screamer.ps

   1 %!PS-Adobe-2.0
   2 %%Creator: dvipsk 5.521a Copyright 1986, 1993 Radical Eye Software
   3 %%Title: screamer.dvi
   4 %%Pages: 50
   5 %%PageOrder: Ascend
   6 %%BoundingBox: 0 0 612 792
   7 %%EndComments
   8 %DVIPSCommandLine: dvips screamer
   9 %DVIPSSource:  TeX output 1994.03.10:2311
  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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1661 I<00FE00000303C0000C00E00010007000100038003C003C003E001C003E001E003E001E
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1676 000038E0000038E0000038E0000038E00000387000007070000070380000E01C0001C007
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1714 80000006000180000002000100002E1F7F9E30>119 D E end
1715 %%EndProlog
1716 %%BeginSetup
1717 %%Feature: *Resolution 300dpi
1718 TeXDict begin
1719
1720 %%EndSetup
1721 %%Page: 1 1
1722 1 0 bop 637 369 a FE(Screaming)21 b(Y)-6 b(ello)n(w)22
1723 b(Zonk)n(ers)792 490 y FD(Je\013rey)16 b(Mark)g(Siskind)1234
1724 472 y FC(\003)568 548 y FD(M.)g(I.)f(T.)h(Arti\014cial)f(In)o
1725 (telligence)e(Lab)q(oratory)559 606 y(545)18 b(T)l(ec)o(hnology)e
1726 (Square,)g(Ro)q(om)g(NE43{800b)779 664 y(Cam)o(bridge)f(MA)g(02139)866
1727 722 y(617/253{5)q(659)698 780 y(in)o(ternet:)20 b(Qobi@AI.MIT.EDU)431
1728 878 y(DRAFT)c(of)h(Sunda)o(y)l(,)e(29{Septem)o(b)q(er{1991)j(11:32:08)f
1729 (EDT)928 1069 y FB(Abstract)236 1134 y FA(Nondeterministi)q(c)d
1730 Fz(Lisp)d FA(is)i(a)e(v)n(arian)o(t)i(of)f Fz(Lisp)f
1731 FA(with)h(a)g(nondeterministic)j(c)o(hoice)e(op)q(erator.)k(This)c(man)
1732 o(ual)179 1180 y(describ)q(es)20 b(an)g(e\016cien)o(t)f(implemen)o
1733 (tation)j(of)d(nondeterministi)q(c)i Fz(Lisp)e FA(called)i
1734 Fz(Screamer)p FA(.)34 b Fz(Screamer)19 b FA(is)179 1225
1735 y(implemen)o(ted)14 b(as)e(a)g(fully)h(p)q(ortable)g(macro)g(pac)o(k)n
1736 (age)f(built)i(on)e(top)g(of)g Fz(Common)h(Lisp)p FA(.)j
1737 Fz(Screamer)c FA(functions)179 1271 y(in)o(ter-op)q(erate)f(in)f(the)f
1738 (same)h(en)o(vironmen)o(t)h(as)f(ordinary)h Fz(Lisp)e
1739 FA(functions)i(and)f(a)f(large)i(subset)f(of)f Fz(Common)k(Lisp)179
1740 1317 y FA(is)g(a)o(v)n(ailable)i(when)d(writing)i Fz(Screamer)e
1741 FA(functions.)18 b(In)12 b(addition)j(to)d(the)g(nondeterminis)q(tic)j
1742 (c)o(hoice)f(op)q(erator,)179 1362 y Fz(Screamer)f FA(pro)o(vides)h(a)f
1743 (forw)o(ard)g(c)o(hec)o(king)h(constrain)o(t)g(propagation)h(facilit)o
1744 (y)g(as)e(w)o(ell.)18 b(T)m(ogether)13 b(they)g(mak)o(e)179
1745 1408 y Fz(Screamer)g FA(an)g(e\016cien)o(t)h(mec)o(hanism)h(for)d
1746 (buildin)q(g)k(searc)o(h)d(programs.)75 1499 y Fy(TOPIC)h(AREAS:)g
1747 (nondeterministic)f(searc)o(h,)i(AI)f(programmi)o(ng)d(languages)1106
1748 1591 y(Caution!)18 b(This)13 b(pro)q(duct)i(ma)o(y)d(driv)o(e)i(y)o(ou)
1749 f(zonk)o(ers!)1168 1641 y Fx(F)m(rom)f(the)j(b)q(o)o(x)e(of)h
1750 (Screaming)e(Y)m(ello)o(w)h(Zonk)o(ers)75 1778 y Fw(1)69
1751 b(In)n(tro)r(duction)75 1894 y(2)g(Nondeterministi)o(c)20
1752 b(Expressions,)j(F)-6 b(unctions)23 b(and)h(Con)n(texts)75
1753 1985 y Fy(In)18 b(order)h(to)g(pro)o(vide)f(the)h(abilit)o(y)d(for)i
1754 (bac)o(ktrac)o(king,)h Fv(Screamer)g Fy(compiles)e(nondeterministic)g
1755 (functions)i(dif-)75 2034 y(feren)o(tly)d(than)g(deterministic)f
1756 (functions.)24 b(Accordingly)m(,)15 b(it)h(also)f(compiles)g(calls)g
1757 (to)h(nondeterministic)f(functions)75 2084 y(di\013eren)o(tly)h(than)g
1758 (calls)f(to)h(deterministic)f(functions.)24 b(F)m(or)16
1759 b(the)g(most)f(part)h(the)g(user)h(need)g(not)f(b)q(e)g(a)o(w)o(are)g
1760 (of)f(this)75 2134 y(di\013erence)h(as)f Fv(Screamer)g
1761 Fy(automatically)d(determines)j(whether)h(or)e(not)h(a)f(function)g(is)
1762 h(deterministic)f(and)g(com-)75 2184 y(piles)j(co)q(de)g(appropriately)
1763 m(.)26 b(There)18 b(are)f(certain)h(restriction)f(ho)o(w)o(ev)o(er.)27
1764 b(In)17 b(order)h(to)e(explain)g(these)j(restrictions)75
1765 2234 y(some)13 b(terminology)f(m)o(ust)g(b)q(e)j(de\014ned.)137
1766 2283 y(A)j Fu(deterministic)f(expr)n(ession)g Fy(is)g(an)g(expression)i
1767 (whic)o(h)e Fv(Screamer)h Fy(can)f(determine)h(to)f(yield)f(at)i(most)e
1768 (one)75 2333 y(v)n(alue.)30 b(A)18 b Fu(nondeterministic)g(expr)n
1769 (ession)h Fy(is)f(an)f(expression)i(whic)o(h)f Fv(Screamer)h
1770 Fy(cannot)f(determine)g(to)g(b)q(e)h(de-)75 2383 y(terministic.)29
1771 b(An)18 b(expression)g(migh)o(t)e(yield)h(no)h(more)f(than)g(one)h(v)n
1772 (alue)f(when)i(actually)d(ev)n(aluated)i(and)g(still)e(b)q(e)75
1773 2433 y(classi\014ed)h(as)f(nondeterministic)g(if)g Fv(Screamer)h
1774 Fy(cannot)f(determine)g(at)h(compile)d(time)h(that)i(it)f(is)g
1775 (deterministic.)75 2483 y Fv(Screamer)f Fy(classi\014es)f(the)h(follo)o
1776 (wing)c(expressions)k(as)f(deterministic:)p 75 2517 750
1777 2 v 121 2544 a Ft(\003)139 2556 y Fs(Need)d(thanks.)1002
1778 2723 y Fy(1)p eop
1779 %%Page: 2 2
1780 2 1 bop 137 195 a Fr(\017)21 b Fy(A)14 b(call)f(to)h(the)g
1781 Fq(map-values)e Fy(primitiv)o(e.)137 278 y Fr(\017)21
1782 b Fy(A)13 b(call)g(to)g(the)h Fq(one-value)d Fy(primitiv)o(e)g(pro)o
1783 (vided)j(that)f(the)h Fu(default-expr)n(ession)f Fy(is)g(either)i
1784 (absen)o(t)e(or)h(a)f(deter-)179 328 y(ministic)f(expression.)137
1785 411 y Fr(\017)21 b Fy(A)14 b(call)f(to)h(the)g Fq(all-values)e
1786 Fy(primitiv)o(e.)137 494 y Fr(\017)21 b Fy(A)13 b(call)f(to)g(the)i
1787 Fq(ith-value)d Fy(primitiv)o(e)f(pro)o(vided)j(b)q(oth)g(that)g(the)g
1788 (argumen)o(t)f Fp(i)h Fy(is)g(a)f(deterministic)h(expression)179
1789 544 y(and)g(that)h(the)h(the)f(argumen)o(t)f Fu(default-expr)n(ession)h
1790 Fy(is)g(either)h(absen)o(t)f(or)g(a)g(deterministic)f(expression.)137
1791 627 y Fr(\017)21 b Fy(A)14 b(call)f(to)h(the)g Fq(print-values)d
1792 Fy(primitiv)o(e.)137 710 y Fr(\017)21 b Fy(A)15 b Fq(function)e
1793 Fy(sp)q(ecial)i(form.)k(The)d(expression)g Fq(#'\(lambda)j(\()p
1794 Fp(:)7 b(:)g(:)o Fq(\))21 b Fp(:)7 b(:)g(:)o Fq(\))14
1795 b Fy(alw)o(a)o(ys)g(yields)h(a)f(single)h(v)n(alue)f(and)179
1796 760 y(is)e(th)o(us)g(deterministic)f(ev)o(en)i(though)e(that)h(v)n
1797 (alue)g(ma)o(y)d(itself)j(b)q(e)g(a)g(nondeterministic)f(function)h(ob)
1798 r(ject.)18 b(This)179 809 y(will)c(b)q(e)i(the)f(case)i(if)d(one)i(of)f
1799 (the)g(expressions)i(in)e(the)h(b)q(o)q(dy)f(of)g(the)h(lam)o(b)q(da)d
1800 (expression)k(is)e(nondeterminis-)179 859 y(tic.)23 b(Lik)o(ewise,)15
1801 b(the)i(expression)f Fq(#')p Fu(function-name)g Fy(alw)o(a)o(ys)f(is)g
1802 (deterministic.)23 b(It)15 b(will)g(ev)n(aluate)g(to)g(yield)g(a)179
1803 909 y(nondeterministic)e(function)h(ob)r(ject)g(if)f
1804 Fu(function-name)i Fy(names)e(a)h(nondeterministic)f(function.)137
1805 992 y Fr(\017)21 b Fy(An)14 b Fq(either)e Fy(sp)q(ecial)j(form)d(with)h
1806 (no)h(argumen)o(ts.)137 1075 y Fr(\017)21 b Fy(An)14
1807 b Fq(either)e Fy(sp)q(ecial)j(form)d(with)h(a)h(single)f(deterministic)
1808 h(argumen)o(t.)137 1158 y Fr(\017)21 b Fy(A)13 b(sp)q(ecial)g(form)e
1809 (or)i(a)g(call)f(to)h(a)g(deterministic)f(function)h(pro)o(vided)g
1810 (that)g(ev)o(ery)h(ev)n(aluated)e(sub)q(expression)j(is)179
1811 1208 y(deterministic.)137 1291 y(A)10 b Fu(deterministic)g(function)f
1812 Fy(is)h(a)f(function)g(whic)o(h)g Fv(Screamer)h Fy(can)g(determine)f
1813 (to)h(yield)f(at)g(most)f(one)i(v)n(alue)e(when)75 1341
1814 y(called.)17 b(A)10 b Fu(nondeterministic)i(function)e
1815 Fy(is)h(a)f(function)g(whic)o(h)g Fv(Screamer)h Fy(cannot)f(determine)h
1816 (to)f(b)q(e)h(deterministic.)75 1391 y(Lik)o(e)20 b(expressions,)k(a)c
1817 (function)g(migh)o(t)f(yield)h(no)h(more)e(than)i(one)g(v)n(alue)f
1818 (when)h(actually)f(called)g(and)h(still)e(b)q(e)75 1440
1819 y(classi\014ed)e(as)f(nondeterministic)g(if)g Fv(Screamer)h
1820 Fy(cannot)f(determine)g(at)h(compile)d(time)h(that)i(it)f(is)g
1821 (deterministic.)75 1490 y(Nondeterministic)f(functions,)g(lik)o(e)g
1822 (deterministic)g(functions,)h(are)f(de\014ned)i(with)e(the)h
1823 Fv(Common)h(Lisp)e Fy(primitiv)o(e)75 1540 y Fq(defun)p
1824 Fy(.)22 b(A)16 b(function)f(de\014ned)i(with)e Fq(defun)g
1825 Fy(is)g(deterministic)g(if)g(ev)o(ery)h(expression)h(in)e(its)h(b)q(o)q
1826 (dy)f(is)h(deterministic;)75 1590 y(otherwise)21 b(the)f(function)g(is)
1827 g(nondeterministic.)36 b(F)m(urthermore,)21 b(all)d(primitiv)o(e)g
1828 Fv(Common)f(Lisp)j Fy(functions)g(are)75 1640 y(deterministic.)137
1829 1689 y Fv(Common)d(Lisp)10 b Fy(allo)o(ws)f(one)i(to)f(access)i
1830 (function)e(ob)r(jects)i(using)e(the)h Fq(function)e
1831 Fy(sp)q(ecial)h(form.)15 b Fv(Common)i(Lisp)75 1739 y
1832 Fy(function)22 b(ob)r(jects)i(alw)o(a)o(ys)d(refer)j(to)e
1833 (deterministic)g(functions)h(and)f(are)h(termed)g Fu(deterministic)f
