fl(0)2342 959 y FA(if)28 b(and)f(only)h(if)g
       
  4683 Fe(p)p Fs(e)p Fe(q)22 b Fr(\031)g Fe(p)p Fs(e)3153 929
       
  4684 y Fl(0)3175 959 y Fe(q)p FA(.)523 1106 y Fq(Example)31
       
  4685 b(1)42 b(\(T)-6 b(yp)l(e)l(che)l(cking)25 b(and)e(infer)l(enc)l(e\).)i
       
  4686 FA(First,)20 b(w)n(e)g(consider)g(the)h(problem)f(of)g(t)n(yp)r(e-)523
       
  4687 1206 y(c)n(hec)n(king)26 b Fs(\025)p FA(-terms.)i(The)g(syn)n(tax)e(of)
       
  4688 i(t)n(yp)r(es)f(can)h(b)r(e)g(enco)r(ded)f(as)g(follo)n(ws:)604
       
  4689 1361 y Fs(tid)c Fp(:)g Fn(name)p 1004 1361 25 4 v 30
       
  4690 w(t)m(yp)s(e)p Fs(:)166 b(ty)27 b Fp(:)c Fn(t)m(yp)s(e)p
       
  4691 Fs(:)166 b(tv)s(ar)26 b Fp(:)d Fs(tid)g Fr(!)g Fs(ty)s(:)166
       
  4692 b(ar)r(r)26 b Fp(:)d(\()p Fs(ty)s(;)14 b(ty)s Fp(\))24
       
  4693 b Fr(!)f Fs(ty)s(:)523 1517 y FA(W)-7 b(e)34 b(de\014ne)g(con)n(texts)f
       
  4694 Fs(ctx)h FA(as)f(lists)h(of)f(pairs)g(of)h(iden)n(ti\014ers)g(and)f(t)n
       
  4695 (yp)r(es,)h(and)g(the)g(3-ary)523 1617 y(relation)27
       
  4696 b Fs(ty)s(p)g FA(relating)g(a)g(con)n(text,)h(term,)f(and)h(t)n(yp)r
       
  4697 (e:)727 1767 y Fn(t)m(yp)s(e)g Fs(ctx)22 b Fp(=)h([)p
       
  4698 Fs(id)18 b Fr(\002)g Fs(ty)s Fp(])p Fs(:)727 1867 y Fn(pred)28
       
  4699 b Fs(ty)s(p)p Fp(\()p Fs(ctx;)14 b(tm;)g(ty)s Fp(\))p
       
  4700 Fs(:)727 1966 y(ty)s(p)p Fp(\()p Fs(C)q(;)g(v)s(ar)r
       
  4701 Fp(\()p Fs(X)7 b Fp(\))p Fs(;)14 b(T)e Fp(\))399 b(:)p
       
  4702 Fr(\000)23 b Fs(mem)p Fp(\(\()p Fs(X)r(;)14 b(T)e Fp(\))p
       
  4703 Fs(;)i(C)6 b Fp(\))p Fs(:)727 2066 y(ty)s(p)p Fp(\()p
       
  4704 Fs(C)q(;)14 b(app)p Fp(\()p Fs(E)1198 2078 y Fz(1)1236
       
  4705 2066 y Fs(;)g(E)1334 2078 y Fz(2)1371 2066 y Fp(\))p
       
  4706 Fs(;)g(T)1501 2036 y Fl(0)1522 2066 y Fp(\))219 b(:)p
       
  4707 Fr(\000)23 b Fs(ty)s(p)p Fp(\()p Fs(C)q(;)14 b(E)2192
       
  4708 2078 y Fz(1)2230 2066 y Fs(;)g(ar)r(r)r Fp(\()p Fs(T)7
       
  4709 b(;)14 b(T)2580 2036 y Fl(0)2601 2066 y Fp(\)\))p Fs(;)g(ty)s(p)p
       
  4710 Fp(\()p Fs(C)q(;)g(E)3010 2078 y Fz(2)3049 2066 y Fs(;)g(T)e
       
  4711 Fp(\))p Fs(:)727 2166 y(ty)s(p)p Fp(\()p Fs(C)q(;)i(lam)p
       
  4712 Fp(\()p Fo(x)p Fs(:E)5 b Fp(\))p Fs(;)14 b(ar)r(r)r Fp(\()p
       
  4713 Fs(T)7 b(;)14 b(T)1661 2135 y Fl(0)1685 2166 y Fp(\)\))24
       
  4714 b(:)p Fr(\000)f Fo(x)g Fp(#)g Fs(C)q(;)14 b(ty)s(p)p
       
  4715 Fp(\([\()p Fo(x)p Fs(;)g(T)e Fp(\))p Fr(j)p Fs(C)6 b
       
  4716 Fp(])p Fs(;)14 b(E)5 b(;)14 b(T)2819 2135 y Fl(0)2841
       
  4717 2166 y Fp(\))p Fs(:)523 2322 y FA(The)35 b(predicate)f
       
  4718 Fs(mem)p Fp(\()p Fs(\013;)14 b Fp([)p Fs(\013)p Fp(]\))37
       
  4719 b FA(is)e(the)g(usual)g(predicate)f(for)g(testing)h(list)g(mem)n(b)r
       
  4720 (ership.)523 2422 y(The)26 b(side-condition)g Fs(x)d
       
  4721 Fr(62)g Fs(D)r(om)p Fp(\()p Fs(\000)12 b Fp(\))27 b FA(is)f(translated)
       
  4722 g(to)g(the)g(freshness)g(constrain)n(t)f Fo(x)e Fp(#)h
       
  4723 Fs(C)6 b FA(.)648 2521 y(Consider)32 b(the)h(query)f
       
  4724 Fp(?)p FA({)g Fs(ty)s(p)p Fp(\([])p Fs(;)14 b(lam)p Fp(\()p
       
  4725 Fo(x)p Fs(:lam)p Fp(\()p Fo(y)q Fs(:v)s(ar)r Fp(\()p
       
  4726 Fo(x)p Fp(\)\)\))p Fs(;)g(T)e Fp(\))p FA(.)37 b(W)-7
       
  4727 b(e)34 b(can)e(reduce)h(this)523 2621 y(goal)26 b(b)n(y)i(bac)n(k)n(c)n
       
  4728 (haining)d(against)i(the)h(suitably)f(freshened)g(rule)712
       
  4729 2777 y Fs(ty)s(p)p Fp(\()p Fs(C)921 2789 y Fz(1)959 2777
       
  4730 y Fs(;)14 b(lam)p Fp(\()p Fo(x)1212 2789 y Fz(1)1251
       
  4731 2777 y Fs(:E)1335 2789 y Fz(1)1372 2777 y Fp(\))p Fs(;)g(ar)r(r)r
       
  4732 Fp(\()p Fs(T)1649 2789 y Fz(1)1687 2777 y Fs(;)g(U)1780
       
  4733 2789 y Fz(1)1817 2777 y Fp(\)\))24 b(:)p Fr(\000)e Fo(x)2053
       
  4734 2789 y Fz(1)2114 2777 y Fp(#)h Fs(C)2265 2789 y Fz(1)2303
       
  4735 2777 y Fs(;)14 b(ty)s(p)p Fp(\([\()p Fo(x)2583 2789 y
       
  4736 Fz(1)2621 2777 y Fs(;)g(T)2707 2789 y Fz(1)2744 2777
       
  4737 y Fp(\))p Fr(j)p Fs(C)2858 2789 y Fz(1)2895 2777 y Fp(])p
       
  4738 Fs(;)g(E)3016 2789 y Fz(1)3054 2777 y Fs(;)g(U)3147 2789
       
  4739 y Fz(1)3183 2777 y Fp(\))523 2932 y FA(whic)n(h)21 b(uni\014es)g(with)g
       
  4740 (the)h(goal)d(with)j Fp([)p Fs(C)1758 2944 y Fz(1)1818
       
  4741 2932 y Fp(=)h([])p Fs(;)14 b(E)2050 2944 y Fz(1)2110
       
  4742 2932 y Fp(=)23 b Fs(lam)p Fp(\()p Fo(y)q Fs(:v)s(ar)r
       
  4743 Fp(\()p Fo(x)2639 2944 y Fz(1)2679 2932 y Fp(\)\))p Fs(;)14
       
  4744 b(T)34 b Fp(=)23 b Fs(ar)r(r)r Fp(\()p Fs(T)3159 2944
       
  4745 y Fz(1)3197 2932 y Fs(;)14 b(U)3290 2944 y Fz(1)3327
       
  4746 2932 y Fp(\)])p FA(.)523 3032 y(This)31 b(yields)f(subgoal)f
       
  4747 Fo(x)1293 3044 y Fz(1)1359 3032 y Fp(#)f([])p Fs(;)14
       
  4748 b(ty)s(p)p Fp(\([\()p Fo(x)1782 3044 y Fz(1)1820 3032
       
  4749 y Fs(;)g(T)1906 3044 y Fz(1)1943 3032 y Fp(\))p Fr(j)p
       
  4750 Fs(C)2057 3044 y Fz(1)2095 3032 y Fp(])p Fs(;)g(E)2216
       
  4751 3044 y Fz(1)2253 3032 y Fs(;)g(U)2346 3044 y Fz(1)2383
       
  4752 3032 y Fp(\))p FA(.)31 b(The)g(\014rst)f(conjunct)h(is)g(triv-)523
       
  4753 3132 y(ially)e(v)-5 b(alid)29 b(since)g Fs(C)1173 3144
       
  4754 y Fz(1)1240 3132 y FA(is)g(a)g(constan)n(t.)g(The)g(second)g(is)g(solv)
       
  4755 n(ed)f(b)n(y)h(bac)n(k)n(c)n(haining)e(against)523 3231
       
  4756 y(the)32 b(third)f Fs(ty)s(p)p FA(-rule)g(again,)f(pro)r(ducing)h
       
  4757 (uni\014er)g Fp([)p Fs(C)2183 3243 y Fz(2)2250 3231 y
       
  4758 Fp(=)d([\()p Fo(x)2436 3243 y Fz(1)2474 3231 y Fs(;)14
       
  4759 b(T)2560 3243 y Fz(1)2597 3231 y Fp(\)])p Fs(;)g(E)2750
       
  4760 3243 y Fz(2)2816 3231 y Fp(=)29 b Fs(v)s(ar)r Fp(\()p
       
  4761 Fo(x)3111 3243 y Fz(1)3149 3231 y Fp(\))p Fs(;)14 b(U)3274
       
  4762 3243 y Fz(1)3340 3231 y Fp(=)523 3331 y Fs(ar)r(r)r Fp(\()p
       
  4763 Fs(T)731 3343 y Fz(2)769 3331 y Fs(;)g(U)862 3343 y Fz(2)899
       
  4764 3331 y Fp(\)])28 b FA(and)g(subgoal)e Fo(x)1482 3343
       
  4765 y Fz(2)1543 3331 y Fp(#)e([\()p Fo(x)1729 3343 y Fz(1)1767
       
  4766 3331 y Fs(;)14 b(T)1853 3343 y Fz(1)1889 3331 y Fp(\)])p
       
  4767 Fs(;)g(ty)s(p)p Fp(\([\()p Fo(x)2224 3343 y Fz(2)2263
       
  4768 3331 y Fs(;)g(T)2349 3343 y Fz(2)2386 3331 y Fp(\))p
       
  4769 Fs(;)g Fp(\()p Fo(x)2525 3343 y Fz(1)2563 3331 y Fs(;)g(T)2649
       
  4770 3343 y Fz(1)2685 3331 y Fp(\)])p Fs(;)g(v)s(ar)r Fp(\()p
       
  4771 Fo(x)2978 3343 y Fz(1)3017 3331 y Fp(\))p Fs(;)g(U)3142
       
  4772 3343 y Fz(2)3179 3331 y Fp(\))p FA(.)28 b(The)523 3430
       
  4773 y(freshness)e(subgoal)f(reduces)g(to)i(the)g(constrain)n(t)e
       
  4774 Fo(x)2135 3442 y Fz(2)2195 3430 y Fp(#)f Fs(T)2337 3442
       
  4775 y Fz(1)2373 3430 y FA(,)j(and)f(the)h Fs(ty)s(p)g FA(subgoal)e(can)h(b)
       
