aaai93.ps

   1 %!PS-Adobe-2.0
   2 %%Creator: dvipsk 5.521a Copyright 1986, 1993 Radical Eye Software
   3 %%Title: aaai93.dvi
   4 %%Pages: 6
   5 %%PageOrder: Ascend
   6 %%BoundingBox: 0 0 612 792
   7 %%EndComments
   8 %DVIPSCommandLine: dvips aaai93
   9 %DVIPSSource:  TeX output 1994.03.10:2313
  10 %%BeginProcSet: tex.pro
  11 /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
  12 /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
  13 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
  14 ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
  15 isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
  16 hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
  17 TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get
  18 round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{
  19 statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0
  20 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn
  21 begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X
  22 array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo
  23 setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx
  24 FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{
  25 pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}
  26 B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup
  27 length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B
  28 /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type
  29 /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp
  30 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2
  31 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff
  32 ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice
  33 ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{
  34 ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn
  35 /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1
  36 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{cc 1 add D
  37 }B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0
  38 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add
  39 .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage
  40 userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook
  41 known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
  42 /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
  43 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0
  44 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
  45 {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7
  46 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
  47 ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley
  48 false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley
  49 scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave
  50 transform round exch round exch itransform moveto rulex 0 rlineto 0
  51 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta
  52 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}
  53 B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{
  54 3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p
  55 -1 w}B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{
  56 3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end
  57 %%EndProcSet
  58 %%BeginProcSet: spline.ps
  59 /@ChaikinSplineSectionDict 20 dict def
  60 /@ChaikinSplineSectionShow {
  61 @ChaikinSplineSectionDict begin
  62 /y4 exch def /x4 exch def
  63 /y3 exch def /x3 exch def
  64 /y2 exch def /x2 exch def
  65 /y1 exch def /x1 exch def
  66 /xm x2 x3 add 2 div def
  67 /ym y2 y3 add 2 div def
  68 x1 xm sub abs 3 lt
  69 y1 ym sub abs 3 lt
  70 and
  71 { x1 y1 moveto xm ym lineto stroke }
  72 {
  73 xm ym x1 y1 x2 y2 x3 y3 x4 y4
  74 x1 y1
  75 x1 x2 add 2 div y1 y2 add 2 div
  76 x2 3 mul x3 add 4 div y2 3 mul y3 add 4 div
  77 xm ym
  78 @ChaikinSplineSectionShow
  79 /y4 exch def /x4 exch def
  80 /y3 exch def /x3 exch def
  81 /y2 exch def /x2 exch def
  82 /y1 exch def /x1 exch def
  83 /ym exch def /xm exch def
  84 } ifelse
  85 xm x4 sub abs 3 lt
  86 ym y4 sub abs 3 lt
  87 and
  88 { xm ym moveto x4 y4 lineto stroke }
  89 {   xm ym
  90 x2 x3 3 mul add 4 div y2 y3 3 mul add 4 div
  91 x3 x4 add 2 div y3 y4 add 2 div
  92 x4 y4
  93 @ChaikinSplineSectionShow
  94 } ifelse
  95 end
  96 } def
  97 /@ChaikinSplineDict 22 dict def
  98 /@ChaikinSplineDraw {
  99 @ChaikinSplineDict begin
 100 /n exch def
 101 n 2 mul -2 roll
 102 /y1 exch def
 103 /x1 exch def
 104 /n n 1 sub def
 105 n 2 mul -2 roll
 106 /y2 exch def
 107 /x2 exch def
 108 /n n 1 sub def
 109 /cx1 x1 x2 add 2 div def
 110 /cy1 y1 y2 add 2 div def
 111 /cx2 x1 3 x2 mul add 4 div def
 112 /cy2 y1 3 y2 mul add 4 div def
 113 newpath x1 y1 moveto cx1 cy1 lineto
 114 {
 115 n 0 eq {exit} if
 116 /x1 x2 def /y1 y2 def
 117 n 2 mul -2 roll
 118 /y2 exch def
 119 /x2 exch def
 120 /n n 1 sub def
 121 /cx3 3 x1 mul x2 add 4 div def
 122 /cy3 3 y1 mul y2 add 4 div def
 123 /cx4 x1 x2 add 2 div def
 124 /cy4 y1 y2 add 2 div def
 125 cx1 cy1 cx2 cy2 cx3 cy3 cx4 cy4 @ChaikinSplineSectionShow
 126 /cx1 cx4 def
 127 /cy1 cy4 def
 128 /cx2 x1 3 x2 mul add 4 div def
 129 /cy2 y1 3 y2 mul add 4 div def
 130 } loop
 131 cx1 cy1 moveto x2 y2 lineto stroke
 132 end
 133 } def
 134 %%EndProcSet
 135 %%BeginProcSet: ellipse.ps
 136 /@ellipsedict 8 dict def
 137 @ellipsedict /mtrx matrix put
 138 /@ellipse
 139 {
 140 @ellipsedict begin
 141 /endangle exch def      /startangle exch def
 142 /yrad exch def  /xrad exch def
 143 /y exch def             /x exch def
 144 /savematrix mtrx currentmatrix def
 145 x y translate
 146 xrad yrad scale
 147 0 0 1 startangle endangle arc
 148 savematrix setmatrix
 149 end
 150 } def
 151 %%EndProcSet
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1193 0007C0380003E0700003F0600001F8C00000F98000007F8000003F0000001F0000001F80
1194 00003FC0000037C0000063E00000C1F00001C0F8000380FC0007007E000E003E00FF80FF
1195 E0FF80FFE01B167F951E>120 D<FFE01FE0FFE01FE01F8007000F8006000FC00E0007C0
1196 0C0007E00C0003E0180003E0180001F0300001F0300000F8600000F86000007CC000007C
1197 C000007FC000003F8000003F8000001F0000001F0000000E0000000E0000000C0000000C
1198 00000018000078180000FC380000FC300000FC60000069C000007F8000001F0000001B20
1199 7F951E>I E /Fu 21 118 df<000003FF80018000003FFFF003800001FFFFFC0F800007
1200 FF007F1F80001FF8000FBF80003FE00003FF8000FF800000FF8001FF0000007F8003FE00
1201 00003F8007FC0000003F8007FC0000001F800FF80000001F801FF80000000F801FF00000
1202 000F803FF000000007803FF000000007807FF000000007807FE000000007807FE0000000
1203 00007FE00000000000FFE00000000000FFE00000000000FFE00000000000FFE000000000
1204 00FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000
1205 7FE000000000007FE000000000007FE000000000007FF000000003803FF000000003803F
1206 F000000003801FF000000003801FF800000007800FF8000000070007FC000000070007FC
1207 0000000E0003FE0000001E0001FF0000003C0000FF8000007800003FE00000F000001FF8
1208 0003E0000007FF003F80000001FFFFFE000000003FFFF80000000003FF80000031317BB0
1209 3C>67 D<FFFFFFF00000FFFFFFF00000FFFFFFF0000000FFC000000000FFC000000000FF
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1213 C000000000FFC000000000FFC000000000FFC000000000FFC000000000FFC000000000FF
1214 C000000000FFC000007000FFC000007000FFC000007000FFC00000F000FFC00000F000FF
1215 C00000E000FFC00000E000FFC00001E000FFC00001E000FFC00003E000FFC00003E000FF
1216 C00007E000FFC0000FE000FFC0001FE000FFC0007FC000FFC003FFC0FFFFFFFFFFC0FFFF
1217 FFFFFFC0FFFFFFFFFFC02C317EB032>76 D<FFFFC000007FFFF0FFFFE000007FFFF0FFFF
1218 F000007FFFF000FFF8000000F80000FFFC000000700000FFFE000000700000EFFF000000
1219 700000E7FF800000700000E3FF800000700000E1FFC00000700000E0FFE00000700000E0
1220 7FF00000700000E07FF80000700000E03FFC0000700000E01FFE0000700000E00FFF0000
1221 700000E007FF8000700000E003FF8000700000E001FFC000700000E000FFE000700000E0
1222 007FF000700000E0007FF800700000E0003FFC00700000E0001FFE00700000E0000FFF00
1223 700000E00007FF80700000E00003FF80700000E00001FFC0700000E00000FFE0700000E0
1224 00007FF0700000E000007FF8700000E000003FFC700000E000001FFE700000E000000FFF
1225 700000E0000007FFF00000E0000003FFF00000E0000001FFF00000E0000000FFF00000E0
1226 0000007FF00000E00000007FF00000E00000003FF00000E00000001FF00000E00000000F
1227 F00000E000000007F00000E000000003F00001F000000001F000FFFFE0000000F000FFFF
1228 E00000007000FFFFE000000070003C317EB041>78 D<FFFFFFFFE000FFFFFFFFFE00FFFF
1229 FFFFFF8000FFC001FFE000FFC0003FF000FFC0001FF800FFC0000FFC00FFC0000FFC00FF
1230 C00007FE00FFC00007FE00FFC00007FF00FFC00007FF00FFC00007FF00FFC00007FF00FF
1231 C00007FF00FFC00007FF00FFC00007FF00FFC00007FE00FFC00007FE00FFC0000FFC00FF
1232 C0000FFC00FFC0001FF800FFC0003FF000FFC001FFE000FFFFFFFF8000FFFFFFFE0000FF
1233 FFFFE00000FFC000000000FFC000000000FFC000000000FFC000000000FFC000000000FF
1234 C000000000FFC000000000FFC000000000FFC000000000FFC000000000FFC000000000FF
1235 C000000000FFC000000000FFC000000000FFC000000000FFC000000000FFC000000000FF
1236 C000000000FFC0000000FFFFFFC00000FFFFFFC00000FFFFFFC0000030317EB038>80
1237 D<001FF0018000FFFF038003FFFFC78007F00FFF800FC001FF801F00007F803F00001F80
1238 3E00000F807E00000F807E00000780FE00000780FE00000780FE00000380FF00000380FF
1239 00000380FF80000000FFE00000007FFC0000007FFFE000007FFFFE00003FFFFFC0001FFF
1240 FFF0000FFFFFF80007FFFFFC0003FFFFFE0001FFFFFF00007FFFFF80001FFFFF800000FF
1241 FFC0000007FFC0000000FFE00000007FE00000003FE00000001FE06000001FE0E000000F
1242 E0E000000FE0E000000FE0E000000FC0F000000FC0F000000FC0F800001F80FC00001F80
1243 FF00003F00FFC0007E00FFFC01FC00F1FFFFF800E03FFFE000C007FF000023317BB02E>
1244 83 D<007FF8000003FFFF000007FFFFC0000FE01FE0001FF007F0001FF003F8001FF003
1245 FC001FF001FE000FE001FE0007C001FE00010001FE00000001FE00000001FE000001FFFE
1246 00003FFFFE0001FFF1FE0007FE01FE000FF001FE001FC001FE003F8001FE007F8001FE00
1247 FF0001FE00FF0001FE00FF0001FE00FF0001FE00FF0003FE007F8003FE007FC00EFE003F
1248 F03CFF000FFFF87FF807FFF03FF800FF800FF825207E9F28>97 D<01F8000000FFF80000
1249 00FFF8000000FFF80000000FF800000007F800000007F800000007F800000007F8000000
1250 07F800000007F800000007F800000007F800000007F800000007F800000007F800000007
1251 F800000007F800000007F80FF00007F87FFE0007F9FFFF8007FFE03FC007FF000FE007FE
1252 0007F007F80003F807F80003FC07F80003FC07F80001FE07F80001FE07F80001FE07F800
1253 01FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001
1254 FF07F80001FE07F80001FE07F80001FE07F80003FC07F80003FC07FC0007F807FE0007F0
1255 07F7001FE007E3E07FC007C1FFFF0007807FFE0007001FE00028327EB12E>I<0007FF00
1256 007FFFE000FFFFF003FC03F807F007FC0FE007FC1FE007FC3FC007FC3FC003F87FC001F0
1257 7F8000407F800000FF800000FF800000FF800000FF800000FF800000FF800000FF800000
