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moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def 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dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 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97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20; patched MV 10-09-99 00:36 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: 8r.enc 0 0 +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, +% W. Schmidt, P. Lehman", +% version = "2.0", +% date = "30 October 2002", +% filename = "8r.enc", +% email = "tex-fonts@@tug.org", +% docstring = "This is the encoding vector for Type1 and TrueType +% fonts to be used with TeX. This file is part of the +% PSNFSS bundle, version 9" +% @} +% +% The idea is to have all the characters normally included in Type 1 fonts +% available for typesetting. This is effectively the characters in Adobe +% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, +% MacRoman, and some extra characters from Lucida. +% +% Character code assignments were made as follows: +% +% (1) the Windows ANSI characters are almost all in their Windows ANSI +% positions, because some Windows users cannot easily reencode the +% fonts, and it makes no difference on other systems. The only Windows +% ANSI characters not available are those that make no sense for +% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen +% (173). quotesingle and grave are moved just because it's such an +% irritation not having them in TeX positions. +% +% (2) Remaining characters are assigned arbitrarily to the lower part +% of the range, avoiding 0, 10 and 13 in case we meet dumb software. +% +% (3) Y&Y Lucida Bright includes some extra text characters; in the +% hopes that other PostScript fonts, perhaps created for public +% consumption, will include them, they are included starting at 0x12. +% These are /dotlessj /ff /ffi /ffl. +% +% (4) hyphen appears twice for compatibility with both ASCII and Windows. +% +% (5) /Euro was assigned to 128, as in Windows ANSI +% +% (6) Missing characters from MacRoman encoding incorporated as follows: +% +% PostScript MacRoman TeXBase1 +% -------------- -------------- -------------- +% /notequal 173 0x16 +% /infinity 176 0x17 +% /lessequal 178 0x18 +% /greaterequal 179 0x19 +% /partialdiff 182 0x1A +% /summation 183 0x1B +% /product 184 0x1C +% /pi 185 0x1D +% /integral 186 0x81 +% /Omega 189 0x8D +% /radical 195 0x8E +% /approxequal 197 0x8F +% /Delta 198 0x9D +% /lozenge 215 0x9E +% +/TeXBase1Encoding [ +% 0x00 + /.notdef /dotaccent /fi /fl + /fraction /hungarumlaut /Lslash /lslash + /ogonek /ring /.notdef /breve + /minus /.notdef /Zcaron /zcaron +% 0x10 + /caron /dotlessi /dotlessj /ff + /ffi /ffl /notequal /infinity + /lessequal /greaterequal /partialdiff /summation + /product /pi /grave /quotesingle +% 0x20 + /space /exclam /quotedbl /numbersign + /dollar /percent /ampersand /quoteright + /parenleft /parenright /asterisk /plus + /comma /hyphen /period /slash +% 0x30 + /zero /one /two /three + /four /five /six /seven + /eight /nine /colon /semicolon + /less /equal /greater /question +% 0x40 + /at /A /B /C + /D /E /F /G + /H /I /J /K + /L /M /N /O +% 0x50 + /P /Q /R /S + /T /U /V /W + /X /Y /Z /bracketleft 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Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@Y /N@X InitNC { /AngleA 0. def /AngleB 130. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 7537 3829 a + tx@Dict begin tx@NodeDict begin {-81.09048 35.56592 } false /N@U 10 +{InitPnode } NewNode end end + 7537 3829 +a 5075 3891 a + tx@Dict begin tx@NodeDict begin {12.01903 6.01901 56.34294 28.17146 +3.0 } false /N@V 16 {InitRnode } NewNode end end + 5075 3891 a Red Black 1 1 0.8 TeXcolorrgb +Black 78 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.06 true +3.8 neg 6.01901 neg 52.54294 12.01903 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -17 +x FI(new)66 b(type)p Red Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@V /N@U InitNC { /AngleA 90. def /AngleB 190. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 +a 6840 3298 a FI(isomorphism)7537 3829 y @beginspecial +@setspecial + tx@Dict begin STP newpath 1.13809 SLW 0 setgray /ArrowA { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow moveto } def /ArrowB +{ } def [ -47.23164 36.98865 47.23164 36.98865 /Lineto /lineto load +def false Line gsave 1.13809 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial Black Green Black Green Black +OliveGreen Black 4893 4716 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + + +@endspecial Black 284 w(You)g(could)h(de\002ne)f(the)g(type)h(of)g +(lists)h(containing)f(only)p Blue 5177 4977 a FH(1)p +Black FI(s,)p Blue 67 w FH(2)p Black FI(s)g(and)p Blue +66 w FH(3)p Black FI(s)h(from)f(the)f(existing)i(type)e(of)h(lists.)p +Black Green Black Green Black OliveGreen Black 4893 5333 +a @beginspecial @setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + +@endspecial Black 284 w(The)f(polymorphic) +h(type)p Blue 66 w FG(\013)60 b FF(\002)h FG(\014)p Black +74 w FI(is)66 b(de\002ned)g(as)g(a)g(subset)5177 5603 +y(of)h(the)f(type)p Blue 67 w FG(\013)79 b FF(\))g FG(\014)87 +b FF(\))79 b FI(bool)p Black 1 w(.)j(The)66 b(pair)p +Blue 67 w FH(\()p FG(a;)48 b(b)p FH(\))p Black 67 w FI(is)5177 +5863 y(represented)67 b(as)g(the)f(function:)p Blue 6428 +6160 a FG(\025x)48 b(y)9 b(:)80 b FH(\()p FG(x)g FH(=)f +FG(a)p FH(\))64 b FF(^)f FH(\()p FG(y)89 b FH(=)79 b +FG(b)p FH(\))p Black Red Black 1 1 0.8 TeXcolorrgb Black +5025 3378 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.05 true +3.8 neg 43.45027 neg 259.8748 49.45029 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -731 +x FN(Implemented)i(Barendregt's:)5025 3132 y FD(Convention)p +5025 3188 1348 12 v -1 w FN(:)99 b(Terms)80 b(that)g(are)h +FC(\013)p FN(-congruent)5025 3435 y(are)f(identi\002ed.)100 +b(So)79 b(now)g(we)h(write)p Blue 5025 3713 a FC(\025x:x)p +Blue 94 w FB(\021)p Blue 95 w FC(\025y)11 b(:y)p Black +90 w FN(etcetera.)p 1 1 0.8 TeXcolorrgb 5319 4122 a FA(=)80 +b FN(is)f(equality)i(in)f(HOL)p Black 0 TeXcolorgray +10797 5925 a + 0 setgray + 10797 5925 a 0.5 TeXcolorgray 9124 6307 +a FL(London,)26 b(6.)h(December)g(2005)g(\226)g(p.3)h(\(1/5\))p +0 TeXcolorgray 4360 6416 a + tx@Dict begin -90 Rot end + 4360 6416 a eop end +%%Page: 3 4 +TeXDict begin 3 3 bop 0 TeXcolorgray 4360 6416 a + tx@Dict begin 90 Rot end + 4360 +6416 a 4585 1909 a +SDict begin /product where{pop product(Distiller)search{pop pop pop +version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto +closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show +grestore}if}{pop}ifelse}{pop}ifelse}if end + 4585 1909 a 4585 1909 a +SDict begin H.S end + 4585 1909 +a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a +SDict begin H.R end + 4585 1909 +a 4585 1909 a +SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark +end + 4585 1909 a 4585 1909 a +SDict begin [ {ThisPage}<> >> /PUT pdfmark end + 4585 1909 a Gray +5056 2027 a FK(\013)p FR(-Equi)-5 b(v)g(alence)127 b(Classes)p +0 TeXcolorgray Black Black Black 7537 3829 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 106.69778 21.33955 +78.24504 5.69046 45.52455 14.22636 34.1432 42.67911 54.06003 76.82231 +79.66776 82.51277 108.1205 56.90549 1. 