  4776 r(e)523 3530 y(solv)n(ed)h(b)n(y)g(bac)n(k)n(c)n(haining)e(against)1187
       
  4777 3686 y Fs(ty)s(p)p Fp(\()p Fs(C)1396 3698 y Fz(3)1434
       
  4778 3686 y Fs(;)14 b(v)s(ar)r Fp(\()p Fs(X)1702 3698 y Fz(3)1739
       
  4779 3686 y Fp(\))p Fs(;)g(T)1857 3698 y Fz(3)1894 3686 y
       
  4780 Fp(\))23 b(:)p Fr(\000)g Fs(mem)p Fp(\(\()p Fs(X)2382
       
  4781 3698 y Fz(3)2421 3686 y Fs(;)14 b(T)2507 3698 y Fz(3)2543
       
  4782 3686 y Fp(\))p Fs(;)g(C)2671 3698 y Fz(3)2709 3686 y
       
  4783 Fp(\))523 3841 y FA(using)35 b(uni\014er)h Fp([)p Fs(C)1097
       
  4784 3853 y Fz(3)1171 3841 y Fp(=)g([\()p Fo(x)1365 3853 y
       
  4785 Fz(2)1403 3841 y Fs(;)14 b(T)1489 3853 y Fz(2)1525 3841
       
  4786 y Fp(\))p Fs(;)g Fp(\()p Fo(x)1664 3853 y Fz(1)1702 3841
       
  4787 y Fs(;)g(T)1788 3853 y Fz(1)1825 3841 y Fp(\)])p Fs(;)g(X)1985
       
  4788 3853 y Fz(3)2059 3841 y Fp(=)36 b Fo(x)2198 3853 y Fz(1)2235
       
  4789 3841 y Fs(;)14 b(T)2321 3853 y Fz(3)2395 3841 y Fp(=)36
       
  4790 b Fs(U)2552 3853 y Fz(2)2588 3841 y Fp(])p FA(.)g(Finally)-7
       
  4791 b(,)36 b(the)g(remain-)523 3941 y(ing)f(subgoal)f Fs(mem)p
       
  4792 Fp(\(\()p Fo(x)1269 3953 y Fz(1)1308 3941 y Fs(;)14 b(U)1401
       
  4793 3953 y Fz(2)1438 3941 y Fp(\))p Fs(;)g Fp([\()p Fo(x)1600
       
  4794 3953 y Fz(2)1638 3941 y Fs(;)g(T)1724 3953 y Fz(2)1761
       
  4795 3941 y Fp(\))p Fs(;)g Fp(\()p Fo(x)1900 3953 y Fz(1)1938
       
  4796 3941 y Fs(;)g(T)2024 3953 y Fz(1)2061 3941 y Fp(\)]\))36
       
  4797 b FA(clearly)e(has)h(most)g(general)g(solution)523 4041
       
  4798 y Fp([)p Fs(U)602 4053 y Fz(2)676 4041 y Fp(=)i Fs(T)827
       
  4799 4053 y Fz(1)864 4041 y Fp(])p FA(.)f(Solving)g(for)g
       
  4800 Fs(T)12 b FA(,)35 b(w)n(e)h(ha)n(v)n(e)f Fs(T)48 b Fp(=)37
       
  4801 b Fs(ar)r(r)r Fp(\()p Fs(T)2241 4053 y Fz(1)2279 4041
       
  4802 y Fs(;)14 b(U)2372 4053 y Fz(1)2409 4041 y Fp(\))37 b(=)g
       
  4803 Fs(ar)r(r)r Fp(\()p Fs(T)2788 4053 y Fz(1)2826 4041 y
       
  4804 Fs(;)14 b(ar)r(r)r Fp(\()p Fs(T)3071 4053 y Fz(2)3109
       
  4805 4041 y Fs(;)g(U)3202 4053 y Fz(2)3238 4041 y Fp(\)\))38
       
  4806 b(=)523 4140 y Fs(ar)r(r)r Fp(\()p Fs(T)731 4152 y Fz(1)769
       
  4807 4140 y Fs(;)14 b(ar)r(r)r Fp(\()p Fs(T)1014 4152 y Fz(2)1051
       
  4808 4140 y Fs(;)g(T)1137 4152 y Fz(1)1174 4140 y Fp(\)\))p
       
  4809 FA(.)26 b(This)f(solution)g(corresp)r(onds)e(to)i(the)g(principal)g(t)n
       
  4810 (yp)r(e)g(of)g Fs(\025x:\025y)s(:x)p FA(.)523 4288 y
       
  4811 Fq(Example)31 b(2)42 b(\(Captur)l(e-avoiding)f(substitution\).)c
       
  4812 FA(Although)h(capture-a)n(v)n(oiding)c(substi-)523 4387
       
  4813 y(tution)28 b(is)g(not)f(a)g(built-in)i(op)r(erator)c(in)j
       
  4814 Fs(\013)p FA(Prolog)n(,)g(it)g(is)f(easy)g(to)h(de\014ne)f(via)g(the)h
       
  4815 (clauses:)760 4537 y Fn(func)g Fs(subst)p Fp(\()p Fs(exp;)14
       
  4816 b(exp;)g(id)p Fp(\))53 b(=)23 b Fs(exp:)760 4637 y(subst)p
       
  4817 Fp(\()p Fs(v)s(ar)r Fp(\()p Fs(X)7 b Fp(\))p Fs(;)14
       
  4818 b(E)5 b(;)14 b(X)7 b Fp(\))182 b(=)23 b Fs(E)5 b(:)760
       
  4819 4737 y(subst)p Fp(\()p Fs(v)s(ar)r Fp(\()p Fs(Y)20 b
       
  4820 Fp(\))p Fs(;)14 b(E)5 b(;)14 b(X)7 b Fp(\))190 b(=)23
       
  4821 b Fs(v)s(ar)r Fp(\()p Fs(Y)c Fp(\))k(:)p Fr(\000)g Fs(X)29
       
  4822 b Fp(#)24 b Fs(Y)5 b(:)760 4836 y(subst)p Fp(\()p Fs(app)p
       
  4823 Fp(\()p Fs(E)1209 4848 y Fz(1)1247 4836 y Fs(;)14 b(E)1345
       
  4824 4848 y Fz(2)1382 4836 y Fp(\))p Fs(;)g(E)5 b(;)14 b(X)7
       
  4825 b Fp(\))23 b(=)g Fs(app)p Fp(\()p Fs(subst)p Fp(\()p
       
  4826 Fs(E)2221 4848 y Fz(1)2259 4836 y Fs(;)14 b(E)5 b(;)14
       
  4827 b(X)7 b Fp(\))p Fs(;)14 b(subst)p Fp(\()p Fs(E)2829 4848
       
  4828 y Fz(2)2867 4836 y Fs(;)g(E)5 b(;)14 b(X)7 b Fp(\)\))p
       
  4829 Fs(:)760 4936 y(subst)p Fp(\()p Fs(lam)p Fp(\()p Fo(y)q
       
  4830 Fs(:E)1291 4906 y Fl(0)1316 4936 y Fp(\))p Fs(;)14 b(E)5
       
  4831 b(;)14 b(X)7 b Fp(\))89 b(=)23 b Fs(lam)p Fp(\()p Fo(y)q
       
  4832 Fs(:subst)p Fp(\()p Fs(E)2303 4906 y Fl(0)2328 4936 y
       
  4833 Fs(;)14 b(E)5 b(;)14 b(X)7 b Fp(\)\))22 b(:)p Fr(\000)h
       
  4834 Fo(y)h Fp(#)g(\()p Fs(X)r(;)14 b(E)5 b Fp(\))p Fs(:)p
       
  4835 eop end
       
  4836 %%Page: 8 8
       
  4837 TeXDict begin 8 7 bop 523 448 a FA(Note)29 b(the)f(t)n(w)n(o)g
       
  4838 (freshness)g(side-conditions:)f(the)i(constrain)n(t)e
       
  4839 Fs(X)k Fp(#)25 b Fs(Y)47 b FA(prev)n(en)n(ts)27 b(the)i(\014rst)523
       
  4840 548 y(and)24 b(second)f(clauses)g(from)g(o)n(v)n(erlapping;)f(the)i
       
  4841 (constrain)n(t)f Fo(y)h Fp(#)f(\()p Fs(X)r(;)14 b(E)5
       
  4842 b Fp(\))24 b FA(ensures)f(capture-)523 648 y(a)n(v)n(oidance,)18
       
  4843 b(b)n(y)h(restricting)g(the)h(application)f(of)h(the)g(fourth)g(clause)
       
  4844 f(to)g(when)h Fo(y)h FA(is)f(fresh)g(for)523 747 y Fs(X)28
       
  4845 b FA(and)22 b Fs(E)5 b FA(.)21 b(Despite)h(these)g(side-conditions,)f
       
  4846 (this)h(de\014nition)g(is)g(total)f(and)h(deterministic.)523
       
  4847 847 y(Determinism)29 b(is)f(immediate:)h(no)f(t)n(w)n(o)g(clauses)f(o)n
       
  4848 (v)n(erlap.)g(T)-7 b(otalit)n(y)28 b(follo)n(ws)f(b)r(ecause,)h(b)n(y)
       
  4849 523 946 y(nominal)20 b(logic's)g Fq(fr)l(eshness)k(principle)p
       
  4850 FA(,)f(the)e(b)r(ound)g(name)g Fo(y)h FA(in)f Fs(lam)p
       
  4851 Fp(\()p Fo(y)q Fs(:E)2839 916 y Fl(0)2862 946 y Fp(\))g
       
  4852 FA(can)g(alw)n(a)n(ys)e(b)r(e)523 1046 y(renamed)g(to)g(a)g(fresh)h
       
  4853 Fo(z)f FA(c)n(hosen)g(so)g(that)h Fo(z)j Fp(#)g(\()p
       
  4854 Fs(X)r(;)14 b(E)5 b Fp(\))p FA(.)20 b(It)f(is)h(straigh)n(tforw)n(ard)c
       
  4855 (to)k(pro)n(v)n(e)e(that)523 1146 y Fs(subst)p Fp(\()p
       
  4856 Fe(p)p Fs(t)p Fe(q)p Fs(;)c Fe(p)p Fs(t)971 1116 y Fl(0)993
       
  4857 1146 y Fe(q)p Fs(;)g Fo(x)p Fp(\))22 b FA(coincides)g(with)h(the)f
       
  4858 (traditional)f(capture-a)n(v)n(oiding)f(substitution)i(on)523
       
  4859 1245 y Fs(\025)p FA(-terms)27 b Fs(t)p Fp([)p Fs(t)913
       
  4860 1215 y Fl(0)936 1245 y Fs(=x)p Fp(])p FA(.)648 1345 y(Consider)i(the)h
       
  4861 (goal)e Fs(X)34 b Fp(=)26 b Fs(subst)p Fp(\()p Fs(lam)p
       
  4862 Fp(\()p Fo(x)p Fs(:v)s(ar)r Fp(\()p Fo(y)q Fp(\)\))p
       
  4863 Fs(;)14 b(v)s(ar)r Fp(\()p Fo(x)p Fp(\))p Fs(;)g Fo(y)q
       
  4864 Fp(\))q FA(.)36 b(The)30 b(substitution)g(on)523 1445
       
  4865 y(the)36 b(righ)n(t-hand)e(side)h(is)g(in)g(danger)f(of)i(capturing)e
       
  4866 (the)i(free)f(v)-5 b(ariable)34 b Fs(v)s(ar)r Fp(\()p
       
  4867 Fo(x)p Fp(\))p FA(.)i(Ho)n(w)f(is)523 1544 y(capture)28
       
  4868 b(a)n(v)n(oided)e(in)i Fs(\013)p FA(Prolog)n(?)h(First,)f(note)g(that)g
       
  4869 (function)h(de\014nitions)f(are)f(translated)523 1644
       
  4870 y(to)38 b(a)g(\015attened)h(clausal)e(form)h(in)h Fs(\013)p
       
  4871 FA(Prolog)n(,)f(so)g(w)n(e)g(m)n(ust)g(solv)n(e)f(the)i(equiv)-5
       
  4872 b(alen)n(t)38 b(goal)523 1743 y Fs(subst)716 1713 y Fl(0)740
       
  4873 1743 y Fp(\()p Fs(lam)p Fp(\()p Fo(x)p Fs(:v)s(ar)r Fp(\()p
       
  4874 Fo(y)q Fp(\)\))p Fs(;)14 b(v)s(ar)r Fp(\()p Fo(x)p Fp(\))p
       
  4875 Fs(;)g Fo(y)q Fs(;)g(X)7 b Fp(\))38 b FA(sub)5 b(ject)33
       
  4876 b(to)h(an)f(appropriately)f(translated)h(de\014-)523
       
  4877 1843 y(nition)28 b(of)f Fs(subst)1050 1813 y Fl(0)1074
       
  4878 1843 y FA(.)h(The)f(freshened,)h(\015attened)g(clause)635
       
  4879 2021 y Fs(subst)828 1987 y Fl(0)851 2021 y Fp(\()p Fs(lam)p
       
  4880 Fp(\()p Fo(y)1099 2033 y Fz(1)1138 2021 y Fs(:E)1227
       
  4881 1987 y Fl(0)1222 2041 y Fz(1)1259 2021 y Fp(\))p Fs(;)14
       
  4882 b(E)1389 2033 y Fz(1)1427 2021 y Fs(;)g(X)1532 2033 y
       
  4883 Fz(1)1569 2021 y Fs(;)g(lam)p Fp(\()p Fo(y)1822 2033
       
  4884 y Fz(1)1860 2021 y Fs(;)g(E)1963 1987 y Fl(00)1958 2041
       
  4885 y Fz(1)2003 2021 y Fp(\))23 b(:)p Fr(\000)g Fo(y)2207
       
  4886 2033 y Fz(1)2268 2021 y Fp(#)g Fs(E)2421 2033 y Fz(1)2458
       
  4887 2021 y Fs(;)14 b(subst)2688 1987 y Fl(0)2711 2021 y Fp(\()p
       
  4888 Fs(E)2809 1987 y Fl(0)2804 2041 y Fz(1)2842 2021 y Fs(;)g(E)2940
       
  4889 2033 y Fz(1)2977 2021 y Fs(;)g(X)3082 2033 y Fz(1)3119
       
  4890 2021 y Fs(;)g(E)3222 1987 y Fl(00)3217 2041 y Fz(1)3261
       
  4891 2021 y Fp(\))523 2199 y FA(uni\014es)31 b(with)g(substitution)g
       
  4892 Fp([)p Fs(E)1531 2168 y Fl(0)1526 2219 y Fz(1)1591 2199
       
  4893 y Fp(=)d Fs(v)s(ar)r Fp(\()p Fo(y)q Fp(\))p Fs(;)14 b(X)2023
       
  4894 2211 y Fz(1)2089 2199 y Fp(=)28 b Fo(y)q Fs(;)14 b(E)2319
       
  4895 2211 y Fz(1)2384 2199 y Fp(=)28 b Fs(v)s(ar)r Fp(\()p
       
  4896 Fo(x)p Fp(\))p Fs(;)14 b(X)35 b Fp(=)28 b Fs(lam)p Fp(\()p
       
  4897 Fo(y)3159 2211 y Fz(1)3198 2199 y Fs(:E)3287 2168 y Fl(00)3282
       
  4898 2219 y Fz(1)3327 2199 y Fp(\)])p FA(.)523 2298 y(The)21
       
  4899 b(freshness)e(constrain)n(t)h Fo(y)1451 2310 y Fz(1)1511
       
  4900 2298 y Fp(#)k Fs(v)s(ar)r Fp(\()p Fo(x)p Fp(\))d FA(guaran)n(tees)e
       
  4901 (that)i Fs(v)s(ar)r Fp(\()p Fo(x)p Fp(\))g FA(cannot)f(b)r(e)h
       
  4902 (captured.)523 2398 y(It)37 b(is)f(easily)f(v)n(eri\014ed,)g(so)h(the)h
       
  4903 (goal)d(reduces)i(to)g Fs(subst)2327 2368 y Fl(0)2350
       
  4904 2398 y Fp(\()p Fs(v)s(ar)r Fp(\()p Fo(y)q Fp(\))p Fs(;)14
       
  4905 b(v)s(ar)r Fp(\()p Fo(x)p Fp(\))p Fs(;)g Fo(y)q Fs(;)g(E)3065
       
  4906 2367 y Fl(00)3060 2418 y Fz(1)3108 2398 y Fp(\))p FA(.)36
       
  4907 b(Using)523 2498 y(the)27 b(freshened)g(rule)f Fs(subst)1390
       
  4908 2467 y Fl(0)1414 2498 y Fp(\()p Fs(v)s(ar)r Fp(\()p Fs(X)1677
       
  4909 2510 y Fz(2)1714 2498 y Fp(\))p Fs(;)14 b(E)1844 2510
       
  4910 y Fz(2)1882 2498 y Fs(;)g(X)1987 2510 y Fz(2)2024 2498
       
  4911 y Fs(;)g(E)2122 2510 y Fz(2)2159 2498 y Fp(\))27 b FA(with)g(unifying)g
       
  4912 (substitution)g Fp([)p Fs(X)3280 2510 y Fz(2)3340 2498
       
  4913 y Fp(=)523 2597 y Fo(y)q Fs(;)14 b(E)660 2609 y Fz(2)721
       
  4914 2597 y Fp(=)22 b Fs(v)s(ar)r Fp(\()p Fo(x)p Fp(\))p Fs(;)14
       
  4915 b(E)1144 2567 y Fl(00)1139 2617 y Fz(1)1208 2597 y Fp(=)22
       
  4916 b Fs(v)s(ar)r Fp(\()p Fo(x)p Fp(\)])p FA(,)29 b(w)n(e)e(obtain)h(the)g
       
  4917 (solution)f Fs(X)i Fp(=)23 b Fs(lam)p Fp(\()p Fo(y)2842
       
  4918 2609 y Fz(1)2881 2597 y Fs(:v)s(ar)r Fp(\()p Fo(x)p Fp(\)\))p
       
  4919 FA(.)523 2767 y Fq(Example)31 b(3)42 b(\(Parsing\).)80
       
  4920 b FA(Logic)38 b(programming)f(languages)g(often)j(pro)n(vide)e(adv)-5
       
  4921 b(anced)523 2866 y(supp)r(ort)21 b(for)g(parsing)e(using)i(de\014nite)h
       
  4922 (clause)e(grammars)f(\(DCGs\).)j(DCG)g(parsing)e(can)h(b)r(e)523
       
  4923 2966 y(implemen)n(ted)29 b(in)g Fs(\013)p FA(Prolog)d(b)n(y)i
       
  4924 (translating)f(DCG)i(rules)f Fs(h)d Fr(\000)-15 b(!)25
       
  4925 b Fs(t)j FA(to)g(ordinary)f Fs(\013)p FA(Prolog)523 3066
       
  4926 y(programs.)d(W)-7 b(e)26 b(assume)f(familiarit)n(y)g(with)h(DCG)g(syn)
       
  4927 n(tax)f(in)h(this)g(example.)g(W)-7 b(e)26 b(assume)523
       
  4928 3165 y(that)i Fs(v)s Fp(\()p Fs(str)r(ing)s Fp(\))p Fs(;)14
       
  4929 b(w)r(s)p 1191 3165 25 4 v 32 w(opt;)g(w)r(s;)g(tok)r(en)p
       
  4930 Fp(\()p Fs(str)r(ing)s Fp(\))30 b FA(are)d(prede\014ned)g(non)n
       
  4931 (terminals)g(recogniz-)523 3265 y(ing)37 b(v)-5 b(ariable)36
       
  4932 b(names,)h(\(optional\))g(whitespace,)g(and)g(string)g(tok)n(ens.)f
       
  4933 (Here)h(is)h(a)e(small)523 3364 y(example)j(of)h(parsing)f
       
  4934 Fs(\025)p FA(-terms)h(from)f(strings.)g(\(Here,)h Fs(mem)p
       
  4935 Fp(1\()p Fs(S;)14 b(X)r(;)g(M)9 b Fp(\))40 b FA(holds)g(when)523
       
  4936 3464 y Fs(S;)14 b(X)34 b FA(is)28 b(the)g(\014rst)f(binding)h(of)f
       
  4937 Fs(S)33 b FA(in)27 b Fs(M)9 b FA(.\))619 3641 y Fn(t)m(yp)s(e)28
       
  4938 b Fs(map)23 b Fp(=)g([\()p Fs(str)r(ing)s(;)14 b(id)p
       
  4939 Fp(\)])619 3741 y Fs(ltm)p Fp(\()p Fs(M)t(;)g(v)s(ar)r
       
  4940 Fp(\()p Fs(X)7 b Fp(\)\))381 b Fr(\000)-14 b(!)23 b Fs(v)s
       
  4941 Fp(\()p Fs(S)5 b Fp(\))p Fs(;)14 b Fr(f)p Fs(mem)p Fp(1\()p
       
  4942 Fs(S;)g(X)r(;)g(M)9 b Fp(\))p Fr(g)p Fs(:)619 3840 y(ltm)p
       
  4943 Fp(\()p Fs(M)t(;)14 b(app)p Fp(\()p Fs(E)1126 3852 y
       
  4944 Fz(1)1164 3840 y Fs(;)g(E)1262 3852 y Fz(2)1299 3840
       
  4945 y Fp(\)\))222 b Fr(\000)-14 b(!)23 b Fs(tok)r(en)p Fp(\(\\\("\))p
       
  4946 Fs(;)14 b(w)r(s)p 2275 3840 V 30 w(opt;)g(ltm)p Fp(\()p
       
  4947 Fs(M)t(;)g(E)2794 3852 y Fz(1)2832 3840 y Fp(\))p Fs(;)g(w)r(s;)1742
       
  4948 3940 y(ltm)p Fp(\()p Fs(M)t(;)g(E)2086 3952 y Fz(2)2124
       
  4949 3940 y Fp(\))p Fs(;)g(w)r(s)p 2300 3940 V 31 w(opt;)g(tok)r(en)p
       
  4950 Fp(\(\\\)"\))619 4040 y Fs(ltm)p Fp(\()p Fs(M)t(;)g(lam)p
       
  4951 Fp(\()p Fo(x)p Fs(:E)5 b Fp(\)\))314 b Fr(\000)-14 b(!)23
       
  4952 b(f)p Fo(x)g Fp(#)g Fs(M)9 b Fr(g)p Fs(;)14 b(tok)r(en)p
       
  4953 Fp(\(\\)p Fr(n)p Fp("\))p Fs(;)g(w)r(s)p 2647 4040 V
       
  4954 29 w(opt;)g(v)s Fp(\()p Fs(X)7 b Fp(\))p Fs(;)14 b(w)r(s)p
       
  4955 3149 4040 V 29 w(opt;)1742 4139 y(tok)r(en)p Fp(\(\\)p
       
  4956 Fs(:)p Fp("\))p Fs(;)g(w)r(s)p 2266 4139 V 30 w(opt;)g(ltm)p
       
  4957 Fp(\([\()p Fs(S;)g Fo(x)p Fp(\))p Fr(j)p Fs(M)9 b Fp(])p
       
  4958 Fs(;)14 b(E)5 b Fp(\))p Fs(:)523 4318 y FA(This)28 b(program)d(parses)h
       
  4959 Fp(\\)p Fr(n)p Fs(x:)p Fr(n)p Fs(y)s(:x)p Fp(")g FA(to)h
       
  4960 Fs(lam)p Fp(\()p Fo(x)p Fs(:lam)p Fp(\()p Fo(y)q Fs(:)p
       
  4961 Fo(x)p Fp(\)\))p FA(.)523 4563 y Fn(4.1)95 b(Extending)31
       
  4962 b(to)g(the)h Fs(\025\026)p Fn(-calculus)523 4725 y FA(The)g
       
  4963 Fs(\025\026)p FA(-calculus,)g(in)n(v)n(en)n(ted)g(b)n(y)g(P)n(arigot)e
       
  4964 ([17],)i(extends)g(the)h Fs(\025)p FA(-calculus)f(with)g
       
  4965 Fq(c)l(ontin-)523 4825 y(uations)44 b Fs(\013)p FA(;)38
       
  4966 b(terms)f(ma)n(y)g(b)r(e)h(\\named")e(b)n(y)h(con)n(tin)n(uations)g(\()
       