1834 (function)h(ob-)75 1789 y(je)n(cts)p Fy(.)f Fv(Screamer)15
1835 b Fy(supp)q(orts)i(a)e(new)g(t)o(yp)q(e)h(of)f(ob)r(ject,)h(the)g
1836 Fu(nondeterministic)g(function)g(obje)n(ct)p Fy(.)22
1837 b(The)16 b(expression)75 1839 y Fq(#'\(lambda)k(\()p
1838 Fp(:)7 b(:)g(:)n Fq(\))22 b Fp(:)7 b(:)g(:)n Fq(\))18
1839 b Fy(will)e(\(deterministically\))g(ev)n(aluate)h(to)h(yield)f(an)g
1840 (ordinary)g Fv(Common)g(Lisp)h Fy(determin-)75 1889 y(istic)e(function)
1841 g(ob)r(ject)h(if)f(ev)o(ery)h(expression)g(in)f(the)h(b)q(o)q(dy)f(of)g
1842 (the)h(lam)o(b)q(da)d(expression)j(is)f(deterministic.)25
1843 b(It)16 b(will)75 1939 y(\(deterministically\))11 b(ev)n(aluate)g(to)h
1844 (yield)g(a)g(nondeterministic)f(function)h(ob)r(ject)h(if)e(some)g
1845 (expression)i(in)f(the)g(b)q(o)q(dy)h(of)75 1988 y(the)g(lam)o(b)q(da)d
1846 (expression)k(is)f(nondeterministic.)k(Lik)o(ewise,)12
1847 b(the)h(expression)h Fq(#')p Fu(function-name)f Fy(will)e
1848 (\(deterministi-)75 2038 y(cally\))g(ev)n(aluate)g(to)h(yield)f(an)g
1849 (ordinary)g Fv(Common)17 b(Lisp)12 b Fy(deterministic)f(function)g(ob)r
1850 (ject)h(if)f Fu(function-name)i Fy(names)75 2088 y(a)h(deterministic)f
1851 (function.)19 b(It)14 b(will)e(\(deterministically\))h(ev)n(aluate)h
1852 (to)g(yield)f(a)h(nondeterministic)f(function)h(ob)r(ject)75
1853 2138 y(if)i Fu(function-name)h Fy(names)f(a)g(nondeterministic)g
1854 (function)g(\(de\014ned)h(using)g Fq(defun)p Fy(\).)24
1855 b(The)17 b Fv(Screamer)g Fy(primitiv)o(e)75 2188 y Fq
1856 (nondeterministic-)o(funct)o(ion?)c Fy(can)k(b)q(e)h(used)f(to)g
1857 (determine)f(whether)i(or)f(not)g(an)f(ob)r(ject)i(is)e(a)h
1858 (nondetermin-)75 2237 y(istic)g(function.)25 b(While)16
1859 b(deterministic)g(function)g(ob)r(jects)i(can)f(b)q(e)g(called)f(using)
1860 h(the)g Fv(Common)f(Lisp)h Fy(primitiv)o(es)75 2287 y
1861 Fq(funcall)d Fy(and)i Fq(apply)p Fy(,)e(nondeterministic)h(function)g
1862 (ob)r(jects)i(m)o(ust)e(b)q(e)h(called)f(using)h(the)g(analogous)e
1863 Fv(Screamer)75 2337 y Fy(primitiv)o(es)d Fq(funcall-nondetermini)o
1864 (stic)f Fy(and)j Fq(apply-nondetermin)o(istic)o Fy(.)i(A)o(ttempting)d
1865 (to)h(call)g(a)g(nondeter-)75 2387 y(ministic)i(function)i(ob)r(ject)h
1866 (with)f Fq(funcall)f Fy(or)h Fq(apply)f Fy(will)g(signal)g(a)h(run)g
1867 (time)f(error.)29 b(The)18 b Fv(Screamer)f Fy(calling)75
1868 2437 y(primitiv)o(es)c(accept)i(either)h(deterministic)e(or)g
1869 (nondeterministic)g(function)h(ob)r(jects.)21 b(Irresp)q(ectiv)o(e)c
1870 (of)c(whether)j(the)75 2487 y Fu(function)i Fy(argumen)o(t)e(to)i
1871 Fq(funcall-nondeter)o(minis)o(tic)c Fy(or)k Fq(apply-nondeterm)o(inist)
1872 o(ic)c Fy(is)k(a)f(deterministic)g(or)75 2536 y(nondeterministic)g
1873 (function)g(ob)r(ject,)i(a)e(call)g(to)g Fq(funcall-nondetermini)o
1874 (stic)d Fy(or)k Fq(apply-nondeterm)o(inist)o(ic)1002
1875 2723 y Fy(2)p eop
1876 %%Page: 3 3
1877 3 2 bop 75 195 a Fy(is)16 b(alw)o(a)o(ys)f(a)g(nondeterministic)h
1878 (expression)h(since)f(it)g(is)g(imp)q(ossible,)e(in)h(general,)i(to)e
1879 (determine)h(the)h(t)o(yp)q(e)f(of)f(the)75 245 y Fu(function)f
1880 Fy(argumen)o(t)f(at)h(compile)e(time.)137 295 y Fv(Screamer)j
1881 Fy(includes)f(sev)o(eral)h(nondeterministic)e(functions)h(as)g
1882 (primitiv)o(es.)i(These)f(include:)137 378 y Fr(\017)21
1883 b Fq(funcall-nondeter)o(minis)o(tic)p Fy(,)137 461 y
1884 Fr(\017)g Fq(apply-nondetermi)o(nisti)o(c)p Fy(,)137
1885 544 y Fr(\017)g Fq(member-of)p Fy(,)137 627 y Fr(\017)g
1886 Fq(integer-between)p Fy(,)137 710 y Fr(\017)g Fq(decide)p
1887 Fy(,)137 793 y Fr(\017)g Fq(linear-force)p Fy(,)137 876
1888 y Fr(\017)g Fq(divide-and-conqu)o(er-fo)o(rce)p Fy(,)137
1889 959 y Fr(\017)g Fq(solution)12 b Fy(and)137 1042 y Fr(\017)21
1890 b Fq(best-value)p Fy(.)75 1125 y(\(Actually)m(,)10 b
1891 Fq(decide)f Fy(and)h Fq(best-value)f Fy(are)h(macros.\))17
1892 b(The)10 b(man)o(ual)e(en)o(tries)k(in)e(this)g(do)q(cumen)o(t)g
1893 (explicitly)g(annotate)75 1175 y(when)19 b(a)f(primitiv)o(e)e(is)i
1894 (nondeterministic)g(in)f(the)i(\014rst)g(line)f(of)g(the)g(en)o(try)h
1895 (for)f(that)h(primitiv)o(e.)28 b(Primitiv)o(es)17 b(not)75
1896 1225 y(annotated)d(as)g(nondeterministic)f(are)i(deterministic.)137
1897 1274 y(A)j(men)o(tioned)f(previously)m(,)h Fv(Screamer)g
1898 Fy(m)o(ust)f(compile)f(nondeterministic)i(expressions)h(sp)q(ecially)m
1899 (.)29 b(It)18 b(do)q(es)75 1324 y(so)h(b)o(y)g(w)o(alking)e(the)j(co)q
1900 (de)f(and)g(p)q(erforming)e(an)i(op)q(eration)g(kno)o(wn)f(as)h(CPS)h
1901 (con)o(v)o(ersion)f(on)g(nondeterministic)75 1374 y(expressions)i
1902 (\(see)g(section)g(14\).)34 b Fv(Screamer)21 b Fy(only)d(w)o(alks)h(co)
1903 q(de)i(app)q(earing)e(in)g(certain)i(con)o(texts.)36
1904 b(The)20 b(main)75 1424 y(implication)13 b(of)j(this)g(is)g(that)g
1905 (nondeterministic)g(expression)h(ma)o(y)d(app)q(ear)j(only)e(in)h(con)o
1906 (texts)h(whic)o(h)f Fv(Screamer)75 1474 y Fy(w)o(alks.)h(These)c(con)o
1907 (texts)g(are)g(termed)f Fu(nondeterministic)h(c)n(ontexts)p
1908 Fy(.)18 b(A)12 b(con)o(text)h(whic)o(h)f Fv(Screamer)h
1909 Fy(do)q(es)g(not)f(w)o(alk)75 1523 y(is)i(termed)g(a)f
1910 Fu(deterministic)h(c)n(ontext)p Fy(.)k(The)d(follo)o(wing)c(is)j(a)f
1911 (list)h(of)f(all)g(nondeterministic)g(con)o(texts:)137
1912 1606 y Fr(\017)21 b Fy(The)14 b(b)q(o)q(dy)f(of)g Fq(defun)p
1913 Fy(.)j(This)e(is)f(accomplished)f(b)o(y)h(ha)o(ving)g
1914 Fv(Screamer)h Fy(shado)o(w)f(the)h(ordinary)f(de\014nition)g(of)179
1915 1656 y Fq(defun)p Fy(.)137 1739 y Fr(\017)21 b Fy(The)14
1916 b Fu(expr)n(ession)g Fy(argumen)o(t)f(of)g(a)h(call)f(to)h(the)g
1917 Fq(map-values)e Fy(primitiv)o(e.)137 1822 y Fr(\017)21
1918 b Fy(The)14 b Fu(expr)n(ession)g Fy(argumen)o(t)f(of)g(a)h(call)f(to)h
1919 (the)g Fq(one-value)e Fy(primitiv)o(e.)137 1905 y Fr(\017)21
1920 b Fy(The)14 b(b)q(o)q(dy)g(of)f(a)h(call)f(to)h(the)g
1921 Fq(all-values)e Fy(primitiv)o(e.)137 1988 y Fr(\017)21
1922 b Fy(The)14 b Fu(expr)n(ession)g Fy(argumen)o(t)f(of)g(a)h(call)f(to)h
1923 (the)g Fq(ith-value)e Fy(primitiv)o(e.)137 2071 y Fr(\017)21
1924 b Fy(The)14 b(b)q(o)q(dy)g(of)f(a)h(call)f(to)h(the)g
1925 Fq(print-values)e Fy(primitiv)o(e.)75 2154 y(Curren)o(tly)m(,)k(the)g
1926 (only)f(top-lev)o(el)h(de\014ning)f(expression)i(whic)o(h)f(allo)o(ws)f
1927 (a)g(nondeterministic)h(b)q(o)q(dy)g(is)f Fq(defun)p
1928 Fy(.)23 b(This)75 2204 y(excludes)12 b(other)f(de\014ning)f
1929 (expressions)i(suc)o(h)f(as)g Fq(defvar)p Fy(,)e Fq(defconstant)p
1930 Fy(,)f Fq(defparameter)p Fy(,)g Fq(defmacro)p Fy(,)h
1931 Fq(defstruct)p Fy(,)75 2254 y Fq(defclass)p Fy(,)j(and)j(particularly)e
1932 Fq(defmethod)p Fy(.)18 b(F)m(uture)d(implemen)o(tatio)o(ns)d(of)i
1933 Fv(Screamer)h Fy(ma)o(y)e(supp)q(ort)i(additional)75
1934 2304 y(de\014ning)f(expressions)h(b)q(ey)o(ond)f Fq(defun)p
1935 Fy(.)j(The)e(general)f(rule)g(is)g(simply:)p 179 2351
1936 1333 2 v 179 2413 2 62 v 193 2392 a Fu(Nondeterministic)g(expr)n
1937 (essions)h(must)g(app)n(e)n(ar)g(in)g(nondeterministic)g(c)n(ontexts.)p
1938 1510 2413 V 179 2415 1333 2 v 1002 2723 a Fy(3)p eop
1939 %%Page: 4 4
1940 4 3 bop 75 195 a Fy(A)14 b(run)g(time)f(or)h(compile)e(time)g(error)j
1941 (should)f(b)q(e)g(signalled)f(if)g(this)h(rule)g(is)g(violated.)137
1942 245 y(Since,)j(the)f Fv(Common)h(Lisp)f Fy(primitiv)o(e)d
1943 Fq(eval)i Fy(is)h(a)f(deterministic)h(function,)f(it)h(can)g(only)f(ev)
1944 n(aluate)h(lists)f(rep-)75 295 y(resen)o(ting)k(deterministic)f
1945 (expressions.)33 b(Lik)o(e)18 b(an)o(y)g(call)f(to)h(a)g(deterministic)
1946 g(function,)h(the)g(argumen)o(t)e(to)h Fq(eval)75 345
1947 y Fy(can)g(b)q(e)g(a)g(nondeterministic)f(expression,)i(but)f(the)g
1948 (argumen)o(t)f(cannot)h(ev)n(aluate)f(to)h(a)f(list)g(whic)o(h)h
1949 (represen)o(ts)i(a)75 394 y(nondeterministic)13 b(expression.)19
1950 b(This)13 b(implies)e(that)i(y)o(ou)g(ma)o(y)f(not)h(t)o(yp)q(e)h(a)f
1951 (nondeterministic)f(expression)j(directly)75 444 y(to)d(a)g
1952 Fv(Lisp)h Fy(listener.)18 b(T)m(o)11 b(ev)n(aluate)h(a)h
1953 (nondeterministic)e(expression,)j(con)o(v)o(ert)f(it)f(to)g(a)g
1954 (deterministic)g(expression)h(b)o(y)75 494 y(enclosing)f(it)f(in)h(one)
1955 g(of)f(the)h(primitiv)o(es)e Fq(map-values)p Fy(,)g Fq(one-value)p
1956 Fy(,)g Fq(all-values)p Fy(,)f Fq(ith-value)h Fy(or)i
1957 Fq(print-values)p Fy(.)137 544 y(The)i(curren)o(t)h(implem)o(en)o
1958 (tation)10 b(imp)q(oses)j(one)g(further)i(restriction.)j(The)c
1959 (initialization)d(expressions)j(for)f Fq(&aux)p Fy(,)75
1960 594 y Fq(&optional)8 b Fy(and)i Fq(&key)f Fy(v)n(ariables)h(app)q
1961 (earing)g(in)g(a)f(lam)o(b)q(da)f(list)i(for)g(a)g Fq(defun)f