0.1 0. /c ED /b ED /a ED false +ClosedCurve gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial 0.76 0.76 0.76 TeXcolorrgb Black +@beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 71.13185 21.33955 +51.21501 28.45274 56.90549 49.7923 73.9773 54.06003 85.35823 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial 0.76 0.76 0.76 +TeXcolorrgb Black @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ -59.75093 21.33955 +-81.09048 35.56592 -73.9773 49.7923 -56.90549 54.06003 -49.7923 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +7537 3829 a + tx@Dict begin tx@NodeDict begin {106.69778 21.33955 } false /N@A 10 +{InitPnode } NewNode end end + 7537 3829 a 9189 4185 a + tx@Dict begin tx@NodeDict begin {17.96753 11.96753 50.65204 25.32602 +3.0 } false /N@B 16 {InitRnode } NewNode end end + 9189 4185 a Red Black +1 1 0.8 TeXcolorrgb Black 78 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.15 true +3.8 neg 11.96753 neg 46.85204 17.96753 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + + +@endspecial -130 x FI(existing)9267 4291 y(type)p Red +Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@B /N@A InitNC { /AngleA 90. def /AngleB 300. def 0.9 + 0.9 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 7537 3829 a + tx@Dict begin tx@NodeDict begin {56.90549 49.7923 } false /N@X 10 +{InitPnode } NewNode end end + 7537 3829 a +6779 2569 a + tx@Dict begin tx@NodeDict begin {16.86595 10.86594 67.72386 33.86192 +3.0 } false /N@Y 16 {InitRnode } NewNode end end + 6779 2569 a Red Black 1 1 0.8 TeXcolorrgb +Black 79 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.06 true +3.8 neg 10.86594 neg 63.92386 16.86595 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -117 +x FI(non-empty)6858 2707 y(subset)p Red Black 7537 3829 +a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@Y /N@X InitNC { /AngleA 0. def /AngleB 130. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 7537 3829 a + tx@Dict begin tx@NodeDict begin {-81.09048 35.56592 } false /N@U 10 +{InitPnode } NewNode end end + 7537 3829 a 5075 3891 a + tx@Dict begin tx@NodeDict begin {12.01903 6.01901 56.34294 28.17146 +3.0 } false /N@V 16 {InitRnode } NewNode end end + 5075 +3891 a Red Black 1 1 0.8 TeXcolorrgb Black 78 w @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.06 true +3.8 neg 6.01901 neg 52.54294 12.01903 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -17 x FI(new)66 b(type)p Red +Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@V /N@U InitNC { /AngleA 90. def /AngleB 190. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 6840 3298 a FI(isomorphism)7537 +3829 y @beginspecial @setspecial + tx@Dict begin STP newpath 1.13809 SLW 0 setgray /ArrowA { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow moveto } def /ArrowB +{ } def [ -47.23164 36.98865 47.23164 36.98865 /Lineto /lineto load +def false Line gsave 1.13809 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial Black Green +Black Green Black OliveGreen Black 4893 4716 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + +@endspecial Black 284 w(You)g(could)h(de\002ne)f(the)g +(type)h(of)g(lists)h(containing)f(only)p Blue 5177 4977 +a FH(1)p Black FI(s,)p Blue 67 w FH(2)p Black FI(s)g(and)p +Blue 66 w FH(3)p Black FI(s)h(from)f(the)f(existing)i(type)e(of)h +(lists.)p Black Green Black Green Black OliveGreen Black +4893 5333 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + +@endspecial Black +284 w(The)f(polymorphic)h(type)p Blue 66 w FG(\013)60 +b FF(\002)h FG(\014)p Black 74 w FI(is)66 b(de\002ned)g(as)g(a)g +(subset)5177 5603 y(of)h(the)f(type)p Blue 67 w FG(\013)79 +b FF(\))g FG(\014)87 b FF(\))79 b FI(bool)p Black 1 w(.)j(The)66 +b(pair)p Blue 67 w FH(\()p FG(a;)48 b(b)p FH(\))p Black +67 w FI(is)5177 5863 y(represented)67 b(as)g(the)f(function:)p +Blue 6428 6160 a FG(\025x)48 b(y)9 b(:)80 b FH(\()p FG(x)g +FH(=)f FG(a)p FH(\))64 b FF(^)f FH(\()p FG(y)89 b FH(=)79 +b FG(b)p FH(\))p Black Red Black 1 1 0.8 TeXcolorrgb +Black 5025 3378 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.05 true +3.8 neg 43.45027 neg 259.8748 49.45029 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial +-731 x FN(Implemented)i(Barendregt's:)5025 3132 y FD(Convention)p +5025 3188 1348 12 v -1 w FN(:)99 b(Terms)80 b(that)g(are)h +FC(\013)p FN(-congruent)5025 3435 y(are)f(identi\002ed.)100 +b(So)79 b(now)g(we)h(write)p Blue 5025 3713 a FC(\025x:x)p +Red 94 w FA(=)p Blue 96 w FC(\025y)11 b(:y)p Black 89 +w FN(etcetera.)p Red 5319 4122 a FA(=)80 b FN(is)f(equality)i(in)f(HOL) +p Black 0 TeXcolorgray 10797 5925 a + 0 setgray + 10797 5925 a 0.5 +TeXcolorgray 9109 6307 a FL(London,)26 b(6.)i(December)e(2005)h(\226)h +(p.3)f(\(2/5\))p 0 TeXcolorgray 4360 6416 a + tx@Dict begin -90 Rot end + 4360 6416 +a eop end +%%Page: 3 5 +TeXDict begin 3 4 bop 0 TeXcolorgray 4360 6416 a + tx@Dict begin 90 Rot end + 4360 +6416 a 4585 1909 a +SDict begin /product where{pop product(Distiller)search{pop pop pop +version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto +closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show +grestore}if}{pop}ifelse}{pop}ifelse}if end + 4585 1909 a 4585 1909 a +SDict begin H.S end + 4585 1909 +a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a +SDict begin H.R end + 4585 1909 +a 4585 1909 a +SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark +end + 4585 1909 a 4585 1909 a +SDict begin [ {ThisPage}<> >> /PUT pdfmark end + 4585 1909 a Gray +5056 2027 a FK(\013)p FR(-Equi)-5 b(v)g(alence)127 b(Classes)p +0 TeXcolorgray Black Black Black 7537 3829 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 106.69778 21.33955 +78.24504 5.69046 45.52455 14.22636 34.1432 42.67911 54.06003 76.82231 +79.66776 82.51277 108.1205 56.90549 1. 0.1 0. /c ED /b ED /a ED false +ClosedCurve gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial 0.76 0.76 0.76 TeXcolorrgb Black +@beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 71.13185 21.33955 +51.21501 28.45274 56.90549 49.7923 73.9773 54.06003 85.35823 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial 0.76 0.76 0.76 +TeXcolorrgb Black @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ -59.75093 21.33955 +-81.09048 35.56592 -73.9773 49.7923 -56.90549 54.06003 -49.7923 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +7537 3829 a + tx@Dict begin tx@NodeDict begin {106.69778 21.33955 } false /N@A 10 +{InitPnode } NewNode end end + 7537 3829 a 9189 4185 a + tx@Dict begin tx@NodeDict begin {17.96753 11.96753 50.65204 25.32602 +3.0 } false /N@B 16 {InitRnode } NewNode end end + 9189 4185 a Red Black +1 1 0.8 TeXcolorrgb Black 78 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.15 true +3.8 neg 11.96753 neg 46.85204 17.96753 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + + +@endspecial -130 x FI(existing)9267 4291 y(type)p Red +Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@B /N@A InitNC { /AngleA 90. def /AngleB 300. def 0.9 + 0.9 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 