  4967 p Fp([)p Fs(\013)p Fp(])p Fs(e)p FA(\))h(and)f(con)n(tin)n(uations)523
       
  4968 4924 y(ma)n(y)25 b(b)r(e)i(in)n(tro)r(duced)e(with)i
       
  4969 Fs(\026)p FA(-binding)e(\()p Fs(\026\013:e)p FA(\).)i(In)n(tuitiv)n
       
  4970 (ely)-7 b(,)26 b Fs(\025\026)p FA(-terms)f(are)g(pro)r(of)g(terms)p
       
  4971 eop end
       
  4972 %%Page: 9 9
       
  4973 TeXDict begin 9 8 bop 549 508 a Fv(T)-7 b(erms,)28 b(T)n(yp)r(es,)g
       
  4974 (and)h(Con)n(texts)569 623 y Fu(e)24 b Fk(::=)f Fu(x)e
       
  4975 Fi(j)h Fk(\()p Fu(e)j(e)992 591 y Fd(0)1013 623 y Fk(\))d
       
  4976 Fi(j)f Fu(\025x:e)g Fi(j)h Fk([)p Fu(\013)p Fk(])p Fu(e)g
       
  4977 Fi(j)g Fu(\026\013:e)562 714 y(\034)33 b Fk(::=)23 b
       
  4978 Fu(b)e Fi(j)h Fu(\034)30 b Fi(!)22 b Fu(\034)1060 683
       
  4979 y Fd(0)1102 714 y Fi(j)f(?)549 806 y Fu(\000)35 b Fk(::=)23
       
  4980 b Fi(\001)f(j)g Fu(\000)r(;)13 b(x)21 b Fk(:)h Fu(\034)30
       
  4981 b Fi(j)22 b Fu(\000)r(;)14 b(\013)21 b Fk(:)p 1336 762
       
  4982 44 4 v 22 w Fu(\034)1869 508 y Fv(Replacemen)n(t)28 b(Op)r(eration)2060
       
  4983 623 y Fu(x)p Fi(f)p Fu(e=\013)p Fi(g)d Fk(=)e Fu(x)1885
       
  4984 714 y Fk(\()p Fu(e)1952 722 y Fy(1)2012 714 y Fu(e)2049
       
  4985 722 y Fy(2)2084 714 y Fk(\))p Fi(f)p Fu(t=\013)p Fi(g)h
       
  4986 Fk(=)f(\()p Fu(e)2480 722 y Fy(1)2514 714 y Fi(f)p Fu(e=\013)p
       
  4987 Fi(g)28 b Fu(e)2780 722 y Fy(2)2814 714 y Fi(f)p Fu(e=\013)p
       
  4988 Fi(g)p Fk(\))1878 806 y(\()p Fu(\025y)s(:e)2053 774 y
       
  4989 Fd(0)2074 806 y Fk(\))p Fi(f)p Fu(e=\013)p Fi(g)d Fk(=)e
       
  4990 Fu(\025y)s(:e)2558 774 y Fd(0)2579 806 y Fi(f)p Fu(e=\013)p
       
  4991 Fi(g)1894 897 y Fk(\([)p Fu(\013)p Fk(])p Fu(e)2053 865
       
  4992 y Fd(0)2074 897 y Fk(\))p Fi(f)p Fu(e=\013)p Fi(g)i Fk(=)e([)p
       
  4993 Fu(\013)p Fk(]\()p Fu(e)2572 865 y Fd(0)2594 897 y Fi(f)p
       
  4994 Fu(e=\013)p Fi(g)k Fu(e)p Fk(\))1895 988 y(\([)p Fu(\014)t
       
  4995 Fk(])p Fu(e)2053 957 y Fd(0)2074 988 y Fk(\))p Fi(f)p
       
  4996 Fu(e=\013)p Fi(g)e Fk(=)e([)p Fu(\014)t Fk(]\()p Fu(e)2571
       
  4997 957 y Fd(0)2592 988 y Fi(f)p Fu(e=\013)p Fi(g)p Fk(\))78
       
  4998 b(\()p Fu(\014)25 b Fi(6)p Fk(=)c Fu(\013)p Fk(\))1869
       
  4999 1080 y(\()p Fu(\026\014)t(:e)2054 1048 y Fd(0)2074 1080
       
  5000 y Fk(\))p Fi(f)p Fu(e=\013)p Fi(g)k Fk(=)e Fu(\026\014)t(:e)2568
       
  5001 1048 y Fd(0)2589 1080 y Fi(f)p Fu(e=\013)p Fi(g)78 b
       
  5002 Fk(\()p Fu(\014)25 b Fi(62)c Fu(F)11 b(N)d Fk(\()p Fu(e;)13
       
  5003 b(\013)p Fk(\)\))588 1250 y Fv(Some)29 b(T)n(yping-Rules)588
       
  5004 1366 y Fu(\013)p Fk(:)p 660 1323 V 1 w Fu(\034)h Fi(2)21
       
  5005 b Fu(\000)88 b(\000)33 b Fi(`)21 b Fu(e)g Fk(:)h Fu(\034)p
       
  5006 588 1391 636 4 v 705 1464 a(\000)33 b Fi(`)21 b Fk([)p
       
  5007 Fu(\013)p Fk(])p Fu(e)h Fk(:)g Fi(?)1400 1363 y Fu(\000)32
       
  5008 b Fi(`)21 b Fu(e)1583 1371 y Fy(1)1639 1363 y Fk(:)h
       
  5009 Fi(?)76 b Fu(\000)32 b Fi(`)21 b Fu(e)2002 1371 y Fy(2)2058
       
  5010 1363 y Fk(:)h Fu(\034)p 1400 1391 746 4 v 1523 1464 a(\000)32
       
  5011 b Fi(`)22 b Fk(\()p Fu(e)1737 1472 y Fy(1)1797 1464 y
       
  5012 Fu(e)1834 1472 y Fy(2)1868 1464 y Fk(\))f(:)h Fi(?)2322
       
  5013 1357 y Fu(\000)r(;)13 b(\013)p Fk(:)p 2476 1313 44 4
       
  5014 v 1 w Fu(\034)30 b Fi(`)22 b Fu(e)f Fk(:)h Fi(?)75 b
       
  5015 Fk(\()p Fu(\013)22 b Fi(62)f Fu(D)r(om)p Fk(\()p Fu(\000)11
       
  5016 b Fk(\)\))p 2322 1396 1019 4 v 2625 1464 a Fu(\000)33
       
  5017 b Fi(`)21 b Fu(\026\013:e)h Fk(:)g Fu(\034)1152 1668
       
  5018 y Fv(Fig.)13 b(2.)26 b Fx(A)f(sligh)n(t)h(v)l(arian)n(t)g(of)g(P)n
       
  5019 (arigot's)i Fu(\025\026)p Fx(-calculus.)523 1949 y FA(for)35
       
  5020 b(classical)e(natural)i(deduction,)g(and)g Fs(\026)p
       
  5021 FA(-abstractions)e(represen)n(t)h(pro)r(ofs)g(b)n(y)h(double)523
       
  5022 2049 y(negation.)23 b(In)h(addition)g(to)f(capture-a)n(v)n(oiding)e
       
  5023 (substitution)k(of)e(terms)h(for)f(v)-5 b(ariables,)23
       
  5024 b(the)523 2148 y Fs(\025\026)p FA(-calculus)30 b(in)n(tro)r(duces)g(a)h
       
  5025 (capture-a)n(v)n(oiding)d Fq(r)l(eplac)l(ement)39 b FA(op)r(erator)29
       
  5026 b Fs(e)2923 2118 y Fl(0)2945 2148 y Fr(f)p Fs(e=\013)p
       
  5027 Fr(g)h FA(whic)n(h)523 2248 y(replaces)36 b(eac)n(h)h(o)r(ccurrence)f
       
  5028 (of)h(the)h(pattern)f Fp([)p Fs(\013)p Fp(])p Fs(e)2169
       
  5029 2260 y Fz(0)2245 2248 y FA(in)g Fs(e)2391 2218 y Fl(0)2451
       
  5030 2248 y FA(with)h Fp([)p Fs(\013)p Fp(]\()p Fs(e)2822
       
  5031 2260 y Fz(0)2897 2248 y Fs(e)p Fp(\))p FA(.)g(W)-7 b(e)38
       
  5032 b(giv)n(e)e(a)523 2347 y(v)-5 b(arian)n(t)25 b(of)h(the)h
       
  5033 Fs(\025\026)p FA(-calculus)f(in)g(Figure)g(2.)g(In)g(con)n(texts)f
       
  5034 Fs(\000)12 b FA(,)26 b(the)h(bar)e(o)n(v)n(er)f(the)j(t)n(yp)r(e)f(of)h
       
  5035 Fs(\013)523 2447 y FA(indicates)h(that)g(it)h(is)e(not)h(a)g(v)-5
       
  5036 b(alue)28 b(of)g(t)n(yp)r(e)g Fs(\034)10 b FA(,)29 b(but)f(a)g(con)n
       
  5037 (tin)n(uation)f(accepting)g(the)i(t)n(yp)r(e)523 2547
       
  5038 y Fs(\034)10 b FA(.)648 2646 y(W)-7 b(e)28 b(ma)n(y)g(extend)h(the)g
       
  5039 Fs(\025)p FA(-calculus)f(enco)r(ding)g(with)h(a)f(new)g(name)g(t)n(yp)r
       
  5040 (e)h Fs(con)g FA(for)f(con-)523 2746 y(tin)n(uations)f(and)h(term)f
       
  5041 (constructors)f(for)h Fs(\025\026)p FA(-terms:)665 2921
       
  5042 y Fs(con)c Fp(:)g Fn(name)p 1090 2921 25 4 v 30 w(t)m(yp)s(e)166
       
  5043 b Fs(pass)24 b Fp(:)f(\()p Fs(con;)14 b(exp)p Fp(\))23
       
  5044 b Fr(!)g Fs(exp)165 b(mu)24 b Fp(:)f Fr(h)p Fs(con)p
       
  5045 Fr(i)p Fs(exp)g Fr(!)g Fs(exp)523 3098 y FA(and)31 b(enco)r(ding)g
       
  5046 Fe(p)p Fp([)p Fs(\013)p Fp(])p Fs(t)p Fe(q)d Fp(=)h Fs(pass)p
       
  5047 Fp(\()p Fs(\013;)14 b Fe(p)p Fs(t)p Fe(q)p Fp(\))32 b
       
  5048 FA(and)f Fe(p)p Fs(\026\013:t)o Fe(q)e Fp(=)g Fs(mu)p
       
  5049 Fp(\()p Fs(\013:)p Fe(p)p Fs(t)p Fe(q)p Fp(\))p FA(.)i(Again,)g(it)h
       
  5050 (is)f(easy)523 3197 y(to)d(sho)n(w)e(that)i(ground)f
       
  5051 Fs(exp)p FA(-terms)f(are)h(in)g(bijectiv)n(e)h(corresp)r(ondence)e
       
  5052 (with)i Fs(\025\026)p FA(-terms.)648 3297 y(The)i(standard)f(approac)n
       
  5053 (h)g(to)h(t)n(yp)r(ec)n(hec)n(king)f Fs(\025\026)p FA(-terms)h(is)g(to)
       
  5054 g(use)h(t)n(w)n(o)e(con)n(texts,)h Fs(\000)523 3397 y
       
  5055 FA(and)24 b Fs(\001)p FA(,)g(for)f(v)-5 b(ariable-)23
       
  5056 b(and)g(con)n(tin)n(uation-bindings)g(resp)r(ectiv)n(ely)-7
       
  5057 b(.)23 b(W)-7 b(e)24 b(instead)g(consider)523 3496 y(a)34
       
  5058 b(single)f(con)n(text)h(with)g(v)-5 b(ariable-bindings)33
       
  5059 b Fs(x)g Fp(:)h Fs(\034)44 b FA(and)34 b(con)n(tin)n(uation-bindings)f
       
  5060 Fs(\013)h Fp(:)p 3335 3448 48 4 v 34 w Fs(\034)10 b FA(.)523
       
  5061 3596 y(Therefore)26 b(w)n(e)i(mo)r(dify)g(the)g(enco)r(ding)f(of)g(con)
       
  5062 n(texts)g(sligh)n(tly)g(as)g(follo)n(ws:)541 3772 y Fs(bind)d
       
  5063 Fp(:)f Fn(t)m(yp)s(e)p Fs(:)107 b(v)s(b)23 b Fp(:)g(\()p
       
  5064 Fs(id;)14 b(ty)s Fp(\))24 b Fr(!)f Fs(bind)107 b(cb)23
       
  5065 b Fp(:)g(\()p Fs(con;)14 b(ty)s Fp(\))24 b Fr(!)f Fs(bind)107
       
  5066 b Fn(t)m(yp)s(e)28 b Fs(ctx)22 b Fp(=)h([)p Fs(bind)p
       
  5067 Fp(])p Fs(:)523 3948 y FA(Then)33 b(the)g(t)n(yp)r(ec)n(hec)n(king)e
       
  5068 (rules)h(from)g(the)h(previous)f(section)g(ma)n(y)f(b)r(e)i(adapted)g
       
  5069 (b)n(y)f(re-)523 4047 y(placing)27 b(bindings)h Fp(\()p
       
  5070 Fo(x)p Fs(;)14 b(T)e Fp(\))27 b FA(with)h Fs(v)s(b)p
       
  5071 Fp(\()p Fo(x)p Fs(;)14 b(T)e Fp(\))p FA(,)28 b(and)f(adding)g(three)h
       
  5072 (new)f(rules:)676 4206 y Fs(ty)s(p)p Fp(\()p Fs(C)q(;)14
       
  5073 b(pass)p Fp(\()p Fs(X)r(;)g(E)5 b Fp(\))p Fs(;)14 b(bot)p
       
  5074 Fp(\))25 b(:)p Fr(\000)e Fs(mem)p Fp(\()p Fs(cb)p Fp(\()p
       
  5075 Fs(X)r(;)14 b(T)e Fp(\))p Fs(;)i(C)6 b Fp(\))p Fs(;)14
       
  5076 b(ty)s(p)p Fp(\()p Fs(C)q(;)g(E)5 b(;)14 b(T)e Fp(\))p
       
  5077 Fs(:)676 4305 y(ty)s(p)p Fp(\()p Fs(C)q(;)i(app)p Fp(\()p
       
  5078 Fs(E)5 b(;)14 b(E)1255 4275 y Fl(0)1277 4305 y Fp(\))p
       
  5079 Fs(;)g(bot)p Fp(\))42 b(:)p Fr(\000)23 b Fs(ty)s(p)p
       
  5080 Fp(\()p Fs(C)q(;)14 b(E)5 b(;)14 b(bot)p Fp(\))p Fs(;)g(ty)s(p)p
       
  5081 Fp(\()p Fs(C)q(;)g(E)2473 4275 y Fl(0)2497 4305 y Fs(;)g(T)e
       
  5082 Fp(\))p Fs(:)676 4405 y(ty)s(p)p Fp(\()p Fs(C)q(;)i(mu)p
       
  5083 Fp(\()p Fo(a)p Fs(:E)5 b Fp(\))p Fs(;)14 b(T)e Fp(\))154
       
  5084 b(:)p Fr(\000)23 b Fo(a)g Fp(#)g Fs(C)q(;)14 b(ty)s(p)p
       
  5085 Fp(\([)p Fs(cb)p Fp(\()p Fo(a)p Fs(;)g(T)e Fp(\))p Fr(j)p
       
  5086 Fs(C)6 b Fp(])p Fs(;)14 b(E)5 b(;)14 b(bot)p Fp(\))p
       
  5087 Fs(:)523 4566 y FA(The)20 b(follo)n(wing)f(query)h(illustrates)f(the)i
       
  5088 (t)n(yp)r(ec)n(hec)n(king)e(for)h(the)g(term)g Fs(\025x:\026\013:)p
       
  5089 Fp(\()p Fs(x)g Fp(\()p Fs(\025y)s(:)p Fp([)p Fs(\013)p
       
  5090 Fp(])p Fs(y)s Fp(\)\))523 4666 y FA(whose)27 b(principal)g(t)n(yp)r(e)h
       
  5091 (corresp)r(onds)e(to)h(the)h(classical)e(double)i(negation)e(la)n(w.)
       