1962 Fy(or)h(lam)o(b)q(da)e(expression)j(are)g(considered)75
1963 643 y(deterministic)19 b(con)o(texts.)35 b(Th)o(us)20
1964 b(suc)o(h)g(initialization)c(expressions)21 b(ma)o(y)c(not)j(b)q(e)f
1965 (nondeterministic.)34 b(A)19 b(future)75 693 y(v)o(ersion)14
1966 b(of)f Fv(Screamer)i Fy(ma)o(y)d(remo)o(v)o(e)h(this)h(restriction.)75
1967 828 y Fw(3)69 b(Side)22 b(E\013ects)75 919 y Fy(Adding)12
1968 b(nondeterminism)f(to)h(an)h(imp)q(erativ)o(e)e(language)h(lik)o(e)g
1969 Fv(Common)k(Lisp)d Fy(o\013ers)g(t)o(w)o(o)g(design)f(alternativ)o(es)h
1970 (for)75 968 y(side)j(e\013ects.)26 b(Should)16 b(side)g(e\013ects)i(b)q
1971 (e)e(undone)h(up)q(on)e(bac)o(ktrac)o(king?)24 b Fv(Screamer)17
1972 b Fy(supp)q(orts)g(b)q(oth)f(alternativ)o(es)75 1018
1973 y(since)k(b)q(oth)f(turn)h(out)f(to)g(b)q(e)h(useful.)34
1974 b Fu(L)n(o)n(c)n(al)19 b Fy(side)h(e\013ects)h(are)f(undone)g(up)q(on)f
1975 (bac)o(ktrac)o(king)g(while)g Fu(glob)n(al)g Fy(side)75
1976 1068 y(e\013ects)e(are)f(not.)21 b Fv(Screamer)16 b Fy(pro)o(vides)g(t)
1977 o(w)o(o)e(new)i(sp)q(ecial)f(forms,)f Fq(local)g Fy(and)h
1978 Fq(global)p Fy(,)f(whic)o(h)h(con)o(trol)g(whether)75
1979 1118 y(side)k(e\013ects)h(are)f(lo)q(cal)f(or)h(global.)30
1980 b(The)19 b(expression)h Fq(\(local)g(\(setf)h(x)h(0\)\))17
1981 b Fy(causes)j(a)f(lo)q(cal)e(side)i(e\013ect)h(to)f Fp(x)p
1982 Fy(,)75 1168 y(while)13 b Fq(\(global)21 b(\(setf)f(x)i(0\)\))13
1983 b Fy(causes)j(a)d(global)f(side)j(e\013ect.)137 1218
1984 y(The)f(co)q(de)f(generated)i(for)d(global)g(side)h(e\013ects)i
1985 (consists)f(of)e(ordinary)h Fv(Common)j(Lisp)d Fy(side)g(e\013ects.)20
1986 b(Lo)q(cal)13 b(side)75 1267 y(e\013ects)20 b(generate)f(co)q(de)g
1987 (whic)o(h)f(\014rst)g(stores)i(the)e(prior)g(v)n(alue)f(of)g(the)i(v)n
1988 (ariable)e(on)g(a)h Fx(trail)f Fy(b)q(efore)i(up)q(dating)e(the)75
1989 1317 y(v)n(ariable,)e(and)h(then)g(restoring)h(the)f(prior)g(v)n(alue)f
1990 (when)i(bac)o(ktrac)o(king.)24 b(This)15 b(has)h(t)o(w)o(o)g
1991 (implications.)21 b(First,)c(one)75 1367 y(can)d(only)e(p)q(erform)g(a)
1992 i(lo)q(cal)e(side)i(e\013ect)h(on)e(a)g(v)n(ariable)f(that)h(is)g(b)q
1993 (ound.)18 b Fv(Screamer)c Fy(cannot)g(p)q(erform)e(a)h(lo)q(cal)g(side)
1994 75 1417 y(e\013ect)h(on)f(an)f(un)o(b)q(ound)g(v)n(ariable)g(since)h
1995 (it)f(will)g(not)g(b)q(e)h(able)f(to)h(access)h(and)f(store)g(the)g
1996 (prior)g(v)n(alue)e(of)h(the)i(v)n(ariable.)75 1467 y(Second,)j(lo)q
1997 (cal)e(side)i(e\013ects)h(can)f(b)q(e)g(p)q(erformed)e(only)h(when)h
1998 (there)g(is)f(at)g(least)h(one)f(c)o(hoice)h(p)q(oin)o(t)f(on)g(the)g
1999 (c)o(hoice)75 1516 y(p)q(oin)o(t)e(stac)o(k,)i(since)f(the)h(p)q
2000 (ortion)e(of)h(the)g(trail)f(to)h(b)q(e)g(un)o(w)o(ound)g(up)q(on)g
2001 (bac)o(ktrac)o(king)g(is)f(k)o(ept)i(as)f(part)g(of)f(a)g(c)o(hoice)75
2002 1566 y(p)q(oin)o(t.)j(Dep)q(ending)c(on)f(the)h Fv(Common)k(Lisp)12
2003 b Fy(implemen)o(tatio)o(n,)e(an)i(error)h(ma)o(y)e(or)h(ma)o(y)f(not)h
2004 (b)q(e)h(generated)h(if)e(these)75 1616 y(restrictions)j(are)f
2005 (violated.)137 1666 y Fq(Local)f Fy(and)h Fq(global)f
2006 Fy(sp)q(ecial)h(forms)f(b)q(eha)o(v)o(e)i(lik)o(e)e Fq(progn)p
2007 Fy(.)18 b(They)c(allo)o(w)f(a)g(b)q(o)q(dy)h(consisting)h(of)e(sev)o
2008 (eral)i(expres-)75 1716 y(sions,)f(returning)h(the)f(v)n(alue)g(of)f
2009 (the)i(last)f(expression.)20 b(All)13 b Fq(setf)h Fy(and)g
2010 Fq(setq)f Fy(op)q(erations)h(that)h(are)f Fu(lexic)n(al)r(ly)h(neste)n
2011 (d)75 1765 y Fy(in)f(a)g Fq(local)f Fy(or)h Fq(global)e
2012 Fy(expression)k(generate)f(side)g(e\013ects)h(of)d(the)i(appropriate)f
2013 (t)o(yp)q(e.)19 b(F)m(urthermore,)14 b Fq(local)f Fy(and)75
2014 1815 y Fq(global)i Fy(expressions)j(ma)o(y)d(b)q(e)i(nested)h(inside)f
2015 (one)f(another.)27 b(In)16 b(this)h(case,)h(the)f(most)e(closely)i
2016 (nested)h Fq(local)d Fy(or)75 1865 y Fq(global)i Fy(expressions)j
2017 (determines)f(whether)h(a)e Fq(setf)g Fy(or)h Fq(setq)e
2018 Fy(causes)j(a)f(lo)q(cal)e(or)i(global)e(side)i(e\013ect.)34
2019 b(Finally)m(,)75 1915 y Fq(setf)12 b Fy(and)g Fq(setq)g
2020 Fy(expression)i(whic)o(h)e(are)i(not)e(nested)i(in)f(either)g(a)f
2021 Fq(local)g Fy(or)h Fq(global)e Fy(expression)j(cause)g(global)d(side)75
2022 1965 y(e\013ects.)22 b(Th)o(us)15 b(the)h(side)f(e\013ects)h(to)f
2023 Fp(y)h Fy(and)f Fp(w)g Fy(in)f(the)i(follo)o(wing)c(will)h(b)q(e)i(lo)q
2024 (cal,)f(while)g(the)h(side)g(e\013ects)i(to)d Fp(v)i
2025 Fy(and)f Fp(z)75 2015 y Fy(will)d(b)q(e)j(global.)204
2026 2082 y Fq(\(defun)20 b(f)i(\(x)f(u\))h(\(setf)e(v)i(u\)\))204
2027 2182 y(\(local)e(\(if)h(\(p)h(x\))443 2231 y(\(setf)f(y)h(\(f)f(x)h
2028 (1\)\))443 2281 y(\(global)f(\(setf)g(z)g(\(f)g(x)h(2\)\)\)\))356
2029 2331 y(\(setq)f(w)h(\(f)f(x)h(3\)\)\))75 2399 y Fy(Note)10
2030 b(that)g(a)f Fq(local)g Fy(or)h Fq(global)e Fy(expression)j(a\013ects)g
2031 (only)e(side)h(e\013ects)i(that)d(are)h(lexically)f(nested)i(in)e(that)
2032 h(expression)75 2449 y(and)j(not)h(side)g(e\013ects)i(in)d(functions)g
2033 (called)h(b)o(y)f(those)h(expressions.)20 b(Th)o(us)14
2034 b(the)g(side)g(e\013ect)h(to)f Fp(v)h Fy(inside)e Fp(f)19
2035 b Fy(is)13 b(alw)o(a)o(ys)75 2499 y(a)h(global)e(side)i(e\013ect,)h(ev)
2036 o(en)g(when)f Fp(f)19 b Fy(is)13 b(called)h(from)e(inside)i(a)g
2037 Fq(local)e Fy(expression.)137 2549 y Fq(Local)g Fy(and)h
2038 Fq(global)e Fy(expression)j(a\013ect)g(an)o(y)e(side)i(e\013ect)g
2039 (caused)g(b)o(y)f(a)f(lexically)g(nested)i Fq(setq)e
2040 Fy(or)h Fq(setf)f Fy(expres-)75 2599 y(sion.)k(Side)9
2041 b(e\013ects)j(caused)e(b)o(y)f(other)h Fv(Common)17 b(Lisp)9
2042 b Fy(primitiv)o(es)e(are)j(alw)o(a)o(ys)e(global.)15
2043 b(Th)o(us)10 b Fq(\(local)20 b(\(delete)h(x)g(y\)\))1002
2044 2723 y Fy(4)p eop
2045 %%Page: 5 5
2046 5 4 bop 75 195 a Fy(will)9 b(cause)j(a)e(global)f(side)h(e\013ect)j
2047 Fu(not)d Fy(a)h(lo)q(cal)e(one.)862 180 y Fo(1)898 195
2048 y Fq(Local)g Fy(and)i Fq(global)e Fy(do)h(ho)o(w)o(ev)o(er,)h(a\013ect)
2049 h(macros)d(whic)o(h)i(expand)75 245 y(in)o(to)j Fq(setq)f
2050 Fy(or)h Fq(setf)g Fy(expressions.)20 b Fv(Common)d(Lisp)d
2051 Fy(con)o(tains)g(a)g(n)o(um)o(b)q(er)g(of)f(side)i(e\013ect)h(primitiv)
2052 o(es)c(implemen)o(ted)75 295 y(as)17 b(macros.)26 b(These)18
2053 b(include)f Fq(psetq)p Fy(,)f Fq(psetf)p Fy(,)g Fq(shiftf)p
2054 Fy(,)f Fq(rotatef)p Fy(,)h Fq(incf)p Fy(,)g Fq(decf)p
2055 Fy(,)g Fq(push)p Fy(,)h Fq(pushnew)e Fy(and)h Fq(pop)p
2056 Fy(.)27 b(Ac-)75 345 y(cording)14 b(to)g(the)h Fv(Common)i(Lisp)d
2057 Fy(sp)q(ec,)i(the)f(expansion)f(of)g(primitiv)o(e)e(macros)i(is)g(allo)
2058 o(w)o(ed)f(to)h(b)q(e)h(implemen)o(tation)75 394 y(dep)q(enden)o(t.)272
2059 379 y Fo(2)322 394 y Fy(Th)o(us)j(some)f(implemen)o(tati)o(ons)e(ma)o
2060 (y)h(expand)i(primitiv)o(e)e(side)i(e\013ect)h(macros,)e(either)i
2061 (directly)f(or)75 444 y(indirectly)i(in)o(to)f(expressions)j(con)o
2062 (taining)d Fq(setf)g Fy(or)h Fq(setq)f Fy(expressions.)38
2063 b(In)20 b(those)h(implem)o(en)o(tations,)e(calls)g(to)75
2064 494 y Fv(Common)e(Lisp)e Fy(primitiv)o(e)f(side)i(e\013ect)h(macros)e
2065 (will)g(b)q(e)h(a\013ected)h(b)o(y)f(surrounding)g Fq(local)f
2066 Fy(and)g Fq(global)g Fy(expres-)75 544 y(sions.)28 b(In)18
2067 b(other)f(implemen)o(tations,)e(calls)i(to)g(primitiv)o(e)e(side)j
2068 (e\013ect)h(macros)d(do)h(not)g(expand)h(in)o(to)e(expressions)75
2069 594 y(con)o(taining)d Fq(setf)g Fy(and)h Fq(setq)f Fy(and)g(th)o(us)i
2070 (cause)f(global)f(side)h(e\013ects)i(irresp)q(ectiv)o(e)g(of)d(their)h
2071 (con)o(text.)1686 579 y Fo(3)137 643 y Fv(Screamer)19
2072 b Fy(supp)q(orts)h(lo)q(cal)e(side)h(e\013ects)h(to)f(generalized)g(v)n
2073 (ariables)f(using)g Fq(setf)p Fy(.)31 b(Th)o(us)19 b(it)f(is)g(p)q
2074 (ossible)h(to)75 693 y(write)i(expressions)h(lik)o(e)d
2075 Fq(\(local)i(\(setf)g(\(car)f(x\)\))i(y\))e Fy(and)g
2076 Fq(\(local)g(\(setf)h(\(aref)g(x)g(n\)\))h(y\))d Fy(and)i(ac)o(hiev)o
2077 (e)75 743 y(the)e(exp)q(ected)h(results.)31 b(When)18
2078 b(ev)n(aluating)e(an)i(expression)h(lik)o(e)e Fq(\(local)k(\(setf)g
2079 Fp(v)i(e)p Fq(\)\))p Fy(,)18 b Fv(Screamer)h Fy(ma)o(y)d(ac-)75
2080 793 y(cess)23 b Fp(v)g Fy(sev)o(eral)e(times,)h(once)g(to)f(trail)g
2081 (its)g(v)n(alue)f(prior)h(to)h(the)f(lo)q(cal)g(side)g(e\013ect)i(and)e
2082 (t)o(wice)h(p)q(er)g(bac)o(ktrac)o(k,)75 843 y(once)d(to)g(up)q(date)g
2083 (its)g(v)n(alue)f(and)g(once)i(to)e(restore)j(its)d(prior)h(v)n(alue.)
2084 32 b Fv(Screamer)19 b Fy(tak)o(es)g(care)h(to)e(ev)n(aluate)g(an)o(y)75
2085 892 y(sub)q(expressions)i(in)e Fp(v)h Fy(only)f(once)g(and)g(use)h(the)
2086 g(result)g(of)e(that)h(ev)n(aluation)f(for)g(all)g(suc)o(h)i(accesses.)