7537 3829 a + tx@Dict begin tx@NodeDict begin {56.90549 49.7923 } false /N@X 10 +{InitPnode } NewNode end end + 7537 3829 a +6779 2569 a + tx@Dict begin tx@NodeDict begin {16.86595 10.86594 67.72386 33.86192 +3.0 } false /N@Y 16 {InitRnode } NewNode end end + 6779 2569 a Red Black 1 1 0.8 TeXcolorrgb +Black 79 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.06 true +3.8 neg 10.86594 neg 63.92386 16.86595 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -117 +x FI(non-empty)6858 2707 y(subset)p Red Black 7537 3829 +a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@Y /N@X InitNC { /AngleA 0. def /AngleB 130. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 7537 3829 a + tx@Dict begin tx@NodeDict begin {-81.09048 35.56592 } false /N@U 10 +{InitPnode } NewNode end end + 7537 3829 a 5075 3891 a + tx@Dict begin tx@NodeDict begin {12.01903 6.01901 56.34294 28.17146 +3.0 } false /N@V 16 {InitRnode } NewNode end end + 5075 +3891 a Red Black 1 1 0.8 TeXcolorrgb Black 78 w @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.06 true +3.8 neg 6.01901 neg 52.54294 12.01903 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -17 x FI(new)66 b(type)p Red +Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@V /N@U InitNC { /AngleA 90. def /AngleB 190. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 6840 3298 a FI(isomorphism)7537 +3829 y @beginspecial @setspecial + tx@Dict begin STP newpath 1.13809 SLW 0 setgray /ArrowA { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow moveto } def /ArrowB +{ } def [ -47.23164 36.98865 47.23164 36.98865 /Lineto /lineto load +def false Line gsave 1.13809 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial Black Green +Black Green Black OliveGreen Black 4893 4716 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + +@endspecial Black 284 w(You)g(could)h(de\002ne)f(the)g +(type)h(of)g(lists)h(containing)f(only)p Blue 5177 4977 +a FH(1)p Black FI(s,)p Blue 67 w FH(2)p Black FI(s)g(and)p +Blue 66 w FH(3)p Black FI(s)h(from)f(the)f(existing)i(type)e(of)h +(lists.)p Black Green Black Green Black OliveGreen Black +4893 5333 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + +@endspecial Black +284 w(The)f(polymorphic)h(type)p Blue 66 w FG(\013)60 +b FF(\002)h FG(\014)p Black 74 w FI(is)66 b(de\002ned)g(as)g(a)g +(subset)5177 5603 y(of)h(the)f(type)p Blue 67 w FG(\013)79 +b FF(\))g FG(\014)87 b FF(\))79 b FI(bool)p Black 1 w(.)j(The)66 +b(pair)p Blue 67 w FH(\()p FG(a;)48 b(b)p FH(\))p Black +67 w FI(is)5177 5863 y(represented)67 b(as)g(the)f(function:)p +Blue 6428 6160 a FG(\025x)48 b(y)9 b(:)80 b FH(\()p FG(x)g +FH(=)f FG(a)p FH(\))64 b FF(^)f FH(\()p FG(y)89 b FH(=)79 +b FG(b)p FH(\))p Black 0 TeXcolorgray 10797 5925 a + 0 setgray + 10797 +5925 a 0.5 TeXcolorgray 9109 6307 a FL(London,)26 b(6.)i(December)e +(2005)h(\226)h(p.3)f(\(3/5\))p 0 TeXcolorgray 4360 6416 +a + tx@Dict begin -90 Rot end + 4360 6416 a eop end +%%Page: 3 6 +TeXDict begin 3 5 bop 0 TeXcolorgray 4360 6416 a + tx@Dict begin 90 Rot end + 4360 +6416 a 4585 1909 a +SDict begin /product where{pop product(Distiller)search{pop pop pop +version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto +closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show +grestore}if}{pop}ifelse}{pop}ifelse}if end + 4585 1909 a 4585 1909 a +SDict begin H.S end + 4585 1909 +a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a +SDict begin H.R end + 4585 1909 +a 4585 1909 a +SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark +end + 4585 1909 a 4585 1909 a +SDict begin [ {ThisPage}<> >> /PUT pdfmark end + 4585 1909 a Gray +5056 2027 a FK(\013)p FR(-Equi)-5 b(v)g(alence)127 b(Classes)p +0 TeXcolorgray Black Black Black 7537 3829 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 106.69778 21.33955 +78.24504 5.69046 45.52455 14.22636 34.1432 42.67911 54.06003 76.82231 +79.66776 82.51277 108.1205 56.90549 1. 