1258 FF8000007F8000007FC000007FC000003FC0000E3FE0000E1FE0001C0FF0001C07F80078
1259 03FF01F000FFFFE0007FFF800007FC001F207D9F25>I<00000007E0000003FFE0000003
1260 FFE0000003FFE00000003FE00000001FE00000001FE00000001FE00000001FE00000001F
1261 E00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE00000001FE0
1262 0000001FE0000FF81FE0007FFF1FE001FFFFDFE003FE03FFE007F800FFE00FE0003FE01F
1263 E0001FE03FC0001FE03FC0001FE07F80001FE07F80001FE07F80001FE0FF80001FE0FF80
1264 001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE0FF80001FE07F8000
1265 1FE07F80001FE07F80001FE03FC0001FE03FC0001FE01FC0003FE00FE0007FE007F001FF
1266 E003FC07DFF001FFFF9FFF007FFE1FFF000FF01FFF28327DB12E>I<0007FC0000003FFF
1267 800000FFFFE00003FC07F00007F801F8000FE000FC001FE0007E003FC0007E003FC0003F
1268 007FC0003F007F80003F007F80003F80FF80003F80FF80003F80FFFFFFFF80FFFFFFFF80
1269 FFFFFFFF80FF80000000FF80000000FF800000007F800000007F800000003FC00000003F
1270 C00003801FC00003801FE00007800FF0000F0007F8001E0003FE00FC0000FFFFF800003F
1271 FFE0000003FF000021207E9F26>I<0000FF000007FFC0001FFFE0003FC7F0007F0FF800
1272 FE0FF801FE0FF801FC0FF803FC07F003FC03E003FC01C003FC000003FC000003FC000003
1273 FC000003FC000003FC000003FC0000FFFFFC00FFFFFC00FFFFFC0003FC000003FC000003
1274 FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003
1275 FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003
1276 FC000003FC000003FC000003FC000003FC000003FC00007FFFF0007FFFF0007FFFF0001D
1277 327EB119>I<001FF803E000FFFF1FF001FFFFBFF807F81FF9F80FE007F1F80FE007F0F0
1278 1FC003F8601FC003F8003FC003FC003FC003FC003FC003FC003FC003FC003FC003FC001F
1279 C003F8001FC003F8000FE007F0000FE007F00007F81FE00007FFFF800006FFFF00000E1F
1280 F800000E000000001E000000001E000000001F000000001F800000001FFFFFC0000FFFFF
1281 F8000FFFFFFE0007FFFFFF0003FFFFFF8007FFFFFFC01FFFFFFFE03F00007FE07E00000F
1282 F0FC000007F0FC000003F0FC000003F0FC000003F0FC000003F07E000007E03F00000FC0
1283 1FC0003F800FF801FF0007FFFFFE0000FFFFF000001FFF8000252F7E9F29>I<01C00007
1284 F0000FF8000FF8001FFC001FFC001FFC000FF8000FF80007F00001C00000000000000000
1285 000000000000000000000000000000000001F800FFF800FFF800FFF80007F80007F80007
1286 F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007
1287 F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800FFFF80FF
1288 FF80FFFF8011337DB217>105 D<03F007F8000FF000FFF03FFF007FFE00FFF07FFF80FF
1289 FF00FFF0F03FC1E07F800FF1C01FE3803FC007F3000FE6001FC007F6000FFC001FE007FE
1290 000FFC001FE007FC000FF8001FE007FC000FF8001FE007F8000FF0001FE007F8000FF000
1291 1FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8
1292 000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF000
1293 1FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8
1294 000FF0001FE007F8000FF0001FE007F8000FF0001FE007F8000FF0001FE0FFFFC1FFFF83
1295 FFFFFFFFC1FFFF83FFFFFFFFC1FFFF83FFFF40207D9F45>109 D<03F007F80000FFF03F
1296 FF0000FFF07FFF8000FFF0F03FC0000FF1C01FE00007F3000FE00007F6000FF00007FE00
1297 0FF00007FC000FF00007FC000FF00007F8000FF00007F8000FF00007F8000FF00007F800
1298 0FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F800
1299 0FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F800
1300 0FF00007F8000FF00007F8000FF00007F8000FF000FFFFC1FFFF80FFFFC1FFFF80FFFFC1
1301 FFFF8029207D9F2E>I<0007FE0000003FFFC00000FFFFF00003FC03FC0007F000FE000F
1302 E0007F001FC0003F803FC0003FC03FC0003FC07F80001FE07F80001FE07F80001FE0FF80
1303 001FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF80001FF0FF8000
1304 1FF07F80001FE07F80001FE07F80001FE03FC0003FC03FC0003FC01FE0007F800FE0007F
1305 0007F801FE0003FE07FC0001FFFFF800003FFFC0000007FE000024207E9F29>I<01F80F
1306 F000FFF87FFE00FFF9FFFF80FFFFE07FC00FFF001FE007FE000FF007F80007F807F80007
1307 FC07F80003FC07F80003FE07F80003FE07F80001FE07F80001FF07F80001FF07F80001FF
1308 07F80001FF07F80001FF07F80001FF07F80001FF07F80001FF07F80001FE07F80003FE07
1309 F80003FE07F80003FC07F80007FC07FC0007F807FE000FF007FF001FE007FBE07FC007F9
1310 FFFF0007F87FFE0007F81FE00007F800000007F800000007F800000007F800000007F800
1311 000007F800000007F800000007F800000007F800000007F800000007F8000000FFFFC000
1312 00FFFFC00000FFFFC00000282E7E9F2E>I<03F03F00FFF07FC0FFF1FFE0FFF1C7F00FF3
1313 8FF807F70FF807F60FF807FE0FF807FC07F007FC03E007FC008007F8000007F8000007F8
1314 000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8
1315 000007F8000007F8000007F8000007F8000007F8000007F80000FFFFE000FFFFE000FFFF
1316 E0001D207E9F22>114 D<00FF870007FFEF001FFFFF003F007F003C001F0078000F00F8
1317 000700F8000700F8000700FC000700FF000000FFF800007FFFC0003FFFF0003FFFFC000F
1318 FFFE0007FFFF0001FFFF80001FFF800000FFC000001FC060000FC0E00007C0E00007C0F0
1319 0007C0F8000780F8000F80FE000F00FF803E00FFFFFC00F3FFF800C07FC0001A207D9F21
1320 >I<001C0000001C0000001C0000001C0000003C0000003C0000003C0000007C0000007C
1321 000000FC000001FC000003FC000007FC00001FFC0000FFFFFF00FFFFFF00FFFFFF0003FC
1322 000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC
1323 000003FC000003FC000003FC000003FC000003FC000003FC000003FC01C003FC01C003FC
1324 01C003FC01C003FC01C003FC01C003FC01C001FC038001FE038000FF0700007FFE00003F
1325 FC000007F0001A2E7FAD20>I<01F80003F000FFF801FFF000FFF801FFF000FFF801FFF0
1326 000FF8001FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF0
1327 0007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF0
1328 0007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF00007F8000FF0
1329 0007F8000FF00007F8000FF00007F8001FF00007F8001FF00003F8003FF00003F8006FF0
1330 0001FE03CFF80000FFFF8FFF80007FFF0FFF80000FFC0FFF8029207D9F2E>I
1331 E end
1332 %%EndProlog
1333 %%BeginSetup
1334 %%Feature: *Resolution 300dpi
1335 TeXDict begin
1336
1337 %%EndSetup
1338 %%Page: 1 1
1339 1 0 bop -17 125 a Fu(Nondeterministic)25 b(Lisp)h(as)h(a)h(Substrate)f
1340 (for)g(Constrain)n(t)567 208 y(Logic)g(Programming)223
1341 298 y Ft(Je\013rey)17 b(Mark)h(Siskind)735 280 y Fs(\003)129
1342 356 y Fr(Univ)o(ersit)o(y)13 b(of)k(P)o(ennsylv)m(ania)f(IR)o(CS)138
1343 414 y(3401)i(W)l(aln)o(ut)e(Street)g(Ro)q(om)g(407C)235
1344 472 y(Philadelphia)g(P)l(A)g(19104)332 530 y(215/898{0)q(367)128
1345 588 y(in)o(ternet:)k(Qobi@CIS.UP)o(enn.EDU)1079 298 y
1346 Ft(Da)n(vid)e(Allen)g(McAllester)1662 280 y Fs(y)925
1347 356 y Fr(M.)e(I.)f(T.)h(Arti\014cial)f(In)o(telligence)e(Lab)q(oratory)
1348 937 414 y(545)k(T)l(ec)o(hnology)f(Square)g(Ro)q(om)g(NE43{412)1136
1349 472 y(Cam)o(bridge)f(MA)g(02139)1223 530 y(617/253{6)q(599)1061
1350 588 y(in)o(ternet:)20 b(dam@AI.MIT.)o(EDU)271 708 y Ft(Abstract)-71
1351 791 y Fq(W)m(e)9 b(ha)o(v)o(e)g(implemen)o(ted)e(a)i(comprehensiv)o(e)h
1352 (constrain)o(t-)-71 837 y(based)18 b(programming)d(language)h(as)i(an)g
1353 (extension)g(to)-71 883 y Fp(Common)f(Lisp)p Fq(.)h(This)c(constrain)o
1354 (t)g(pac)o(k)n(age)g(pro)o(vides)-71 928 y(a)f(uni\014ed)h(framew)o
1355 (ork)d(for)i(solving)f(b)q(oth)i(n)o(umeric)e(and)-71
1356 974 y(non-n)o(umeric)j(systems)i(of)e(constrain)o(ts)j(using)e(a)g
1357 (com-)-71 1019 y(bination)10 b(of)h(lo)q(cal)g(propagation)f(tec)o
1358 (hniques)j(including)-71 1065 y(binding)e(propagation,)f(Bo)q(olean)h
1359 (constrain)o(t)h(propaga-)-71 1111 y(tion,)f(generalized)i(forw)o(ard)e
1360 (c)o(hec)o(king,)h(propagation)f(of)-71 1156 y(b)q(ounds,)g(and)g
1361 (uni\014cation.)16 b(The)11 b(bac)o(ktrac)o(king)f(facilit)o(y)-71
1362 1202 y(of)15 b(the)i(nondeterministic)e(dialect)g(of)h
1363 Fp(Common)g(Lisp)-71 1248 y Fq(used)e(to)f(implemen)o(t)d(this)j
1364 (constrain)o(t)h(pac)o(k)n(age)e(acts)i(as)-71 1293 y(a)g(general)h
1365 (fallbac)o(k)e(constrain)o(t)i(solving)e(metho)q(d)h(mit-)-71
1366 1339 y(igating)e(the)j(incompleteness)f(of)f(lo)q(cal)g(propagation.)
1367 223 1469 y Ft(In)n(tro)r(duction)-112 1537 y Fq(Recen)o(t)e(y)o(ears)f
1368 (ha)o(v)o(e)g(seen)i(signi\014can)o(t)d(in)o(terest)j(in)d(constrain)o
1369 (t)-112 1583 y(logic)j(programming)e(languages.)18 b(Numerous)13
1370 b(implemen)o(ta-)-112 1629 y(tions)g(of)g(suc)o(h)h(languages)g(ha)o(v)
1371 o(e)f(b)q(een)i(describ)q(ed)g(in)e(the)i(lit-)-112 1674
1372 y(erature,)g(notably)f Fp(clp)p Fq(\()p Fo(<)p Fq(\))h(\(Ja\013ar)g
1373 (and)f(Lassez)i(1987\))e(and)-112 1720 y Fp(CHiP)c Fq(\(V)m(an)i(Hen)o
1374 (tenryc)o(k)i(1989\).)i(The)d(p)q(oin)o(t)f(of)f(departure)-112
1375 1766 y(leading)18 b(to)h(these)i(systems)f(is)f(the)h(observ)n(ation)g
1376 (that)f(the)-112 1811 y(uni\014cation)12 b(op)q(eration)g(at)h(the)h
1377 (core)f(of)g(logic)e(programming)-112 1857 y(can)i(b)q(e)h(view)o(ed)f
1378 (as)g(a)g(metho)q(d)g(for)f(solving)h(equational)f(con-)-112
1379 1903 y(strain)o(ts)17 b(b)q(et)o(w)o(een)i(logic)d(v)n(ariables)g(whic)
1380 o(h)h(range)h(o)o(v)o(er)f(the)-112 1948 y(univ)o(erse)i(of)g(Herbrand)
1381 h(terms.)33 b(A)19 b(natural)g(extension)g(of)-112 1994
1382 y(suc)o(h)f(a)f(view)h(is)f(to)g(allo)o(w)f(v)n(ariables)h(to)h(range)f
1383 (o)o(v)o(er)h(other)-112 2040 y(domains)e(and)j(augmen)o(t)e(the)i
1384 (programming)c(language)j(to)-112 2085 y(supp)q(ort)23
1385 b(the)f(form)o(ulation)e(and)i(solution)f(of)h(systems)g(of)-112
1386 2131 y(constrain)o(ts)e(appropriate)h(to)f(these)h(new)g(domains.)35
1387 b(The)p -112 2179 250 2 v -61 2201 a Fn(\003)-43 2217
1388 y Fm(Supp)q(orted)17 b(in)f(part)g(b)o(y)g(a)g(Presiden)o(tial)i(Y)m
1389 (oung)e(In)o(v)o(estiga-)-112 2259 y(tor)d(Aw)o(ard)f(to)h(Professor)h
1390 (Rob)q(ert)g(C.)e(Berwic)o(k)i(under)g(National)-112
1391 2300 y(Science)e(F)m(oundation)g(Gran)o(t)f(DCR{85552543,)i(b)o(y)e(a)g
1392 (gran)o(t)g(from)-112 2342 y(the)e(Siemens)h(Corp)q(oration,)h(b)o(y)f
1393 (the)f(Kap)q(or)g(F)m(amily)i(F)m(oundation,)-112 2383
1394 y(b)o(y)20 b(AR)o(O)f(gran)o(t)i(D)o(AAL)e(03{89{C{0031,)k(b)o(y)d(D)o
1395 (ARP)m(A)g(gran)o(t)-112 2425 y(N00014{90{J{1863,)g(b)o(y)e(NSF)g(gran)
1396 o(t)g(IRI)g(90{16592,)i(and)e(b)o(y)-112 2466 y(Ben)13
1397 b(F)m(ranklin)i(gran)o(t)e(91S.3078C{1)-60 2496 y Fn(y)-43
1398 2512 y Fm(Supp)q(orted)h(in)g(part)f(b)o(y)g(the)h(Adv)n(anced)f
1399 (Researc)o(h)h(Pro)r(jects)-112 2553 y(Agency)d(of)f(the)h(Departmen)o
1400 (t)g(of)g(Defense)g(under)g(O\016ce)g(of)f(Na)o(v)n(al)-112
1401 2595 y(Researc)o(h)j(con)o(tract)h(N00014-91-J-4038.)980
1402 708 y Fq(notion)j(of)f(extending)i(a)f(programmi)o(ng)d(language)i(to)h
1403 (sup-)980 753 y(p)q(ort)10 b(constrain)o(t-based)g(programming)c(need)
1404 11 b(not)e(b)q(e)h(unique)980 799 y(to)19 b(logic)e(programming.)29
1405 b(In)19 b(this)f(pap)q(er)i(w)o(e)f(presen)o(t)h(the)980
1406 844 y(constrain)o(t)f(pac)o(k)n(age)e(included)i(with)f
1407 Fp(Screamer)p Fq(,)h(a)f(non-)980 890 y(deterministic)j(dialect)g(of)g
1408 Fp(Common)16 b(Lisp)22 b Fq(describ)q(ed)h(b)o(y)980
1409 936 y(Siskind)g(and)g(McAllester)i(\(1993\).)46 b(This)24