  5092 814 4836 y Fp(?)p FA({)d Fs(ty)s(p)p Fp(\([])p Fs(;)14
       
  5093 b(lam)p Fp(\()p Fo(x)p Fs(:mu)p Fp(\()p Fo(a)p Fs(:app)p
       
  5094 Fp(\()p Fs(v)s(ar)r Fp(\()p Fo(x)p Fp(\))p Fs(;)g(lam)p
       
  5095 Fp(\()p Fo(y)q Fs(:pass)q Fp(\()p Fo(a)p Fs(;)g(v)s(ar)r
       
  5096 Fp(\()p Fo(y)r Fp(\)\)\)\))q(\)\))p Fs(;)g(T)e Fp(\))p
       
  5097 Fs(:)814 4936 y(T)35 b Fp(=)22 b Fs(ar)r(r)r Fp(\()p
       
  5098 Fs(ar)r(r)r Fp(\()p Fs(ar)r(r)r Fp(\()p Fs(T)1511 4948
       
  5099 y Fz(162)1617 4936 y Fs(;)14 b(bot)p Fp(\))p Fs(;)g(bot)p
       
  5100 Fp(\))p Fs(;)g(T)2051 4948 y Fz(162)2155 4936 y Fp(\))p
       
  5101 eop end
       
  5102 %%Page: 10 10
       
  5103 TeXDict begin 10 9 bop 648 448 a FA(Capture-a)n(v)n(oiding)33
       
  5104 b(substitution)j(can)f(b)r(e)h(extended)g(to)g Fs(\025\026)p
       
  5105 FA(-terms)f(easily)-7 b(.)35 b(F)-7 b(or)35 b(re-)523
       
  5106 548 y(placemen)n(t,)f(w)n(e)g(sho)n(w)f(the)i(in)n(teresting)f(cases)f
       
  5107 (for)h(con)n(tin)n(uation)f(applications)g(and)i Fs(\026)p
       
  5108 FA(-)523 648 y(abstractions:)815 794 y Fn(func)29 b Fs(r)r(epl)p
       
  5109 Fp(\()p Fs(exp;)14 b(exp;)g(con)p Fp(\))23 b(=)f Fs(exp:)815
       
  5110 894 y(r)r(epl)p Fp(\()p Fs(pass)p Fp(\()p Fs(A;)14 b(E)1359
       
  5111 864 y Fl(0)1383 894 y Fp(\))p Fs(;)g(E)5 b(;)14 b(A)p
       
  5112 Fp(\))74 b(=)22 b Fs(pass)p Fp(\()p Fs(A;)14 b(app)p
       
  5113 Fp(\()p Fs(r)r(epl)p Fp(\()p Fs(E)2516 864 y Fl(0)2540
       
  5114 894 y Fs(;)g(E)5 b(;)14 b(A)p Fp(\))p Fs(;)g(E)5 b Fp(\)\))p
       
  5115 Fs(:)815 994 y(r)r(epl)p Fp(\()p Fs(pass)p Fp(\()p Fs(B)t(;)14
       
  5116 b(E)1365 963 y Fl(0)1389 994 y Fp(\))p Fs(;)g(E)5 b(;)14
       
  5117 b(A)p Fp(\))68 b(=)22 b Fs(pass)p Fp(\()p Fs(B)t(;)14
       
  5118 b(r)r(epl)p Fp(\()p Fs(E)2359 963 y Fl(0)2383 994 y Fs(;)g(E)5
       
  5119 b(;)14 b(A)p Fp(\)\))23 b(:)p Fr(\000)g Fs(A)g Fp(#)g
       
  5120 Fs(B)t(:)815 1093 y(r)r(epl)p Fp(\()p Fs(mu)p Fp(\()p
       
  5121 Fo(b)p Fs(:E)1286 1063 y Fl(0)1310 1093 y Fp(\))p Fs(;)14
       
  5122 b(E)5 b(;)14 b(A)p Fp(\))147 b(=)22 b Fs(mu)p Fp(\()p
       
  5123 Fo(b)p Fs(:r)r(epl)p Fp(\()p Fs(E)2280 1063 y Fl(0)2304
       
  5124 1093 y Fs(;)14 b(E)5 b(;)14 b(A)p Fp(\)\))23 b(:)p Fr(\000)g
       
  5125 Fo(b)g Fp(#)g(\()p Fs(A;)14 b(E)5 b Fp(\))p Fs(:)648
       
  5126 1258 y FA(This)21 b(\014rst-order)e(NAS)j(enco)r(ding)e(is)i(quite)f
       
  5127 (di\013eren)n(t)g(in)h(\015a)n(v)n(or)d(from)i(a)f(HO)n(AS)h(enco)r(d-)
       
  5128 523 1357 y(ing)26 b(of)g(the)g Fs(\025\026)p FA(-calculus)f(due)h(to)g
       
  5129 (Ab)r(el)h([1].)e(There,)h Fs(\026\013:t)g FA(is)g(enco)r(ded)g(as)f
       
  5130 Fs(mu)p Fp(\()p Fs(\025)p Fe(p)p Fs(\013)p Fe(q)p Fs(:)p
       
  5131 Fe(p)p Fs(t)p Fe(q)p Fp(\))p FA(,)523 1457 y(where)k
       
  5132 Fs(mu)e Fp(:)g(\(\()p Fs(tm)k(A)26 b Fr(!)h Fs(nam)p
       
  5133 Fp(\))h Fr(!)e Fs(nam)p Fp(\))i Fr(!)e Fs(tm)k(A)p FA(,)h(and)e
       
  5134 Fs(tm)h(A)g FA(is)g(the)g(t)n(yp)r(e)g(of)f(terms)523
       
  5135 1557 y(of)38 b(t)n(yp)r(e)g Fs(A)g FA(and)g Fs(nam)h
       
  5136 FA(the)f(t)n(yp)r(e)h(of)e(named)h(terms.)g(Con)n(tin)n(uations)f(are)g
       
  5137 (enco)r(ded)h(as)523 1656 y(v)-5 b(ariables)31 b Fe(p)p
       
  5138 Fs(\013)p Fe(q)f Fp(:)h(\()p Fs(tm)i(A)e Fr(!)g Fs(nam)p
       
  5139 Fp(\))i FA(and)f(named)g(terms)g Fp([)p Fs(\013)p Fp(])p
       
  5140 Fs(t)h FA(are)e(enco)r(ded)h(as)g(applica-)523 1756 y(tions)26
       
  5141 b Fe(p)p Fs(\013)p Fe(q)g(p)p Fs(t)p Fe(q)p FA(.)f(While)i(elegan)n(t,)
       
  5142 e(this)i(third-order)d(enco)r(ding)i(is)g(seman)n(tically)f(complex,)
       