2087 33 b(Lo)q(cal)18 b(side)75 942 y(e\013ects)c(are)f(supp)q(orted)g(for)f
2088 (an)o(y)g Fq(setf)f Fy(metho)q(d)h(including)f(slot)h(accessors)i
2089 (created)g(b)o(y)e Fq(defstruct)e Fy(and)i Fq(defclass)p
2090 Fy(.)75 992 y(There)21 b(is)e(one)h(minor)e(exception)i(ho)o(w)o(ev)o
2091 (er.)35 b(While)19 b(it)g(is)g(p)q(ossible)h(to)g(do)f(lo)q(cal)g(side)
2092 h(e\013ects)h(on)e(hash)h(tables,)75 1042 y(i.e.)14 b
2093 Fq(\(local)21 b(\(setf)g(\(gethash)f(key)h(table\))f(value\)\))p
2094 Fy(,)14 b Fv(Screamer)i Fy(is)f(not)g(able)g(to)g(distinguish)g(b)q(et)
2095 o(w)o(een)h(the)75 1092 y(situation)e(where)h Fq(table)e
2096 Fy(lac)o(k)o(ed)h(an)g(en)o(try)h(for)f Fq(key)g Fy(prior)g(to)g(the)h
2097 (lo)q(cal)e(side)i(e\013ect)g(and)g(the)f(situation)g(where)h(the)75
2098 1142 y(en)o(try)e(for)g Fq(key)f Fy(w)o(as)h Fq(nil)p
2099 Fy(.)k(In)c(either)g(case,)h Fq(table)e Fy(will)f(ha)o(v)o(e)i(an)g(en)
2100 o(try)g(pairing)f Fq(key)g Fy(with)g Fq(nil)h Fy(after)g(bac)o(ktrac)o
2101 (king.)75 1191 y(The)j(reason)h(for)e(this)h(is)f(that)h(when)g
2102 Fv(Screamer)h Fy(ev)n(aluates)e Fq(\(gethash)21 b(key)g(table\))14
2103 b Fy(to)i(access)h(its)f(v)n(alue)f(prior)75 1241 y(to)g(the)h(lo)q
2104 (cal)f(side)h(e\013ect,)h(it)e(utilizes)g(only)g(the)h(\014rst)g(v)n
2105 (alue)f(returned)i(b)o(y)f Fq(gethash)p Fy(.)21 b(In)15
2106 b(b)q(oth)h(cases)h(this)e(v)n(alue)g(is)75 1291 y Fq(nil)p
2107 Fy(.)21 b Fv(Screamer)16 b Fy(is)f(not)g(able)g(to)g(utilize)g(the)h
2108 (second)g(v)n(alue)f(returned)i(b)o(y)e Fq(gethash)f
2109 Fy(whic)o(h)h(w)o(ould)f(di\013eren)o(tiate)75 1341 y(these)h
2110 (situations.)137 1391 y(One)j(m)o(ust)d(b)q(e)i(careful)g(using)g
2111 (iteration)f(constructs)i(con)o(taining)e(nondeterministic)g
2112 (expressions.)28 b(These)18 b(in-)75 1440 y(clude)10
2113 b(the)g Fv(Common)17 b(Lisp)9 b Fy(primitiv)o(es)f Fq(do)p
2114 Fy(,)i Fq(do*)p Fy(,)f Fq(dolist)p Fy(,)g Fq(dotimes)p
2115 Fy(,)f Fq(do-all-symbols)p Fy(,)f Fq(do-external-symbols)o
2116 Fy(,)75 1490 y Fq(do-symbols)j Fy(and)i Fq(loop)f Fy(as)i(w)o(ell)e(as)
2117 i(the)f Fq(iterate)f Fy(macro.)16 b(Suc)o(h)d(macros)e(usually)h(p)q
2118 (erform)f(side)i(e\013ect)g(during)f(the)75 1540 y(iteration.)21
2119 b(The)15 b(desired)h(iteration)f(b)q(eha)o(vior)g(o)o(v)o(er)g(a)f
2120 (nondeterministic)h(b)q(o)q(dy)g(usually)f(requires)i(the)g(side)f
2121 (e\013ects)75 1590 y(to)h(b)q(e)h(lo)q(cal.)24 b(It)16
2122 b(ma)o(y)f(b)q(e)i(p)q(ossible)f(to)g(get)h(the)f(correct)i(b)q(eha)o
2123 (vior)e(b)o(y)g(wrapping)g(the)h(lo)q(oping)e(expression)i(inside)75
2124 1640 y(a)g Fq(local)f Fy(expression)i(though)f(for)g(reasons)i(describ)
2125 q(ed)g(ab)q(o)o(v)o(e,)e(whether)h(this)g(w)o(orks)f(or)g(not)g(is)g
2126 (implemen)o(tation)75 1689 y(dep)q(enden)o(t.)137 1739
2127 y(Lo)q(cal)11 b(side)h(e\013ects)h(in)o(teract)f(with)f
2128 Fv(Screamer)h Fy(primitiv)o(es)d(lik)o(e)i Fq(all-values)e
2129 Fy(in)i(predictable)h(w)o(a)o(ys)f(whic)o(h)g(ma)o(y)75
2130 1789 y(app)q(ear)17 b(coun)o(terin)o(tuitiv)o(e)f(at)g(\014rst)h
2131 (glance.)25 b(Lo)q(cal)16 b(side)g(e\013ect)i(p)q(erformed)e(inside)g
2132 (the)h(b)q(o)q(dy)f(of)g(an)g Fq(all-values)75 1839 y
2133 Fy(expression)h(are)g(undone)f(up)q(on)g(exit)g(from)e(the)j
2134 Fq(all-values)d Fy(expression.)25 b(One)17 b(ma)o(y)d(try)i
2135 (unsuccessfully)h(to)f(use)75 1889 y(the)e(follo)o(wing)e(co)q(de)i(to)
2136 g(pro)q(duce)h(a)f(list)f(of)h(all)e(bit)i(strings)g(of)f(length)h
2137 Fp(n)p Fy(.)204 1958 y Fq(\(all-values)19 b(\(local)i(\(loop)g(for)g(i)
2138 g(from)g(0)h(below)f(n)g(collect)g(\(either)f(0)h(1\)\)\)\))75
2139 2028 y Fy(The)16 b(ab)q(o)o(v)o(e)f(co)q(de)i(do)q(es)f(not)g(pro)q
2140 (duce)h(the)f(desired)h(result,)f(ev)o(en)g(for)g(an)f(implemen)o
2141 (tatio)o(n)e(whic)o(h)j(mak)o(es)e(all)h(side)75 2077
2142 y(e\013ects)h(caused)g(b)o(y)e Fq(loop)f Fy(to)h(b)q(e)h(lo)q(cal,)e
2143 (since)i Fq(collect)d Fy(adds)j(eac)o(h)g(new)f(elemen)o(t)g(to)g(the)h
2144 (list)e(b)q(eing)i(generated)g(b)o(y)75 2127 y(side)d(e\013ecting)h
2145 (the)f(tail)f(of)g(that)h(list.)17 b(If)11 b(suc)o(h)i(side)f
2146 (e\013ects)i(w)o(ere)e(lo)q(cal,)f(the)i(constructed)g(list)f(w)o(ould)
2147 f(b)q(e)h(una)o(v)n(ailable)75 2177 y(for)i(use)g(up)q(on)g(exiting)f
2148 (the)i Fq(all-values)d Fy(expression.)p 75 2205 750 2
2149 v 121 2232 a Fn(1)139 2243 y Fs(T)m(ec)o(hnically)m(,)i(the)g
2150 Fm(Common)f(Lisp)i Fs(de\014nition)e(allo)o(ws)i(an)g(implemen)o(tat)o
2151 (ion)d(to)j(in-line)f(expand)f(a)j(call)e(to)i(a)f(primitiv)o(e)e(suc)o
2152 (h)h(as)75 2283 y Fl(delete)p Fs(.)28 b(F)m(urthermore)o(,)15
2153 b(in)h(some)f(implemen)o(ta)o(tio)o(ns,)f(the)i(function)e
2154 Fl(macroexpan)o(d)f Fs(p)q(erforms)h(in-line)h(substitution,)f(ev)o(en)
2155 h(though)75 2322 y(this)f(is)h(not)f(allo)o(w)o(ed)g(b)o(y)h(the)f
2156 Fm(Common)f(Lisp)h Fs(sp)q(ec.)25 b(On)15 b(an)g(implemen)o(ta)o(tio)o
2157 (n)d(whic)o(h)j(exhibited)d(b)q(oth)i(of)g(these)g(\015a)o(ws,)i
2158 Fl(local)d Fs(and)75 2362 y Fl(global)c Fs(expressions)f(could)i
2159 (a\013ect)g(in-line)f(expanded)f(calls)i(to)h Fm(Common)i(Lisp)d
2160 Fs(side)h(e\013ect)e(primitiv)o(es)g(suc)o(h)h(as)g Fl(delete)p
2161 Fs(.)k(I)c(kno)o(w)h(of)g(no)75 2401 y(implemen)o(ta)o(tion)d(whic)o(h)
2162 j(su\013ers)f(from)g(this)h(problem.)121 2429 y Fn(2)139
2163 2441 y Fs(In)g(m)o(y)f(opinion)g(this)h(is)g(a)h(\015a)o(w)f(in)g(the)g
2164 (design)f(of)h Fm(Common)i(Lisp)e Fs(for)g(reasons)f(made)g(apparen)o
2165 (t)f(in)i(this)g(paragraph.)121 2469 y Fn(3)139 2480
2166 y Fs(The)k(Sym)o(b)q(olics)f(implemen)o(t)o(ati)o(on)f(b)q(eha)o(v)o
2167 (es)h(lik)o(e)h(the)g(former)f(while)h(the)h(Lucid)e(implemen)o(tat)o
2168 (ion)f(b)q(eha)o(v)o(es)g(partially)h(lik)o(e)h(the)75
2169 2520 y(former)g(and)h(partially)f(lik)o(e)h(the)g(later.)30
2170 b(In)17 b(Lucid,)g(side)f(e\013ect)f(macros)g(expand)g(in)o(to)h
2171 Fl(setq)g Fs(when)h(called)e(on)h(v)n(ariables)f(but)h(not)75
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2173 b(Th)o(us)14 b(expressions)e(lik)o(e)h Fl(\(local)i(\(push)h(a)i(x\)\))
2174 13 b Fs(cause)g(lo)q(cal)g(side)g(e\013ects)g(while)h(ones)f(lik)o(e)75
2175 2599 y Fl(\(local)i(\(push)h(a)i(\(aref)d(x)j(n\)\)\))10
2176 b Fs(cause)g(global)g(side)h(e\013ects.)j(This)d(is)h(an)f(unfortunate)
2177 d(screw.)1002 2723 y Fy(5)p eop
2178 %%Page: 6 6
2179 6 5 bop 75 195 a Fw(4)69 b(Gotc)n(has)75 311 y(5)g(The)23
2180 b(Constrain)n(t)f(P)n(ac)n(k)l(age)75 402 y Fy(It)14
2181 b(is)g(often)h(said)e(that)i Fv(Pr)o(olog)f Fy(added)h(t)o(w)o(o)f
2182 (inno)o(v)n(ations)e(to)i(programming)d(language)i(design:)19
2183 b(nondeterminism)75 452 y(and)g(logic)f(v)n(ariables)h
2184 (\(uni\014cation\).)677 437 y Fo(4)729 452 y Fy(The)g(basic)h
2185 Fv(Screamer)f Fy(mec)o(hanisms)e(of)i Fq(either)f Fy(and)h
2186 Fq(fail)f Fy(describ)q(ed)75 501 y(in)f(the)h(previous)f(sections)i
2187 (add)e(nondeterminism)e(to)i Fv(Common)f(Lisp)p Fy(.)28
2188 b(This)18 b(section)f(describ)q(es)j(an)d(additional)75
2189 551 y(set)g(of)f(mec)o(hanisms)e(pro)o(vided)i(with)g
2190 Fv(Screamer)h Fy(whic)o(h)f(add)g(logic)f(v)n(ariables)h(to)g
2191 Fv(Common)g(Lisp)p Fy(.)25 b(This)16 b(set)i(of)75 601
2192 y(mec)o(hanisms)c(is)h(collectiv)o(ely)g(called)g(the)h
2193 Fu(c)n(onstr)n(aint)h(p)n(ackage)p Fy(.)23 b(These)17
2194 b(mec)o(hanisms)d(go)h(a)g(lot)g(further)i(than)e(pro-)75
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2196 (they)i(pro)o(vide)f(m)o(uc)o(h)f(of)h(the)h(capabilit)o(y)d(t)o
2197 (ypically)h(incorp)q(orated)75 701 y(in)j(constrain)o(t-based)h(logic)e
2198 (programmi)o(ng)e(languages)j(suc)o(h)h(as)f Fv(clp)p
2199 Fy(\()p Fr(<)p Fy(\))g(\(Ja\013ar)h(and)f(Mic)o(ha)o(ylo)o(v,)e(1987;)h
2200 (Hein)o(tze)75 751 y(et)k(al.)f(1987\))g(and)h Fv(CHiP)e
2201 Fy(\(V)m(an)i(Hen)o(tenryc)o(k,)h(1989\).)29 b(In)18
2202 b(con)o(trast,)h Fv(Screamer)f Fy(uses)h(constrain)o(t)f(satisfaction)
2203 75 800 y(metho)q(ds)e(based)i(on)f(range)g(propagation)e(rather)j(than)
2204 f(the)h(linear)e(programmi)o(ng)e(tec)o(hniques)k(used)g(b)o(y)f
2205 Fv(clp)p Fy(\()p Fr(<)p Fy(\))75 850 y(and)d Fv(CHiP)n
2206 Fy(.)k(Hence)e(the)e(name)f(constrain)o(t)h(pac)o(k)n(age.)137
2207 900 y(The)21 b(constrain)o(t)f(pac)o(k)n(age)f(adds)i(a)e(single)h(new)
2208 g(data)g(t)o(yp)q(e)g(to)g Fv(Common)c(Lisp)p Fy(:)30
2209 b(the)21 b Fu(variable)p Fy(.)36 b(V)m(ariables)75 950
2210 y(pro)o(vide)19 b(a)g(sup)q(erset)i(of)d(the)i(functionalit)o(y)d(of)i
2211 (logic)f(v)n(ariables.)32 b(In)19 b(addition)f(to)h(b)q(eing)g(able)g
2212 (to)f(b)q(e)i(b)q(ound)f(to)75 1000 y(arbitrary)e(v)n(alues,)f(they)i
2213 (ma)o(y)d(also)h(b)q(e)h(dynamically)d(annotated)j(at)g(run)g(time)e
2214 (with)i(constrain)o(ts)g(on)g(the)g(v)n(alues)75 1049
2215 y(to)f(whic)o(h)h(they)g(ma)o(y)e(b)q(e)i(b)q(ound.)26
2216 b(V)m(ariables)16 b(are)h(created)h(with)e(the)h(function)g