1410 b(pac)o(k)n(age)f(pro-)980 981 y(vides)15 b(functionalit)o(y)e
1411 (analogous)h(to)g Fp(clp)p Fq(\()p Fo(<)p Fq(\))h(and)g
1412 Fp(CHiP)e Fq(in)980 1027 y(a)f Fp(Common)17 b(Lisp)12
1413 b Fq(framew)o(ork)e(instead)j(of)e(a)h Fp(Pr)o(olog)h
1414 Fq(one.)1022 1073 y Fp(Screamer)21 b Fq(augmen)o(ts)e
1415 Fp(Common)d(Lisp)21 b Fq(with)f(the)g(ca-)980 1119 y(pacit)o(y)d(for)g
1416 (writing)f(nondeterministic)g(functions)h(and)g(ex-)980
1417 1164 y(pressions.)j(Nondeterministic)14 b(functions)g(and)g
1418 (expressions)980 1210 y(can)f(return)g(m)o(ultiple)d(v)n(alues)h(up)q
1419 (on)i(bac)o(ktrac)o(king)e(initiated)980 1255 y(b)o(y)i(failure.)j
1420 Fp(Screamer)e Fq(also)e(pro)o(vides)g(the)h(abilit)o(y)e(to)i(p)q(er-)
1421 980 1301 y(form)18 b Fl(lo)q(cal)h Fq(side)h(e\013ects,)i(ones)e(whic)o
1422 (h)g(are)f(undone)h(up)q(on)980 1347 y(bac)o(ktrac)o(king.)32
1423 b(Nondeterminism)16 b(and)j(lo)q(cal)f(side)g(e\013ects)980
1424 1392 y(form)9 b(the)i(substrate)h(on)e(top)g(of)g(whic)o(h)g(the)h
1425 Fp(Screamer)g Fq(con-)980 1438 y(strain)o(t)j(pac)o(k)n(age)g(is)f
1426 (constructed.)1153 1532 y Ft(V)-5 b(ariables)19 b(and)g(Constrain)n(ts)
1427 980 1590 y Fp(Screamer)37 b Fq(includes)f(the)g(function)f
1428 Fk(make-variable)980 1636 y Fq(whic)o(h)29 b(returns)i(a)d(data)h
1429 (structure)i(called)d(a)h Fl(v)n(ariable)p Fq(.)980 1682
1430 y Fp(Screamer)18 b Fq(v)n(ariables)e(are)i(a)f(generalization)f(of)h
1431 Fp(Pr)o(olog)980 1727 y Fq(logic)h(v)n(ariables.)34 b(Initially)m(,)17
1432 b(new)j(v)n(ariables)f(are)g(un)o(b)q(ound)980 1773 y(and)14
1433 b(unconstrained.)19 b(V)m(ariables)13 b(ma)o(y)f(b)q(e)j(b)q(ound)f(to)
1434 g(v)n(alues)980 1819 y(b)o(y)g(the)h(pro)q(cess)h(of)d(solving)g
1435 (constrain)o(ts)i(asserted)h(b)q(et)o(w)o(een)980 1864
1436 y(sets)e(of)e(v)n(ariables.)17 b(Both)12 b(the)i(assertion)f(of)e
1437 (constrain)o(ts)j(and)980 1910 y(the)f(ensuing)g(binding)e(of)h(v)n
1438 (ariables)g(is)g(done)h(with)f(lo)q(cal)f(side)980 1956
1439 y(e\013ects.)38 b(Th)o(us)21 b(constrain)o(ts)f(are)g(remo)o(v)o(ed)f
1440 (and)h(v)n(ariables)980 2001 y(b)q(ecome)14 b(un)o(b)q(ound)g(again)f
1441 (up)q(on)h(bac)o(ktrac)o(king.)1022 2047 y Fp(Screamer)h
1442 Fq(pro)o(vides)g(a)f(v)n(ariet)o(y)g(of)g(primitiv)o(es)f(for)h(con-)
1443 980 2093 y(straining)24 b(v)n(ariables.)47 b(Eac)o(h)24
1444 b(constrain)o(t)g(primitiv)o(e)e(is)i(a)980 2138 y(\\constrain)o(t)11
1445 b(v)o(ersion")f(of)g(a)g(corresp)q(onding)h Fp(Common)16
1446 b(Lisp)980 2184 y Fq(primitiv)o(e.)34 b(F)m(or)20 b(example,)f(the)i
1447 (constrain)o(t)f(primitiv)o(e)e Fk(+v)980 2230 y Fq(is)23
1448 b(a)f(constrain)o(t)h(v)o(ersion)g(of)f Fk(+)p Fq(.)43
1449 b(An)23 b(expression)h(of)e(the)980 2275 y(form)11 b
1450 Fk(\(+v)21 b Fj(x)h(y)q Fk(\))13 b Fq(returns)i(a)d(new)h(v)n(ariable)f
1451 Fj(z)r Fq(,)g(whic)o(h)h(it)f(con-)980 2321 y(strains)18
1452 b(to)e(b)q(e)i(the)g(sum)e(of)g Fj(x)g Fq(and)h Fj(y)i
1453 Fq(b)o(y)e(adding)f(the)h(con-)980 2367 y(strain)o(t)j
1454 Fj(z)k Fq(=)e Fk(\(+)g Fj(x)f(y)q Fk(\))q Fq(.)36 b(By)20
1455 b(con)o(v)o(en)o(tion,)h(a)f Fp(Screamer)980 2412 y Fq(primitiv)o(e)12
1456 b(ending)j(in)e(the)i(letter)g Fk(v)g Fq(is)f(a)g(constrain)o(t)g(v)o
1457 (ersion)980 2458 y(of)i(a)f(corresp)q(onding)i Fp(Common)g(Lisp)f
1458 Fq(primitiv)o(e.)22 b(T)m(able)16 b(1)980 2504 y(lists)d(the)g
1459 (constrain)o(t)f(primitiv)o(es)f(pro)o(vided)h(b)o(y)g
1460 Fp(Screamer)q Fq(.)980 2549 y(All)21 b(of)f(these)j(primitiv)o(es)c(ha)
1461 o(v)o(e)i(the)h(prop)q(ert)o(y)g(that)f(they)980 2595
1462 y(accept)c(v)n(ariables)d(as)i(argumen)o(ts|in)d(addition)h(to)i
1463 (ground)p eop
1464 %%Page: 2 2
1465 2 1 bop -112 -53 979 2 v -113 -7 2 46 v -87 -21 a Fq(T)o(yp)q(e)14
1466 b(Restrictions:)50 b Fk(numberpv)20 b(realpv)h(integerpv)p
1467 866 -7 V -113 39 V 297 25 a(booleanpv)f(memberv)p 866
1468 39 V -113 84 V -87 71 a Fq(Bo)q(olean:)226 b Fk(andv)21
1469 b(orv)g(notv)p 866 84 V -113 130 V -87 116 a Fq(Numeric:)218
1470 b Fk(<v)22 b(<=v)f(>v)g(>=v)g(=v)h(/=v)p 866 130 V -113
1471 176 V 297 162 a(+v)g(-v)f(*v)g(/v)h(minv)f(maxv)p 866
1472 176 V -113 221 V -87 208 a Fq(Expression:)177 b Fk(equalv)p
1473 866 221 V -113 267 V -87 253 a Fq(F)m(unctions:)196 b
1474 Fk(funcallv)20 b(applyv)p 866 267 V -112 269 979 2 v
1475 -112 364 a Fq(T)m(able)31 b(1:)53 b(The)33 b(constrain)o(t)f(primitiv)o
1476 (es)e(pro)o(vided)i(b)o(y)-112 410 y Fp(Screamer)p Fq(.)-112
1477 537 y(v)n(alues|and)11 b(return)i(a)f(v)n(ariable)f(as)h(their)h
1478 (result.)18 b(The)13 b(con-)-112 583 y(strain)o(t)j(primitiv)o(e)e
1479 (installs)h(a)h(constrain)o(t)h(b)q(et)o(w)o(een)g(the)g(ar-)-112
1480 629 y(gumen)o(ts)h(and)h(the)h(returned)h(v)n(ariable)d(stating)h
1481 (that,)h(un-)-112 674 y(der)g(an)o(y)f(in)o(terpretation)i(of)e(the)h
1482 (v)n(ariables)g(in)o(v)o(olv)o(ed,)f(the)-112 720 y(v)n(alue)25
1483 b(of)g(the)h(result)h(v)n(ariable)d(m)o(ust)h(equal)g(the)i(corre-)-112
1484 765 y(sp)q(onding)14 b Fp(Common)j(Lisp)e Fq(primitiv)o(e)e(applied)h
1485 (to)h(the)h(v)n(al-)-112 811 y(ues)k(of)f(the)h(argumen)o(ts.)34
1486 b(As)20 b(another)g(example,)f(the)i(ex-)-112 857 y(pression)c
1487 Fk(\(<v)22 b Fj(x)f(y)q Fk(\))d Fq(returns)h(a)d(v)n(ariable)h
1488 Fj(z)i Fq(and)e(adds)g(the)-112 902 y(constrain)o(t)i
1489 Fj(z)i Fq(=)f Fk(\(<)g Fj(x)f(y)q Fk(\))q Fq(.)33 b(This)18
1490 b(constrain)o(t)h(is)g(satis\014ed)-112 948 y(when)10
1491 b Fj(z)i Fq(is)e(either)h Fk(t)f Fq(or)f Fk(nil)h Fq(dep)q(ending)g(on)
1492 g(whether)i Fj(x)d Fq(is)h(less)-112 994 y(than)16 b
1493 Fj(y)q Fq(.)28 b(F)m(or)16 b(the)i(most)d(part,)i(eac)o(h)h(constrain)o
1494 (t)f(primitiv)o(e)-112 1039 y(ob)q(eys)f(the)h(same)f(calling)e(con)o
1495 (v)o(en)o(tion)i(as)g(the)h(corresp)q(ond-)-112 1085
1496 y(ing)f Fp(Common)g(Lisp)h Fq(primitiv)o(e.)25 b Fp(Screamer)18
1497 b Fq(p)q(erforms)e(a)-112 1131 y(v)n(ariet)o(y)11 b(of)g(optimizations)
1498 e(to)j(impro)o(v)o(e)d(run)j(time)f(e\016ciency)m(.)-112
1499 1176 y(In)16 b(particular,)g(if)f(the)i(v)n(alue)f(of)f(a)h(v)n
1500 (ariable)f(returned)j(b)o(y)e(a)-112 1222 y(constrain)o(t)c(primitiv)o
1501 (e)d(can)j(b)q(e)h(determined)f(at)f(the)i(time)d(the)-112
1502 1268 y(function)15 b(is)i(called)f(then)g(that)h(v)n(alue)e(is)h
1503 (returned)i(directly)-112 1313 y(without)13 b(creating)h(a)g(new)g(v)n
1504 (ariable.)-71 1361 y(In)f Fp(Screamer)q Fq(,)g(most)f(constrain)o(ts)h
1505 (are)h(of)f(the)g(form)f Fj(z)h Fq(=)-112 1406 y Fk(\(f)18
1506 b Fj(x)-26 1412 y Fi(1)19 1406 y Fj(:)7 b(:)g(:)24 b(x)117
1507 1412 y Fh(n)140 1406 y Fk(\))18 b Fq(where)h Fk(f)g Fq(is)f(the)h
1508 Fp(Common)d(Lisp)j Fq(primi-)-112 1452 y(tiv)o(e)13 b(corresp)q(onding)
1509 i(to)f(some)f(constrain)o(t)i(primitiv)o(e.)h(Con-)-112
1510 1498 y(strain)o(ts)21 b(of)g(this)g(form)f(can)i(imply)c(t)o(yp)q(e)k
1511 (restrictions)h(on)-112 1543 y(the)c(v)n(ariables)f(in)o(v)o(olv)o(ed.)
1512 32 b(F)m(or)18 b(example,)h(a)f(constrain)o(t)h(of)-112
1513 1589 y(the)h(form)e Fj(z)23 b Fq(=)f Fk(\(<)f Fj(x)g(y)q
1514 Fk(\))f Fq(implies)e(that)h Fj(z)j Fq(is)e(\\Bo)q(olean",)-112
1515 1635 y(i.e.,)14 b(either)i Fk(t)f Fq(or)g Fk(nil)p Fq(.)21
1516 b(F)m(urthermore,)15 b(this)g(constrain)o(t)h(im-)-112
1517 1680 y(plies)d(that)h Fj(x)g Fq(and)g Fj(y)i Fq(are)e(n)o(umeric.)k(In)
1518 c(practice,)g(a)g(v)n(ariable)-112 1726 y(usually)k(has)i(a)f(w)o(ell)g
1519 (de\014ned)h(t)o(yp)q(e,)h(e.g.,)f(it)f(is)g(kno)o(wn)g(to)-112
1520 1772 y(b)q(e)e(Bo)q(olean,)h(kno)o(wn)f(b)q(e)g(real,)h(kno)o(wn)f(to)g
1521 (b)q(e)h(a)e(cons)i(cell,)-112 1817 y(etc.)26 b(Kno)o(wledge)17
1522 b(ab)q(out)f(the)h(t)o(yp)q(e)g(of)f(a)g(v)n(ariable)g(has)g(sig-)-112
1523 1863 y(ni\014can)o(t)c(rami\014cations)f(for)h(the)i(e\016ciency)f(of)f
1524 Fp(Screamer)q Fq('s)-112 1909 y(constrain)o(t)d(satisfaction)h
1525 (algorithms.)k Fp(Screamer)c Fq(has)g(sp)q(e-)-112 1954
1526 y(cial)h(pro)q(cedures)j(for)d(inferring)h(the)g(t)o(yp)q(es)h(of)e(v)n
1527 (ariables.)17 b(Be-)-112 2000 y(cause)22 b(kno)o(wledge)f(of)f(the)i(t)
1528 o(yp)q(es)g(of)e(v)n(ariables)h(is)g(imp)q(or-)-112 2046
1529 y(tan)o(t)e(for)f(e\016ciency)m(,)j(in)d(con)o(trast)i(to)f(the)h
1530 Fp(Common)d(Lisp)-112 2091 y Fq(primitiv)o(es)g Fk(and)p
1531 Fq(,)i Fk(or)p Fq(,)h(and)f Fk(not)g Fq(whic)o(h)g(accept)h(an)o(y)f
1532 (argu-)-112 2137 y(men)o(ts)f(of)g(an)o(y)g(t)o(yp)q(e,)i(the)f
1533 Fp(Screamer)g Fq(constrain)o(t)g(primi-)-112 2183 y(tiv)o(es)d
1534 Fk(andv)p Fq(,)f Fk(orv)p Fq(,)h(and)g Fk(notv)g Fq(require)h(their)f
1535 (argumen)o(ts)g(to)-112 2228 y(b)q(e)e(Bo)q(olean.)j(This)d(allo)o(ws)e
1536 (the)j(use)f(of)f(Bo)q(olean)g(constrain)o(t)-112 2274
1537 y(satisfaction)i(tec)o(hniques)j(for)d(an)o(y)h(constrain)o(ts)h(in)o
1538 (tro)q(duced)-112 2320 y(b)o(y)c(these)j(primitiv)o(es.)h(Similarly)l
1539 (,)11 b(constrain)o(t)k(\\predicates")-112 2365 y(return)h(Bo)q(olean)f
1540 (v)n(ariables.)20 b(F)m(or)15 b(example,)f(in)g(con)o(trast)i(to)-112
1541 2411 y(the)d Fp(Common)j(Lisp)d Fq(primitiv)o(e)e Fk(member)g
1542 Fq(whic)o(h)i(can)g(return)-112 2456 y(the)c(sub-list)h(of)e(the)i
1543 (second)h(argumen)o(t)d(whose)i(head)g(satis\014es)-112
1544 2502 y(the)j(equalit)o(y)f(c)o(hec)o(k,)h(the)h(result)f(of)f(the)i
1545 Fk(memberv)d Fq(primitiv)o(e)-112 2548 y(is)i(constrained)i(to)f(b)q(e)
1546 g(Bo)q(olean.)-71 2595 y Fp(Screamer)23 b Fq(includes)g(the)g(primitiv)
1547 o(e)d Fk(assert!)h Fq(whic)o(h)980 -33 y(can)13 b(b)q(e)g(used)g(to)g
1548 (add)f(constrain)o(ts)h(other)g(than)g(those)g(added)980
1549 12 y(b)o(y)18 b(the)i(constrain)o(t)e(primitiv)o(es.)30
1550 b(Ev)n(aluating)17 b(the)i(expres-)980 58 y(sion)26 b
1551 Fk(\(assert!)20 b Fj(x)p Fk(\))26 b Fq(constrains)h Fj(x)f
1552 Fq(to)g(equal)g Fk(t)p Fq(.)56 b(This)980 103 y(can)28
1553 b(b)q(e)g(used)g(in)f(conjunction)h(with)f(other)h(constrain)o(t)980
1554 149 y(primitiv)o(es)d(to)g(install)g(a)h(wide)g(v)n(ariet)o(y)g(of)f
1555 (constrain)o(ts.)980 195 y(F)m(or)14 b(example,)f Fk(\(assert!)20
1556 b(\(<v)i Fj(x)f(y)q Fk(\)\))15 b Fq(e\013ectiv)o(ely)g(installs)980
1557 240 y(the)24 b(constrain)o(t)g(that)f Fj(x)g Fq(m)o(ust)g(b)q(e)h(less)
1558 g(than)f Fj(y)q Fq(.)1816 225 y Fi(1)1882 240 y Fq(Cer-)980
1559 286 y(tain)28 b(constrain)o(t)h(primitiv)o(es)e(in)h(table)g(1,)j(in)d
1560 (conjunc-)980 332 y(tion)17 b(with)g Fk(assert!)p Fq(,)f(can)h(b)q(e)h
1561 (used)g(to)f(directly)g(constrain)980 377 y(the)29 b(t)o(yp)q(e)f(of)f
1562 (a)g(v)n(ariable.)58 b(F)m(or)28 b(example,)h(ev)n(aluating)980
1563 423 y Fk(\(assert!)20 b(\(numberpv)g Fj(x)p Fk(\)\))14
1564 b Fq(e\013ectiv)o(ely)h(installs)f(the)h(con-)980 469
1565 y(strain)o(t)k(that)g Fj(x)f Fq(m)o(ust)g(b)q(e)h(a)f(n)o(um)o(b)q(er.)