  5143 523 1856 y(making)i(pro)r(ofs)g(of)g(in)n(teresting)g(prop)r(erties)g
       
  5144 (di\016cult.)523 2110 y Ft(5)112 b(Example:)39 b(the)e
       
  5145 Ff(\031)t Ft(-calculus)523 2298 y FA(The)21 b Fs(\031)s
       
  5146 FA(-calculus)f(is)h(a)f(calculus)h(of)g(concurren)n(t,)e(mobile)i(pro)r
       
  5147 (cesses.)f(Its)h(syn)n(tax)f(\(follo)n(wing)523 2397
       
  5148 y(Milner,)33 b(P)n(arro)n(w,)d(and)j(W)-7 b(alk)n(er)32
       
  5149 b([14]\))h(is)g(describ)r(ed)g(b)n(y)f(the)i(grammar)d(rules)h(sho)n
       
  5150 (wn)h(in)523 2497 y(Figure)20 b(3.)g(The)h(sym)n(b)r(ols)f
       
  5151 Fs(x;)14 b(y)s(;)g(:)g(:)g(:)20 b FA(are)f Fq(channel)25
       
  5152 b(names)p FA(.)20 b(The)h(inactiv)n(e)f(pro)r(cess)f
       
  5153 Fp(0)i FA(is)f(inert.)523 2596 y(The)j Fs(\034)5 b(:p)24
       
  5154 b FA(pro)r(cess)e(p)r(erforms)h(a)g Fq(silent)i(action)31
       
  5155 b Fs(\034)j FA(and)23 b(then)g(do)r(es)g Fs(p)p FA(.)g(P)n(arallel)f
       
  5156 (comp)r(osition)523 2696 y(is)j(denoted)f Fs(p)p Fr(j)p
       
  5157 Fs(q)k FA(and)d(nondeterministic)f(c)n(hoice)g(b)n(y)g
       
  5158 Fs(p)13 b Fp(+)g Fs(q)s FA(.)24 b(The)h(pro)r(cess)e
       
  5159 Fs(x)p Fp(\()p Fs(y)s Fp(\))p Fs(:p)i FA(inputs)g(a)523
       
  5160 2796 y(c)n(hannel)j(name)f(from)h Fs(x)p FA(,)g(binds)g(it)h(to)e
       
  5161 Fs(y)s FA(,)i(and)f(then)g(do)r(es)g Fs(p)p FA(.)g(The)g(pro)r(cess)p
       
  5162 2941 2748 48 4 v 27 w Fs(x)o(y)s(:p)h FA(outputs)523
       
  5163 2895 y Fs(y)k FA(to)d Fs(x)g FA(and)f(then)i(do)r(es)e
       
  5164 Fs(p)p FA(.)h(The)g(matc)n(h)g(op)r(erator)e Fp([)p Fs(x)e
       
  5165 Fp(=)h Fs(y)s Fp(])p Fs(p)j FA(is)g Fs(p)f FA(pro)n(vided)g
       
  5166 Fs(x)e Fp(=)f Fs(y)s FA(,)k(but)523 2995 y(is)d(inactiv)n(e)f(if)h
       
  5167 Fs(x)22 b Fr(6)p Fp(=)h Fs(y)s FA(.)k(The)g(restriction)e(op)r(erator)g
       
  5168 Fp(\()p Fs(y)s Fp(\))p Fs(p)i FA(restricts)f Fs(y)k FA(to)c
       
  5169 Fs(p)p FA(.)h(P)n(aren)n(thesized)523 3095 y(names)d(\(e.g.)g
       
  5170 Fs(y)k FA(in)c Fs(x)p Fp(\()p Fs(y)s Fp(\))p Fs(:p)h
       
  5171 FA(and)f Fp(\()p Fs(y)s Fp(\))p Fs(p)p FA(\))i(are)d(binding,)h(and)h
       
  5172 Fs(f)8 b(n)p Fp(\()p Fs(p)p Fp(\))p FA(,)25 b Fs(bn)p
       
  5173 Fp(\()p Fs(p)p Fp(\))h FA(and)e Fs(n)p Fp(\()p Fs(p)p
       
  5174 Fp(\))h FA(denote)523 3194 y(the)e(sets)g(of)g(free,)f(b)r(ound,)h(and)
       
  5175 g(all)g(names)f(o)r(ccurring)f(in)i Fs(p)p FA(.)g(Capture-a)n(v)n
       
  5176 (oiding)d(renaming)523 3294 y(is)28 b(written)f Fs(t)p
       
  5177 Fr(f)p Fs(x=y)s Fr(g)p FA(.)648 3393 y(Milner)g(et)h(al.'s)f(original)f
       
  5178 (op)r(erational)g(seman)n(tics)g(\(sho)n(wn)h(in)h(Figure)f(3,)g
       
  5179 (symmetric)523 3505 y(cases)e(omitted\))i(is)f(a)g(lab)r(eled)h
       
  5180 (transition)e(system)h(with)h(relation)e Fs(p)2760 3457
       
  5181 y Fm(a)2711 3505 y Fr(\000)-14 b(!)23 b Fs(q)30 b FA(indicating)c(\\)p
       
  5182 Fs(p)812 3776 y Fx(Pro)r(cess)i(terms)d Fu(p)e Fk(::=)h(0)e
       
  5183 Fi(j)f Fu(\034)5 b(:p)21 b Fi(j)h Fu(p)p Fi(j)p Fu(q)i
       
  5184 Fi(j)d Fu(p)c Fk(+)g Fu(q)24 b Fi(j)d Fu(x)p Fk(\()p
       
  5185 Fu(y)s Fk(\))p Fu(:p)g Fi(j)p 2427 3732 44 4 v 22 w Fu(xy)s(:p)g
       
  5186 Fi(j)h Fk([)p Fu(x)f Fk(=)g Fu(y)s Fk(])p Fu(p)h Fi(j)f
       
  5187 Fk(\()p Fu(x)p Fk(\))p Fu(p)812 3867 y Fx(Actions)235
       
  5188 b Fu(a)23 b Fk(::=)h Fu(\034)30 b Fi(j)22 b Fu(x)p Fk(\()p
       
  5189 Fu(y)s Fk(\))f Fi(j)p 1809 3823 V 21 w Fu(xy)k Fi(j)p
       
  5190 1959 3823 V 21 w Fu(x)p Fk(\()p Fu(y)s Fk(\))959 4156
       
  5191 y Fu(\034)5 b(:p)1126 4113 y Fg(\034)1081 4156 y Fi(\000)-13
       
  5192 b(!)21 b Fu(p)1343 4026 y(p)1449 3983 y Fg(a)1404 4026
       
  5193 y Fi(\000)-13 b(!)21 b Fu(p)1589 3995 y Fd(0)1686 4026
       
  5194 y Fu(bn)p Fk(\()p Fu(a)p Fk(\))16 b Fi(\\)i Fu(f)8 b(n)p
       
  5195 Fk(\()p Fu(q)s Fk(\))19 b(=)i Fi(;)p 1343 4065 944 4
       
  5196 v 1623 4156 a Fu(p)p Fi(j)p Fu(q)1788 4113 y Fg(a)1742
       
  5197 4156 y Fi(\000)-13 b(!)21 b Fu(p)1927 4124 y Fd(0)1948
       
  5198 4156 y Fi(j)p Fu(q)2363 4031 y(p)p 2453 3954 34 3 v 2453
       
  5199 3984 a Fg(xy)2424 4031 y Fi(\000)-13 b(!)22 b Fu(p)2610
       
  5200 3999 y Fd(0)2707 4031 y Fu(q)2771 3981 y Fg(x)p Fy(\()p
       
  5201 Fg(z)r Fy(\))2766 4031 y Fi(\000)-13 b(!)21 b Fu(q)2949
       
  5202 3999 y Fd(0)p 2363 4065 606 4 v 2365 4156 a Fu(p)p Fi(j)p
       
  5203 Fu(q)2529 4113 y Fg(\034)2484 4156 y Fi(\000)-13 b(!)21
       
  5204 b Fu(p)2669 4124 y Fd(0)2690 4156 y Fi(j)p Fu(q)2749
       
  5205 4124 y Fd(0)2770 4156 y Fi(f)p Fu(y)s(=z)t Fi(g)975 4289
       
  5206 y Fu(p)1081 4246 y Fg(a)1036 4289 y Fi(\000)-13 b(!)21
       
  5207 b Fu(p)1221 4257 y Fd(0)p 909 4323 398 4 v 909 4414 a
       
  5208 Fu(p)c Fk(+)g Fu(q)1147 4371 y Fg(a)1101 4414 y Fi(\000)-13
       
  5209 b(!)21 b Fu(p)1286 4383 y Fd(0)p 1384 4371 44 4 v 1384
       
  5210 4414 a Fu(xy)s(:p)p 1581 4338 34 3 v 1581 4368 a Fg(x)o(y)1552
       
  5211 4414 y Fi(\000)-13 b(!)21 b Fu(p)1905 4264 y(w)32 b(=)-46
       
  5212 b Fi(2)21 b Fu(f)8 b(n)p Fk(\(\()p Fu(z)t Fk(\))p Fu(p)p
       
  5213 Fk(\))p 1814 4303 630 4 v 1814 4414 a Fu(x)p Fk(\()p
       
  5214 Fu(z)t Fk(\))p Fu(:p)2040 4365 y Fg(x)p Fy(\()p Fg(w)q
       
  5215 Fy(\))2042 4414 y Fi(\000)-13 b(!)23 b Fu(p)p Fi(f)p
       
  5216 Fu(w)r(=z)t Fi(g)2636 4289 y Fu(p)2742 4246 y Fg(a)2697
       
  5217 4289 y Fi(\000)-13 b(!)21 b Fu(p)2882 4257 y Fd(0)p 2520
       
  5218 4323 500 4 v 2520 4414 a Fk([)p Fu(x)g Fk(=)g Fu(x)p
       
  5219 Fk(])p Fu(p)2859 4371 y Fg(a)2813 4414 y Fi(\000)-13
       
  5220 b(!)21 b Fu(p)2998 4383 y Fd(0)738 4581 y Fu(p)p 799
       
  5221 4501 34 3 v 799 4532 a Fg(x)p Fy(\()p Fg(w)q Fy(\))801
       
  5222 4581 y Fi(\000)-13 b(!)23 b Fu(p)988 4549 y Fd(0)1085
       
  5223 4581 y Fu(q)1144 4532 y Fg(x)p Fy(\()p Fg(w)q Fy(\))1145
       
  5224 4581 y Fi(\000)-13 b(!)23 b Fu(q)1330 4549 y Fd(0)p 738
       
  5225 4615 613 4 v 753 4706 a Fu(p)p Fi(j)p Fu(q)917 4663 y
       
  5226 Fg(\034)873 4706 y Fi(\000)-14 b(!)22 b Fk(\()p Fu(w)r
       
  5227 Fk(\)\()p Fu(p)1206 4674 y Fd(0)1226 4706 y Fi(j)p Fu(q)1285
       
  5228 4674 y Fd(0)1306 4706 y Fk(\))1427 4576 y Fu(p)1534 4533
       
  5229 y Fg(a)1488 4576 y Fi(\000)-13 b(!)21 b Fu(p)1673 4545
       
  5230 y Fd(0)1771 4576 y Fu(y)33 b(=)-47 b Fi(2)22 b Fu(n)p
       
  5231 Fk(\()p Fu(a)p Fk(\))p 1427 4615 630 4 v 1507 4706 a(\()p
       
  5232 Fu(y)s Fk(\))p Fu(p)1715 4663 y Fg(a)1670 4706 y Fi(\000)-13
       
  5233 b(!)21 b Fk(\()p Fu(y)s Fk(\))p Fu(p)1957 4674 y Fd(0)2134
       
  5234 4556 y Fu(p)p 2223 4480 34 3 v 2223 4510 a Fg(xy)2195
       
  5235 4556 y Fi(\000)-13 b(!)21 b Fu(p)2380 4524 y Fd(0)2477
       
  5236 4556 y Fu(y)j Fi(6)p Fk(=)e Fu(x)76 b(w)32 b(=)-46 b
       
  5237 Fi(2)21 b Fu(f)8 b(n)p Fk(\(\()p Fu(y)s Fk(\))p Fu(p)p
       
  5238 Fk(\))p 2134 4595 1057 4 v 2368 4706 a(\()p Fu(y)s Fk(\))p
       
  5239 Fu(p)p 2531 4627 34 3 v 2531 4657 a Fg(x)o Fy(\()p Fg(w)q
       
  5240 Fy(\))2532 4706 y Fi(\000)-13 b(!)23 b Fu(p)2719 4674
       
  5241 y Fd(0)2740 4706 y Fi(f)p Fu(w)r(=y)s Fi(g)1587 4910
       
  5242 y Fv(Fig.)13 b(3.)26 b Fx(The)g Fu(\031)s Fx(-calculus)p
       
  5243 eop end
       
  5244 %%Page: 11 11
       
  5245 TeXDict begin 11 10 bop 659 509 a Fv(func)26 b Fu(r)r(en)p
       
  5246 978 509 24 4 v 28 w(p)p Fk(\()p Fu(pr)r(oc;)13 b(chan;)f(chan)p
       
  5247 Fk(\))23 b(=)g Fu(pr)r(oc:)j Fx(\(*)g(de\014nition)f(omitted)h(*\))659
       
  5248 600 y Fv(pred)g Fu(saf)8 b(e)p Fk(\()p Fu(act;)k(pr)r
       
  5249 Fk(\))p Fu(:)251 b Fx(\(*)26 b(tests)g Fu(bn)p Fk(\()p
       
  5250 Fu(A)p Fk(\))16 b Fi(\\)h Fu(f)8 b(n)p Fk(\()p Fu(P)j
       
  5251 Fk(\))20 b(=)h Fi(;)26 b Fx(*\))659 691 y Fu(saf)8 b(e)p
       
  5252 Fk(\()p Fu(tau)p 972 691 V 26 w(a;)13 b(P)e Fk(\))p Fu(:)659
       
  5253 782 y(saf)d(e)p Fk(\()p Fu(f)g(out)p 1013 782 V 26 w(a)p
       
  5254 Fk(\()p Fu(X)r(;)k(Y)17 b Fk(\))p Fu(;)c(P)e Fk(\))p
       
  5255 Fu(:)659 874 y(saf)d(e)p Fk(\()p Fu(bout)p 1000 874 V
       
  5256 26 w(a)p Fk(\()p Fu(X)r(;)k(Y)17 b Fk(\))p Fu(;)c(P)e
       
  5257 Fk(\))56 b(:)q Fi(\000)23 b Fu(Y)38 b Fk(#)21 b Fu(P)r(:)659
       
  5258 965 y(saf)8 b(e)p Fk(\()p Fu(in)p 932 965 V 26 w(a)p
       
  5259 Fk(\()p Fu(X)r(;)k(Y)17 b Fk(\))p Fu(;)c(P)e Fk(\))124
       
  5260 b(:)q Fi(\000)23 b Fu(Y)38 b Fk(#)21 b Fu(P)r(:)659 1067
       
  5261 y Fv(pred)26 b Fu(step)p Fk(\()p Fu(pr)n(;)12 b(act;)h(pr)r
       
  5262 Fk(\))p Fu(:)770 b Fx(\(*)26 b(enco)r(des)h Fu(p)2659
       
  5263 1024 y Fg(a)2614 1067 y Fi(\000)-13 b(!)21 b Fu(p)2799
       
  5264 1035 y Fd(0)2845 1067 y Fx(*\))659 1158 y Fu(step)p Fk(\()p
       
  5265 Fu(tau)p Fk(\()p Fu(P)11 b Fk(\))p Fu(;)g(tau)p 1221
       
  5266 1158 V 27 w(a;)i(P)e Fk(\))p Fu(:)659 1250 y(step)p Fk(\()p
       
  5267 Fu(par)r Fk(\()p Fu(P)r(;)h(Q)p Fk(\))p Fu(;)h(A;)g(par)r
       
  5268 Fk(\()p Fu(P)1490 1218 y Fd(0)1509 1250 y Fu(;)h(Q)p
       
  5269 Fk(\)\))405 b(:)q Fi(\000)22 b Fu(step)p Fk(\()p Fu(P)r(;)13
       
  5270 b(A;)g(P)2581 1218 y Fd(0)2601 1250 y Fk(\))p Fu(;)g(saf)8
       
  5271 b(e)p Fk(\()p Fu(A;)k(Q)p Fk(\))p Fu(:)659 1341 y(step)p
       
  5272 Fk(\()p Fu(par)r Fk(\()p Fu(P)r(;)g(Q)p Fk(\))p Fu(;)h(tau)p
       
  5273 1311 1341 V 27 w(a;)g(par)r Fk(\()p Fu(P)1619 1309 y
       
  5274 Fd(0)1638 1341 y Fu(;)g(Q)1733 1309 y Fd(00)1771 1341
       
  5275 y Fk(\)\))239 b(:)q Fi(\000)22 b Fu(step)p Fk(\()p Fu(P)r(;)13
       
  5276 b(f)8 b(out)p 2593 1341 V 26 w(a)p Fk(\()p Fu(X)r(;)k(Y)17
       
  5277 b Fk(\))p Fu(;)c(P)2969 1309 y Fd(0)2989 1341 y Fk(\))p
       
  5278 Fu(;)2174 1432 y(step)p Fk(\()p Fu(Q;)g(in)p 2522 1432
       
  5279 V 27 w(a)p Fk(\()p Fu(X)r(;)f(Z)5 b Fk(\))p Fu(;)13 b(Q)2896
       
  5280 1400 y Fd(0)2917 1432 y Fk(\))p Fu(;)2174 1524 y(Q)2235
       
  5281 1492 y Fd(00)2294 1524 y Fk(=)21 b Fu(r)r(en)p 2504 1524
       
  5282 V 28 w(p)p Fk(\()p Fu(Q)2658 1492 y Fd(0)2678 1524 y
       
  5283 Fu(;)13 b(Y)t(;)g(Z)5 b Fk(\))p Fu(:)659 1615 y(step)p
       
  5284 Fk(\()p Fu(sum)p Fk(\()p Fu(P)r(;)12 b(Q)p Fk(\))p Fu(;)h(A;)g(P)1373
       
  5285 1583 y Fd(0)1393 1615 y Fk(\))647 b(:)q Fi(\000)22 b
       
  5286 Fu(step)p Fk(\()p Fu(P)r(;)13 b(A;)g(P)2581 1583 y Fd(0)2601
       
  5287 1615 y Fk(\))p Fu(:)659 1706 y(step)p Fk(\()p Fu(out)p
       
  5288 Fk(\()p Fu(X)r(;)e(Y)t(;)i(P)e Fk(\))p Fu(;)i(f)8 b(out)p
       
  5289 1438 1706 V 26 w(a)p Fk(\()p Fu(X)r(;)k(Y)17 b Fk(\))p
       
  5290 Fu(;)c(P)e Fk(\))p Fu(:)659 1798 y(step)p Fk(\()p Fu(in)p
       
  5291 Fk(\()p Fu(X)r(;)g(z)t(:P)g Fk(\))p Fu(;)h(in)p 1301
       
  5292 1798 V 27 w(a)p Fk(\()p Fu(X)r(;)g(W)f Fk(\))p Fu(;)i(P)1700
       
  5293 1766 y Fd(0)1720 1798 y Fk(\))320 b(:)q Fi(\000)22 b
       
  5294 Fu(W)32 b Fk(#)21 b Fu(z)t(:P)r(;)13 b(P)2570 1766 y
       
  5295 Fd(0)2612 1798 y Fk(=)21 b Fu(r)r(en)p 2822 1798 V 28
       
  5296 w(p)p Fk(\()p Fu(P)r(;)12 b(W)n(;)h(z)t Fk(\))p Fu(:)659
       
  5297 1889 y(step)p Fk(\()p Fu(match)p Fk(\()p Fu(X)r(;)e(X)r(;)i(P)e
       
  5298 Fk(\))p Fu(;)h(A;)h(P)1549 1857 y Fd(0)1569 1889 y Fk(\))471
       
  5299 b(:)q Fi(\000)22 b Fu(step)p Fk(\()p Fu(P)r(;)13 b(A;)g(P)2581
       
  5300 1857 y Fd(0)2601 1889 y Fk(\))p Fu(:)659 1980 y(step)p
       
  5301 Fk(\()p Fu(par)r Fk(\()p Fu(P)r(;)f(Q)p Fk(\))p Fu(;)h(tau)p
       
  5302 1311 1980 V 27 w(a;)g(r)r(es)p Fk(\()p Fu(z)t(:par)r
       
  5303 Fk(\()p Fu(P)1822 1948 y Fd(0)1842 1980 y Fu(;)g(Q)1937
       
  5304 1948 y Fd(0)1957 1980 y Fk(\)\)\))23 b(:)q Fi(\000)f
       
  5305 Fu(step)p Fk(\()p Fu(P)r(;)13 b(bout)p 2580 1980 V 27
       
  5306 w(a)p Fk(\()p Fu(X)r(;)f(z)t Fk(\))p Fu(;)h(P)2937 1948
       
  5307 y Fd(0)2957 1980 y Fk(\))p Fu(;)2174 2071 y(step)p Fk(\()p
       
  5308 Fu(Q;)g(in)p 2522 2071 V 27 w(a)p Fk(\()p Fu(X)r(;)f(z)t
       
  5309 Fk(\))p Fu(;)g(Q)2879 2040 y Fd(0)2900 2071 y Fk(\))p
       
  5310 Fu(:)659 2163 y(step)p Fk(\()p Fu(r)r(es)p Fk(\()p Fu(y)s(:P)f
       
  5311 Fk(\))p Fu(;)i(A;)g(r)r(es)p Fk(\()p Fu(y)s(:P)1513 2131
       
  5312 y Fd(0)1533 2163 y Fk(\)\))477 b(:)q Fi(\000)22 b Fu(y)j
       
  5313 Fk(#)c Fu(A;)13 b(step)p Fk(\()p Fu(P)r(;)g(A;)f(P)2820
       
  5314 2131 y Fd(0)2841 2163 y Fk(\))p Fu(:)659 2254 y(step)p
       
  5315 Fk(\()p Fu(r)r(es)p Fk(\()p Fu(y)s(:P)f Fk(\))p Fu(;)i(bout)p
       