0.1 0. /c ED /b ED /a ED false +ClosedCurve gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial 0.76 0.76 0.76 TeXcolorrgb Black +@beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 71.13185 21.33955 +51.21501 28.45274 56.90549 49.7923 73.9773 54.06003 85.35823 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial 0.76 0.76 0.76 +TeXcolorrgb Black @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ -59.75093 21.33955 +-81.09048 35.56592 -73.9773 49.7923 -56.90549 54.06003 -49.7923 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +7537 3829 a + tx@Dict begin tx@NodeDict begin {106.69778 21.33955 } false /N@A 10 +{InitPnode } NewNode end end + 7537 3829 a 9189 4185 a + tx@Dict begin tx@NodeDict begin {17.96753 11.96753 50.65204 25.32602 +3.0 } false /N@B 16 {InitRnode } NewNode end end + 9189 4185 a Red Black +1 1 0.8 TeXcolorrgb Black 78 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.15 true +3.8 neg 11.96753 neg 46.85204 17.96753 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + + +@endspecial -130 x FI(existing)9267 4291 y(type)p Red +Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@B /N@A InitNC { /AngleA 90. def /AngleB 300. def 0.9 + 0.9 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 7537 3829 a + tx@Dict begin tx@NodeDict begin {56.90549 49.7923 } false /N@X 10 +{InitPnode } NewNode end end + 7537 3829 a +6779 2569 a + tx@Dict begin tx@NodeDict begin {16.86595 10.86594 67.72386 33.86192 +3.0 } false /N@Y 16 {InitRnode } NewNode end end + 6779 2569 a Red Black 1 1 0.8 TeXcolorrgb +Black 79 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.06 true +3.8 neg 10.86594 neg 63.92386 16.86595 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -117 +x FI(non-empty)6858 2707 y(subset)p Red Black 7537 3829 +a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@Y /N@X InitNC { /AngleA 0. def /AngleB 130. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a 7537 3829 a + tx@Dict begin tx@NodeDict begin {-81.09048 35.56592 } false /N@U 10 +{InitPnode } NewNode end end + 7537 3829 a 5075 3891 a + tx@Dict begin tx@NodeDict begin {12.01903 6.01901 56.34294 28.17146 +3.0 } false /N@V 16 {InitRnode } NewNode end end + 5075 +3891 a Red Black 1 1 0.8 TeXcolorrgb Black 78 w @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.06 true +3.8 neg 6.01901 neg 52.54294 12.01903 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + +@endspecial -17 x FI(new)66 b(type)p Red +Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. Arrow EndArrow } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg +0.0 0.0 0 0 /N@V /N@U InitNC { /AngleA 90. def /AngleB 190. def 0.7 + 0.7 NCCurve } if end gsave 0.8 SLW TeXDict begin Red end 0 setlinecap +stroke grestore grestore end + 7537 3829 a Blue 8882 3151 a FH(?)p +Black Blue 5989 3111 a(\003)6184 3148 y Fz(=)p Fy(\031)p +Black Blue 9000 2564 a FH(?)p Black 6840 3298 a FI(isomorphism)7537 +3829 y @beginspecial @setspecial + tx@Dict begin STP newpath 1.13809 SLW 0 setgray /ArrowA { BeginArrow +1. 