1566 32 b(Lik)o(ewise)18 b(ev)n(aluat-)980 514 y(ing)13 b
1567 Fk(\(assert!)21 b(\(booleanpv)e Fj(x)p Fk(\)\))13 b Fq(installs)h(the)g
1568 (constrain)o(t)980 560 y(that)j Fj(x)e Fq(m)o(ust)h(b)q(e)g(Bo)q
1569 (olean.)25 b(This)16 b(is)g(e\013ectiv)o(ely)i(the)e(same)980
1570 606 y(as)e(ev)n(aluating)f Fk(\(assert!)20 b(\(memberv)g
1571 Fj(x)h Fk('\(t)h(nil\)\)\))p Fq(.)1022 651 y(All)12 b(constrain)o(ts)j
1572 (in)e Fp(Screamer)h Fq(are)g(installed)e(either)j(b)o(y)980
1573 697 y Fk(assert!)g Fq(or)h(b)o(y)g(one)h(of)f(the)h(constrain)o(t)f
1574 (primitiv)o(es)f(in)h(ta-)980 743 y(ble)i(1.)29 b(A)18
1575 b(constrain)o(t)g(installed)f(b)o(y)g Fk(assert!)g Fq(states)h(that)980
1576 788 y(a)23 b(certain)h(v)n(ariable)e(m)o(ust)g(ha)o(v)o(e)h(the)g(v)n
1577 (alue)g Fk(t)p Fq(.)45 b(A)23 b(con-)980 834 y(strain)o(t)17
1578 b(installed)g(b)o(y)g(a)g(constrain)o(t)g(primitiv)o(e)e(alw)o(a)o(ys)h
1579 (has)980 880 y(the)23 b(form)e Fj(z)28 b Fq(=)f Fk(\(f)e
1580 Fj(x)1366 886 y Fi(1)1418 880 y Fj(:)7 b(:)g(:)31 b(x)1523
1581 886 y Fh(n)1545 880 y Fk(\))23 b Fq(where)h Fk(f)e Fq(is)g(either)i(a)
1582 980 925 y Fp(Common)17 b(Lisp)23 b Fq(primitiv)o(e)f(or)h(a)g(sligh)o
1583 (t)g(v)n(ariation)f(on)h(a)980 971 y Fp(Common)17 b(Lisp)11
1584 b Fq(primitiv)o(e.)16 b(The)c(v)n(ariations)e(arise)i(for)f(con-)980
1585 1017 y(strain)o(t)k(primitiv)o(es)d(suc)o(h)k(as)e Fk(orv)g
1586 Fq(and)g Fk(memberv)f Fq(where)j(the)980 1062 y(seman)o(tics)11
1587 b(of)g(the)h(constrain)o(t)g(v)o(ersion)g(di\013ers)g(sligh)o(tly)e
1588 (from)980 1108 y(the)27 b(seman)o(tics)f(of)g(the)h(corresp)q(onding)h
1589 Fp(Common)16 b(Lisp)980 1154 y Fq(primitiv)o(e)c(as)i(discussed)h(ab)q
1590 (o)o(v)o(e.)1022 1199 y(An)i(attempt)f(to)g(add)h(a)f(constrain)o(t)h
1591 (fails)f(if)g Fp(Screamer)980 1245 y Fq(determines)36
1592 b(that)f(the)h(resulting)f(set)h(of)f(constrain)o(ts)980
1593 1291 y(w)o(ould)20 b(b)q(e)i(unsatis\014able.)39 b(F)m(or)20
1594 b(example,)h(after)g(ev)n(aluat-)980 1336 y(ing)d Fk(\(assert!)i(\(<v)h
1595 Fj(x)h Fk(0\)\))c Fq(a)g(subsequen)o(t)i(ev)n(aluation)d(of)980
1596 1382 y Fk(\(assert!)j(\(>v)i Fj(x)f Fk(0\)\))15 b Fq(will)g(fail.)23
1597 b(A)16 b(call)f(to)h(a)g(constrain)o(t)980 1428 y(primitiv)o(e)c(can)j
1598 (fail)e(when)h(it)g(w)o(ould)g(generate)h(a)f(constrain)o(t)980
1599 1473 y(inconsisten)o(t)i(with)e(kno)o(wn)h(t)o(yp)q(e)g(information.)j
1600 (F)m(or)d(exam-)980 1519 y(ple,)20 b(if)d Fj(x)i Fq(is)f(kno)o(wn)g(to)
1601 h(b)q(e)g(Bo)q(olean)f(then)h(an)g(ev)n(aluation)980
1602 1565 y(of)14 b Fk(\(+v)21 b Fj(x)g(y)q Fk(\))15 b Fq(will)d(fail.)1181
1603 1659 y Ft(Constrain)n(t)19 b(Propagation)980 1717 y Fq(In)28
1604 b(this)h(section)f(w)o(e)h(discuss)g(the)g(\014v)o(e)f(kinds)g(of)f
1605 (con-)980 1762 y(strain)o(t)18 b(propagation)f(inference)i(pro)q
1606 (cesses)i(p)q(erformed)d(b)o(y)980 1808 y Fp(Screamer)q
1607 Fq(.)48 b(First,)26 b Fp(Screamer)e Fq(implemen)o(ts)d(binding)980
1608 1854 y(propagation,)14 b(an)g(incomplete)g(inference)j(tec)o(hnique)e
1609 (some-)980 1899 y(times)k(called)h(v)n(alue)f(propagation.)34
1610 b(Second,)22 b Fp(Screamer)980 1945 y Fq(implemen)o(ts)g(Bo)q(olean)j
1611 (constrain)o(t)g(propagation)e(\(BCP\).)980 1991 y(This)17
1612 b(is)f(an)g(incomplete)g(form)e(of)i(Bo)q(olean)h(inference)g(that)980
1613 2036 y(can)k(b)q(e)g(view)o(ed)f(as)g(a)g(form)f(of)g(unit)h
1614 (resolution.)37 b(Third,)980 2082 y Fp(Screamer)20 b
1615 Fq(implemen)o(ts)e(generalized)i(forw)o(ard)f(c)o(hec)o(king)980
1616 2128 y(\(GF)o(C\).)40 b(This)22 b(is)f(a)g(constrain)o(t)g(propagation)
1617 g(tec)o(hnique)980 2173 y(for)k(discrete)i(constrain)o(ts)f(used)g(in)f
1618 (the)g Fp(CHiP)f Fq(system.)980 2219 y(F)m(ourth,)f Fp(Screamer)g
1619 Fq(implemen)o(ts)c(b)q(ounds)k(propagation)980 2265 y(on)h(n)o(umeric)g
1620 (v)n(ariables.)49 b(Suc)o(h)24 b(b)q(ounds)h(propagation|)980
1621 2310 y(when)12 b(com)o(bined)e(with)h(the)h(divide-and-conquer)g(tec)o
1622 (hnique)p 980 2345 250 2 v 1032 2372 a Fg(1)1049 2387
1623 y Fm(T)m(o)h(mitigate)h(the)f(apparen)o(t)g(ine\016ciency)i(of)e(this)g
1624 (conceptu-)980 2429 y(ally)18 b(clean)g(language)h(design,)f(the)f
1625 (implemen)o(tation)i(optimizes)980 2470 y(most)e(calls)i(to)e
1626 Ff(assert!)p Fm(,)e(suc)o(h)i(as)g(the)g(calls)i Ff(\(assert!)d(\(notv)
1627 980 2512 y(\(realpv)h Fe(x)p Ff(\)\)\))9 b Fm(and)j Ff(\(assert!)k
1628 (\(<=v)j Fe(x)g(y)q Ff(\)\))p Fm(,)10 b(to)h(eliminate)i(the)980
1629 2553 y(creation)f(of)e(the)g(in)o(termediate)i(Bo)q(olean)g(v)n
1630 (ariable\(s\))g(and)f(the)g(re-)980 2595 y(sulting)k(lo)q(cal)g
1631 (propagation.)p eop
1632 %%Page: 3 3
1633 3 2 bop -112 -33 a Fq(discussed)20 b(later)f(in)g(this)g(pap)q
1634 (er|implemen)o(ts)e(a)i(general-)-112 12 y(ization)g(of)g(the)i(in)o
1635 (terv)n(al)e(metho)q(d)h(of)f(solving)g(systems)h(of)-112
1636 58 y(nonlinear)d(equations)h(prop)q(osed)h(b)o(y)f(Hansen)h(\(1968\).)
1637 29 b(Fi-)-112 103 y(nally)m(,)14 b Fp(Screamer)i Fq(implemen)o(ts)d
1638 (uni\014cation.)23 b(Uni\014cation)-112 149 y(is)17 b(view)o(ed)h(as)g
1639 (a)g(constrain)o(t)g(propagation)f(inference)i(tec)o(h-)-112
1640 195 y(nique)d(whic)o(h)h(can)g(b)q(e)h(applied)e(to)h(equational)f
1641 (constrain)o(ts)-112 240 y(in)o(v)o(olving)11 b(v)n(ariables)h(that)i
1642 (range)f(o)o(v)o(er)h(S-expressions.)19 b(The)-112 286
1643 y(constrain)o(t)k(propagation)f(tec)o(hniques)j(are)e(incremen)o(tally)
1644 -112 332 y(run)d(to)h(completion)e(whenev)o(er)j(a)e(new)h(constrain)o
1645 (t)g(is)f(in-)-112 377 y(stalled)12 b(b)o(y)h Fk(assert!)e
1646 Fq(or)i(one)g(of)f(the)i(constrain)o(t)f(primitiv)o(es.)-112
1647 423 y(The)g(\014v)o(e)g(forms)e(of)h(constrain)o(t)h(propagation)f(are)
1648 h(describ)q(ed)-112 469 y(in)g(more)g(detail)g(b)q(elo)o(w.)-71
1649 521 y(Eac)o(h)j(form)d(of)i(constrain)o(t)g(propagation)f(can)i(b)q(e)g
1650 (view)o(ed)-112 567 y(as)23 b(an)g(inference)h(pro)q(cess)i(whic)o(h)d
1651 (lo)q(cally)f(deriv)o(es)i(infor-)-112 612 y(mation)e(ab)q(out)i(v)n
1652 (ariables.)50 b(All)24 b(forms)f(of)h(propagation)-112
1653 658 y(are)i(capable)g(of)g(inferring)f(v)n(alues)h(for)g(v)n(ariables.)
1654 54 b(F)m(or)-112 704 y(example,)15 b(after)i(ev)n(aluating)e
1655 Fk(\(assert!)20 b(\(orv)h Fj(x)h(y)q Fk(\)\))17 b Fq(and)-112
1656 749 y Fk(\(assert!)j(\(notv)g Fj(x)p Fk(\)\))12 b Fq(BCP)g(will)e
1657 (infer)i(that)g Fj(y)i Fq(m)o(ust)d(ha)o(v)o(e)-112 795
1658 y(the)16 b(v)n(alue)f Fk(t)p Fq(.)24 b(If)15 b(some)g(constrain)o(t)i
1659 (propagation)d(inference)-112 841 y(pro)q(cess)d(has)f(determined)f(a)g
1660 (v)n(alue)g(for)h(some)e(v)n(ariable)h Fj(x)g Fq(then)-112
1661 886 y(w)o(e)16 b(sa)o(y)f(that)h Fj(x)g Fq(is)g Fl(b)q(ound)g
1662 Fq(and)g(the)g(inferred)h(v)n(alue)e(of)g Fj(x)h Fq(is)-112
1663 932 y(called)d(the)i Fl(binding)e Fq(of)g Fj(x)p Fq(.)-71
1664 984 y Fd(Binding)27 b(Propagation:)40 b Fq(As)27 b(noted)f(ab)q(o)o(v)o
1665 (e,)j(most)-112 1030 y(constrain)o(ts)j(in)f Fp(Screamer)h
1666 Fq(are)g(of)f(the)h(form)d Fj(z)43 b Fq(=)-112 1075 y
1667 Fk(\(f)14 b Fj(x)-30 1081 y Fi(1)11 1075 y Fj(:)7 b(:)g(:)21
1668 b(x)106 1081 y Fh(n)128 1075 y Fq(\))16 b(where)i Fj(f)j
1669 Fq(is)16 b(a)g Fp(Common)g(Lisp)g Fq(primitiv)o(e,)-112
1670 1121 y Fj(z)k Fq(is)e(a)g(v)n(ariable,)g(and)g(eac)o(h)h
1671 Fj(x)392 1127 y Fh(i)424 1121 y Fq(is)f(either)h(a)f(v)n(ariable)g(or)g
1672 (a)-112 1167 y(sp)q(eci\014c)c(v)n(alue.)j(F)m(or)c(an)o(y)f(suc)o(h)i
1673 (constrain)o(t)f Fp(Screamer)h Fq(im-)-112 1212 y(plemen)o(ts)k(a)h
1674 (certain)g(v)n(alue)f(propagation)g(pro)q(cess.)35 b(More)-112
1675 1258 y(sp)q(eci\014cally)m(,)20 b(if)e(bindings)h(ha)o(v)o(e)g(b)q(een)
1676 i(determined)e(for)g(all)-112 1304 y(but)9 b(one)h(of)f(the)i(v)n
1677 (ariables)e(in)g(the)h(constrain)o(t,)h(and)e(a)h(binding)-112
1678 1349 y(for)k(the)i(remaining)d(v)n(ariable)h(follo)o(ws)f(from)h(the)h
1679 (constrain)o(t)-112 1395 y(and)i(the)i(existing)f(bindings,)g(then)h
1680 (this)f(additional)e(bind-)-112 1441 y(ing)c(is)h(inferred.)19
1681 b(This)13 b(general)g(principle)h(is)f(called)g Fl(binding)-112
1682 1486 y(propagation)p Fq(.)i(Binding)10 b(propagation)g(will)f(alw)o(a)o
1683 (ys)h(bind)g(the)-112 1532 y(output)j(v)n(ariable)f(of)g(a)h(constrain)
1684 o(t)g(primitiv)o(e)e(whenev)o(er)j(the)-112 1578 y(input)e(v)n
1685 (ariables)f(b)q(ecome)h(b)q(ound.)18 b(F)m(or)12 b(example,)e(giv)o(en)
1686 i(the)-112 1623 y(constrain)o(t)18 b Fj(z)j Fq(=)e Fk(\(+)g
1687 Fj(x)f(y)q Fk(\))q Fq(,)h(if)e Fj(x)h Fq(is)g(b)q(ound)h(to)f(2)g(and)g
1688 Fj(y)i Fq(is)-112 1669 y(b)q(ound)12 b(to)h(3,)f(then)i(binding)e
1689 (propagation)f(will)g(bind)i Fj(z)i Fq(to)d(5.)-112 1715
1690 y(Often,)e(ho)o(w)o(ev)o(er,)g(binding)f(propagation)f(will)g(deriv)o
1691 (e)i(a)f(bind-)-112 1760 y(ing)i(for)g(an)h(input)g(from)e(a)i(binding)
1692 f(for)h(the)g(output.)18 b(F)m(or)12 b(ex-)-112 1806
1693 y(ample,)g(giv)o(en)i(the)h(constrain)o(t)f Fj(z)h Fq(=)d
1694 Fk(\(+)g Fj(x)g(y)q Fk(\))q Fq(,)i(if)f Fj(z)j Fq(is)f(b)q(ound)-112
1695 1852 y(to)10 b(5)h(and)g Fj(x)g Fq(is)g(b)q(ound)g(to)g(2,)g(then)h
1696 (binding)e(propagation)g(will)-112 1897 y(bind)j Fj(y)j
1697 Fq(to)d(3.)-71 1949 y Fd(Bo)q(olean)k(Constrain)o(t)e(Propagation:)k
1698 Fq(BCP)d(is)f(sim-)-112 1995 y(ply)j(arc)h(consistency)i(\(cf.)d(Mac)o
1699 (kw)o(orth)h(1992\))f(relativ)o(e)h(to)-112 2041 y(the)11
1700 b(Bo)q(olean)f(constrain)o(t)h(primitiv)o(es)d Fk(andv)p
1701 Fq(,)i Fk(orv)p Fq(,)g(and)g Fk(notv)p Fq(.)-112 2086
1702 y(BCP)m(,)15 b(lik)o(e)g(arc)h(consistency)m(,)h(is)f(seman)o(tically)d
1703 (incomplete.)-112 2132 y(F)m(or)j(example,)f(after)i(ev)n(aluating)e
1704 Fk(\(assert!)20 b(\(orv)h Fj(z)j(w)q Fk(\)\))-112 2178
1705 y Fq(and)17 b Fk(\(assert!)j(\(orv)h(\(notv)g Fj(z)r
1706 Fk(\))h Fj(w)q Fk(\)\))p Fq(,)17 b(an)o(y)h(v)n(ariable)e(in-)-112
1707 2223 y(terpretation)k(satisfying)e(the)h(installed)g(constrain)o(ts)h
1708 (m)o(ust)-112 2269 y(assign)e Fj(w)i Fq(the)f(v)n(alue)f
1709 Fk(t)p Fq(.)33 b(Ho)o(w)o(ev)o(er,)20 b(BCP)f(will)e(not)i(mak)o(e)-112
1710 2315 y(this)f(inference.)34 b(Seman)o(tic)18 b(incompleteness)h(is)g
1711 (necessary)-112 2360 y(in)11 b(order)h(to)f(ensure)j(that)d(the)h
1712 (constrain)o(t)g(propagation)f(pro-)-112 2406 y(cess)21