  5316 1308 2254 V 27 w(a)p Fk(\()p Fu(X)r(;)f(W)f Fk(\))p Fu(;)h(P)1706
       
  5317 2222 y Fd(00)1743 2254 y Fk(\))297 b(:)q Fi(\000)22 b
       
  5318 Fu(step)p Fk(\()p Fu(P)r(;)13 b(f)8 b(out)p 2593 2254
       
  5319 V 26 w(a)p Fk(\()p Fu(X)r(;)k(y)s Fk(\))p Fu(;)i(P)2951
       
  5320 2222 y Fd(0)2971 2254 y Fk(\))p Fu(;)f(y)24 b Fk(#)d
       
  5321 Fu(X)r(;)2174 2345 y(W)32 b Fk(#)21 b Fu(y)s(:P)r(;)14
       
  5322 b(P)2572 2314 y Fd(00)2630 2345 y Fk(=)21 b Fu(r)r(en)p
       
  5323 2840 2345 V 28 w(p)p Fk(\()p Fu(P)2993 2314 y Fd(0)3012
       
  5324 2345 y Fu(;)13 b(W)n(;)g(y)s Fk(\))p Fu(:)1270 2587 y
       
  5325 Fv(Fig.)h(4.)25 b Fu(\031)s Fx(-calculus)i(transitions)f(in)g
       
  5326 Fu(\013)p Fx(Prolog)523 2931 y FA(steps)j(to)f Fs(q)33
       
  5327 b FA(b)n(y)28 b(p)r(erforming)g(action)g Fs(a)p FA(".)h(Actions)g
       
  5328 Fs(\034)10 b FA(,)p 2239 2882 48 4 v 29 w Fs(x)o(y)s
       
  5329 FA(,)30 b Fs(x)p Fp(\()p Fs(y)s Fp(\))p FA(,)p 2593 2882
       
  5330 V 29 w Fs(x)p Fp(\()p Fs(y)s Fp(\))g FA(are)d(referred)h(to)h(as)523
       
  5331 3030 y Fq(silent)p FA(,)24 b Fq(fr)l(e)l(e)j(output)p
       
  5332 FA(,)c Fq(input)p FA(,)h(and)g Fq(b)l(ound)i(output)31
       
  5333 b FA(actions)24 b(resp)r(ectiv)n(ely;)f(the)h(\014rst)g(t)n(w)n(o)f
       
  5334 (are)523 3130 y(called)j Fq(fr)l(e)l(e)32 b FA(and)26
       
  5335 b(the)g(second)g(t)n(w)n(o)f(are)g(called)h Fq(b)l(ound)34
       
  5336 b FA(actions.)25 b(F)-7 b(or)26 b(an)f(action)h Fs(a)p
       
  5337 FA(,)g Fs(n)p Fp(\()p Fs(a)p Fp(\))h FA(is)523 3229 y(the)h(set)g(of)f
       
  5338 (all)g(names)h(app)r(earing)e(in)i Fs(a)p FA(,)g(and)f
       
  5339 Fs(bn)p Fp(\()p Fs(a)p Fp(\))i FA(is)f(empt)n(y)f(if)h
       
  5340 Fs(a)g FA(is)g(a)f(free)g(action)g(and)523 3329 y(is)f
       
  5341 Fr(f)p Fs(y)s Fr(g)f FA(if)h Fs(a)g FA(is)f(a)h(b)r(ound)g(action)f
       
  5342 Fs(x)p Fp(\()p Fs(y)s Fp(\))h FA(or)p 1837 3281 V 25
       
  5343 w Fs(x)p Fp(\()p Fs(y)s Fp(\))p FA(.)h(Pro)r(cesses)c(and)j(actions)f
       
  5344 (can)g(b)r(e)h(enco)r(ded)523 3429 y(using)h(the)h(follo)n(wing)f(syn)n
       
  5345 (tax:)615 3663 y Fs(chan)d Fp(:)f Fn(name)p 1095 3663
       
  5346 25 4 v 29 w(t)m(yp)s(e)q Fs(:)166 b(pr)r(oc)23 b Fp(:)g
       
  5347 Fn(t)m(yp)s(e)p Fs(:)146 b(ina)24 b Fp(:)f Fs(pr)r(oc:)166
       
  5348 b(tau)23 b Fp(:)g Fs(pr)r(oc)g Fr(!)g Fs(pr)r(oc:)615
       
  5349 3763 y(par)n(;)14 b(sum)23 b Fp(:)h(\()p Fs(pr)r(oc;)14
       
  5350 b(pr)r(oc)p Fp(\))23 b Fr(!)g Fs(pr)r(oc:)414 b(in)24
       
  5351 b Fp(:)f(\()p Fs(chan;)14 b Fr(h)p Fs(chan)p Fr(i)p Fs(pr)r(oc)p
       
  5352 Fp(\))25 b Fr(!)e Fs(pr)r(oc:)615 3862 y(out;)14 b(match)24
       
  5353 b Fp(:)f(\()p Fs(chan;)14 b(chan;)g(pr)r(oc)p Fp(\))24
       
  5354 b Fr(!)f Fs(pr)r(oc:)106 b(r)r(es)24 b Fp(:)f(\()p Fr(h)p
       
  5355 Fs(chan)p Fr(i)p Fs(pr)r(oc)p Fp(\))i Fr(!)e Fs(pr)r(oc:)615
       
  5356 3962 y(act)g Fp(:)g Fn(t)m(yp)s(e)p Fs(:)166 b(tau)p
       
  5357 1298 3962 V 30 w(a)23 b Fp(:)h Fs(act:)165 b(in)p 1824
       
  5358 3962 V 31 w(a;)14 b(f)8 b(out)p 2106 3962 V 30 w(a;)14
       
  5359 b(bout)p 2373 3962 V 31 w(a)23 b Fp(:)g(\()p Fs(chan;)14
       
  5360 b(chan)p Fp(\))25 b Fr(!)e Fs(act:)648 4227 y FA(Muc)n(h)31
       
  5361 b(of)h(the)g(complexit)n(y)f(of)h(the)g(rules)f(is)g(due)h(to)g(the)g
       
  5362 (need)f(to)h(handle)f Fq(sc)l(op)l(e)k(ex-)523 4327 y(trusion)p
       
  5363 FA(,)i(whic)n(h)h(o)r(ccurs)f(when)g(restricted)g(names)g(\\escap)r(e")
       
  5364 f(their)i(scop)r(e)f(b)r(ecause)g(of)523 4426 y(comm)n(unication.)22
       
  5365 b(In)g Fp(\(\()p Fs(x)p Fp(\))p 1362 4378 46 4 v Fs(ax:p)p
       
  5366 Fp(\))p Fr(j)p Fp(\()p Fs(a)p Fp(\()p Fs(z)t Fp(\))p
       
  5367 Fs(:z)t Fp(\()p Fs(x)p Fp(\))p Fs(:)p Fp(0\))2110 4379
       
  5368 y Fm(\034)2062 4426 y Fr(\000)-15 b(!)23 b Fp(\()p Fs(x)2298
       
  5369 4396 y Fl(0)2320 4426 y Fp(\)\()p Fs(p)p Fr(j)p Fs(x)2498
       
  5370 4396 y Fl(0)2520 4426 y Fp(\()p Fs(x)p Fp(\))p Fs(:)p
       
  5371 Fp(0\)\))p FA(,)g(for)f(example,)f(it)i(is)523 4526 y(necessary)17
       
  5372 b(to)i(\\freshen")e Fs(x)i FA(to)f Fs(x)1540 4496 y Fl(0)1581
       
  5373 4526 y FA(in)h(order)e(to)i(a)n(v)n(oid)e(capturing)h(the)h(free)g
       
  5374 Fs(x)f FA(in)h Fs(a)p Fp(\()p Fs(z)t Fp(\))p Fs(:z)t
       
  5375 Fp(\()p Fs(x)p Fp(\))p Fs(:)p Fp(0)p FA(.)523 4625 y(Bound)28
       
  5376 b(output)g(actions)f(are)g(used)h(to)g(lift)h(the)f(scop)r(e)g(of)g(an)
       
  5377 f(escaping)g(name)h(out)g(to)g(the)523 4725 y(p)r(oin)n(t)d(where)f(it)
       
  5378 h(is)f(receiv)n(ed.)g(The)h(rules)f(can)g(b)r(e)h(translated)f
       
  5379 (directly)g(in)n(to)h Fs(\013)p FA(Prolog)d(\(see)523
       
  5380 4825 y(Figure)h(4\).)h(The)g(function)h Fs(r)r(en)p 1529
       
  5381 4825 25 4 v 30 w(p)p Fp(\()p Fs(P)r(;)14 b(Y)5 b(;)14
       
  5382 b(X)7 b Fp(\))24 b FA(p)r(erforming)f(capture-a)n(v)n(oiding)e
       
  5383 (renaming)i(is)523 4924 y(not)28 b(sho)n(wn,)f(but)h(easy)e(to)i
       
  5384 (de\014ne.)p eop end
       
  5385 %%Page: 12 12
       
  5386 TeXDict begin 12 11 bop 648 448 a FA(W)-7 b(e)21 b(can)f(c)n(hec)n(k)g
       
  5387 (that)h(this)g(implemen)n(tation)g(of)g(the)g(op)r(erational)f(seman)n
       
  5388 (tics)g(pro)r(duces)523 548 y(correct)26 b(answ)n(ers)g(for)h(the)h
       
  5389 (follo)n(wing)f(queries:)727 732 y Fp(?)p FA({)c Fs(step)p
       
  5390 Fp(\()p Fs(r)r(es)p Fp(\()p Fo(x)p Fs(:par)r Fp(\()p
       
  5391 Fs(r)r(es)p Fp(\()p Fo(y)q Fs(:out)p Fp(\()p Fo(x)p Fs(;)14
       
  5392 b Fo(y)q Fs(;)g(ina)p Fp(\)\))p Fs(;)g(in)p Fp(\()p Fo(x)q
       
  5393 Fs(;)g Fo(z)p Fs(:out)p Fp(\()p Fo(z)p Fs(;)g Fo(x)p
       
  5394 Fs(;)g(in)q(a)p Fp(\)\)\))q(\))p Fs(;)g(A;)g(P)e Fp(\))p
       
  5395 Fs(:)727 832 y(A)24 b Fp(=)e Fs(tau)p 1029 832 25 4 v
       
  5396 30 w(a;)14 b(P)35 b Fp(=)22 b Fs(r)r(es)p Fp(\()p Fo(y)1501
       
  5397 844 y Fz(58)1573 832 y Fs(:r)r(es)p Fp(\()p Fo(z)1784
       
  5398 844 y Fz(643)1889 832 y Fs(:par)r Fp(\()p Fs(ina;)14
       
  5399 b(out)p Fp(\()p Fo(z)2425 844 y Fz(643)2529 832 y Fs(;)g
       
  5400 Fo(y)2604 844 y Fz(58)2675 832 y Fs(;)g(ina)p Fp(\)\)\)\))727
       
  5401 932 y(?)p FA({)23 b Fs(step)p Fp(\()p Fs(r)r(es)p Fp(\()p
       
  5402 Fo(x)p Fs(:out)p Fp(\()p Fo(x)p Fs(;)14 b Fo(y)q Fs(;)g(ina)p
       
  5403 Fp(\)\))p Fs(;)g(A;)g(P)e Fp(\))p Fs(:)727 1031 y(N)d(o:)523
       
  5404 1242 y FA(This)32 b Fs(\013)p FA(Prolog)f(session)g(sho)n(ws)h(that)g
       
  5405 Fp(\()p Fs(x)p Fp(\)\(\()p Fs(y)s Fp(\))p 2000 1194 48
       
  5406 4 v Fs(x)q(y)s(:)p Fp(0)f Fr(j)g Fs(x)p Fp(\()p Fs(y)s
       
  5407 Fp(\))p Fs(:)p 2424 1194 46 4 v(y)t(x:)p Fp(0\))2694
       
  5408 1195 y Fm(\034)2646 1242 y Fr(\000)-14 b(!)31 b Fp(\()p
       
  5409 Fs(x)p Fp(\)\()p Fs(y)s Fp(\)\(0)h Fr(j)p 3192 1194 V
       
  5410 31 w Fs(y)s(x:)p Fp(0\))p FA(,)523 1342 y(but)i Fp(\()p
       
  5411 Fs(x)p Fp(\)\()p Fs(x)p Fp(\()p Fs(y)s Fp(\))p Fs(:)p
       
  5412 Fp(0\))g FA(cannot)f(mak)n(e)f(an)n(y)g(transition.)h(Moreo)n(v)n(er,)d
       
  5413 (the)k(answ)n(er)e(to)h(the)g(\014rst)523 1442 y(query)27
       
  5414 b(is)g(unique)h(\(up)g(to)g(renaming\).)648 1545 y(R\177)-42
       
  5415 b(oc)n(kl)29 b([20])h(and)h(Gabba)n(y)e([6])i(ha)n(v)n(e)e(also)h
       
  5416 (considered)f(enco)r(dings)h(of)h(the)g Fs(\031)s FA(-calculus)523
       
  5417 1645 y(using)k(nominal)h(abstract)e(syn)n(tax.)h(R\177)-42
       
  5418 b(oc)n(kl)35 b(considered)g(only)g(mo)r(deling)g(the)h(syn)n(tax)f(of)
       
  5419 523 1744 y(terms)f(up)h(to)g Fs(\013)p FA(-equiv)-5 b(alence)34
       
  5420 b(using)g(sw)n(apping,)g(whereas)g(Gabba)n(y)f(w)n(en)n(t)i(further,)f
       
  5421 (en-)523 1844 y(co)r(ding)j(transitions)g(and)g(the)h(bisim)n(ulation)g
       
  5422 (relation)e(and)i(pro)n(ving)e(basic)h(prop)r(erties)523
       
  5423 1943 y(thereof.)25 b(By)h([6,)f(Thm)h(4.5],)e(Gabba)n(y's)h(v)n(ersion)
       
  5424 f(of)h(the)h Fs(\031)s FA(-calculus)f(is)g(equiv)-5 b(alen)n(t)25
       
  5425 b(to)h(our)523 2043 y(con)n(v)n(en)n(tional)g(represen)n(tation.)g(In)h
       
  5426 (fact,)h(Gabba)n(y's)f(presen)n(tation)f(is)i(a)f(bit)h(simpler)f(and)
       
  5427 523 2143 y(easier)h(to)h(reason)e(ab)r(out,)j(but)f(w)n(e)g(ha)n(v)n(e)
       
  5428 f(c)n(hosen)g(Milner)h(et)h(al.'s)f(original)e(presen)n(tation)523
       
  5429 2242 y(to)33 b(emphasize)g(that)h(informal)f(\\pap)r(er")f(presen)n
       
  5430 (tations)g(\(ev)n(en)h(for)g(fairly)f(complicated)523
       
  5431 2342 y(calculi\))c(can)f(b)r(e)h(translated)f(directly)g(to)g
       
  5432 Fs(\013)p FA(Prolog)f(programs.)523 2626 y Ft(6)112 b(Concluding)39
       
  5433 b(Remarks)523 2843 y Fn(6.1)95 b(Related)31 b(w)m(ork)523
       
  5434 3028 y(F)-8 b(reshML)34 b FA([22]:)g(an)g(extension)g(of)g(the)h(ML)g
       
  5435 (programming)d(language)g(with)j(Gabba)n(y-)523 3127
       
  5436 y(Pitts)30 b(names,)g(name-binding)g(with)h(pattern)f(matc)n(hing,)f
       
  5437 (and)h(fresh)g(name)g(generation.)523 3227 y Fs(\013)p
       
  5438 FA(Prolog)21 b(is)i(related)f(to)h(F)-7 b(reshML)23 b(in)g(man)n(y)f(w)
       
  5439 n(a)n(ys,)g(and)h(it)g(is)g(fair)f(to)h(sa)n(y)f(that)h
       
  5440 Fs(\013)p FA(Prolog)e(is)523 3327 y(to)29 b(logic)f(programming)f(what)
       
  5441 i(F)-7 b(reshML)29 b(is)g(to)g(functional)h(programming.)d(W)-7
       
  5442 b(e)29 b(b)r(eliev)n(e)523 3426 y(ho)n(w)n(ev)n(er)d(that)i(the)h
       
  5443 (di\013erences)f(b)r(et)n(w)n(een)g(F)-7 b(reshML)27
       
  5444 b(and)h Fs(\013)p FA(Prolog)e(are)i(more)f(than)h(cos-)523
       
  5445 3526 y(metic.)f Fs(\013)p FA(Prolog)d(lends)i(itself)g(to)g(a)g
       
  5446 (declarativ)n(e)e(st)n(yle)i(of)g(nameful)g(programming)e(whic)n(h)523
       
  5447 3626 y(is)29 b(refreshingly)e(close)h(to)g(informal)g(declarativ)n(e)f
       
  5448 (presen)n(tations)g(of)i(op)r(erational)e(seman-)523
       
  5449 3725 y(tics,)g(t)n(yp)r(e)h(systems)f(and)g(logics,)f(in)i(con)n(trast)
       
  5450 e(to)h(F)-7 b(reshML)27 b(whic)n(h)g(remains)f(pro)r(cedural)523
       
  5451 3825 y(\(and)21 b(e\013ectful\))h(at)f(heart.)f(There)g(are)g(also)g
       
  5452 (ma)5 b(jor)19 b(di\013erences)i(from)f(a)h(tec)n(hnical)f(p)r(oin)n(t)
       
  5453 h(of)523 3924 y(view:)26 b(in)g(F)-7 b(reshML)25 b(m)n(uc)n(h)g
       
  5454 (researc)n(h)f(w)n(en)n(t)i(in)n(to)f(designing)g(an)g(expressiv)n(e)f
       
  5455 (t)n(yp)r(e-system,)523 4024 y(while)32 b(the)g(problems)f(w)n(e)g
       
  5456 (face)g(in)h Fs(\013)p FA(Prolog)e(concern)h(the)h(design)f(of)g(an)h
       
  5457 (e\016cien)n(t)g(pro)r(of)523 4124 y(searc)n(h)26 b(pro)r(cedure)h
       
  5458 (\(see)g([26]\).)648 4227 y Fn(Qu-Prolog)32 b FA([24]:)h(an)g
       
  5459 (extension)g(of)h(Prolog)d(with)j(built-in)g(names,)f(binding,)h(and)
       
  5460 523 4327 y(explicit)26 b(capture-a)n(v)n(oiding)c(substitutions)k(and)f
       
  5461 (uni\014cation)h(up)f(to)h(b)r(oth)f Fs(\013)p FA(-equiv)-5
       
  5462 b(alence)523 4426 y(and)27 b(substitution)h(ev)-5 b(aluation.)27
       
  5463 b(Qu-Prolog)d(includes)j(\\not)g(free)g(in")g(constrain)n(ts)f(corre-)
       
  5464 523 4526 y(sp)r(onding)k(to)g(our)f(freshness)g(constrain)n(ts.)f(Nev)n
       
  5465 (ertheless,)h(there)h(are)f(signi\014can)n(t)g(di\013er-)523
       
  5466 4625 y(ences;)34 b Fs(\013)p FA(Prolog)f(is)h(not)h(a)f(rein)n(v)n(en)n
       
  5467 (tion)f(of)h(Qu-Prolog.)e(First,)i Fs(\013)p FA(Prolog)f(is)h(a)g
       
  5468 (strongly)523 4725 y(t)n(yp)r(ed)28 b(p)r(olymorphic)f(language,)f(in)h
       
  5469 (con)n(trast)f(to)i(Qu-Prolog,)c(whic)n(h)k(is)f(un)n(t)n(yp)r(ed)h(in)
       
  5470 g(the)523 4825 y(Prolog)33 b(tradition.)h(Second,)h Fs(\013)p
       
  5471 FA(Prolog)e(is)i(based)f(on)h(a)g(simpler)f(uni\014cation)h(algorithm)
       
  5472 523 4924 y(that)30 b(uni\014es)g(up)g(to)f Fs(\013)p
       
  5473 FA(-equiv)-5 b(alence)29 b(but)h(not)g(up)g(to)f(substitution.)h
       
  5474 (Finally)-7 b(,)30 b(Qu-Prolog)p eop end
       
  5475 %%Page: 13 13
       
  5476 TeXDict begin 13 12 bop 523 448 a FA(lac)n(ks)30 b(a)h(logical)f(seman)
       
  5477 n(tics,)h(and)g(b)r(ecause)g(of)h(its)g(in)n(ternalized)e(treatmen)n(t)
       
  5478 h(of)h(capture-)523 548 y(a)n(v)n(oiding)23 b(substitution,)i(dev)n
       
  5479 (eloping)f(one)g(w)n(ould)g(lik)n(ely)g(b)r(e)h(di\016cult.)g(In)g(con)
       