1. scale false 0.4 1.4 1.5 2. Arrow EndArrow moveto } def /ArrowB +{ } def [ -47.23164 36.98865 47.23164 36.98865 /Lineto /lineto load +def false Line gsave 1.13809 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial 4665 4689 +a(Question:)p Black Green Black Green Black OliveGreen +Black 4893 5028 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + +@endspecial +Black 284 w(What)g(is)h(a)g(suitable)h(existing)f(type)g(and)f(a)g +(suitable)5177 5289 y(subset)i(to)e(represent)h FG(\013)p +FI(-equivalent)g(lambda-terms?)5177 5549 y(\(And)f FG(\013)p +FI(-equivalence)h(classes)h(in)e(general?\))p Black Green +Black Green Black OliveGreen Black 4893 5906 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end 0. true +0.0 0.0 9.14807 9.14807 .5 Frame gsave 2.0 -45. PtoC Shadow TeXDict +begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict +begin Green end gsave fill grestore stroke grestore gsave TeXDict begin +Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap +stroke grestore end + +@endspecial Black 284 w(Answer:)83 b(this)67 +b(talk.)p 0 TeXcolorgray 10797 5925 a + 0 setgray + 10797 5925 a 0.5 +TeXcolorgray 9109 6307 a FL(London,)26 b(6.)i(December)e(2005)h(\226)h +(p.3)f(\(4/5\))p 0 TeXcolorgray 4360 6416 a + tx@Dict begin -90 Rot end + 4360 6416 +a eop end +%%Page: 3 7 +TeXDict begin 3 6 bop 0 TeXcolorgray 4360 6416 a + tx@Dict begin 90 Rot end + 4360 +6416 a 4585 1909 a +SDict begin /product where{pop product(Distiller)search{pop pop pop +version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto +closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show +grestore}if}{pop}ifelse}{pop}ifelse}if end + 4585 1909 a 4585 1909 a +SDict begin H.S end + 4585 1909 +a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a +SDict begin H.R end + 4585 1909 +a 4585 1909 a +SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark +end + 4585 1909 a 4585 1909 a +SDict begin [ {ThisPage}<> >> /PUT pdfmark end + 4585 1909 a Gray +5056 2027 a FK(\013)p FR(-Equi)-5 b(v)g(alence)127 b(Classes)p +0 TeXcolorgray Black Black Black 7537 3829 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 106.69778 21.33955 +78.24504 5.69046 45.52455 14.22636 34.1432 42.67911 54.06003 76.82231 +79.66776 82.51277 108.1205 56.90549 1. 0.1 0. /c ED /b ED /a ED false +ClosedCurve gsave 0.8 SLW 0 setgray 0 setlinecap stroke grestore +end + +@endspecial 0.76 0.76 0.76 TeXcolorrgb Black +@beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ 71.13185 21.33955 +51.21501 28.45274 56.90549 49.7923 73.9773 54.06003 85.35823 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial 0.76 0.76 0.76 +TeXcolorrgb Black @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0 setgray [ -59.75093 21.33955 +-81.09048 35.56592 -73.9773 49.7923 -56.90549 54.06003 -49.7923 35.56592 + 1. 0.1 0. /c ED /b ED /a ED false ClosedCurve gsave 0.76 0.76 0.76 + setrgbcolor fill grestore gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +7537 3829 a + tx@Dict begin tx@NodeDict begin {106.69778 21.33955 } false /N@A 10 +{InitPnode } NewNode end end + 7537 3829 a 9189 4185 a + tx@Dict begin tx@NodeDict begin {17.96753 11.96753 50.65204 25.32602 +3.0 } false /N@B 16 {InitRnode } NewNode end end + 9189 4185 a Red Black +1 1 0.8 TeXcolorrgb Black 78 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW TeXDict begin Red end 0.15 true +3.8 neg 11.96753 neg 46.85204 17.96753 .5 Frame gsave 1 1 0.8 setrgbcolor +fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke + grestore end + + +@endspecial -130 x FI(existing)9267 4291 y(type)p Red +Black 7537 3829 a + tx@Dict begin gsave STV newpath 0.8 SLW TeXDict begin Red end /ArrowA +{ moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4 1.4 1.5 +2. 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