1713 b(terminates)f(quic)o(kly)m(.)35 b(Later)21 b(in)e(the)i(pap)q(er)g(w)o
1714 (e)f(dis-)-112 2452 y(cuss)d(ho)o(w)f(w)o(e)g(in)o(terlea)o(v)o(e)g
1715 (bac)o(ktrac)o(king)g(searc)o(h)i(with)e(con-)-112 2497
1716 y(strain)o(t)g(propagation)f(to)g(mitigate)f(the)j(incompleteness)f(of)
1717 -112 2543 y(lo)q(cal)d(propagation.)-71 2595 y Fd(Generalized)21
1718 b(F)l(orw)o(ard)i(Chec)o(king:)32 b Fq(GF)o(C)20 b(applies)980
1719 -33 y(to)25 b(v)n(ariables)f(for)h(whic)o(h)g(a)g(\014nite)g(set)h(of)e
1720 (p)q(ossible)i(v)n(al-)980 12 y(ues)f(has)e(b)q(een)i(established.)47
1721 b(Suc)o(h)24 b(a)f(set)h(is)g(called)f(an)980 58 y Fl(en)o(umerated)c
1722 (domain)p Fq(.)30 b(V)m(ariables)19 b(with)f(en)o(umerated)h(do-)980
1723 103 y(mains)f(are)i(called)f Fl(discrete)p Fq(.)36 b(F)m(or)19
1724 b(example,)g(after)g(ev)n(alu-)980 149 y(ating)d Fk(\(assert!)k
1725 (\(memberv)g Fj(x)i Fk('\(a)f(b)g(c)h(d\)\)\))16 b Fq(the)h(v)n(ari-)
1726 980 195 y(able)10 b Fj(x)g Fq(is)g(discrete)h(b)q(ecause)h(its)e(v)n
1727 (alue)g(is)f(kno)o(wn)h(to)g(b)q(e)h(either)980 240 y
1728 Fk(a)p Fq(,)17 b Fk(b)p Fq(,)f Fk(c)p Fq(,)h(or)g Fk(d)p
1729 Fq(.)28 b(Bo)q(olean)17 b(v)n(ariables)g(are)g(a)g(sp)q(ecial)h(case)g
1730 (of)980 286 y(discrete)g(v)n(ariables)e(where)i(the)f(en)o(umerated)f
1731 (domain)e(con-)980 332 y(tains)g(only)f Fk(t)h Fq(and)g
1732 Fk(nil)p Fq(.)k(Similarly)m(,)10 b(b)q(ounded)15 b(in)o(teger)g(v)n
1733 (ari-)980 377 y(ables)h(are)h(considered)g(to)f(b)q(e)h(discrete.)26
1734 b(F)m(or)15 b(eac)o(h)i(discrete)980 423 y(v)n(ariable)i
1735 Fp(Screamer)h Fq(main)o(tains)d(a)j(list)f(represen)o(ting)i(its)980
1736 469 y(en)o(umerated)f(domain.)35 b(The)20 b(en)o(umerated)g(domain)e
1737 (for)i(a)980 514 y(giv)o(en)d(v)n(ariable)g(can)g(b)q(e)i(up)q(dated)f
1738 (b)o(y)f(the)h(GF)o(C)f(inference)980 560 y(pro)q(cess.)25
1739 b(The)16 b(GF)o(C)e(inference)j(pro)q(cess)g(op)q(erates)g(on)e(con-)
1740 980 606 y(strain)o(ts)c(of)e(the)i(form)d Fj(z)14 b Fq(=)e
1741 Fk(\(funcall)d Fj(f)17 b(x)1654 612 y Fi(1)1691 606 y
1742 Fj(:)7 b(:)g(:)16 b(x)1781 612 y Fh(n)1804 606 y Fk(\))o
1743 Fq(.)h(These)980 651 y(constrain)o(ts)27 b(are)g(generated)h(b)o(y)e
1744 (the)h(constrain)o(t)g(primi-)980 697 y(tiv)o(e)15 b
1745 Fk(funcallv)p Fq(.)j(Unlik)o(e)13 b(most)h(constrain)o(t)h(primitiv)o
1746 (es,)d(the)980 743 y(primitiv)o(e)k Fk(funcallv)g Fq(will)g(signal)h
1747 (an)g(error|rather)i(than)980 788 y(fail|)e(if)h(its)h(\014rst)h
1748 (argumen)o(t)e(is)g(b)q(ound)h(to)g(an)o(ything)f(but)980
1749 834 y(a)24 b(deterministic)g(pro)q(cedure.)51 b(No)o(w)24
1750 b(consider)h(the)g(con-)980 880 y(strain)o(t)18 b Fj(z)j
1751 Fq(=)d Fk(\(funcall)f Fj(f)23 b(x)1467 886 y Fi(1)1511
1752 880 y Fj(:)7 b(:)g(:)23 b(x)1608 886 y Fh(n)1630 880
1753 y Fk(\))p Fq(.)30 b(GF)o(C)18 b(will)e(only)980 925 y(op)q(erate)d(on)f
1754 (this)g(constrain)o(t)g(when)g Fj(f)17 b Fq(is)12 b(b)q(ound)g(and)g
1755 (all)e(but)980 971 y(one)17 b(of)f(the)i(remaining)c(v)n(ariables)i(in)
1756 g(the)i(constrain)o(t)f(ha)o(v)o(e)980 1017 y(b)q(een)k(b)q(ound.)37
1757 b(If)19 b(the)i(un)o(b)q(ound)f(v)n(ariable)f(is)h(the)g(output)980
1758 1062 y(v)n(ariable)d Fj(z)r Fq(,)i(then)g(GF)o(C)f(simply)e(deriv)o(es)
1759 j(a)f(binding)f(for)h Fj(z)980 1108 y Fq(b)o(y)f(applying)e
1760 Fj(f)t Fq(.)27 b(If)17 b(the)g(un)o(b)q(ound)g(v)n(ariable)e(is)i(one)g
1761 (of)f(the)980 1154 y(argumen)o(ts)i Fj(x)1211 1160 y
1762 Fh(i)1244 1154 y Fq(then)h(GF)o(C)g(tests)h(eac)o(h)g(elemen)o(t)e
1763 Fj(v)j Fq(of)d(the)980 1199 y(en)o(umerated)13 b(domain)d(of)i(the)h
1764 (discrete)i(v)n(ariable)c Fj(x)1796 1205 y Fh(i)1822
1765 1199 y Fq(for)h(con-)980 1245 y(sistency)21 b(relativ)o(e)e(to)g(this)h
1766 (constrain)o(t.)34 b(Elemen)o(ts)19 b(of)g(the)980 1291
1767 y(en)o(umerated)10 b(domain)e(of)i Fj(x)1413 1297 y Fh(i)1436
1768 1291 y Fq(that)h(are)f(inconsisten)o(t)h(with)f(the)980
1769 1336 y(constrain)o(t)j(are)g(remo)o(v)o(ed.)k(F)m(or)12
1770 b(example,)g(supp)q(ose)h(that)g(w)o(e)980 1382 y(ha)o(v)o(e)30
1771 b(ev)n(aluated)f Fk(\(assert!)20 b(\(memberv)h Fj(x)g
1772 Fk('\(1)g(5)h(9\)\)\))p Fq(,)980 1428 y Fk(\(assert!)e(\(memberv)h
1773 Fj(y)i Fk('\(3)e(7)h(12\)\)\))31 b Fq(and)g Fk(\(assert!)980
1774 1473 y(\(funcallv)20 b(#'<)h Fj(x)h(y)q Fk(\)\))p Fq(.)27
1775 b(In)17 b(this)g(case)h(the)f(output)h(v)n(ari-)980 1519
1776 y(able)f(of)g(the)h Fk(funcallv)d Fq(constrain)o(t)j(is)f(b)q(ound)h
1777 (to)f Fk(t)p Fq(.)28 b(No)o(w)980 1565 y(supp)q(ose)c(that)f(some)f
1778 (constrain)o(t)h(propagation)e(inference)980 1610 y(pro)q(cess)e
1779 (infers)f(that)f Fj(y)i Fq(is)d(3.)28 b(In)17 b(this)g(case)h(GF)o(C)f
1780 (will)e(run)980 1656 y(on)g(the)h Fk(funcallv)d Fq(constrain)o(t)j(and)
1781 f(remo)o(v)o(e)f(5)g(and)h(9)g(from)980 1702 y(the)i(en)o(umerated)g
1782 (domain)d(of)h Fj(x)p Fq(.)26 b(Whenev)o(er)17 b(the)g(en)o(umer-)980
1783 1747 y(ated)11 b(domain)d(of)i(a)h(discrete)h(v)n(ariable)d(is)i
1784 (reduced)h(to)f(a)f(single)980 1793 y(v)n(alue,)h(GF)o(C)g(binds)g(the)
1785 h(v)n(ariable)e(to)i(that)f(v)n(alue.)16 b(An)c(exam-)980
1786 1839 y(ple)g(of)g(GF)o(C)g(running)g(on)g(the)g Fj(N)5
1787 b Fq(-Queens)14 b(problem)d(is)h(giv)o(en)980 1884 y(later)i(in)g(the)g
1788 (pap)q(er.)1022 1956 y Fd(Bounds)23 b(Propagation:)32
1789 b Fq(Bounds)23 b(propagation)e(ap-)980 2001 y(plies)14
1790 b(to)f(n)o(umeric)g(v)n(ariables.)k(F)m(or)c(eac)o(h)h(n)o(umeric)f(v)n
1791 (alue)g(the)980 2047 y(system)19 b(main)o(tains)e(an)i(upp)q(er)h(and)g
1792 (lo)o(w)o(er)e(b)q(ound)i(on)f(the)980 2093 y(p)q(ossible)f(v)n(alues)f
1793 (of)f(that)h(v)n(ariable.)27 b(These)19 b(b)q(ounds)f(prop-)980
1794 2138 y(agate)f(through)h(constrain)o(ts)f(generated)i(b)o(y)e(n)o
1795 (umeric)f(con-)980 2184 y(strain)o(t)d(primitiv)o(es)f(suc)o(h)h(as)h
1796 Fk(+v)p Fq(,)e Fk(*v)g Fq(and)h Fk(<v)p Fq(.)18 b(F)m(or)12
1797 b(example,)980 2230 y(after)k(ev)n(aluating)f Fk(\(assert!)20
1798 b(\(=v)h Fj(z)j Fk(\(+v)d Fj(x)h(y)q Fk(\)\)\))p Fq(,)16
1799 b(if)f Fj(z)j Fq(is)980 2275 y(kno)o(wn)c(to)g(b)q(e)h(no)g(larger)f
1800 (than)g(5)p Fj(:)p Fq(7,)f(and)h Fj(x)g Fq(is)h(kno)o(wn)f(to)g(b)q(e)
1801 980 2321 y(no)d(smaller)e(than)h(2)p Fj(:)p Fq(2,)g(then)h(b)q(ounds)g
1802 (propagation)e(will)h(infer)980 2367 y(that)16 b Fj(y)h
1803 Fq(is)e(no)g(larger)g(than)g(3)p Fj(:)p Fq(5.)21 b(Bounds)16
1804 b(propagation)e(can)980 2412 y(also)h(deriv)o(e)i(v)n(alues)e(for)g
1805 (the)i(Bo)q(olean)e(output)h(v)n(ariables)f(of)980 2458
1806 y(n)o(umeric)g(constrain)o(t)g(predicates)i(suc)o(h)f(as)f
1807 Fk(<v)g Fq(and)g Fk(=v)p Fq(.)22 b(F)m(or)980 2504 y(example,)16
1808 b(if)f(w)o(e)i(ha)o(v)o(e)g(the)g(constrain)o(t)g Fj(z)h
1809 Fq(=)e Fk(\(<)g Fj(x)f(y)q Fq(\))p Fk(\))j Fq(and)980
1810 2549 y(the)d(system)e(has)h(determined)g(that)f Fj(x)h
1811 Fq(is)f(at)h(least)g(2)p Fj(:)p Fq(0)f(but)h Fj(y)980
1812 2595 y Fq(is)g(no)f(larger)h(than)g(1)p Fj(:)p Fq(0,)e(then)j(the)f
1813 (system)g(will)e(infer)i(that)f Fj(z)p eop
1814 %%Page: 4 4
1815 4 3 bop -112 -33 a Fq(is)13 b Fk(nil)p Fq(.)-71 13 y(Bounds)25
1816 b(propagation)f(will)f(not)i(infer)g(a)f(new)i(b)q(ound)-112
1817 59 y(unless)g(the)h(new)g(b)q(ound)f(reduces)i(the)f(kno)o(wn)f(in)o
1818 (terv)n(al)-112 105 y(of)21 b(the)h(v)n(ariable)e(in)o(v)o(olv)o(ed)h
1819 (b)o(y)g(at)h(least)g(a)f(certain)h(mini-)-112 150 y(m)o(um)11
1820 b(p)q(ercen)o(tage.)23 b(This)15 b(ensures)h(that)f(the)h(b)q(ounds)f
1821 (prop-)-112 196 y(agation)23 b(pro)q(cess)k(terminates)e(fairly)f(quic)
1822 o(kly)m(.)50 b(F)m(or)25 b(ex-)-112 242 y(ample,)c Fp(Screamer)h
1823 Fq(a)o(v)o(oids)e(the)j(v)o(ery)e(large)h(n)o(um)o(b)q(er)e(of)-112
1824 287 y(b)q(ounds)12 b(up)q(dates)h(that)f(w)o(ould)f(result)h(from)f
1825 (the)h(constrain)o(ts)-112 333 y Fk(\(assert!)20 b(\(>v)h
1826 Fj(x)g Fk(0\)\))p Fq(,)j Fk(\(assert!)d(\(<v)g Fj(x)g
1827 Fk(1000\)\))h Fq(and)-112 379 y Fk(\(assert!)e(\(<v)h
1828 Fj(x)g Fk(\(-v)h Fj(x)f Fk(0.001\)\)\))p Fq(.)-71 425
1829 y Fd(Uni\014cation:)33 b Fq(Uni\014cation)22 b(op)q(erates)i(on)e
1830 (constrain)o(ts)-112 471 y(of)27 b(the)h(form)f Fj(w)35
1831 b Fq(=)h Fk(\(equal)d Fj(u)i(v)q Fk(\))28 b Fq(whic)o(h)g(are)h(gen-)
1832 -112 517 y(erated)k(b)o(y)e(the)i(constrain)o(t)f(primitiv)o(e)e
1833 Fk(equalv)p Fq(.)71 b(A)o(t)-112 562 y(an)o(y)23 b(giv)o(en)g(time)g
1834 (there)i(is)f(a)g(system)f(of)h(equations)f(de-)-112
1835 608 y(\014ned)i(b)o(y)f(the)h(set)g(of)f Fk(equalv)g
1836 Fq(constrain)o(ts)h(whose)g(out-)-112 654 y(put)d(v)n(ariable)f(has)h
1837 (b)q(een)h(b)q(ound)f(to)g Fk(t)p Fq(.)42 b Fp(Screamer)22
1838 b Fq(in-)-112 699 y(cremen)o(tally)g(main)o(tains)f(a)j(most)e(general)
1839 i(uni\014er)g Fj(\033)h Fq(for)-112 745 y(this)e(system)g(of)g
1840 (equations.)46 b(F)m(or)23 b(example,)h(ev)n(aluating)-112
1841 791 y Fk(\(assert!)c(\(equalv)g(\(cons)h Fj(x)g(x)p Fk(\))h(\(cons)e
1842 Fj(y)k(w)q Fk(\)\)\))30 b Fq(will)-112 836 y(result)21
1843 b(in)f(a)h(uni\014er)g Fj(\033)h Fq(that)e(equates)i
1844 Fj(x)p Fq(,)e Fj(y)q Fq(,)h(and)f Fj(w)q Fq(,)i(i.e.,)-112
1845 882 y(a)i(uni\014er)i Fj(\033)g Fq(suc)o(h)g(that)f Fj(\033)q
1846 Fq([)p Fj(x)p Fq(],)e Fj(\033)q Fq([)p Fj(y)q Fq(],)28
1847 b(and)c Fj(\033)q Fq([)p Fj(w)q Fq(])g(are)i(all)-112
1848 928 y(equal.)35 b Fp(Screamer)20 b Fq(also)f(implemen)o(ts)f
1849 (disuni\014cation)h(as)-112 973 y(in)c Fp(Pr)o(olog-I)q(I)i
1850 Fq(\(Colmerauer)e(1984\).)25 b(Th)o(us,)17 b(after)g(ev)n(alu-)-112
1851 1019 y(ating)9 b Fk(\(assert!)21 b(\(notv)f(\(equalv)h
1852 Fj(x)g(y)q Fk(\)\)\))p Fq(,)11 b(an)o(y)f(attempt)-112
1853 1065 y(to)j(bind)h Fj(x)f Fq(or)h Fj(y)i Fq(to)e(b)q(e)g(equal)g(will)e
1854 (fail.)-71 1112 y(The)f(di\013eren)o(t)h(forms)d(of)h(constrain)o(t)h
1855 (propagation)e(can)i(in-)-112 1157 y(teract)16 b(with)f(eac)o(h)h
1856 (other.)22 b(F)m(or)15 b(example,)f(a)h(giv)o(en)g(v)n(ariable)-112
1857 1203 y(can)10 b(b)q(e)h(b)q(oth)g(discrete)h(and)e(n)o(umeric.)16
1858 b(The)11 b(system)f(remo)o(v)o(es)-112 1249 y(non-n)o(umeric)f(elemen)o
1859 (ts)h(from)f(the)i(en)o(umerated)g(domains)d(of)-112
1860 1294 y(discrete)15 b(n)o(umeric)e(v)n(ariables.)18 b(F)m(urthermore,)13
1861 b(if)g(a)h(b)q(ound)g(is)-112 1340 y(kno)o(wn)k(for)g(a)h(discrete)h(n)