2217 Fq(make-variable)p Fy(.)23 b(Initially)14 b(they)75 1099
2218 y(are)19 b Fu(unb)n(ound)h Fy(but)f(ma)o(y)d(b)q(ecome)j
2219 Fu(b)n(ound)g Fy(as)g(a)f(result)h(of)f(constrain)o(ts)i(whic)o(h)e
2220 (are)h(asserted)h(b)q(et)o(w)o(een)g(v)n(ariables.)75
2221 1149 y(V)m(ariables)14 b(are)h(b)q(ound)g(if)e Fv(Screamer)j
2222 Fy(can)e(determine)h(that)g(only)e(a)i(single)f(v)n(alue)g(can)h
2223 (satisfy)f(the)h(constrain)o(ts)g(in)75 1199 y(whic)o(h)d(the)h(v)n
2224 (ariable)f(participates.)18 b(Otherwise,)13 b(v)n(ariables)f(remain)f
2225 (un)o(b)q(ound.)18 b(All)11 b(of)h(the)h(primitiv)o(es)e(pro)o(vided)h
2226 (b)o(y)75 1249 y Fv(Screamer)g Fy(accept)g(either)g(b)q(ound)f(v)n
2227 (ariables,)f(un)o(b)q(ound)h(v)n(ariables)g(or)g(non-v)n(ariables)f(as)
2228 h(argumen)o(ts.)16 b(Collectiv)o(ely)75 1298 y(w)o(e)f(will)f(refer)i
2229 (to)e(an)o(y)h(suc)o(h)h(en)o(tit)o(y)f(as)g(a)f Fu(value)p
2230 Fy(.)22 b(Unlik)o(e)14 b Fv(Pr)o(olog)i Fy(and)e(its)h(deriv)n(ativ)o
2231 (es,)g(whic)o(h)g(usually)f(allo)o(w)f(all)75 1348 y(primitiv)o(es)f
2232 (to)i(tak)o(e)g(v)n(ariables)f(as)h(argumen)o(ts,)f(the)i(primitiv)o
2233 (es)d(pro)o(vided)i(b)o(y)f Fv(Common)k(Lisp)d Fy(ho)o(w)o(ev)o(er,)g
2234 (can)g(tak)o(e)75 1398 y(only)h(non-v)n(ariable)g(v)n(alues)g(as)h
2235 (argumen)o(ts.)24 b(Dep)q(ending)16 b(on)g(the)g(implemen)o(tation)c
2236 (and)k(the)h(setting)f(of)f(compiler)75 1448 y(optimization)d(switc)o
2237 (hes,)j(most)e Fv(Common)j(Lisp)e Fy(primitiv)o(es)f(will)g(signal)g
2238 (an)h(error)h(message)f(when)h(passed)g(a)f(v)n(ari-)75
2239 1498 y(able)i(as)h(an)g(argumen)o(t.)25 b(The)17 b Fv(Screamer)g
2240 Fy(primitiv)o(es)e Fq(value-of)g Fy(and)h Fq(apply-substitution)d
2241 Fy(can)k(b)q(e)h(used)f(to)75 1548 y(access)f(the)e(v)n(alue)g(of)f(a)h
2242 (b)q(ound)g(v)n(ariable)f(b)q(efore)i(calling)d(a)i Fv(Common)j(Lisp)d
2243 Fy(primitiv)o(e.)1498 1532 y Fo(5)1533 1548 y Fy(In)g(most)e(cases)k
2244 (un)o(b)q(ound)75 1597 y(v)n(ariables)c(can)h(b)q(e)g(forced)h(to)e
2245 (tak)o(e)h(on)f(a)h(unique)f(v)n(alue)h(b)o(y)f(using)g(the)i
2246 Fv(Screamer)f Fy(primitiv)o(es)e Fq(linear-force)f Fy(and)75
2247 1647 y Fq(divide-and-conque)o(r-for)o(ce)p Fy(.)k(These)g(are)e
2248 (nondeterministic)g(functions)g(whic)o(h)g(pro)o(vide)f(the)i(in)o
2249 (terface)g(b)q(et)o(w)o(een)75 1697 y(constrain)o(t)g(propagation)e
2250 (and)h(bac)o(ktrac)o(king)g(searc)o(h.)19 b(Bound)13
2251 b(v)n(ariables)e(are)i(alw)o(a)o(ys)f(dereferenced)j(when)e(prin)o
2252 (ted.)75 1747 y(Un)o(b)q(ound)i(v)n(ariables)g(prin)o(t)f(in)h(some)f
2253 (form)f(whic)o(h)i(is)g(not)g(parsable)h(b)o(y)e(the)i
2254 Fv(Lisp)f Fy(reader,)h(designed)g(to)f(mak)o(e)e(the)75
2255 1797 y(iden)o(tit)o(y)h(and)g(simple)f(prop)q(erties)j(of)d(the)i(v)n
2256 (ariable)e(readily)h(apparen)o(t.)20 b(The)15 b Fv(Screamer)g
2257 Fy(primitiv)o(es)d Fq(bound?)h Fy(and)75 1846 y Fq(ground?)k
2258 Fy(can)j(b)q(e)f(used)h(to)f(determine)f(whether)j(a)d(v)n(alue)h(is)f
2259 (b)q(ound)h(or)g(un)o(b)q(ound.)33 b(The)20 b(primitiv)o(e)c
2260 Fq(bound?)i Fy(is)75 1896 y(analogous)11 b(to)g(the)i(extra-logic)e
2261 (predicates)i Fq(var)f Fy(and)f Fq(nonvar)g Fy(t)o(ypically)g(included)
2262 h(in)f(a)h Fv(Pr)o(olog)g Fy(implemen)o(tatio)o(n.)137
2263 1946 y(V)m(ariables)k(can)h(participate)g(in)f(constrain)o(ts.)27
2264 b Fv(Screamer)18 b Fy(pro)o(vides)f(a)f(ric)o(h)h(set)g(of)f(primitiv)o
2265 (es)f(for)i(m)o(utually)75 1996 y(constraining)e(v)n(ariables.)22
2266 b(Constrain)o(t)15 b(satisfaction)g(is)h(implem)o(en)o(ted)e(in)h
2267 Fv(Screamer)h Fy(b)o(y)f(a)g(com)o(bination)e(of)i(con-)75
2268 2046 y(strain)o(t)c(propagation)f(and)i(bac)o(ktrac)o(king)e(searc)o
2269 (h.)19 b(The)11 b(constrain)o(t)h(primitiv)o(es)d(attac)o(h)j(pro)q
2270 (cedures)h(called)e Fu(notic)n(ers)75 2095 y Fy(on)o(to)16
2271 b(v)n(ariables.)27 b(Whenev)o(er)18 b(the)f(domain,)e(range)i(or)g(t)o
2272 (yp)q(e)g(of)g(a)f(v)n(ariable)g(is)h(restricted,)i(the)e(noticers)h
2273 (attac)o(hed)75 2145 y(on)o(to)13 b(that)g(v)n(ariable)f(are)i(run)g
2274 (to)f(propagate)g(the)h(e\013ect)h(of)e(that)g(restriction)h(to)f
2275 (other)h(m)o(utually)d(constrained)j(v)n(ari-)75 2195
2276 y(ables.)k(Noticers)c(implemen)o(t)c(constrain)o(t)k(propagation.)i
2277 (Since)e(constrain)o(t)f(propagation)f(alone)h(is)g(not)g(a)g(complete)
2278 75 2245 y(constrain)o(t)j(satisfaction)f(tec)o(hnique,)h(it)f(is)g
2279 (augmen)o(ted)g(b)o(y)g(bac)o(ktrac)o(king)g(searc)o(h.)24
2280 b(Constrain)o(t)15 b(propagation)f(and)p 75 2280 750
2281 2 v 121 2306 a Fn(4)139 2318 y Fs(Some)6 b(p)q(eople)g(add)h(a)h(third)
2282 f(inno)o(v)n(ation)o(,)f(pattern)g(directed)f(in)o(v)o(o)q(cation.)12
2283 b(In)7 b(m)o(y)g(opinion,)g(pattern)e(directed)h(in)o(v)o(o)q(cation)f
2284 (is)j(primarily)75 2358 y(a)j(syn)o(tactic)f(con)o(v)o(enienc)o(e)f
2285 (while)i(the)g(other)f(t)o(w)o(o)h(inno)o(v)n(ations)e(add)h
2286 (signi\014can)o(t)f(expressiv)o(eness)f(to)k(an)o(y)e(programmin)o(g)f
2287 (language.)121 2385 y Fn(5)139 2397 y Fs(This)15 b(op)q(eration)d(is)j
2288 (sometimes)d(called)i Fk(der)n(efer)n(encing)p Fs(.)29
2289 b Fm(Pr)o(olog)16 b Fs(and)e(its)g(deriv)n(ativ)o(es)f(pro)o(vide)f
2290 (automatic)h(dereferenci)o(ng.)23 b(It)75 2437 y(w)o(ould)12
2291 b(b)q(e)g(nice)g(if)g Fm(Common)h(Lisp)g Fs(pro)o(vided)d(a)i(ho)q(ok)g
2292 (to)g(allo)o(w)g(an)g(arbitrary)f(dereferenc)o(ing)e(function)i(to)h(b)
2293 q(e)g(de\014ned)f(on)h(a)g(p)q(er)g(t)o(yp)q(e)75 2476
2294 y(basis)f(and)h(sp)q(ecify)e(that)h(an)o(y)h(primitiv)o(e)d(op)q
2295 (eration)h(that)h(w)o(as)i(unde\014ned)c(giv)o(en)i(the)g(t)o(yp)q(es)g
2296 (of)h(argumen)o(ts)e(it)i(w)o(as)g(called)f(with)h(w)o(ould)75
2297 2515 y(\014rst)h(call)g(the)g(appropriat)o(e)e(dereferencin)o(g)g
2298 (functions)g(on)i(it)h(argumen)o(ts.)19 b(Suc)o(h)12
2299 b(an)h(extension)e(w)o(ould)i(b)q(e)h(useful)e(not)h(only)f(for)h
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2301 i(futures)e(\(Halstead,)h(19??\))k(as)d(w)o(ell.)1002
2302 2723 y Fy(6)p eop
2303 %%Page: 7 7
2304 7 6 bop 75 195 a Fy(bac)o(ktrac)o(king)15 b(searc)o(h)h(run)f
2305 (automatically)d(in)j(an)f(in)o(terlea)o(v)o(ed)h(opp)q(ortunistic)h
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2307 (the)h(attac)o(hing)e(and)h(running)g(noticers;)h(that)f(is)g
2308 (automatically)d(handled)j(b)o(y)g Fv(Screamer)q Fy(.)21
2309 b(The)16 b(user)75 295 y(simply)c(creates)k(v)n(ariables,)d(asserts)j
2310 (constrain)o(ts)e(b)q(et)o(w)o(een)i(them)d(and)h(asks)h
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2312 (helpful)g(to)g(kno)o(w)g(a)g(little)f(bit)h(ab)q(out)g(the)h(implemen)
2313 o(tatio)o(n)d(details)i(since)h(at)f(one)g(lev)o(el,)h(the)f(precise)75
2314 394 y(seman)o(tics)c(of)h(the)g Fv(Screamer)h Fy(primitiv)o(es)d(dep)q
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2316 (principles)g(p)q(ertaining)g(to)g(noticers)g(hold)f(throughout)h(the)h
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2318 (deterministic.)j(Constrain)o(t)c(propagation)f(th)o(us)i(is)f(a)f
2319 (deterministic)h(pro)q(cess.)21 b(Noticers)15 b(ma)o(y)d(fail)h(ho)o
2320 (w-)75 544 y(ev)o(er.)18 b(Lik)o(e)10 b(all)g(failures,)h(this)g
2321 (causes)h(bac)o(ktrac)o(king)f(to)f(the)i(most)e(recen)o(t)i(c)o(hoice)
2322 g(p)q(oin)o(t.)k(Choice)11 b(p)q(oin)o(ts)g(are)g(created)75
2323 594 y(b)o(y)j(the)g(primitiv)o(e)e Fv(Screamer)i Fy(solution)f(forcing)
2324 g(functions)h Fq(linear-force)d Fy(and)j Fq(divide-and-conque)o(r-for)o
2325 (ce)75 643 y Fy(in)e(addition)f(to)i(an)o(y)f(other)h(c)o(hoice)g(p)q
2326 (oin)o(ts)f(explicitly)g(created)i(b)o(y)e(the)h(user.)19
2327 b(Second,)13 b(all)f(noticers)h(are)g(attac)o(hed)g(to)75
2328 693 y(v)n(ariables)g(b)o(y)g(lo)q(cal)f(side)i(e\013ect.)19
2329 b(Th)o(us)14 b(constrain)o(ts)g(asserted)h(b)q(et)o(w)o(een)g(v)n
2330 (ariables)e(disapp)q(ear)g(up)q(on)h(bac)o(ktrac)o(king.)137
2331 743 y(Constrain)o(t)c(propagation)e(ma)o(y)g(restrict)j(the)f(v)n(alue)
2332 f(that)h(a)g(v)n(ariable)e(ma)o(y)g(tak)o(e)h(on.)17
2333 b(Sev)o(eral)10 b(forms)e(of)h(restriction)75 793 y(are)19
2334 b(curren)o(tly)h(implemen)o(ted)d(in)i Fv(Screamer)q
2335 Fy(.)33 b(These)20 b(include)g(domain)c(restrictions,)21
2336 b(range)f(restrictions)g(and)75 843 y(t)o(yp)q(e)d(restrictions.)26
2337 b(The)17 b(kinds)f(of)g(restriction)h(will)e(b)q(e)i(discussed)h(in)e
2338 (greater)h(detail)f(in)g(the)h(follo)o(wing)c(sections.)75
2339 892 y(Sev)o(eral)k(general)g(principles)g(p)q(ertaining)f(to)h
2340 (restrictions)h(hold)e(throughout)h(the)g(implemen)o(tation.)23
2341 b(First,)18 b(there)75 942 y(is)e(only)g(one)h(kind)f(of)g(v)n
2342 (ariable.)25 b(An)o(y)16 b(v)n(ariable)g(ma)o(y)e(ha)o(v)o(e)j(an)o(y)f
2343 (com)o(bination)e(of)i(restrictions)i(placed)f(on)f(it)g(and)75
2344 992 y(ma)o(y)e(participate)i(in)f(an)o(y)h(form)e(of)h(constrain)o(t.)