  5480 n(trast,)e(nom-)523 648 y(inal)k(logic)g([19])g(pro)n(vides)f(a)h
       
  5481 (solid)h(seman)n(tic)f(foundation)g(for)g Fs(\013)p FA(Prolog)n(.)648
       
  5482 754 y Fn(Logic)45 b(programming)g(with)g(binding)g(algebras)p
       
  5483 FA(:)40 b(Hamana)f([9])g(has)g(formal-)523 853 y(ized)30
       
  5484 b(a)f(logic)g(programming)f(language)g(based)i(on)f(Fiore,)g(T)-7
       
  5485 b(uri,)30 b(and)g(Plotkin's)f Fq(binding)523 953 y(algebr)l(as)38
       
  5486 b FA([5].)29 b(No)h(implemen)n(tation)f(of)h(this)g(language)e(app)r
       
  5487 (ears)g(to)h(b)r(e)h(a)n(v)-5 b(ailable.)29 b(Ho)n(w-)523
       
  5488 1052 y(ev)n(er,)i(since)h(binding)g(algebras)f(are)g(a)g(formalization)
       
  5489 g(of)h(HO)n(AS,)h(w)n(e)e(b)r(eliev)n(e)h(that)h(this)523
       
  5490 1152 y(approac)n(h)26 b(will)i(also)e(share)h(the)h(seman)n(tic)f
       
  5491 (complexit)n(y)g(of)g(HO)n(AS.)648 1258 y Fs(L)704 1270
       
  5492 y Fm(\025)746 1258 y FA(:)21 b(Miller)f([12])g(disco)n(v)n(ered)f(a)h
       
  5493 (restricted)g(form)g(of)g(higher-order)e(logic)i(programming)523
       
  5494 1358 y(called)31 b Fs(L)818 1370 y Fm(\025)892 1358 y
       
  5495 FA(in)g(whic)n(h)h(uni\014cation)f(is)g(e\016cien)n(tly)g(decidable)g
       
  5496 (and)g(HO)n(AS)g(enco)r(dings)g(are)523 1457 y(p)r(ossible,)j(but)h
       
  5497 (built-in)g(capture-a)n(v)n(oiding)d(substitution)i(is)h(not)f(a)n(v)-5
       
  5498 b(ailable.)33 b(There)h(are)523 1557 y(sev)n(eral)d(in)n(teresting)i
       
  5499 (parallels)f(b)r(et)n(w)n(een)h Fs(L)1932 1569 y Fm(\025)2008
       
  5500 1557 y FA(and)g Fs(\013)p FA(Prolog)e(\(and)i(nominal)g(uni\014cation)
       
  5501 523 1657 y(and)27 b Fs(L)740 1669 y Fm(\025)811 1657
       
  5502 y FA(uni\014cation\);)h(relating)e(these)i(languages)e(is)h(future)h(w)
       
  5503 n(ork.)648 1762 y Fn(Delphin)p FA(:)35 b(Sc)n(h)r(\177)-44
       
  5504 b(urmann)36 b(et)h(al.)f([21])g(are)f(dev)n(eloping)h(a)g(functional)g
       
  5505 (programming)523 1862 y(language)31 b(called)i(Delphin)h(whic)n(h)e
       
  5506 (supp)r(orts)h(adv)-5 b(anced)32 b(meta-programming)e(with)k(re-)523
       
  5507 1962 y(cursion)d(o)n(v)n(er)e(higher-order)h(abstract)g(syn)n(tax.)h
       
  5508 (This)g(approac)n(h)f(seems)h(v)n(ery)g(p)r(o)n(w)n(erful,)523
       
  5509 2061 y(but)d(also)f(v)n(ery)f(complex)h(b)r(ecause)h(it)g(is)f(based)g
       
  5510 (on)g(HO)n(AS.)523 2342 y Fn(6.2)95 b(Status)32 b(and)g(F)-8
       
  5511 b(uture)32 b(W)-8 b(ork)523 2540 y FA(W)h(e)31 b(ha)n(v)n(e)f(implemen)
       
  5512 n(ted)i(an)f(in)n(terpreter)f(for)g Fs(\013)p FA(Prolog)f(based)i(on)f
       
  5513 (nominal)h(uni\014cation)523 2639 y(as)g(outlined)g(in)h(this)f(pap)r
       
  5514 (er,)g(along)f(with)i(man)n(y)f(additional)f(example)h(programs,)e(suc)
       
  5515 n(h)523 2739 y(as)g(translation)f(to)i(a)f(small)g(t)n(yp)r(ed)h(assem)
       
  5516 n(bly)f(language,)f(ev)-5 b(aluation)29 b(for)g(a)g(core)f(ob)5
       
  5517 b(ject)523 2839 y(calculus,)25 b(and)g(mo)r(deling)f(a)h(cryptographic)
       
  5518 e(authen)n(tication)i(proto)r(col.)f(The)h(implemen-)523
       
  5519 2938 y(tation)g(is)f(a)n(v)-5 b(ailable)24 b(online.)1424
       
  5520 2908 y Fc(1)1486 2938 y FA(Some)g(additional)g(applications)g(of)h(in)n
       
  5521 (terest,)f(suc)n(h)h(as)f(t)n(yp)r(e)523 3038 y(inference)g(for)g(a)g
       
  5522 (small)g(ML-lik)n(e)g(language)f(and)h(translations)f(from)h(regular)f
       
  5523 (expressions)523 3138 y(to)33 b(\014nite)h(automata,)f(do)g(not)g(w)n
       
  5524 (ork)f(prop)r(erly)g(b)r(ecause)h(of)h Fs(\013)p FA(Prolog)n('s)f
       
  5525 (curren)n(t)f(incom-)523 3237 y(plete)25 b(implemen)n(tation.)g
       
  5526 (Therefore)f(w)n(e)h(are)f(v)n(ery)g(in)n(terested)g(in)h(dev)n
       
  5527 (eloping)f(tec)n(hniques)523 3337 y(for)j(equiv)-5 b(arian)n(t)27
       
  5528 b(uni\014cation)g(and)h(resolution.)648 3443 y(F)-7 b(ollo)n(wing)35
       
  5529 b(Miller)i(et)g(al.)f([13],)g(w)n(e)h(ha)n(v)n(e)e(form)n(ulated)h(a)h
       
  5530 (uniform)f(pro)r(of)g(theoretic)523 3542 y(seman)n(tics)30
       
  5531 b(for)h Fq(nominal)i(her)l(e)l(ditary)i(Harr)l(op)e(formulas)39
       
  5532 b FA(based)31 b(on)f(a)h(sequen)n(t)g(calculus)523 3642
       
  5533 y(for)f(nominal)h(logic)e([7].)i(A)g(more)f(traditional)f(mo)r
       
  5534 (del-theoretic)h(seman)n(tics)g(is)h(in)g(dev)n(el-)523
       
  5535 3742 y(opmen)n(t.)g(W)-7 b(e)31 b(also)f(plan)h(to)g(dev)n(elop)g(mo)r
       
  5536 (de)g(and)g(determinism)g(analyses)e(for)i Fs(\013)p
       
  5537 FA(Prolog)n(.)523 3841 y(Another)19 b(in)n(teresting)g(direction)g(is)g
       
  5538 (the)h(p)r(ossibilit)n(y)f(of)g(in)n(tegrating)f Fs(\013)p
       
  5539 FA(Prolog)n('s)h(constrain)n(t)523 3941 y(domain)27 b(in)n(to)h(an)f
       
  5540 (existing)g(constrain)n(t)g(logic)f(programming)g(system.)648
       
  5541 4047 y(One)j(de\014ciency)h(of)f Fs(\013)p FA(Prolog)f(relativ)n(e)g
       
  5542 (to)i(HO)n(AS)g(systems)f(and)g(Qu-Prolog)e(is)j(that)523
       
  5543 4146 y(capture-a)n(v)n(oiding)22 b(substitution)j(is)f(not)h(built-in,)
       
  5544 g(but)g(m)n(ust)g(b)r(e)g(written)g(b)n(y)f(hand)h(when)523
       
  5545 4246 y(needed.)e(W)-7 b(e)22 b(are)g(curren)n(tly)f(exp)r(erimen)n
       
  5546 (ting)h(with)h(an)f(op)r(eration)g Fr(\001f\001)p Fs(=)p
       
  5547 Fr(\001g)g Fp(:)h(\()p Fs(\013;)14 b(\014)t(;)g(\014)t
       
  5548 Fp(\))24 b Fr(!)f Fs(\013)p FA(,)523 4346 y(suc)n(h)29
       
  5549 b(that)i Fs(t)p Fr(f)p Fs(u=v)s Fr(g)d FA(denotes)h(the)h(result)g(of)g
       
  5550 (replacing)e(the)i(term)g Fs(v)j FA(with)d Fs(u)g FA(ev)n(erywhere)523
       
  5551 4445 y(in)35 b Fs(t)p FA(,)g(renaming)e(abstractions)g(to)i(a)n(v)n
       
  5552 (oid)e(capture.)h(Th)n(us,)g Fs(subst)p Fp(\()p Fs(t;)14
       
  5553 b(u;)g Fo(x)p Fp(\))37 b FA(for)d Fs(\025)h FA(or)f Fs(\025\026)p
       
  5554 FA(-)523 4545 y(terms)i(can)h(b)r(e)g(written)f(as)g
       
  5555 Fs(t)p Fr(f)p Fs(u=v)s(ar)r Fp(\()p Fo(x)p Fp(\))p Fr(g)p
       
  5556 FA(,)h(and)f Fs(r)r(en)p 2264 4545 25 4 v 31 w(p)p Fp(\()p
       
  5557 Fs(p;)14 b Fo(a)p Fs(;)g Fo(b)p Fp(\))36 b FA(as)g Fs(p)p
       
  5558 Fr(f)p Fo(a)p Fs(=)p Fo(b)p Fr(g)p FA(.)f(Curren)n(tly)523
       
  5559 4645 y(there)28 b(are)f Fq(ad)k(ho)l(c)j FA(restrictions)27
       
  5560 b(suc)n(h)g(as)h(that)g Fs(t)g FA(and)g Fs(v)j FA(m)n(ust)e(b)r(e)f
       
  5561 (ground)f(when)i Fs(t)p Fr(f)p Fs(u=v)s Fr(g)523 4744
       
  5562 y FA(is)i(ev)-5 b(aluated.)30 b(Also,)g(this)h(do)r(es)f(not)h(help)g
       
  5563 (with)g(un)n(usual)f(substitution-lik)n(e)g(op)r(erations)p
       
  5564 523 4839 473 4 v 546 4893 a Fb(1)606 4924 y Fw
       
  5565 (http://www.cs.cornell.edu/Peo)q(ple/)q(jchen)q(ey/a)q(prol)q(og/)p
       
  5566 eop end
       
  5567 %%Page: 14 14
       
  5568 TeXDict begin 14 13 bop 523 448 a FA(suc)n(h)25 b(as)f
       
  5569 Fs(\025\026)p FA(-calculus)h(replacemen)n(t.)f(Dev)n(eloping)h(a)g
       
  5570 (logical)e(accoun)n(t)i(of)g(substitution)h(in)523 548
       
  5571 y(nominal)h(logic)g(and)g Fs(\013)p FA(Prolog)f(is)h(an)h(imp)r(ortan)n
       
  5572 (t)f(area)f(for)h(future)h(w)n(ork.)523 802 y Fn(6.3)95
       
  5573 b(Summary)523 972 y FA(Though)21 b(still)h(a)f(w)n(ork)g(in)g
       
  5574 (progress,)f Fs(\013)p FA(Prolog)f(sho)n(ws)i(great)f(promise.)h
       
  5575 (Although)h Fs(\013)p FA(Prolog)523 1072 y(is)32 b(not)f(the)h(\014rst)
       