1862 o(umeric)e(v)n(ariable)f(then)j(elemen)o(ts)-112 1386
1863 y(violating)14 b(that)i(b)q(ound)g(are)h(eliminated)d(from)g(its)i(en)o
1864 (umer-)-112 1431 y(ated)11 b(domain.)k Fp(Screamer)e
1865 Fq(also)e(deriv)o(es)h(b)q(ounds)g(informa-)-112 1477
1866 y(tion)g(from)f(the)i(en)o(umerated)g(domains)e(of)h(discrete)i(n)o
1867 (umeric)-112 1523 y(v)n(ariables.)29 b(Uni\014cation)17
1868 b(also)h(in)o(teracts)g(with)g Fp(Screamer)-112 1568
1869 y Fq(bindings.)28 b(F)m(or)18 b(example,)e(if)h Fj(\033)i
1870 Fq(is)f(the)g(most)e(general)i(uni-)-112 1614 y(\014er)g(main)o(tained)
1871 e(b)o(y)i Fp(Screamer)q Fq(,)g(and)g Fj(x)g Fq(and)g
1872 Fj(y)i Fq(are)e(t)o(w)o(o)-112 1660 y(v)n(ariables)h(suc)o(h)h(that)g
1873 Fj(\033)q Fq([)p Fj(x)p Fq(])f(equals)h Fj(\033)q Fq([)p
1874 Fj(y)q Fq(],)h(then)g(an)o(y)e(bind-)-112 1705 y(ing)d(for)h
1875 Fj(x)g Fq(b)q(ecomes)h(a)f(binding)g(for)g Fj(y)i Fq(and)e(vice)h(v)o
1876 (ersa.)29 b(If)-112 1751 y Fj(\033)q Fq([)p Fj(x)p Fq(])12
1877 b(equals)j Fj(\033)q Fq([)p Fj(y)q Fq(],)e(and)h Fj(x)g
1878 Fq(and)g Fj(y)h Fq(ha)o(v)o(e)f(incompatible)e(bind-)-112
1879 1797 y(ings,)h(then)h(a)g(failure)f(is)h(generated.)-3
1880 1894 y Ft(Solving)j(Systems)g(of)i(Constrain)n(ts)-112
1881 1956 y Fq(By)12 b(design,)h(all)e(of)h(the)i(constrain)o(t)e(primitiv)o
1882 (es)f(describ)q(ed)k(so)-112 2001 y(far)i(use)j(only)d(fast)h(lo)q(cal)
1883 g(propagation)f(tec)o(hniques.)32 b(Suc)o(h)-112 2047
1884 y(tec)o(hniques)15 b(are)g(necessarily)h(incomplete;)d(they)i(cannot)g
1885 (al-)-112 2093 y(w)o(a)o(ys)k(solv)o(e)h(systems)h(of)e(constrain)o(ts)
1886 i(or)f(determine)h(that)-112 2138 y(they)f(are)g(unsolv)n(able.)35
1887 b Fp(Screamer)20 b Fq(pro)o(vides)g(a)f(n)o(um)o(b)q(er)-112
1888 2184 y(of)h(primitiv)o(es)f(for)h(augmen)o(ting)f(lo)q(cal)g
1889 (propagation)h(with)-112 2230 y(bac)o(ktrac)o(king)f(searc)o(h)h(to)g
1890 (pro)o(vide)f(a)g(general)h(mec)o(hanism)-112 2275 y(for)f(solving)g
1891 (systems)h(of)g(constrain)o(ts.)37 b(One)21 b(suc)o(h)g(primi-)-112
1892 2321 y(tiv)o(e,)e Fk(linear-force)p Fq(,)f(can)h(b)q(e)h(applied)f(to)g
1893 (a)g(v)n(ariable)f(to)-112 2367 y(cause)13 b(it)f(to)g
1894 (nondeterministically)f(tak)o(e)h(on)h(one)f(of)g(the)h(v)n(al-)-112
1895 2412 y(ues)i(in)f(its)h(domain.)j Fk(Linear-force)12
1896 b Fq(can)j(b)q(e)g(applied)f(only)-112 2458 y(to)k(discrete)i(v)n
1897 (ariables)e(or)g(in)o(teger)h(v)n(ariables.)31 b(Constrain-)-112
1898 2504 y(ing)14 b(a)h(v)n(ariable)f(to)g(tak)o(e)i(on)e(a)h(v)n(alue)f
1899 (using)h Fk(linear-force)-112 2549 y Fq(ma)o(y)j(cause)k(lo)q(cal)d
1900 (propagation.)37 b(Th)o(us)21 b(a)f(single)g(call)g(to)-112
1901 2595 y Fk(linear-force)12 b Fq(ma)o(y)g(cause)k(a)e(n)o(um)o(b)q(er)g
1902 (of)g(v)n(ariables)g(to)g(b)q(e)980 -33 y(b)q(ound,)g(or)g(alternativ)o
1903 (ely)f(ma)o(y)f(fail)h(if)g(the)h(v)n(ariable)f(cannot)980
1904 12 y(consisten)o(tly)20 b(tak)o(e)g(on)f(an)o(y)g(v)n(alue.)34
1905 b(A)20 b(second)g(primitiv)o(e,)980 58 y Fk(divide-and-conquer-)o(forc)
1906 o(e)p Fq(,)9 b(can)j(b)q(e)g(applied)f(to)g(a)h(v)n(ari-)980
1907 103 y(able)i(to)g(nondeterministically)f(reduce)j(the)e(set)i(of)d(p)q
1908 (ossible)980 149 y(v)n(alues)19 b(it)g(ma)o(y)f(tak)o(e)h(on.)34
1909 b Fk(Divide-and-conquer-f)o(orce)980 195 y Fq(can)17
1910 b(b)q(e)g(applied)f(only)f(to)h(discrete)i(v)n(ariables)e(or)g(real)h
1911 (v)n(ari-)980 240 y(ables)g(with)f(\014nite)h(upp)q(er)h(and)f(lo)o(w)o
1912 (er)f(b)q(ounds.)27 b(When)17 b(ap-)980 286 y(plied)f(to)h(discrete)h
1913 (v)n(ariables,)e(the)i(en)o(umerated)e(domain)f(is)980
1914 332 y(split)j(in)o(to)g(t)o(w)o(o)g(subsets)i(and)e(the)h(v)n(ariable)e
1915 (nondetermin-)980 377 y(istically)d(constrained)i(to)f(tak)o(e)g(on)g
1916 (v)n(alues)g(from)e(either)j(the)980 423 y(\014rst)g(or)f(second)i
1917 (subset.)23 b(When)15 b(applied)g(to)g(b)q(ounded)h(real)980
1918 469 y(v)n(ariables,)f(the)h(in)o(terv)n(al)f(is)h(split)f(in)g(half)g
1919 (and)g(the)i(v)n(ariable)980 514 y(nondeterministically)f(constrained)i
1920 (to)f(tak)o(e)g(on)g(v)n(alues)g(in)980 560 y(either)e(of)e(the)i(t)o
1921 (w)o(o)e(subin)o(terv)n(als.)1022 609 y(The)f(ab)q(o)o(v)o(e)g(t)o(w)o
1922 (o)f(functions)h(op)q(erate)h(on)f(single)g(v)n(ariables.)980
1923 654 y(More)f(generally)m(,)e(one)h(m)o(ust)f(\014nd)h(the)h(v)n(alues)f
1924 (of)f(sev)o(eral)i(v)n(ari-)980 700 y(ables)16 b(whic)o(h)g(satisfy)g
1925 (the)h(giv)o(en)f(constrain)o(ts.)25 b Fp(Screamer)980
1926 746 y Fq(pro)o(vides)h(t)o(w)o(o)f(primitiv)o(es)f(to)i(accomplish)e
1927 (this.)53 b(Both)980 791 y(are)22 b(higher-order)h(functions)f(whic)o
1928 (h)g(tak)o(e)g(a)f(single)h(v)n(ari-)980 837 y(able)11
1929 b(force)h(function)f(as)g(an)g(argumen)o(t)f(\(e.g.)h
1930 Fk(linear-force)980 882 y Fq(or)16 b Fk(divide-and-conquer-f)o(orce)p
1931 Fq(\))d(and)j(pro)q(duce)h(a)f(func-)980 928 y(tion)j(capable)h(of)f
1932 (forcing)g(a)h(list)f(of)g(v)n(ariables)g(using)g(that)980
1933 974 y(force)e(function.)23 b(Eac)o(h)16 b(incorp)q(orates)h(a)f
1934 (di\013eren)o(t)h(strategy)980 1019 y(for)h(c)o(ho)q(osing)g(whic)o(h)g
1935 (v)n(ariable)g(to)g(force)h(next.)31 b(The)19 b(\014rst,)980
1936 1065 y Fk(static-ordering)p Fq(,)d(simply)h(forces)i(the)g(v)n
1937 (ariables)f(in)g(the)980 1111 y(order)h(giv)o(en.)28
1938 b(The)18 b(single)g(v)n(ariable)e(force)i(function)g(is)f(re-)980
1939 1156 y(p)q(eatedly)h(applied)f(to)g(eac)o(h)h(v)n(ariable,)f(un)o(til)f
1940 (that)i(v)n(ariable)980 1202 y(tak)o(es)h(on)f(a)g(ground)g(v)n(alue,)h
1941 (b)q(efore)g(pro)q(ceeding)g(with)f(the)980 1248 y(next)f(v)n(ariable.)
1942 23 b(All)15 b(v)n(ariables)g(are)h(b)q(ound)g(up)q(on)g(termina-)980
1943 1293 y(tion.)28 b(The)18 b(second,)g Fk(reorder)p Fq(,)f(selects)i(the)
1944 f(v)n(ariable)e(with)980 1339 y(the)i(smallest)d(domain,)g(applies)i
1945 (the)h(single)e(v)n(ariable)g(force)980 1385 y(function)f(to)f(this)h
1946 (v)n(ariable,)f(and)h(rep)q(eats)h(this)f(pro)q(cess)i(un-)980
1947 1430 y(til)f(all)g(v)n(ariables)g(are)h(b)q(ound.)27
1948 b(Since)17 b(the)g(c)o(hoice)h(of)e(single)980 1476 y(v)n(ariable)h
1949 (force)i(function)e(is)h(orthogonal)f(to)h(the)h(c)o(hoice)f(of)980
1950 1522 y(v)n(ariable)h(ordering)i(strategy)m(,)h Fp(Screamer)f
1951 Fq(th)o(us)f(pro)o(vides)980 1567 y(four)f(distinct)f(constrain)o(t)h
1952 (solving)f(strategies.)33 b(More)19 b(can)980 1613 y(easily)14
1953 b(b)q(e)g(added.)1353 1716 y Ft(Examples)980 1782 y Fq(W)m(e)20
1954 b(will)f(illustrate)h(the)h(p)q(o)o(w)o(er)f(of)g(the)h
1955 Fp(Screamer)f Fq(con-)980 1828 y(strain)o(t)d(language)g(with)f(t)o(w)o
1956 (o)h(small)e(examples.)27 b(The)17 b(\014rst,)980 1873
1957 y(sho)o(wn)e(in)f(\014gure)h(1,)g(solv)o(es)g(the)g Fj(N)5
1958 b Fq(-Queens)16 b(problem.)j(The)980 1919 y(function)11
1959 b Fk(n-queensv)e Fq(creates)j(a)f(v)n(ariable)e(for)i(eac)o(h)g(ro)o(w)
1960 g(and)980 1965 y(constrains)k(eac)o(h)g(ro)o(w)g(v)n(ariable)e(to)h
1961 (tak)o(e)h(on)f(an)g(in)o(teger)h(b)q(e-)980 2010 y(t)o(w)o(een)20
1962 b(1)f(and)g Fj(n)g Fq(indicating)f(the)i(column)e(o)q(ccupied)i(b)o(y)f
1963 (a)980 2056 y(queen)14 b(in)e(that)g(ro)o(w.)18 b(The)13
1964 b(function)f Fk(\(a-member-ofv)19 b Fj(s)p Fk(\))13 b
1965 Fq(is)980 2102 y(simply)f(syn)o(tactic)j(sugar)f(for)f(the)i(follo)o
1966 (wing.)1005 2168 y Ff(\(let)j(\(\(v)h(\(make-var)o(ia)o(ble)o(\)\)\))
1967 1025 2209 y(\(assert!)d(\(memberv)h(v)i Fe(s)p Ff(\)\))1025
1968 2251 y(v\))980 2318 y Fq(The)12 b Fp(Screamer)g Fq(primitiv)o(e)d
1969 Fk(\(solution)20 b Fj(x)i(f)t Fk(\))12 b Fq(gathers)g(all)980
1970 2364 y(of)k(the)h(v)n(ariables)e(nested)j(inside)e(the)h(structure)h
1971 Fj(x)p Fq(,)e(applies)980 2410 y(the)h(m)o(ultiple)c(v)n(ariable)i
1972 (forcing)g(function)h Fj(f)k Fq(to)c(this)g(list)f(of)980
1973 2455 y(v)n(ariables,)f(and)g(returns)i(a)f(cop)o(y)f(of)g
1974 Fj(x)g Fq(where)i(the)f(v)n(ariables)980 2501 y(ha)o(v)o(e)f(b)q(een)h
1975 (replaced)g(b)o(y)e(their)i(b)q(ound)f(v)n(alues.)1022
1976 2549 y(In)k(the)g(ab)q(o)o(v)o(e)g(example,)f Fp(Screamer)h
1977 Fq(applies)g(GF)o(C)f(as)980 2595 y(the)12 b(tec)o(hnique)f(for)g
1978 (solving)e(the)j(underlying)e(constrain)o(t)h(sat-)p
1979 eop
1980 %%Page: 5 5
1981 5 4 bop -66 -53 1981 2 v -66 720 2 773 v -27 -11 a Ff(\(defun)17
1982 b(attacks?)g(\(qi)h(qj)h(distance\))d(\(or)i(\(=)h(qi)g(qj\))g(\(=)f
1983 (\(abs)g(\(-)h(qi)g(qj\)\))f(distance\)\))o(\))-27 30
1984 y(\(defun)f(n-queensv)f(\(n\))-8 72 y(\(solution)g(\(let)j(\(\(q)f
1985 (\(make-arra)o(y)e(n\)\)\))208 113 y(\(dotimes)h(\(i)h(n\))h(\(setf)f
1986 (\(aref)g(q)h(i\))g(\(an-integ)o(er)o(-be)o(twe)o(en)o(v)e(1)i(n\)\)\))
1987 208 155 y(\(dotimes)e(\(i)h(n\))228 196 y(\(dotimes)e(\(j)j(n\))247
1988 238 y(\(if)g(\(>)g(j)g(i\))g(\(assert!)d(\(notv)i(\(funcallv)e
1989 (#'attacks?)g(\(aref)h(q)j(i\))f(\(aref)e(q)i(j\))g(\(-)g(j)g
1990 (i\)\)\)\)\)\)\))208 280 y(\(coerce)e(q)i('list\)\))188
1991 321 y(\(reorder)e(#'domain-s)o(iz)o(e)g(#'\(lambda)f(\(x\))i(\(declare)
1992 f(\(ignore)g(x\)\))h(nil\))g(#'<)h(#'linear-)o(fo)o(rce)o(\)\))o(\))-27
1993 363 y(\(defun)e(nonlinear)f(\(\))-8 404 y(\(let)i(\(\(x)h(\(a-real-b)o
1994 (etw)o(ee)o(nv)d(-1e40)i(1e40\)\))110 446 y(\(y)h(\(a-real-b)o(etw)o
1995 (ee)o(nv)d(-1e40)i(1e40\)\))110 487 y(\(z)h(\(a-real-b)o(etw)o(ee)o(nv)
1996 d(-1e40)i(1e40\)\)\))12 529 y(\(assert!)e(\(andv)i(\(=v)h(\(+v)f(\(*v)h
1997 (4)g(x)g(x)g(y\))g(\(*v)g(7)g(y)g(z)g(z\))g(\(*v)f(6)i(x)f(x)g(z)g
1998 (z\)\))g(1356.14\))306 570 y(\(=v)g(\(+v)f(\(*v)h(3)g(x)g(y\))g(\(*v)f
1999 (2)i(y)f(y\))g(\(*v)f(5)h(x)g(y)h(z\)\))e(-141.375\))306
2000 612 y(\(=v)h(\(*v)f(\(+v)h(x)g(y\))g(\(+v)f(y)h(z\)\))g(-7.7625\)\))o
2001 (\))12 653 y(\(solution)d(\(list)i(x)h(y)g(z\))208 695
2002 y(\(reorder)e(#'range-s)o(iz)o(e)g(#'\(lambda)f(\(x\))i(\(<)h(x)g
2003 (1e-6\)\))f(#'>)g(#'divide-a)o(nd)o(-co)o(nq)o(uer)o(-fo)o(rc)o(e\)\))o
2004 (\)\))p 1913 720 V -66 722 1981 2 v -112 816 a Fq(Figure)13
2005 b(1:)k(Tw)o(o)12 b(constrain)o(t-based)i Fp(Screamer)g
2006 Fq(programs,)d(one)i(for)g(solving)f(the)h Fj(N)5 b Fq(-Queens)15
2007 b(problem)c(and)i(one)g(for)g(solving)f(a)-112 862 y(system)h(of)g
2008 (nonlinear)h(equations)g(using)f(n)o(umeric)g(b)q(ounds)i(propagation.)