2345 24 b(Second,)17 b(v)n(ariables)e(are)h(alw)o(a)o(ys)f(restricted)j(b)o
2346 (y)e(lo)q(cal)f(side)h(e\013ect.)75 1042 y(Th)o(us)g(an)o(y)e
2347 (restrictions)j(placed)f(on)f(the)h(v)n(alues)f(of)f(v)n(ariables)h
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2349 b(section)g(3)f(for)75 1092 y(a)j(discussion)h(of)g(the)g(implications)
2350 d(of)i(this)g(for)h(the)g(in)o(teraction)f(b)q(et)o(w)o(een)i(lo)q(cal)
2351 e(side)h(e\013ects)i(and)d Fv(Screamer)75 1142 y Fy(primitiv)o(es)12
2352 b(lik)o(e)h Fq(one-value)p Fy(.)75 1279 y Fw(6)69 b(Domain,)22
2353 b(Range)h(and)h(T)n(yp)r(e)f(Restricti)o(ons)75 1370
2354 y Fy(The)14 b Fv(Screamer)h Fy(constrain)o(t)f(pac)o(k)n(age)f(incorp)q
2355 (orates)i(the)f(follo)o(wing)d(simple)i(t)o(yp)q(e)h(system.)k(All)12
2356 b(v)n(alues)i(are)g(either)75 1420 y Fx(n)o(umeric)f
2357 Fy(or)g Fx(non-n)o(umeric)p Fy(.)k(Numeric)c(v)n(alues)g(are)g(in)g
2358 (turn)h(either)g Fx(real)g Fy(or)f Fx(non-real)p Fy(.)18
2359 b(Real)12 b(n)o(um)o(b)q(ers)h(include)h(b)q(oth)75 1469
2360 y(\015oating)g(p)q(oin)o(t)g(n)o(um)o(b)q(ers)h(as)g(w)o(ell)f(as)h
2361 (rational)f(n)o(um)o(b)q(ers.)20 b(Non-real)15 b(n)o(um)o(b)q(ers)f
2362 (include)h(complex)f(n)o(um)o(b)q(ers.)21 b(Real)75 1519
2363 y(v)n(alues)15 b(are)h(in)f(turn)h(either)h Fx(in)o(teger)f
2364 Fy(or)f Fx(non-in)o(teger)p Fy(.)23 b(The)16 b(ab)q(o)o(v)o(e)g
2365 (classes)g(are)g(not)g(disjoin)o(t.)22 b(In)15 b(the)h
2366 Fv(Screamer)75 1569 y Fy(t)o(yp)q(e)e(system,)f(all)g(in)o(tegers)i
2367 (are)f(reals)g(and)g(all)e(real)i(are)g(n)o(um)o(b)q(ers.)k(An)o(y)c(v)
2368 n(alue)f(ho)o(w)o(ev)o(er,)h(can)g(b)q(e)g(classi\014ed)g(in)g(one)75
2369 1619 y(of)f(the)i(follo)o(wing)c(four)j(disjoin)o(t)e(classes:)20
2370 b(in)o(teger,)14 b(non-in)o(teger)g(real,)f(non-real)h(n)o(um)o(b)q
2371 (er,)e(non-n)o(um)o(b)q(er.)137 1669 y(One)21 b(m)o(ust)f(b)q(ear)h(in)
2372 f(mind)e(that)j(the)g Fv(Screamer)g Fy(notion)f(of)g(t)o(yp)q(e)g(is)h
2373 (deriv)o(ed)g(from)d(the)j Fv(Common)c(Lisp)75 1718 y
2374 Fy(represen)o(tation)i(of)e(an)g(ob)r(ject)h(and)f(not)g(its)g
2375 (abstract)i(mathematical)14 b(prop)q(erties.)29 b(Th)o(us)18
2376 b Fv(Screamer)g Fy(do)q(es)g(not)75 1768 y(consider)13
2377 b(the)g(n)o(um)o(b)q(er)e Fq(1.0)h Fy(to)g(b)q(e)g(an)g(in)o(teger)h
2378 (since)g(its)f(underlying)g Fv(Common)k(Lisp)c Fy(represen)o(tation)i
2379 (is)e(a)g(\015oating)75 1818 y(p)q(oin)o(t)e(n)o(um)o(b)q(er)f(and)i
2380 Fv(Common)16 b(Lisp)10 b Fy(nev)o(er)i(automatically)7
2381 b(con)o(v)o(erts)k(a)f(\015oating)g(p)q(oin)o(t)f(n)o(um)o(b)q(er)h(to)
2382 g(an)g(in)o(teger.)18 b(On)75 1868 y(the)d(other)h(hand,)e
2383 Fv(Screamer)i Fy(do)q(es)f(consider)h Fq(4/1)e Fy(to)h(b)q(e)g(an)g(in)
2384 o(teger)g(since)g Fv(Common)i(Lisp)e Fy(will)e(automatically)75
2385 1918 y(con)o(v)o(ert)i(a)g(rational)e(n)o(um)o(b)q(er)h(with)g(one)h
2386 (as)g(its)f(denominator)f(in)o(to)h(an)h(in)o(teger.)20
2387 b(Lik)o(ewise,)14 b Fv(Screamer)i Fy(considers)75 1968
2388 y Fq(#C\(4)21 b(0\))16 b Fy(to)h(b)q(e)g(an)g(in)o(teger)g(since)g
2389 Fv(Common)g(Lisp)f Fy(will)g(con)o(v)o(ert)h(a)g(complex)e(n)o(um)o(b)q
2390 (er)h(whose)h(comp)q(onen)o(ts)g(are)75 2017 y(in)o(tegers)k(and)f
2391 (whose)h(imaginary)d(part)i(is)h(zero)g(in)o(to)f(an)g(in)o(teger.)38
2392 b Fv(Screamer)21 b Fy(ho)o(w)o(ev)o(er,)h(do)q(es)f(not)f(consider)75
2393 2067 y Fq(#C\(4.0)h(0.0\))12 b Fy(to)h(b)q(e)h(real)g(since)g
2394 Fv(Common)i(Lisp)e Fy(will)e(not)h(con)o(v)o(ert)h(a)f(complex)f(n)o
2395 (um)o(b)q(er)h(whose)h(comp)q(onen)o(ts)f(are)75 2117
2396 y(reals)i(in)o(to)f(a)h(real,)f(ev)o(en)h(though)g(its)g(imaginary)c
2397 (part)k(is)g(zero.)21 b(Since)16 b Fv(Common)g(Lisp)f
2398 Fy(represen)o(ts)i(b)q(oth)e(parts)h(of)75 2167 y(a)d(complex)e(n)o(um)
2399 o(b)q(er)i(as)g(the)h(same)e(data)g(t)o(yp)q(e,)i(b)q(oth)f
2400 Fq(#C\(4.0)20 b(0\))13 b Fy(and)g Fq(#C\(4)21 b(0.0\))12
2401 b Fy(are)h(treated)i(as)e Fq(#C\(4.0)20 b(0.0\))p Fy(.)137
2402 2217 y Fv(Screamer)14 b Fy(can)g(optionally)d(restrict)k(a)d(v)n
2403 (ariable)h(to)g(tak)o(e)g(on)g(v)n(alues)g(only)f(of)h(a)g(giv)o(en)f
2404 (t)o(yp)q(e.)19 b(V)m(ariables)12 b(whose)75 2266 y(v)n(alues)j(are)g
2405 (restricted)j(to)d(b)q(e)h(n)o(umeric)e(are)h(termed)h(n)o(umeric)e(v)n
2406 (ariables.)21 b(Similar)12 b(terminology)h(is)i(used)h(for)f(non-)75
2407 2316 y(n)o(umeric,)9 b(real,)h(non-real,)g(in)o(teger)g(and)f(non-in)o
2408 (teger)h(v)n(ariables.)16 b(V)m(ariables)9 b(created)i(with)f
2409 Fq(make-variable)c Fy(initially)75 2366 y(carry)17 b(no)g(t)o(yp)q(e)g
2410 (restrictions.)28 b(Subsequen)o(t)18 b(t)o(yp)q(e)f(restrictions)h(can)
2411 f(b)q(e)g(added)g(using)g(the)g(primitiv)o(es)e Fq(integerv)p
2412 Fy(,)75 2416 y Fq(realv)c Fy(and)h Fq(numberv)p Fy(,)e(p)q(oten)o
2413 (tially)h(com)o(bined)g(with)h Fq(notv)p Fy(,)f(along)g(with)g
2414 Fq(assertv!)p Fy(.)16 b(F)m(or)c(example,)e(a)i(real)g(v)n(ariable)75
2415 2466 y(can)i(b)q(e)h(created)g(using:)1002 2723 y(7)p
2416 eop
2417 %%Page: 8 8
2418 8 7 bop 204 188 a Fq(\(let)21 b(\(\(x)g(\(make-variable\)\)\))225
2419 238 y(\(assert!)g(\(realv)f(x\)\))225 288 y Fp(:)7 b(:)g(:)o
2420 Fq(\))75 369 y Fy(a)14 b(non-n)o(umeric)e(v)n(ariable)h(using:)204
2421 450 y Fq(\(let)21 b(\(\(x)g(\(make-variable\)\)\))225
2422 499 y(\(assert!)g(\(notv)f(\(numberv)h(x\)\)\))225 549
2423 y Fp(:)7 b(:)g(:)o Fq(\))75 630 y Fy(and)14 b(a)f(non-in)o(teger)h
2424 (real)g(using:)204 711 y Fq(\(let)21 b(\(\(x)g(\(make-variable\)\)\))
2425 225 760 y(\(assert!)g(\(notv)f(\(integerv)g(x\)\)\))225
2426 810 y(\(assert!)h(\(realv)f(x\)\))225 860 y Fp(:)7 b(:)g(:)o
2427 Fq(\).)75 941 y Fy(As)15 b(the)g(last)f(example)f(sho)o(ws,)h(sev)o
2428 (eral)h(t)o(yp)q(e)g(restrictions)g(can)g(b)q(e)g(placed)f(sim)o
2429 (ultaneously)f(on)h(the)h(same)e(v)n(ariable)75 991 y(sub)r(ject)e(to)f
2430 (the)h(pro)o(vision)d(that)i(the)h(in)o(tersection)g(of)e(the)h(t)o(yp)
2431 q(es)h(in)f(nonempt)o(y)m(.)15 b(An)10 b(attempt,)f(suc)o(h)i(as)f(the)
2432 g(follo)o(wing,)75 1041 y(to)i(restrict)i(a)e(v)n(ariable)g(to)g(an)g
2433 (empt)o(y)f(set)j(of)e(p)q(ossible)g(v)n(alues)g(fails)g(and)g(bac)o
2434 (ktrac)o(ks)h(to)f(the)h(previous)g(c)o(hoice)g(p)q(oin)o(t.)204
2435 1121 y Fq(\(let)21 b(\(\(x)g(\(make-variable\)\)\))225
2436 1171 y(\(assert!)g(\(notv)f(\(numberv)h(x\)\)\))225 1221
2437 y(\(assert!)g(\(integerv)f(x\)\))225 1271 y Fp(:)7 b(:)g(:)o
2438 Fq(\).)75 1352 y Fy(This)15 b(do)q(es)g(not)g(cause)h(an)f(error)h
2439 (unless)f(the)h(assertion)f(is)g(p)q(erformed)g(outside)g(the)g(con)o
2440 (text)h(of)e(an)o(y)h(c)o(hoice)g(p)q(oin)o(t.)75 1401
2441 y(Remem)o(b)q(er)g(that)h(in)f Fv(Screamer)q Fy(,)h(restricting)h(a)f
2442 (v)n(ariable)f(to)h(b)q(e)h(an)f(in)o(teger)h(inheren)o(tly)f
2443 (restricts)i(it)e(to)g(b)q(e)h(real)75 1451 y(and)c(restricting)g(a)g
2444 (v)n(ariable)f(to)g(b)q(e)i(real)f(inheren)o(tly)g(restricts)i(it)d(to)
2445 h(b)q(e)g(n)o(umeric.)k(Lik)o(ewise,)c(restricting)g(a)g(v)n(ariable)75
2446 1501 y(to)i(b)q(e)h(non-n)o(umeric)e(restricts)k(it)c(to)i(b)q(e)g
2447 (non-real)e(and)i(restricting)g(a)f(v)n(ariable)f(to)h(b)q(e)h
2448 (non-real)f(restricts)i(it)e(to)g(b)q(e)75 1551 y(non-in)o(teger.)j(In)
2449 12 b(the)h(ab)q(o)o(v)o(e)f(example,)f Fq(\(assert!)20
2450 b(\(integerv)g(x\)\))12 b Fy(will)f(fail)f(since)j Fq(x)g
2451 Fy(is)f(already)g(restricted)i(to)e(b)q(e)75 1601 y(non-n)o(umeric)h
2452 (and)h(th)o(us)g(non-in)o(teger.)137 1651 y(All)19 b
2453 Fv(Screamer)i Fy(constrain)o(t)f(primitiv)o(es)e(accept)j(b)q(oth)f(b)q
2454 (ound)g(and)g(un)o(b)q(ound)g(v)n(ariables,)g(as)g(w)o(ell)f(as)h(non-)
2455 75 1700 y(v)n(ariable)15 b(v)n(alues,)h(as)g(their)h(argumen)o(ts.)24
2456 b(This)16 b(includes)h(the)f(t)o(yp)q(e)h(primitiv)o(es)d
2457 Fq(integerv)p Fy(,)h Fq(realv)g Fy(and)h Fq(numberv)p
2458 Fy(.)75 1750 y(Th)o(us)10 b Fq(\(assert!)20 b(\(integerv)g(4.0\)\))8
2459 b Fy(is)h(acceptable)h(and)f(will)f(fail)g(immedia)o(tely)m(.)13
2460 b(Lik)o(ewise)d Fq(\(assert!)20 b(\(integerv)g(x\)\))75
2461 1800 y Fy(will)12 b(also)i(fail)e(immediately)e(if)j
2462 Fq(x)h Fy(ev)n(aluates)g(to)g Fq(4.0)f Fy(or)h(if)f Fq(x)h
2463 Fy(ev)n(aluates)f(to)h(a)g(v)n(ariable)f(whic)o(h)g(is)h(b)q(ound)g(to)
2464 g Fq(4.0)p Fy(.)137 1850 y(In)19 b(the)f(ab)q(o)o(v)o(e)g(examples,)g
2465 (the)h(t)o(yp)q(es)g(of)f(v)n(ariables)g(w)o(ere)h(explicitly)e
2466 (restricted)k(using)d(the)g Fq(assert!)f Fy(primi-)75
2467 1900 y(tiv)o(e.)22 b Fv(Screamer)16 b Fy(ma)o(y)d(restrict)k(the)f(t)o
2468 (yp)q(es)g(of)e(v)n(ariables)h(in)g(t)o(w)o(o)f(other)i(w)o(a)o(ys.)22
2469 b(First,)15 b(a)g(n)o(um)o(b)q(er)g(of)f Fv(Screamer)75
2470 1949 y Fy(primitiv)o(es)f(create)k(and)e(return)h(v)n(ariables)f(whic)o
2471 (h)g(are)g(already)g(t)o(yp)q(ed.)22 b(In)15 b(particular)g(the)h
2472 (primitiv)o(es)d(fo)q(o)i(return)75 1999 y(in)o(teger)i(v)n(ariables,)g
2473 (the)h(primitiv)o(es)d(bar)i(return)h(real)f(v)n(ariables)g(and)f(the)i
2474 (primitiv)o(es)d(baz)j(return)g(n)o(umeric)e(v)n(ari-)75
2475 2049 y(ables.)25 b(Second,)17 b(a)e(n)o(um)o(b)q(er)h(of)f
2476 Fv(Screamer)i Fy(primitiv)o(es)d(restrict)k(the)e(t)o(yp)q(es)h(of)f
2477 (their)g(argumen)o(ts.)24 b(In)16 b(particular)75 2099
2478 y(...)23 b(Remem)o(b)q(er)14 b(that)i(all)f Fv(Screamer)h
2479 Fy(constrain)o(t)h(primitiv)o(es)d(accept)j(b)q(oth)f(b)q(ound)g(and)g
2480 (un)o(b)q(ound)g(v)n(ariables,)f(as)75 2149 y(w)o(ell)f(as)h(non-v)n
2481 (ariable)e(v)n(alues)h(as)h(argumen)o(ts.)20 b(A)15 b(primitiv)o(e)d
2482 (whic)o(h)j(restricts)h(an)f(argumen)o(t)e(to)i(a)f(giv)o(en)g(t)o(yp)q
2483 (e)h(will)75 2198 y(fail)d(immediately)e(if)j(called)g(with)h(a)f
2484 (non-v)n(ariable)f(v)n(alue)h(not)g(meeting)g(the)h(t)o(yp)q(e)g
2485 (restriction.)19 b(Similarly)l(,)11 b(a)i(b)q(ound)75
2486 2248 y(v)n(ariable)k(whose)i(v)n(alue)e(do)q(es)i(not)f(meet)g(the)h(t)
2487 o(yp)q(e)f(restriction)h(will)e(also)g(cause)j(imm)o(ediate)c(failure.)