  5576 g(language)e(to)h(include)h(sp)r(ecial)g(constructs)f(for)g(dealing)g
       
  5577 (with)h(v)-5 b(ariable)523 1172 y(binding,)34 b Fs(\013)p
       
  5578 FA(Prolog)e(allo)n(ws)g(programming)f(m)n(uc)n(h)j(closer)e(to)i
       
  5579 (informal)f(\\pap)r(er")f(de\014ni-)523 1271 y(tions)21
       
  5580 b(than)h(an)n(y)f(other)g(extan)n(t)g(system.)g(W)-7
       
  5581 b(e)22 b(ha)n(v)n(e)e(giv)n(en)h(sev)n(eral)f(examples)g(of)i
       
  5582 (languages)523 1371 y(that)32 b(can)f(b)r(e)h(de\014ned)f(b)r(oth)h
       
  5583 (declarativ)n(ely)e(and)h(concisely)g(in)h Fs(\013)p
       
  5584 FA(Prolog)m(.)g(W)-7 b(e)32 b(ha)n(v)n(e)e(also)523 1470
       
  5585 y(describ)r(ed)j(the)i(op)r(erational)d(seman)n(tics)h(for)g(core)f
       
  5586 Fs(\013)p FA(Prolog)n(,)i(whic)n(h)g(is)f(sound)h(with)g(re-)523
       
  5587 1570 y(sp)r(ect)29 b(to)f(nominal)g(logic,)f(but)i(complete)f(only)g
       
  5588 (for)g(a)g(class)f(of)h(w)n(ell-b)r(eha)n(v)n(ed)f(programs.)523
       
  5589 1670 y(Additional)i(w)n(ork)d(is)j(needed)f(to)g(dev)n(elop)g
       
  5590 (practical)f(tec)n(hniques)h(for)g Fq(e)l(quivariant)j(uni\014-)523
       
  5591 1769 y(c)l(ation)h FA(necessary)23 b(for)h(complete)h(nominal)f
       
  5592 (resolution,)g(and)g(to)h(dev)n(elop)f(static)h(analyses)523
       
  5593 1869 y(and)32 b(other)f(forms)g(of)h(reasoning)e(ab)r(out)i
       
  5594 Fs(\013)p FA(Prolog)d(programs.)h(More)h(broadly)-7 b(,)31
       
  5595 b(w)n(e)g(view)523 1969 y Fs(\013)p FA(Prolog)e(as)h(a)h(mo)r(dest)g
       
  5596 (\014rst)f(step)h(to)n(w)n(ard)f(a)g Fq(nominal)k(lo)l(gic)l(al)g(fr)l
       
  5597 (amework)42 b FA(for)30 b(reason-)523 2068 y(ing)25 b(ab)r(out)h
       
  5598 (programming)d(languages,)g(logics,)i(and)g(t)n(yp)r(e)g(systems)g
       
  5599 (enco)r(ded)h(in)f(nominal)523 2168 y(abstract)i(syn)n(tax.)523
       
  5600 2438 y Ft(References)561 2634 y Fx(1.)43 b(Andreas)17
       
  5601 b(Ab)r(el.)k(A)d(third-order)f(represen)n(tation)h(of)h(the)e
       
  5602 Fu(\025\026)p Fx(-calculus.)22 b(In)17 b(S.J.)h(Am)n(bler,)g(R.L.)663
       
  5603 2725 y(Crole,)33 b(and)d(A.)i(Momigliano,)i(editors,)e
       
  5604 Fa(MERLIN)g(2001:)h(Me)l(chanize)l(d)h(R)l(e)l(asoning)g(ab)l(out)663
       
  5605 2816 y(L)l(anguages)29 b(with)f(V)-6 b(ariable)28 b(Binding)p
       
  5606 Fx(,)e(v)n(olume)g(58\(1\))h(of)f Fa(Ele)l(ctr)l(onic)j(Notes)g(in)e
       
  5607 (The)l(or)l(etic)l(al)663 2908 y(Computer)h(Scienc)l(e)p
       
  5608 Fx(.)f(Elsevier,)g(2001.)561 3000 y(2.)43 b(James)32
       
  5609 b(Cheney)-6 b(.)49 b(The)31 b(complexit)n(y)f(of)i(equiv)l(arian)n(t)e
       
  5610 (uni\014cation.)50 b(In)30 b Fa(Pr)l(o)l(c)l(e)l(e)l(dings)35
       
  5611 b(of)d(the)663 3091 y(31st)23 b(International)g(Col)t(lo)l(quium)e(on)h
       
  5612 (A)n(utomata,)h(L)l(anguages)h(and)e(Pr)l(o)l(gr)l(amming)h(\(ICALP)663
       
  5613 3183 y(2004\))p Fx(,)k(2004.)36 b(T)-6 b(o)26 b(app)r(ear.)561
       
  5614 3275 y(3.)43 b(N.)33 b(G.)i(de)f(Bruijn.)59 b(Lam)n(b)r(da-calculus)35
       
  5615 b(notation)f(with)g(nameless)h(dummies,)g(a)f(to)r(ol)h(for)663
       
  5616 3366 y(automatic)26 b(form)n(ula)h(manipulation.)35 b
       
  5617 Fa(Indag.)28 b(Mat.)p Fx(,)d(34\(5\):381{392,)30 b(1972.)561
       
  5618 3459 y(4.)43 b(Jo)n(\177)-36 b(elle)25 b(Desp)r(eyroux,)d(Am)n(y)g(F)-6
       
  5619 b(elt)n(y)g(,)23 b(and)g(Andr)n(\023)-36 b(e)22 b(Hirsc)n(ho)n(witz.)31
       
  5620 b(Higher-order)23 b(abstract)h(syn-)663 3550 y(tax)32
       
  5621 b(in)h(Co)r(q.)56 b(In)32 b(M.)h(Dezani-Ciancaglini)j(and)c(G.)h
       
  5622 (Plotkin,)h(editors,)f Fa(Pr)l(o)l(c.)i(Int.)f(Conf.)663
       
  5623 3641 y(on)c(T)-6 b(yp)l(e)l(d)31 b(L)l(amb)l(da)g(Calculi)e(and)i
       
  5624 (Applic)l(ations)p Fx(,)f(pages)f(124{138,)j(Edin)n(burgh,)27
       
  5625 b(Scotland,)663 3732 y(1995.)g(Springer-V)-6 b(erlag)26
       
  5626 b(LNCS)f(902.)561 3825 y(5.)43 b(M.)31 b(P)-6 b(.)31
       
  5627 b(Fiore,)h(G.)g(D.)e(Plotkin,)i(and)e(D.)h(T)-6 b(uri.)50
       
  5628 b(Abstract)30 b(syn)n(tax)g(and)h(v)l(ariable)g(binding.)663
       
  5629 3916 y(In)d Fa(Pr)l(o)l(c.)i(14th)i(Symp.)e(on)g(L)l(o)l(gic)h(in)f
       
  5630 (Computer)i(Scienc)l(e)f(\(LICS)f(1999\))p Fx(,)g(pages)g(193{202.)663
       
  5631 4007 y(IEEE,)c(1999.)561 4100 y(6.)43 b(M.)24 b(J.)h(Gabba)n(y)-6
       
  5632 b(.)31 b(The)24 b Fu(\031)s Fx(-calculus)g(in)g(FM.)32
       
  5633 b(In)24 b(F)-6 b(airouz)24 b(Kamareddine,)g(editor,)h
       
  5634 Fa(Thirty-\014ve)663 4191 y(ye)l(ars)k(of)e(Automath)p
       
  5635 Fx(.)g(Klu)n(w)n(er,)f(2003.)561 4283 y(7.)43 b(M.)32
       
  5636 b(J.)f(Gabba)n(y)g(and)g(J.)h(Cheney)-6 b(.)50 b(A)31
       
  5637 b(pro)r(of)h(theory)f(for)h(nominal)g(logic.)52 b(In)31
       
  5638 b Fa(Pr)l(o)l(c)l(e)l(e)l(dings)663 4375 y(of)26 b(the)h(19th)h(A)n
       
  5639 (nnual)e(IEEE)g(Symp)l(osium)h(on)g(L)l(o)l(gic)g(in)f(Computer)i
       
  5640 (Scienc)l(e)f(\(LICS)f(2004\))p Fx(,)663 4466 y(2004.)36
       
  5641 b(T)-6 b(o)26 b(app)r(ear.)561 4558 y(8.)43 b(M.)27 b(J.)g(Gabba)n(y)f
       
  5642 (and)h(A.)f(M.)h(Pitts.)38 b(A)26 b(new)g(approac)n(h)h(to)g(abstract)g
       
  5643 (syn)n(tax)f(with)g(v)l(ariable)663 4649 y(binding.)34
       
  5644 b Fa(F)-6 b(ormal)27 b(Asp)l(e)l(cts)j(of)d(Computing)p
       
  5645 Fx(,)g(13:341{363,)j(2002.)561 4742 y(9.)43 b(Mak)n(oto)31
       
  5646 b(Hamana.)51 b(A)31 b(logic)h(programming)g(language)h(based)e(on)g
       
  5647 (binding)g(algebras.)52 b(In)663 4833 y Fa(Pr)l(o)l(c.)24
       
  5648 b(The)l(or)l(etic)l(al)i(Asp)l(e)l(cts)g(of)e(Computer)h(Scienc)l(e)h
       
  5649 (\(T)-6 b(A)n(CS)24 b(2001\))p Fx(,)g(n)n(um)n(b)r(er)d(2215)i(in)f
       
  5650 (Lec-)663 4924 y(ture)j(Notes)h(in)f(Computer)h(Science,)h(pages)f
       
  5651 (243{262.)j(Springer-V)-6 b(erlag,)26 b(2001.)p eop end
       
  5652 %%Page: 15 15
       
  5653 TeXDict begin 15 14 bop 523 448 a Fx(10.)43 b(Martin)32
       
  5654 b(Hofmann.)51 b(Seman)n(tical)32 b(analysis)h(of)f(higher-order)f
       
  5655 (abstract)h(syn)n(tax.)51 b(In)30 b Fa(Pr)l(o)l(c.)663
       
  5656 540 y(14th)e(Symp.)f(on)h(L)l(o)l(gic)g(in)f(Computer)i(Scienc)l(e)p
       
  5657 Fx(,)e(pages)g(204{213.)h(IEEE,)f(July)e(1999.)523 626
       
  5658 y(11.)43 b(Jo)n(xan)19 b(Ja\013ar,)g(Mic)n(hael)h(J.)g(Maher,)f(Kim)g
       
  5659 (Marriott,)h(and)e(P)n(eter)h(J.)g(Stuc)n(k)n(ey)-6 b(.)21
       
  5660 b(The)e(seman)n(tics)663 718 y(of)26 b(constrain)n(t)g(logic)h
       
  5661 (programs.)36 b Fa(Journal)28 b(of)g(L)l(o)l(gic)g(Pr)l(o)l(gr)l
       
  5662 (amming)p Fx(,)f(37\(1-3\):1{46,)h(1998.)523 804 y(12.)43
       
  5663 b(Dale)37 b(Miller.)68 b(A)36 b(logic)i(programming)f(language)h(with)f
       
  5664 (lam)n(b)r(da-abstraction,)h(function)663 896 y(v)l(ariables,)26
       
  5665 b(and)g(simple)g(uni\014cation.)35 b Fa(J.)27 b(L)l(o)l(gic)h(and)g
       
  5666 (Computation)p Fx(,)f(1\(4\):497{536,)j(1991.)523 982
       
  5667 y(13.)43 b(Dale)35 b(Miller,)i(Gopalan)f(Nadath)n(ur,)f(F)-6
       
  5668 b(rank)34 b(Pfenning,)i(and)f(Andre)f(Scedro)n(v.)61
       
  5669 b(Uniform)663 1074 y(pro)r(ofs)28 b(as)f(a)g(foundation)g(for)g(logic)h
       
  5670 (programming.)39 b Fa(A)n(nnals)29 b(of)f(Pur)l(e)h(and)g(Applie)l(d)f
       
  5671 (L)l(o)l(gic)p Fx(,)663 1165 y(51:125{157,)i(1991.)523
       
  5672 1252 y(14.)43 b(Robin)21 b(Milner,)i(Joac)n(him)h(P)n(arro)n(w,)f(and)f
       
  5673 (Da)n(vid)f(W)-6 b(alk)n(er.)29 b(A)21 b(calculus)i(of)g(mobile)g(pro)r
       
  5674 (cesses,)663 1343 y(I-I)r(I.)33 b Fa(Information)27 b(and)h
       
  5675 (Computation)p Fx(,)g(100\(1\):1{77,)h(Septem)n(b)r(er)c(1992.)523
       
  5676 1430 y(15.)43 b(A.)26 b(Momigliano,)j(S.)d(J.)h(Am)n(bler,)f(and)f(R.)h
       
  5677 (L.)h(Crole.)37 b(A)26 b(comparison)h(of)g(formalizations)i(of)663
       
  5678 1521 y(the)g(meta-theory)h(of)h(a)f(language)h(with)g(v)l(ariable)f
       
  5679 (bindings)g(in)g(Isab)r(elle.)48 b(In)30 b Fa(Informatics)663
       
  5680 1613 y(R)l(ese)l(ar)l(ch)i(R)l(ep)l(ort)g(EDI-INF-RR-0046,)f
       
  5681 (Supplemental)g(Pr)l(o)l(c)l(e)l(e)l(dings)h(of)e(TPHOLs)h(2001)p
       
  5682 Fx(,)663 1704 y(pages)26 b(267{282.)j(Univ)n(ersit)n(y)c(of)h(Edin)n
       
  5683 (burgh,)f(2001.)523 1791 y(16.)43 b(G.)37 b(Nadath)n(ur)e(and)h(D.)h
       
  5684 (Miller.)68 b(Higher-order)36 b(logic)i(programming.)68
       
  5685 b(In)36 b(D.)g(M.)h(Gab-)663 1882 y(ba)n(y)-6 b(,)33
       
  5686 b(C.)i(J.)g(Hogger,)g(and)f(J.)g(A.)g(Robinson,)h(editors,)g
       
  5687 Fa(Handb)l(o)l(ok)h(of)f(L)l(o)l(gic)h(in)f(A)n(rti\014cial)663
       
  5688 1973 y(Intel)t(ligenc)l(e)30 b(and)f(L)l(o)l(gic)h(Pr)l(o)l(gr)l
       
  5689 (amming)p Fx(,)g(v)n(olume)d(5,)i(c)n(hapter)e(8,)i(pages)f(499{590.)j
       
  5690 (Oxford)663 2065 y(Univ)n(ersit)n(y)24 b(Press,)j(1998.)523
       
  5691 2151 y(17.)43 b(Mic)n(hel)34 b(P)n(arigot.)61 b(Lam)n(b)r(da-m)n
       
  5692 (u-calculus:)34 b(An)f(algorithmic)i(in)n(terpretation)g(of)f
       
  5693 (classical)663 2243 y(natural)28 b(deduction.)43 b(In)28
       
  5694 b(A.)g(V)-6 b(oronk)n(o)n(v,)27 b(editor,)j Fa(Pr)l(o)l(c)l(e)l(e)l
       
  5695 (dings)i(of)e(the)h(1992)g(International)663 2334 y(Confer)l(enc)l(e)24
       
  5696 b(on)g(L)l(o)l(gic)f(Pr)l(o)l(gr)l(amming)h(and)g(A)n(utomate)l(d)h(R)l
       
  5697 (e)l(asoning)f(\(LP)-6 b(AR)23 b('92\))p Fx(,)f(n)n(um)n(b)r(er)663
       
  5698 2425 y(624)k(in)g(LNAI,)f(pages)h(190{201,)j(1992.)523
       
  5699 2512 y(18.)43 b(F)-6 b(rank)29 b(Pfenning)h(and)f(Conal)i(Elliott.)47
       
  5700 b(Higher-order)30 b(abstract)g(syn)n(tax.)46 b(In)29
       
  5701 b Fa(Pr)l(o)l(c.)i(A)n(CM)663 2603 y(SIGPLAN)k(Conf.)f(on)i(Pr)l(o)l
       
  5702 (gr)l(amming)g(L)l(anguage)g(Design)g(and)f(Implementation)h(\(PLDI)663
       
  5703 2695 y('89\))p Fx(,)26 b(pages)g(199{208.)j(A)n(CM)d(Press,)h(1989.)523
       
  5704 2781 y(19.)43 b(A.)21 b(M.)i(Pitts.)29 b(Nominal)23 b(logic,)g(a)g
       
  5705 (\014rst)e(order)i(theory)e(of)i(names)f(and)g(binding.)28
       
  5706 b Fa(Information)663 2873 y(and)g(Computation)p Fx(,)f(183:165{193,)j
       
  5707 (2003.)523 2959 y(20.)43 b(Christine)27 b(R\177)-38 b(oc)n(kl.)36
       
  5708 b(A)26 b(\014rst-order)g(syn)n(tax)f(for)j(the)e(pi-calculus)g(in)h
       
  5709 (isab)r(elle/hol)i(using)d(p)r(er-)663 3051 y(m)n(utations.)67
       
  5710 b(In)36 b(S.J.)h(Am)n(bler,)g(R.L.)f(Crole,)j(and)d(A.)g(Momigliano,)k
       
  5711 (editors,)d Fa(MERLIN)663 3142 y(2001:)24 b(Me)l(chanize)l(d)h(R)l(e)l
       
  5712 (asoning)g(ab)l(out)g(L)l(anguages)h(with)e(V)-6 b(ariable)24
       
  5713 b(Binding)p Fx(,)e(v)n(olume)f(58\(1\))663 3233 y(of)26
       
  5714 b Fa(Ele)l(ctr)l(onic)j(Notes)g(in)e(The)l(or)l(etic)l(al)i(Computer)g
       
  5715 (Scienc)l(e)p Fx(.)d(Elsevier,)h(2001.)523 3320 y(21.)43
       
  5716 b(C.)32 b(Sc)n(hrmann,)e(R.)h(F)-6 b(on)n(tana,)31 b(and)g(Y.)g(Liao.)
       
  5717 52 b(Delphin:)31 b(F)-6 b(unctional)31 b(programming)i(with)663
       
  5718 3412 y(deductiv)n(e)h(systems.)65 b(Av)l(ailable)37 b(at)e
       
  5719 Fw(http://cs-www.cs.yale.edu/h)q(omes)q(/cars)q(ten/)q
       
  5720 Fx(,)663 3503 y(2002.)523 3590 y(22.)43 b(M.)30 b(R.)g(Shin)n(w)n(ell,)
       
  5721 g(A.)g(M.)h(Pitts,)f(and)g(M.)h(J.)f(Gabba)n(y)-6 b(.)46
       
  5722 b(F)-6 b(reshML:)31 b(Programmming)h(with)663 3681 y(binders)24
       
  5723 b(made)h(simple.)34 b(In)24 b Fa(Pr)l(o)l(c.)k(8th)f(A)n(CM)g(SIGPLAN)g
       
  5724 (Int.)f(Conf.)g(on)h(F)-6 b(unctional)28 b(Pr)l(o-)663
       
  5725 3772 y(gr)l(amming)f(\(ICFP)h(2003\))p Fx(,)f(pages)f(263{274,)j
       
  5726 (Uppsala,)d(Sw)n(eden,)g(2003.)h(A)n(CM)f(Press.)523
       
  5727 3859 y(23.)43 b(Zoltan)20 b(Somogyi,)g(F)-6 b(ergus)20
       
  5728 b(Henderson,)f(and)g(Thomas)i(Con)n(w)n(a)n(y)-6 b(.)24
       
  5729 b(The)c(execution)g(algorithm)663 3950 y(of)30 b(Mercury:)f(an)g
       
  5730 (e\016cien)n(t)h(purely)e(declarativ)n(e)i(logic)h(programming)f
       
  5731 (language.)47 b Fa(J.)30 b(L)l(o)l(gic)663 4042 y(Pr)l(o)l(gr)l(amming)
       
  5732 p Fx(,)d(29\(1{3\):17{64,)j(Octob)r(er-Decem)n(b)r(er)25
       
  5733 b(1996.)523 4128 y(24.)43 b(J.)22 b(Staples,)g(P)-6 b(.)22
       
  5734 b(J.)h(Robinson,)f(R.)f(A.)h(P)n(aterson,)h(R.)e(A.)h(Hagen,)g(A.)f(J.)
       
  5735 i(Craddo)r(c)n(k,)f(and)f(P)-6 b(.)22 b(C.)663 4220 y(W)-6
       
  5736 b(allis.)54 b(Qu-prolog:)32 b(An)f(extended)g(prolog)i(for)g(meta)f
       
  5737 (lev)n(el)g(programming.)55 b(In)31 b(Harv)n(ey)663 4311
       
  5738 y(Abramson)d(and)f(M.)i(H.)f(Rogers,)h(editors,)g Fa(Meta-Pr)l(o)l(gr)l
       
  5739 (amming)j(in)d(L)l(o)l(gic)i(Pr)l(o)l(gr)l(amming)p Fx(,)663
       
  5740 4402 y(c)n(hapter)25 b(23.)i(MIT)f(Press,)h(1996.)523
       
  5741 4489 y(25.)43 b(C.)21 b(Urban,)f(A.)h(M.)g(Pitts,)h(and)e(M.)i(J.)f
       
  5742 (Gabba)n(y)-6 b(.)26 b(Nominal)21 b(uni\014cation.)26
       
  5743 b(In)21 b(M.)g(Baaz,)h(editor,)663 4580 y Fa(Computer)h(Scienc)l(e)g(L)
       
  5744 l(o)l(gic)f(and)g(8th)h(Kurt)g(G\177)-39 b(odel)22 b(Col)t(lo)l(quium)g
       
  5745 (\(CSL'03)g(&)g(K)n(GC\))p Fx(,)e(v)n(olume)663 4672
       
  5746 y(2803)k(of)f Fa(L)l(e)l(ctur)l(e)j(Notes)g(in)e(Computer)i(Scienc)l(e)
       
  5747 p Fx(,)d(pages)g(513{527,)j(Vienna,)c(Austria,)h(2003.)663
       
  5748 4763 y(Springer-V)-6 b(erlag.)523 4850 y(26.)43 b(Christian)24
       
  5749 b(Urban)f(and)h(James)h(Cheney)-6 b(.)30 b(Av)n(oiding)23
       
  5750 b(equiv)l(arian)n(t)g(uni\014cation.)32 b(Submitted.)p
       
  5751 eop end
       
  5752 %%Trailer
       
  5753 
       
  5754 userdict /end-hook known{end-hook}if
       
  5755 %%EOF