2009 -112 995 y(isfaction)g(problem.)25 b Fp(Screamer)17 b
2010 Fq(c)o(ho)q(oses)h(this)f(tec)o(hnique)-112 1040 y(since)d(all)f(of)g
2011 (the)i(v)n(ariables)e(in)o(v)o(olv)o(ed)f(are)j(discrete.)-71
2012 1103 y(The)k(second)g(example,)e(sho)o(wn)h(in)g(\014gure)g(1,)h
2013 (illustrates)-112 1149 y(ho)o(w)j(b)q(ounds)h(propagation)e(can)i(b)q
2014 (e)h(used)f(to)g(solv)o(e)f(sys-)-112 1194 y(tems)c(of)g(nonlinear)h
2015 (equations)g(expressed)i(as)e(constrain)o(ts)-112 1240
2016 y(b)q(et)o(w)o(een)g(n)o(umeric)e(v)n(ariables.)30 b(The)19
2017 b(function)f Fk(nonlinear)-112 1286 y Fq(\014nds)h(a)f(solution)g(to)g
2018 (the)i(follo)o(wing)c(system)i(of)g(nonlinear)-112 1331
2019 y(equations.)50 1440 y(4)p Fj(x)95 1423 y Fi(2)113 1440
2020 y Fj(y)11 b Fq(+)f(7)p Fj(y)q(z)249 1423 y Fi(2)277 1440
2021 y Fq(+)g(6)p Fj(x)364 1423 y Fi(2)382 1440 y Fj(z)403
2022 1423 y Fi(2)463 1440 y Fq(=)42 b(1356)p Fj(:)p Fq(14)105
2023 1498 y(3)p Fj(xy)11 b Fq(+)e(2)p Fj(y)264 1481 y Fi(2)293
2024 1498 y Fq(+)g(5)p Fj(xy)q(z)44 b Fq(=)e Fo(\000)p Fq(141)p
2025 Fj(:)p Fq(375)167 1556 y(\()p Fj(x)9 b Fq(+)h Fj(y)q
2026 Fq(\)\()p Fj(y)i Fq(+)d Fj(z)r Fq(\))42 b(=)g Fo(\000)p
2027 Fq(7)p Fj(:)p Fq(7625)-112 1665 y(The)15 b(expression)h
2028 Fk(\(a-real-betweenv)j(-1e40)i(1e40\))14 b Fq(cre-)-112
2029 1710 y(ates)20 b(a)f(v)n(ariable)g(constrained)h(to)g(b)q(e)g(a)g(real)
2030 f(n)o(um)o(b)q(er)g(b)q(e-)-112 1756 y(t)o(w)o(een)g(the)g(giv)o(en)f
2031 (upp)q(er)i(and)f(lo)o(w)o(er)f(b)q(ounds.)33 b(After)19
2032 b(the)-112 1802 y(constrain)o(ts)d(ha)o(v)o(e)g(b)q(een)i(asserted)g(b)
2033 q(et)o(w)o(een)f(the)g(v)n(ariables,)-112 1847 y(divide)i(and)h
2034 (conquer)h(searc)o(h|in)o(terlea)o(v)o(ed)g(with)f(b)q(ounds)-112
2035 1893 y(propagation|is)d(used)i(to)g(\014nd)g(a)g(solution)f(to)g(the)i
2036 (equa-)-112 1939 y(tions.)57 b(One)28 b(suc)o(h)g(solution)e(is)h
2037 Fj(x)33 b Fo(\031)h(\000)p Fq(7)p Fj(:)p Fq(311)p Fj(;)39
2038 b(y)c Fo(\031)-112 1984 y Fq(6)p Fj(:)p Fq(113)p Fj(;)16
2039 b(z)e Fo(\031)e Fq(0)p Fj(:)p Fq(367.)j(Note)c(that)g(unlik)o(e)e(the)j
2040 (simplex)d(metho)q(d)-112 2030 y(used)k(in)f Fp(clp)p
2041 Fq(\()p Fo(<)p Fq(\)|whic)o(h)g(is)g(limited)f(to)h(solving)f(linear)h
2042 (sys-)-112 2076 y(tems)f(of)g(equations|the)h(com)o(bination)d(of)i
2043 (divide)g(and)h(con-)-112 2121 y(quer)20 b(searc)o(h)h(in)o(terlea)o(v)
2044 o(ed)e(with)h(b)q(ounds)g(propagation)f(al-)-112 2167
2045 y(lo)o(ws)11 b Fp(Screamer)i Fq(to)f(solv)o(e)g(complex)e(nonlinear)i
2046 (systems)g(of)-112 2213 y(equations.)17 b(These)c(tec)o(hniques)g(also)
2047 e(enable)h Fp(Screamer)h Fq(to)-112 2258 y(solv)o(e)19
2048 b(n)o(umeric)g(constrain)o(t)h(systems)g(with)f(b)q(oth)h(inequal-)-112
2049 2304 y(ities)f(and)h(equational)e(constrain)o(ts.)36
2050 b(F)m(urthermore,)21 b(since)-112 2350 y(all)c(of)i(the)g(constrain)o
2051 (t)h(satisfaction)e(tec)o(hniques)i(are)g(in)o(te-)-112
2052 2395 y(grated,)j Fp(Screamer)f Fq(can)g(solv)o(e)g(disjunctiv)o(e)f
2053 (systems)h(of)-112 2441 y(equations)17 b(as)h(w)o(ell)f(as)h(systems)g
2054 (whic)o(h)f(mix)f(together)j(n)o(u-)-112 2487 y(meric,)12
2055 b(Bo)q(olean,)h(and)h(other)h(forms)d(of)h(constrain)o(ts.)-71
2056 2549 y(W)m(e)d(wish)h(to)f(p)q(oin)o(t)g(out)g(the)h(in)o(ten)o(tional)
2057 f(similarit)o(y)d(in)j(the)-112 2595 y(names)j(of)h(the)h
2058 Fp(Screamer)g Fq(primitiv)o(es)e Fk(a-member-of)f Fq(and)980
2059 995 y Fk(a-member-ofv)p Fq(.)1256 980 y Fi(2)1291 995
2060 y Fq(Both)j(describ)q(e)h(a)d(c)o(hoice)i(b)q(et)o(w)o(een)h(a)e(set)
2061 980 1040 y(of)j(p)q(ossible)g(alternativ)o(es.)27 b(The)17
2062 b(former)f(en)o(umerates)h(that)980 1086 y(set)i(nondeterministically)e
2063 (b)o(y)h(bac)o(ktrac)o(king.)31 b(The)18 b(latter)980
2064 1132 y(instead,)f(creates)h(a)e(v)n(ariable)f(whose)i(v)n(alue)f(is)g
2065 (constrained)980 1177 y(to)j(b)q(e)h(a)e(mem)o(b)q(er)f(of)i(the)g(giv)
2066 o(en)g(set.)34 b(The)19 b(former)f(lends)980 1223 y(itself)c(to)g(a)f
2067 (generate-and-test)j(st)o(yle)e(of)f(programming.)1005
2068 1282 y Ff(\(let)18 b(\(\()p Fe(x)1165 1286 y Fg(1)1201
2069 1282 y Ff(\(a-member-)o(of)e Fe(s)1474 1286 y Fg(1)1491
2070 1282 y Ff(\)\))1123 1325 y(.)1123 1341 y(.)1123 1358
2071 y(.)1123 1399 y(\()p Fe(x)1165 1403 y Fc(n)1205 1399
2072 y Ff(\(a-member-)o(of)g Fe(s)1478 1403 y Fc(n)1499 1399
2073 y Ff(\)\)\))1025 1441 y(\(unless)h Fm(\010[)p Fe(x)1243
2074 1445 y Fg(1)1266 1441 y Fe(:)6 b(:)g(:)g(x)1339 1445
2075 y Fc(n)1360 1441 y Fm(])19 b Ff(\(fail\)\))1025 1482
2076 y(\(list)e Fe(x)1164 1486 y Fg(1)1188 1482 y Fe(:)6 b(:)g(:)g(x)1261
2077 1486 y Fc(n)1282 1482 y Ff(\)\))980 1545 y Fq(The)22
2078 b(latter)g(lends)h(itself)e(to)h(constrain)o(t-based)g(program-)980
2079 1591 y(ming.)1005 1651 y Ff(\(let)c(\(\()p Fe(x)1165
2080 1655 y Fg(1)1201 1651 y Ff(\(a-member-)o(of)o(v)f Fe(s)1494
2081 1655 y Fg(1)1511 1651 y Ff(\)\))1123 1693 y(.)1123 1709
2082 y(.)1123 1726 y(.)1123 1767 y(\()p Fe(x)1165 1771 y Fc(n)1205
2083 1767 y Ff(\(a-member-)o(of)o(v)g Fe(s)1498 1771 y Fc(n)1519
2084 1767 y Ff(\)\)\))1025 1809 y(\(assert!)f(\(funcallv)1221
2085 1850 y(#'\(lambda)g(\()p Fe(x)1459 1854 y Fg(1)1482 1850
2086 y Fe(:)6 b(:)g(:)g(x)1555 1854 y Fc(n)1576 1850 y Ff(\))20
2087 b Fm(\010[)p Fe(x)1677 1854 y Fg(1)1699 1850 y Fe(:)6
2088 b(:)h(:)f(x)1773 1854 y Fc(n)1794 1850 y Fm(])p Ff(\))1221
2089 1892 y Fe(x)1243 1896 y Fg(1)1266 1892 y Fe(:)g(:)g(:)h(x)1340
2090 1896 y Fc(n)1361 1892 y Ff(\)\))1025 1934 y(\(solution)16
2091 b(\(list)i Fe(x)1361 1938 y Fg(1)1384 1934 y Fe(:)6 b(:)g(:)g(x)1457
2092 1938 y Fc(n)1478 1934 y Ff(\))1221 1975 y(\(static-o)o(rde)o(rin)o(g)16
2093 b(#'linear-f)o(orc)o(e\)\))o(\))980 2038 y Fq(Though)e(these)i(t)o(w)o
2094 (o)e(program)e(fragmen)o(ts)h(are)i(structurally)980
2095 2084 y(v)o(ery)i(similar,)e(and)i(sp)q(ecify)g(the)h(same)e(problem,)g
2096 (they)h(en-)980 2129 y(tail)k(drastically)h(di\013eren)o(t)h(searc)o(h)
2097 g(strategies.)44 b(The)22 b(lat-)980 2175 y(ter)e(constitutes)h(a)e
2098 Fl(lifted)g Fq(v)n(arian)o(t)f(of)h(the)h(former.)33
2099 b(A)20 b(fu-)980 2221 y(ture)15 b(pap)q(er)f(will)e(w)o(e)i(discuss)h
2100 (the)f(p)q(ossibilities)f(of)g(p)q(erform-)980 2266 y(ing)19
2101 b(suc)o(h)g(lifting)f(transformations)f(automatically)m(.)30
2102 b(Suc)o(h)p 980 2303 250 2 v 1032 2330 a Fg(2)1049 2346
2103 y Fm(W)m(e)13 b(adopt)h(the)f(\(unenforced\))h(con)o(v)o(en)o(tion)h
2104 (that)e(the)g(names)980 2387 y(of)h(all)i(nondeterministi)q(c)h
2105 (generator)e(functions)h(b)q(egin)g(with)f(the)980 2429
2106 y(pre\014x)d Ff(a-)f Fm(or)g Ff(an-)f Fm(and)i(that)f(functions)i(b)q
2107 (eginning)h(with)e(the)f(pre-)980 2470 y(\014x)18 b Ff(a-)e
2108 Fm(or)g Ff(an-)p Fm(,)h(and)g(also)h(ending)h(with)e
2109 Ff(v)p Fm(,)g(denote)h(lifted)g(gen-)980 2512 y(erators,)12
2110 b(functions)i(whic)o(h)f(deterministicall)q(y)i(return)d(a)g(v)n
2111 (ariable)980 2553 y(ranging)h(o)o(v)o(er)f(the)g(stated)g(domain)h
2112 (instead)g(of)e(nondeterministi)q(-)980 2595 y(cally)k(returning)g(a)e
2113 (v)n(alue)h(in)g(that)f(domain.)p eop
2114 %%Page: 6 6
2115 6 5 bop -112 -33 a Fq(lifting)19 b(is)i(not)g(limited)e(to)j(the)f
2116 Fk(a-member-of)e Fq(primitiv)o(e.)-112 12 y Fp(Screamer)f
2117 Fq(includes)f(the)i(follo)o(wing)14 b(syn)o(tactic)k(sugar)g(for)-112
2118 58 y Fk(\(an-integer-bet)o(weenv)g Fj(l)23 b(h)p Fk(\))p
2119 Fq(.)-88 115 y Ff(\(let)18 b(\(\(v)h(\(make-var)o(iab)o(le\))o(\)\))-68
2120 156 y(\(assert!)-48 198 y(\(andv)e(\(integerpv)f(v\))j(\(<=v)f(v)h
2121 Fe(h)p Ff(\))h(\(>=v)e(v)h Fe(l)q Ff(\)\)\))-68 239 y(v\))-112
2122 299 y Fq(The)14 b(function)g Fk(an-integer-betweenv)d
2123 Fq(is)j(a)g(lifted)g(analog)-112 345 y(to)c(the)i Fp(Screamer)f
2124 Fq(primitiv)o(e)e Fk(an-integer-between)p Fq(.)14 b(All)-112
2125 390 y Fp(Screamer)g Fq(generators)h(ha)o(v)o(e)f(lifted)f(analogs.)207
2126 483 y Ft(Related)k(W)-5 b(ork)-112 540 y Fq(Most)12 b(of)g(the)h
2127 (individual)d(tec)o(hniques)k(describ)q(ed)g(in)e(this)g(pa-)-112
2128 586 y(p)q(er)g(are)g(not)f(new.)18 b(What)11 b(is)g(no)o(v)o(el)g(is)g
2129 (their)h(particular)f(com-)-112 632 y(bination.)16 b(Programming)10
2130 b(languages)k(whic)o(h)f(allo)o(w)f(stating)-112 677
2131 y(n)o(umeric)e(constrain)o(ts)i(date)g(bac)o(k)g(to)f
2132 Fp(Sketchp)m(ad)i Fq(\(Suther-)-112 723 y(land)j(1963\).)25
2133 b(Lo)q(cal)16 b(propagation)g(for)g(solving)f(systems)i(of)-112
2134 769 y(constrain)o(ts)c(w)o(as)g(used)i(b)o(y)e(Borning)f(\(1979\))h(in)
2135 g Fp(Thinglab)p Fq(.)-112 814 y(Steele)d(\(1980\))f(constructs)j
2136 (constrain)o(t)e(primitiv)o(es)e(v)o(ery)i(sim-)-112
2137 860 y(ilar)j(to)h(ours)h(and)f(implemen)o(ts)e(lo)q(cal)h(propagation)h
2138 (b)o(y)g(pro-)-112 906 y(cedural)h(attac)o(hmen)o(t.)21