2488 30 b(When)18 b(an)75 2298 y(un)o(b)q(ound)e(v)n(ariable)f(is)h(passed)h
2489 (to)f(a)f(restricted)j(argumen)o(t,)d(the)i(primitiv)o(e)d(imm)o
2490 (ediately)f(restricts)18 b(that)e(v)n(ariable)75 2348
2491 y(to)e(b)q(e)h(of)f(the)h(requisite)g(t)o(yp)q(e)g(b)q(efore)g(an)o(y)f
2492 (further)h(pro)q(cessing.)21 b(That)14 b(restriction)h(ma)o(y)e(cause)i
2493 (immediate)d(failure)75 2398 y(if)h(the)i(restriction)f(w)o(ould)f
2494 (cause)i(the)g(v)n(ariable's)e(t)o(yp)q(e)h(to)g(b)q(ecome)f(empt)o(y)m
2495 (.)137 2448 y(The)h(t)o(yp)q(e)h(hierarc)o(h)o(y)f(implies)d(that)j(at)
2496 g(an)o(y)f(p)q(oin)o(t)g(in)h(time)e(a)h(v)n(ariable)g(can)h(b)q(e)g
2497 (in)f(one)h(of)f(ten)i(t)o(yp)q(e)f(restriction)75 2497
2498 y(states:)19 b(in)o(teger,)12 b(non-in)o(teger,)h(non-in)o(teger)g(n)o
2499 (um)o(b)q(er,)e(non-in)o(teger)i(real,)f(real,)h(non-real,)f(non-real)g
2500 (n)o(um)o(b)q(er,)g(n)o(um-)75 2547 y(b)q(er,)j(non-n)o(um)o(b)q(er)e
2501 (and)i(unkno)o(wn.)k(In)14 b(all)g(but)g(the)h(last,)f(some)g
2502 (information)d(is)k(kno)o(wn)e(ab)q(out)i(the)g(t)o(yp)q(e)g(of)f(v)n
2503 (alue)75 2597 y(whic)o(h)g(the)g(v)n(ariable)f(ma)o(y)f(tak)o(e)i(on.)k
2504 (Th)o(us)c(a)f(v)n(ariable)g(whic)o(h)h(is)1002 2723
2505 y(8)p eop
2506 %%Page: 9 9
2507 9 8 bop 75 195 a Fw(7)69 b(Binding,)22 b(Dereferencing)f(and)j(Sharing)
2508 75 311 y(8)69 b(Argumen)n(t)23 b(Restricti)o(ons)75 427
2509 y(9)69 b(Aggregate)24 b(Ob)t(jects)75 518 y Fy(A)11 b(n)o(um)o(b)q(er)e
2510 (of)h Fv(Screamer)h Fy(primitiv)o(es)e(deal)h(with)g(aggregate)h(ob)r
2511 (jects,)h(tra)o(v)o(ersing)e(the)h(slots)g(of)f(suc)o(h)h(ob)r(jects)h
2512 (recur-)75 567 y(siv)o(ely)d(to)h(access)h(all)d(of)h(their)h(sub-ob)r
2513 (jects.)19 b(These)10 b(primitiv)o(es)e(include)i Fq(equalv)p
2514 Fy(,)f Fq(ground?)p Fy(,)f Fq(apply-substitution)o Fy(,)75
2515 617 y Fq(domain-size)p Fy(,)k Fq(solution)h Fy(and)h
2516 Fq(template)p Fy(.)k(The)d(only)e(aggregate)i(ob)r(jects)g(whic)o(h)g
2517 Fv(Screamer)g Fy(curren)o(tly)g(kno)o(ws)75 667 y(ho)o(w)i(to)h(tra)o
2518 (v)o(erse)h(are)f(cons)h(cells.)30 b(All)17 b(other)h(aggregate)g(ob)r
2519 (jects)h(are)f(treated)h(as)f(atomic.)28 b(F)m(urthermore,)18
2520 b(an)o(y)75 717 y(primitiv)o(e)12 b(whic)o(h)h(tra)o(v)o(erses)j
2521 (aggregate)e(data)f(ma)o(y)f(lo)q(op)h(if)h(the)g(aggregate)g(ob)r
2522 (ject)h(con)o(tains)e(circular)i(p)q(oin)o(ters.)75 854
2523 y Fw(10)69 b(Un)n(w)n(edging)23 b(Screamer)75 945 y Fy(T)m(o)17
2524 b(compile)f(e\016cien)o(t)i(co)q(de,)h Fv(Screamer)f
2525 Fy(m)o(ust)e(kno)o(w)h(whether)i(or)f(not)f(an)h(expression)h(is)e
2526 (deterministic)g(since)75 995 y Fv(Screamer)d Fy(can)g(generate)h(more)
2527 d(e\016cien)o(t)i(co)q(de)h(for)e(deterministic)g(expressions,)i(sub)q
2528 (expressions)g(and)f(functions)75 1045 y(than)e(for)f(nondeterministic)
2529 g(ones.)18 b(Whether)13 b(or)f(not)g(an)f(expression)i(is)f
2530 (deterministic)f(can)h(dep)q(end)h(on)f(whether)h(or)75
2531 1095 y(not)e(the)h(functions)g(it)e(calls)h(are)h(deterministic.)17
2532 b(Th)o(us)11 b Fv(Screamer)h Fy(main)o(tains)d(a)i(database)h(of)e(the)
2533 i(function)f(calling)75 1144 y(structure)19 b(of)e(an)o(y)f(functions)i
2534 (whic)o(h)f(ha)o(v)o(e)g(b)q(een)h(compiled)d(or)i(loaded)g(in)o(to)g
2535 (the)g Fv(Lisp)g Fy(w)o(orld.)28 b(This)17 b(`who-calls')75
2536 1194 y(database)h(is)g(implemen)o(ted)e(in)i(p)q(ortable)g
2537 Fv(Common)f(Lisp)h Fy(and)g(is)g(part)g(of)g Fv(Screamer)p
2538 Fy(.)31 b(It)18 b(is)g(indep)q(enden)o(t)i(of)75 1244
2539 y(an)o(y)12 b(other)h(nativ)o(e)f(who-calls)g(database)g(that)h(ma)o(y)
2540 d(b)q(e)j(built)f(in)o(to)g(the)h Fv(Common)j(Lisp)c
2541 Fy(implemen)o(tation)d(for)j(other)75 1294 y(purp)q(oses.)137
2542 1344 y(F)m(or)f(the)h(most)f(part,)g(the)i Fv(Screamer)f
2543 Fy(who-calls)e(database)i(is)g(completely)e(transparen)o(t)j(from)c
2544 (the)j(user.)19 b(There)75 1393 y(are)12 b(ho)o(w)o(ev)o(er,)g(a)f(n)o
2545 (um)o(b)q(er)g(of)g(quirky)g(situations)h(where)g(it)g(is)f(helpful)g
2546 (to)g(understand)i(its)f(op)q(eration.)17 b(Some)11 b(of)g(these)75
2547 1443 y(situations)j(are)g(una)o(v)o(oidable.)i(Others)g(are)e(simply)e
2548 (bugs)i(in)g(the)g(curren)o(t)h(implemen)o(tation.)137
2549 1493 y(When)d(compiling)c(an)j(expression)i Fp(e)e Fy(whic)o(h)g(calls)
2550 g(a)g(function)g Fp(f)t Fy(,)h Fv(Screamer)g Fy(needs)g(to)g(kno)o(w)e
2551 (whether)j(or)e(not)g Fp(f)75 1543 y Fy(is)f(deterministic)g(to)h(kno)o
2552 (w)f(ho)o(w)g(to)g(compile)f Fp(e)p Fy(.)17 b(There)12
2553 b(will)d(b)q(e)i(no)f(problem)f(if)h(the)h(de\014nition)f(of)g
2554 Fp(f)15 b Fy(app)q(ears)c(b)q(efore)h Fp(e)75 1593 y
2555 Fy(in)j(the)i(program,)d(i.e.)g(if)h(the)h(call)f(to)h
2556 Fp(f)k Fy(is)c(a)f(bac)o(kw)o(ard)h(reference.)26 b Fv(Screamer)16
2557 b Fy(will)e(already)i(kno)o(w)f(whether)i(or)75 1643
2558 y(not)c Fp(f)18 b Fy(is)13 b(deterministic)g(and)g(th)o(us)h(ho)o(w)f
2559 (to)g(compile)e Fp(e)p Fy(.)18 b(The)c(situation)f(is)g(more)f(complex)
2560 g(for)h(forw)o(ard)g(references.)75 1692 y Fv(Screamer)19
2561 b Fy(assumes)f(b)o(y)g(default)g(that)g Fp(f)24 b Fy(is)18
2562 b(deterministic)g(and)g(compiles)f Fp(e)h Fy(accordingly)m(.)30
2563 b(It)19 b(also)f(sa)o(v)o(es)g(the)75 1742 y(complete)12
2564 b(source)i(co)q(de)g(de\014nition)f(for)f(the)i(function)e
2565 Fp(g)i Fy(whic)o(h)f(con)o(tains)g Fp(e)p Fy(.)18 b(If)12
2566 b Fv(Screamer)i Fy(later)f(disco)o(v)o(ers)g(that)g Fp(f)75
2567 1792 y Fy(is)h(actually)g(nondeterministic,)g(then)h
2568 Fv(Screamer)g Fy(recompiles)f Fp(g)q Fy(.)20 b(This)14
2569 b(recompilation)f(happ)q(ens)i(automatically)l(.)75 1842
2570 y(The)f(user)h(normally)d(need)i(not)g(b)q(e)h(a)o(w)o(are)e(that)h
2571 (this)g(is)g(happ)q(ening.)137 1892 y(When)h(using)e(the)i
2572 Fv(Common)h(Lisp)f Fq(compile-file)c Fy(function,)i(this)h
2573 (recompilation)e(causes)k(the)e(binary)g(\014le)g(to)75
2574 1941 y(con)o(tain)i(t)o(w)o(o)h(de\014nitions)f(for)h(the)g(function)f
2575 Fp(g)q Fy(|one)h(where)h(the)f(original)e(de\014nition)i(app)q(eared)g
2576 (and)g(one)g(at)f(the)75 1991 y(place)c(of)g(recompilation)e(just)i
2577 (prior)g(to)g(the)h(de\014nition)f(of)f Fp(f)t Fy(.)1047
2578 1976 y Fo(6)1084 1991 y Fy(Some)g Fv(Common)16 b(Lisp)d
2579 Fy(implem)o(en)o(tations)d(will)g(issue)75 2041 y(a)15
2580 b(w)o(arning)g(that)h(the)g(binary)f(\014le)h(con)o(tains)f(m)o
2581 (ultiple)f(de\014nitions)h(for)h(functions.)23 b(Suc)o(h)16
2582 b(w)o(arnings)f(can)h(safely)f(b)q(e)75 2091 y(ignored.)221
2583 2076 y Fo(7)257 2091 y Fy(Note)f(that)g(there)g(is)g(no)f(run)g(time)g
2584 (p)q(erformance)g(p)q(enalt)o(y)g(for)g(forw)o(ard)g(references)j(and)e
2585 (recompilation.)75 2141 y(The)f(compiled)e(co)q(de)j(resulting)f(at)f
2586 (the)h(end)h(is)e(the)h(same)f(as)h(for)f(bac)o(kw)o(ard)h(references.)