2139 b(These)16 b(tec)o(hniques)h(w)o(ere)f(expanded)-112
2140 951 y(on)21 b(b)o(y)h(the)h Fp(Ma)o(gritte)d Fq(system)i(\(Gosling)f
2141 (1983\).)41 b(The)-112 997 y(ab)q(o)o(v)o(e)22 b(systems)h(di\013er)g
2142 (from)e Fp(Screamer)i Fq(in)f(t)o(w)o(o)h(w)o(a)o(ys.)-112
2143 1042 y(First,)17 b(they)g(handled)g(only)e(n)o(umeric)h(constrain)o
2144 (ts,)i(lac)o(king)-112 1088 y(the)13 b(GF)o(C)e(capacit)o(y)i(of)f
2145 Fp(Screamer)h Fq(em)o(b)q(o)q(died)e(in)h Fk(memberv)-112
2146 1134 y Fq(and)19 b Fk(funcallv)p Fq(,)g(as)h(w)o(ell)f(as)h
2147 (uni\014cation)f(and)h(disuni\014ca-)-112 1179 y(tion)13
2148 b(em)o(b)q(o)q(died)h(in)g Fk(equalv)p Fq(.)k(More)d(imp)q(ortan)o(tly)
2149 m(,)d(the)j(con-)-112 1225 y(strain)o(t)h(solving)e(tec)o(hniques)k
2150 (incorp)q(orated)e(in)g(all)f(of)g(these)-112 1271 y(systems)h(w)o(ere)
2151 h(incomplete,)f(particularly)g(those)h(based)g(on)-112
2152 1316 y(lo)q(cal)i(propagation.)38 b(None)21 b(of)f(these)i(systems)f
2153 (could)f(re-)-112 1362 y(sort)26 b(to)g(in)o(terlea)o(ving)e(bac)o
2154 (ktrac)o(king)i(searc)o(h)h(with)f(lo)q(cal)-112 1408
2155 y(propagation|as)20 b Fp(Screamer)i Fq(can|to)g(pro)o(vide)g(a)f(slo)o
2156 (w)-112 1453 y(but)e(complete)g(fallbac)o(k)f(to)i(faster)g(but)g
2157 (incomplete)f(lo)q(cal)-112 1499 y(propagation)12 b(tec)o(hniques)j
2158 (when)g(applied)e(alone.)-71 1545 y(More)22 b(recen)o(tly)m(,)i(n)o
2159 (umerous)d(systems)g(suc)o(h)i(as)e Fp(clp)p Fq(\()p
2160 Fo(<)p Fq(\))-112 1590 y(and)10 b Fp(CHiP)g Fq(ha)o(v)o(e)g(b)q(een)i
2161 (constructed)h(in)d(the)i(logic)d(program-)-112 1636
2162 y(ming)17 b(framew)o(ork)i(whic)o(h)g(add)h(some)f(form)f(of)h
2163 (constrain)o(t)-112 1682 y(satisfaction|sometim)o(es)13
2164 b(based)i(on)f(lo)q(cal)g(propagation|)-112 1727 y(to)f(the)h(bac)o
2165 (ktrac)o(king)f(searc)o(h)h(mec)o(hanism)d(already)i(presen)o(t)-112
2166 1773 y(in)20 b(logic)f(programming)e(languages.)38 b
2167 Fp(Screamer)21 b Fq(di\013ers)-112 1819 y(from)f(suc)o(h)j(systems)f
2168 (in)g(a)g(n)o(um)o(b)q(er)f(of)h(w)o(a)o(ys,)h(some)f(mi-)-112
2169 1864 y(nor)h(and)h(some)e(ma)r(jor.)46 b(First,)26 b
2170 Fp(Screamer)e Fq(uses)g(only)-112 1910 y(fast)19 b(lo)q(cal)g
2171 (propagation)f(tec)o(hniques)j(as)f(part)g(of)f(its)h(con-)-112
2172 1956 y(strain)o(t)h(mec)o(hanism.)37 b(The)22 b(n)o(umeric)e(constrain)
2173 o(t)i(mec)o(ha-)-112 2001 y(nism)c(of)i Fp(clp)p Fq(\()p
2174 Fo(<)p Fq(\))h(instead)f(uses)i(more)d(costly)h(tec)o(hniques)-112
2175 2047 y(based)27 b(on)f(the)h(simplex)e(metho)q(d)g(for)h(linear)g
2176 (program-)-112 2093 y(ming.)41 b(These)23 b(tec)o(hniques)h(are)f
2177 (incomplete)e(for)h(nonlin-)-112 2138 y(ear)28 b(constrain)o(ts.)62
2178 b Fp(clp)p Fq(\()p Fo(<)p Fq(\))28 b(and)g Fp(CHiP)f
2179 Fq(do)h(not)g(pro-)-112 2184 y(vide)d(mec)o(hanisms)e(for)j(dealing)e
2180 (with)h(this)h(incomplete-)-112 2230 y(ness.)j Fp(Screamer)q
2181 Fq(,)18 b(on)f(the)h(other)g(hand,)f(can)h(solv)o(e)f(non-)-112
2182 2275 y(linear)j(constrain)o(ts)i(using)f Fk(divide-and-conqu)o(er-fo)o
2183 (rce)-112 2321 y Fq(com)o(bined)16 b(with)h(lo)q(cal)f(propagation.)28
2184 b(The)18 b(second)g(di\013er-)-112 2367 y(ence)h(lies)e(in)h(using)f
2185 Fp(Common)g(Lisp)h Fq(instead)g(of)f Fp(Pr)o(olog)-112
2186 2412 y Fq(as)h(a)g(substrate)j(for)d(constructing)h(constrain)o
2187 (t-based)h(pro-)-112 2458 y(gramm)o(ing)15 b(languages.)32
2188 b(Giv)o(en)17 b(the)j(substrate)g(of)e(nonde-)-112 2504
2189 y(terministic)13 b Fp(Common)j(Lisp)p Fq(|esp)q(ecially)e(its)g
2190 (capacit)o(y)g(for)-112 2549 y(lo)q(cal)j(side)h(e\013ects|the)j
2191 Fp(Screamer)e Fq(constrain)o(t)f(pac)o(k)n(age)-112 2595
2192 y(can)g(b)q(e)g(written)h(totally)e(in)g Fp(Common)g(Lisp)p
2193 Fq(.)30 b(This)18 b(giv)o(es)980 -33 y Fp(Screamer)e
2194 Fq(three)h(adv)n(an)o(tages)e(o)o(v)o(er)g Fp(clp)p Fq(\()p
2195 Fo(<)p Fq(\))h(and)f Fp(CHiP)o Fq(.)980 12 y(First,)10
2196 b Fp(Screamer)h Fq(is)e(p)q(ortable)g(to)h(an)o(y)f Fp(Common)16
2197 b(Lisp)10 b Fq(im-)980 58 y(plemen)o(tation.)16 b(Second,)d
2198 Fp(Screamer)h Fq(can)e(b)q(e)h(easily)g(mo)q(di-)980
2199 103 y(\014ed)g(and)f(extended,)i(to)e(exp)q(erimen)o(t)g(with)f
2200 (alternativ)o(e)h(con-)980 149 y(strain)o(t)j(t)o(yp)q(es)h(and)e
2201 (constrain)o(t)h(satisfaction)g(metho)q(ds.)20 b(Fi-)980
2202 195 y(nally)m(,)e Fp(Screamer)h Fq(can)g(co)q(exist)h(and)e(in)o
2203 (ter-op)q(erate)i(with)980 240 y(other)g(curren)o(t)g(or)f(future)h
2204 (extensions)g(to)f Fp(Common)d(Lisp)980 286 y Fq(suc)o(h)f(as)f
2205 Fp(clos)g Fq(and)g Fp(clim)o Fq(.)1022 332 y(The)e(curren)o(t)g(v)o
2206 (ersion)g(of)e Fp(Screamer)q Fq(,)h(including)g(the)h(full)980
2207 377 y(constrain)o(t)22 b(pac)o(k)n(age,)g(is)f(a)o(v)n(ailable)f(b)o(y)
2208 h(anon)o(ymous)e(FTP)980 423 y(from)f(the)h(\014le)g
2209 Fk(/com/ftp/pub/screame)o(r.tar)o(.Z)d Fq(on)j(the)980
2210 469 y(host)d Fk(ftp.ai.mit.edu)p Fq(.)i(W)m(e)d(encourage)h(y)o(ou)f
2211 (to)f(obtain)h(a)980 514 y(cop)o(y)i(of)f Fp(Screamer)h
2212 Fq(and)f(giv)o(e)g(us)h(feedbac)o(k)h(on)e(y)o(our)g(ex-)980
2213 560 y(p)q(eriences)g(using)e(it.)1339 652 y Ft(References)1001
2214 708 y Fq(Alan)i(Hamilton)d(Borning.)24 b Fp(Thinglab)q
2215 Fb(|A)17 b(Constr)n(aint-)1001 753 y(Oriente)n(d)i(Simulation)g(L)n(ab)
2216 n(or)n(atory)p Fq(.)32 b(PhD)19 b(thesis,)i(Stan-)1001
2217 799 y(ford)12 b(Univ)o(ersit)o(y)m(,)g(July)g(1979.)j(Also)d(a)o(v)n
2218 (ailable)e(as)j(Stanford)1001 845 y(Computer)j(Science)j(Departmen)o(t)
2219 d(rep)q(ort)j(ST)m(AN-CS-79-)1001 890 y(746)10 b(and)h(as)g(XER)o(O)o
2220 (X)g(P)o(alo)f(Alto)h(Researc)o(h)h(Cen)o(ter)g(rep)q(ort)1001
2221 936 y(SSL-79-3.)1001 992 y(A.)k(Colmerauer.)23 b(Equations)15
2222 b(and)h(inequations)g(on)f(\014nite)1001 1038 y(and)22
2223 b(in\014nite)f(trees.)43 b(In)22 b Fb(2d)g(International)h(Confer)n
2224 (enc)n(e)1001 1083 y(on)14 b(Fifth)e(Gener)n(ation)i(Computer)f
2225 (Systems)p Fq(,)f(pages)g(85{99,)1001 1129 y(1984.)1001
2226 1185 y(James)18 b(Gosling.)29 b Fb(A)o(lgebr)n(aic)18
2227 b(Constr)n(aints)p Fq(.)30 b(PhD)18 b(thesis,)1001 1230
2228 y(Carnegie-Mellon)13 b(Univ)o(ersit)o(y)m(,)g(1983.)1001
2229 1286 y(E.)20 b(R.)g(Hansen.)38 b(On)21 b(the)g(solution)e(of)h(linear)g
2230 (algebraic)1001 1332 y(equations)j(using)g(in)o(terv)n(al)f
2231 (arithmetic.)44 b Fb(Mathematic)n(al)1001 1378 y(Computation)p
2232 Fq(,)14 b(22:153{165,)d(1968.)1001 1433 y(Jo)o(xan)i(Ja\013ar)g(and)h
2233 (Jean-Louis)f(Lassez.)18 b(Constrain)o(t)13 b(logic)1001
2234 1479 y(programming)o(.)k(In)d Fb(Pr)n(o)n(c)n(e)n(e)n(dings)h(of)h(the)
2235 f Fq(14)1710 1464 y Fa(th)1756 1479 y Fb(A)o(CM)g(Sym-)1001
2236 1525 y(p)n(osium)f(on)f(the)h(Principles)f(of)g(Pr)n(o)n(gr)n(amming)g
2237 (L)n(anguages)p Fq(,)1001 1570 y(pages)h(111{119,)e(1987.)1001
2238 1626 y(Alan)h(K.)h(Mac)o(kw)o(orth.)k(Constrain)o(t)13
2239 b(satisfaction.)18 b(In)13 b(Stu-)1001 1672 y(art)j(C.)g(Shapiro,)f
2240 (editor,)h Fb(Encyclop)n(e)n(dia)i(of)f(A)o(rti\014cial)e(In-)1001
2241 1717 y(tel)r(ligenc)n(e)p Fq(,)j(pages)g(285{293.)d(John)j(Wiley)f(&)h
2242 (Sons,)f(Inc.,)1001 1763 y(New)d(Y)m(ork,)f(1992.)1001
2243 1819 y(Je\013rey)24 b(Mark)e(Siskind)g(and)g(Da)o(vid)f(Allen)h
2244 (McAllester.)1001 1865 y Fp(Screamer)q Fq(:)32 b(a)21
2245 b(p)q(ortable)h(e\016cien)o(t)f(implemen)o(tation)d(of)1001
2246 1910 y(nondeterministic)h Fp(Common)e(Lisp)p Fq(.)36
2247 b(T)m(ec)o(hnical)20 b(Rep)q(ort)1001 1956 y(IR)o(CS{93{03,)10
2248 b(Univ)o(ersit)o(y)j(of)f(P)o(ennsylv)n(ania)g(Institute)i(for)1001
2249 2002 y(Researc)o(h)h(in)e(Cognitiv)o(e)g(Science,)i(1993.)1001
2250 2057 y(Iv)n(an)g(E.)h(Southerland.)24 b Fp(Sketchp)m(ad)q
2251 Fb(:)e(A)17 b(Man-Machine)1001 2103 y(Gr)n(aphic)n(al)e(Communic)n
2252 (ation)g(System)p Fq(.)j(PhD)c(thesis,)g(Mas-)1001 2149
2253 y(sac)o(h)o(usetts)i(Institute)e(of)g(T)m(ec)o(hnology)m(,)e(Jan)o
2254 (uary)i(1963.)1001 2205 y(Guy)h(Lewis)g(Steele)h(Jr.)23
2255 b Fb(The)16 b(De\014nition)h(and)f(Implemen-)1001 2250
2256 y(tation)h(of)g(a)h(Computer)f(Pr)n(o)n(gr)n(amming)f(L)n(anguage)j
2257 (Base)n(d)1001 2296 y(on)24 b(Constr)n(aints)p Fq(.)47
2258 b(PhD)23 b(thesis,)k(Massac)o(h)o(usetts)f(Insti-)1001
2259 2342 y(tute)21 b(of)f(T)m(ec)o(hnology)m(,)f(August)i(1980.)36
2260 b(Also)20 b(a)o(vilable)e(as)1001 2387 y(M.)13 b(I.)g(T.)g(VLSI)h(Memo)
2261 e(80{32)h(and)g(as)h(M.)f(I.)g(T.)g(Arti\014cial)1001
2262 2433 y(In)o(teligence)i(Lab)q(oratory)e(T)m(ec)o(hnical)h(Rep)q(ort)g
2263 (595.)1001 2489 y(P)o(ascal)20 b(V)m(an)f(Hen)o(tenryc)o(k.)36
2264 b Fb(Constr)n(aint)20 b(Satisfaction)g(in)1001 2534 y(L)n(o)n(gic)11
2265 b(Pr)n(o)n(gr)n(amming)p Fq(.)f(The)g(MIT)f(Press,)j(Cam)o(bridge,)c
2266 (MA,)1001 2580 y(1989.)p eop
2267 %%Trailer
2268 end
2269 userdict /end-hook known{end-hook}if
2270 %%EOF