2587 20 b(Th)o(us)13 b(there)h(should)f(b)q(e)g(no)75 2190
2588 y(temptation)d(to)i(restructure)i(program)d(\014les)h(to)f(minimi)o(ze)
2589 f(forw)o(ard)h(references.)20 b(The)12 b(only)f(p)q(enalties)h(are)h
2590 (increased)75 2240 y(compilation)j(time)i(due)i(to)e(recompilation,)g
2591 (sligh)o(tly)g(increased)i(binary)f(\014le)g(size)h(and)f(sligh)o(tly)e
2592 (increased)k(load)75 2290 y(time.)j(Recompiling)14 b(a)i(\014le)g(a)g
2593 (second)h(time)e(in)h(the)h(same)e Fv(Lisp)i Fy(w)o(orld)e(will)g
2594 (eliminate)g(all)g(duplicate)h(de\014nitions)p 75 2325
2595 750 2 v 121 2352 a Fn(6)139 2363 y Fs(It)d(is)g(actually)e(p)q(ossible)
2596 h(for)g(a)i(function)d(to)i(ha)o(v)o(e)f(sev)o(eral)f(recompilation)o
2597 (s.)18 b(If)13 b Fj(f)k Fs(has)c(forw)o(ard)f(references)f(to)i
2598 Fj(g)i Fs(and)d Fj(h)p Fs(,)i(b)q(oth)f(of)75 2403 y(whic)o(h)e(are)g
2599 (later)g(found)f(to)h(b)q(e)g(nondetermin)o(istic)o(,)e
2600 Fj(f)15 b Fs(will)d(b)q(e)f(recompiled)e(t)o(wice,)i(once)g(prior)f(to)
2601 h(the)g(de\014nition)e(of)j Fj(g)g Fs(and)f(again)f(prior)75
2602 2442 y(to)h(the)f(de\014nition)f(of)i Fj(h)p Fs(.)16
2603 b(It)11 b(is)g(also)g(p)q(ossible)e(for)i(recompilati)o(ons)d(to)j
2604 (cascade.)i(If)e Fj(f)k Fs(has)c(a)g(forw)o(ard)g(reference)d(to)j
2605 Fj(g)i Fs(whic)o(h)e(in)g(turn)f(has)75 2482 y(a)h(forw)o(ard)e
2606 (reference)f(to)j Fj(h)g Fs(then)e(disco)o(v)o(ering)f(that)h
2607 Fj(h)j Fs(is)e(nondetermin)o(istic)d(will)k(cause)e(b)q(oth)h
2608 Fj(g)i Fs(and)d(then)h Fj(f)k Fs(to)d(b)q(e)f(recompiled)d(when)k
2609 Fj(h)75 2521 y Fs(is)g(compiled.)i(It)e(is)h(our)f(exp)q(erience)d
2610 (that)j(suc)o(h)f(m)o(ultiple)f(recompilation)o(s)g(are)i(v)o(ery)f
2611 (rare.)121 2549 y Fn(7)139 2561 y Fs(It)h(w)o(ould)g(b)q(e)g(nice)f(if)
2612 i Fm(Common)g(Lisp)g Fs(pro)o(vided)d(a)i(declaration)d(to)k(disable)d
2613 (suc)o(h)i(w)o(arnings.)1002 2723 y Fy(9)p eop
2614 %%Page: 10 10
2615 10 9 bop 75 195 a Fy(and)12 b(alleviate)f(the)i(increased)h(binary)e
2616 (\014le)g(size)h(and)f(load)f(time)g(p)q(enalties)i(since)g
2617 Fv(Screamer)g Fy(will)e(ha)o(v)o(e)h(a)g(complete)75
2618 245 y(and)i(up-to-date)g(who-calls)f(database)h(for)f(the)i(second)g
2619 (compilation.)137 295 y(This)i(same)f(who-calls)f(database)i(allo)o(ws)
2620 f(users)i(to)e(safely)h(rede\014ne)h(functions,)f(c)o(hanging)f(them)g
2621 (from)f(deter-)75 345 y(ministic)e(to)h(nondeterministic)g(and)g(vica)g
2622 (v)o(ersa.)20 b Fv(Screamer)15 b Fy(will)e(trac)o(k)i(all)e(suc)o(h)i
2623 (c)o(hanges)h(using)e(the)h(who-calls)75 394 y(database)i(and)f
2624 (recompile)g(the)h(necessary)i(functions)e(to)f(k)o(eep)h(the)h(co)q
2625 (de)f(optimal)d(and)i(correct)j(at)d(all)g(times.)25
2626 b(It)75 444 y(is)14 b(p)q(ossible)h(ho)o(w)o(ev)o(er,)g(for)f(there)i
2627 (to)f(b)q(e)g(bugs)g(in)f(the)h(who-calls)f(database)h(co)q(de)h(whic)o
2628 (h)e(migh)o(t)f(cause)i Fv(Screamer)75 494 y Fy(to)h(incorrectly)i
2629 (determine)e(whether)i(or)f(not)f(a)h(function)f(is)h(deterministic)f
2630 (and)g(th)o(us)h(generate)h(incorrect)g(or)f(in-)75 544
2631 y(e\016cien)o(t)h(co)q(de.)29 b(W)m(e)16 b(request)j(that)e(y)o(ou)g
2632 (inform)e(us)j(if)e(y)o(ou)h(disco)o(v)o(er)h(suc)o(h)f(a)g(bug)g(b)o
2633 (y)g(sending)h(a)f(bug)g(rep)q(ort)h(to)75 594 y Fq(Bug-Screamer@AI.M)o
2634 (IT.ED)o(U)13 b Fy(including)i(as)h(m)o(uc)o(h)f(information)e(as)j(p)q
2635 (ossible)h(to)f(allo)o(w)e(us)i(to)g(rep)q(eat)i(that)e(bug.)75
2636 643 y(Nonetheless,)h(ev)o(en)f(if)e(y)o(ou)h(are)h(bitten)g(b)o(y)f(a)g
2637 (bug)g(in)g(the)h(who-calls)e(database)i(managemen)o(t)d(co)q(de,)j(it)
2638 f(is)g(usually)75 693 y(p)q(ossible)g(for)f(y)o(ou)h(to)f(reco)o(v)o
2639 (er)i(and)e(still)g(compile)f(and)i(run)g(y)o(our)f(program.)19
2640 b(W)m(e)c(pro)o(vide)f(t)o(w)o(o)g(functions)h(to)g(allo)o(w)75
2641 743 y(y)o(ou)d(to)g(man)o(ually)e(remo)o(v)o(e)h(en)o(tries)j(from)c
2642 (the)j Fv(Screamer)g Fy(who-calls)f(database.)18 b(The)13
2643 b(\014rst,)g Fq(purge)p Fy(,)e(allo)o(ws)g(y)o(ou)h(to)75
2644 793 y(remo)o(v)o(e)h(individual)e(en)o(tries.)19 b(This)14
2645 b(function)f(w)o(ould)f(t)o(ypically)h(b)q(e)h(used)g(if)f(y)o(ou)g
2646 (encoun)o(ter)i(problems)d(compiling)f(a)75 843 y(function)h
2647 Fp(f)t Fy(.)18 b(In)12 b(this)g(case,)g(y)o(ou)g(should)f(purge)i
2648 Fp(f)j Fy(along)11 b(with)h(all)e(functions)i(called)g(b)o(y)g
2649 Fp(f)k Fy(and)c(then)h(recompile)d(eac)o(h)75 892 y(of)h(the)i
2650 (functions)f(just)g(purged.)18 b(The)12 b(second,)h Fq
2651 (unwedge-screamer)p Fy(,)c(is)i(for)h(more)f(catastrophic)h
2652 (situations.)17 b(It)12 b(will)75 942 y(purge)i(all)f(user)i(de\014ned)
2653 g(functions.)j(Y)m(ou)13 b(will)g(then)h(need)h(to)f(recompile)f(and)h
2654 (reload)f(all)g(user)i(de\014ned)g(functions.)137 992
2655 y(There)d(is)e(one)h(curren)o(tly)g(kno)o(wn)g(bug)f(in)g(the)h
2656 (who-calls)f(database)h(co)q(de.)17 b(It)11 b(arises)g(when)g(a)f
2657 (function)h(calls)f(itself,)75 1042 y(either)k(directly)f(or)g
2658 (indirectly)m(,)f(through)h(a)f(c)o(hain)h(of)f(other)i(functions)f
2659 (\(i.e.)f Fp(f)18 b Fy(calls)12 b Fp(g)i Fy(whic)o(h)f(in)f(turn)i
2660 (calls)e Fp(h)h Fy(whic)o(h)75 1092 y(in)h(turn)i(calls)e
2661 Fp(f)t Fy(\).)21 b(If)15 b(an)o(y)f(function)g(in)h(the)g(call)f(cycle)
2662 h(is)g(nondeterministic)f(than)h(the)g(all)f(functions)h(in)f(the)h
2663 (cycle)75 1142 y(will)f(b)q(e)j(nondeterministic.)23
2664 b Fv(Screamer)17 b Fy(has)f(no)f(problem)g(detecting)i(that)f(this)g
2665 (is)f(the)i(case.)25 b(If)15 b(ho)o(w)o(ev)o(er,)h(eac)o(h)75
2666 1191 y(of)f(the)g(functions)h(in)e(the)i(cycle)g(are)f(rede\014ned)i
2667 (so)f(that)f(they)g(are)h(deterministic,)f(the)g(en)o(tire)h(cycle)g
2668 (can)f(b)q(e)h(made)75 1241 y(deterministic.)g Fv(Screamer)11
2669 b Fy(will)e(not)h(detect)i(this)f(and)f(will)f(still)g(think)h(that)h
2670 (the)g(en)o(tire)g(cycle)g(is)f(nondeterministic.)75
2671 1291 y(Un)o(til)15 b(this)h(bug)g(is)f(\014xed,)i(y)o(ou)e(can)h(man)o
2672 (ually)d(reco)o(v)o(er)k(from)d(suc)o(h)j(a)f(situation)f(b)o(y)h
2673 (simply)d(purging)j(eac)o(h)g(of)f(the)75 1341 y(functions)c(in)f(the)i
2674 (call)e(cycle)h(and)g(then)g(recompiling)e(them.)16 b(Remem)o(b)q(er)9
2675 b(to)i(\014rst)g(purge)h Fu(al)r(l)e Fy(of)g(the)h(functions)g(b)q
2676 (efore)75 1391 y(recompiling)h Fu(any)i Fy(of)g(them)f(or)h
2677 Fv(Screamer)g Fy(will)e(still)h(insist)h(that)g(the)h(en)o(tire)f(call)
2678 f(cycle)i(is)f(nondeterministic.)75 1527 y Fw(11)69 b(Man)n(ual)24
2679 b(En)n(tries)75 1768 y Fq(nondeterministic-)o(funct)o(ion?)18
2680 b Fu(x)824 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p
2681 Fy(])75 1915 y(Returns)d Fq(t)f Fy(if)f Fp(x)h Fy(is)g(a)f
2682 (nondeterministic)h(function)g(ob)r(ject)g(and)g Fq(nil)g
2683 Fy(otherwise.)17 b(Nondeterministic)10 b(function)g(ob)r(jects)75
2684 1965 y(can)g(b)q(e)f(pro)q(duced)i(in)e(t)o(w)o(o)g(w)o(a)o(ys.)16
2685 b(First,)10 b(the)g(sp)q(ecial)f(form)f Fq(\(function)20
2686 b(foo\))8 b Fy(\(i.e.)16 b Fq(#'foo)p Fy(\))9 b(will)e
2687 (\(deterministically\))75 2015 y(ev)n(aluate)20 b(to)f(a)h
2688 (nondeterministic)f(function)h(ob)r(ject)g(if)f Fq(foo)h
2689 Fy(names)f(a)g(nondeterministic)h(function)f(de\014ned)i(b)o(y)75
2690 2065 y Fq(defun)p Fy(.)37 b(Second,)23 b(the)e(sp)q(ecial)g(form)e
2691 Fq(\(function)h(\(lambda)g(\()p Fp(:)7 b(:)g(:)o Fq(\))21
2692 b Fp(:)7 b(:)g(:)o Fq(\)\))20 b Fy(\(i.e.)38 b Fq(#'\(lambda)20
2693 b(\()p Fp(:)7 b(:)g(:)n Fq(\))21 b Fp(:)7 b(:)g(:)o Fq(\))p
2694 Fy(\))20 b(will)75 2115 y(\(deterministically\))13 b(ev)n(aluate)h(to)h
2695 (a)f(nondeterministic)g(function)g(ob)r(ject)h(if)f(the)h(b)q(o)q(dy)g
2696 (of)e(the)j(lam)o(b)q(da)c(expression)75 2164 y(con)o(tains)i(a)f
2697 (nondeterministic)h(expression.)75 2402 y Fq(either)21
2698 b Fr(f)p Fu(expr)n(ession)p Fr(g)455 2387 y Fi(\003)1366
2699 2402 y Fy([)p Fu(Nondeterministic)14 b(Sp)n(e)n(cial)h(F)m(orm)p
2700 Fy(])75 2549 y(Nondeterministically)d(ev)n(aluates)i(and)g(returns)i
2701 (the)f(v)n(alue)e(of)h(one)g(of)f(its)i Fu(expr)n(essions)p
2702 Fy(.)j(It)d(sets)g(up)f(a)g(c)o(hoice)g(p)q(oin)o(t)75
2703 2599 y(and)i(ev)n(aluates)h(the)f(\014rst)i Fu(expr)n(ession)e
2704 Fy(returning)h(its)f(result.)26 b(Whenev)o(er)18 b(bac)o(ktrac)o(king)e
2705 (pro)q(ceeds)i(to)e(this)g(c)o(hoice)992 2723 y(10)p
2706 eop
2707 %%Page: 11 11
2708 11 10 bop 75 195 a Fy(p)q(oin)o(t,)14 b(the)i(next)f
2709 Fu(expr)n(ession)g Fy(is)g(ev)n(aluated)g(and)g(its)g(result)g
2710 (returned.)23 b(When)15 b(no)g(more)f Fu(expr)n(essions)h
2711 Fy(remain,)e(the)75 245 y(curren)o(t)i(c)o(hoice)f(p)q(oin)o(t)e(is)h
2712 (remo)o(v)o(ed)g(and)g(bac)o(ktrac)o(king)g(con)o(tin)o(ues)h(to)f(the)
2713 h(next)f(most)f(recen)o(t)j(c)o(hoice)f(p)q(oin)o(t.)j(As)d(an)75
2714 295 y(optimization,)g(the)j(c)o(hoice)h(p)q(oin)o(t)e(created)i(for)e
2715 (this)h(expression)h(is)e(remo)o(v)o(ed)g(b)q(efore)h(the)h(ev)n
2716 (aluation)d(of)h(the)h(last)75 345 y Fu(expr)n(ession)12
2717 b Fy(so)f(that)h(a)f(failure)f(during)i(the)g(ev)n(aluation)e(of)g(the)
2718 i(last)g Fu(expr)n(ession)f Fy(will)f(bac)o(ktrac)o(k)i(directly)g(to)f
2719 (the)h(par-)75 394 y(en)o(t)h(c)o(hoice)g(p)q(oin)o(t)f(of)g(the)h
2720 Fq(either)f Fy(expression.)19 b Fq(Either)11 b Fy(tak)o(es)i(an)o(y)f
2721 (n)o(um)o(b)q(er)g(of)g(argumen)o(ts.)17 b(With)12 b(no)g(argumen)o
2722 (ts,)75 444 y Fq(\(either\))e Fy(is)h(equiv)n(alen)o(t)g(to)g
2723 Fq(\(fail\))f Fy(and)h(is)g(th)o(us)h(deterministic.)17
2724 b(With)10 b(one)i(argumen)o(t,)e Fq(\(either)21 b Fu(expr)n(ession)p
2725 Fq(\))11 b Fy(is)75 494 y(equiv)n(alen)o(t)h(to)h Fu(expr)n(ession)g
2726 Fy(itself)f(and)h(is)g(th)o(us)g(deterministic)f(only)g(when)i
2727 Fu(expr)n(ession)f Fy(is)f(deterministic.)18 b Fq(Either)11
2728 b Fy(is)75 544 y(a)i(sp)q(ecial)h(form,)d(not)j(a)f(function.)18
2729 b(It)13 b(is)h(an)f(error)i(for)e(the)h(expression)h
2730 Fq(#'either)d Fy(to)h(app)q(ear)h(in)f(a)g(program.)k(Th)o(us)75
2731 594 y Fq(\(funcall)j(#'either)g Fp(:)7 b(:)g(:)o Fq(\))18
2732 b Fy(or)g Fq(\(apply)j(#'either)f Fp(:)7 b(:)g(:)n Fq(\))19
2733 b Fy(are)f(in)g(error)i(and)e(will)f(yield)h(unpredictable)h(results.)
2734 75 643 y(With)c(t)o(w)o(o)f(or)h(more)g(argumen)o(t)f(it)g(is)h
2735 (nondeterministic)g(and)g(can)g(only)g(app)q(ear)h(in)e(a)h
2736 (nondeterministic)g(con)o(text.)75 693 y(See)g(section)f(2)g(for)g(a)f
2737 (discussion)i(of)e(the)h(con)o(texts)h(in)f(whic)o(h)f
2738 Fq(either)g Fy(ma)o(y)f(app)q(ear.)75 931 y Fq(fail)1343
2739 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
2740 1079 y(Bac)o(ktrac)o(ks)22 b(to)f(the)g(most)f(recen)o(t)i(c)o(hoice)f
2741 (p)q(oin)o(t.)39 b(Equiv)n(alen)o(t)20 b(to)g Fq(\(either\))p
2742 Fy(.)37 b(Note)22 b(that)f Fq(fail)f Fy(is)g(a)h(deter-)75
2743 1129 y(ministic)f(function)h(and)g(th)o(us)h(it)f(is)g(p)q(ermissible)g
2744 (to)g(reference)j Fq(#'fail)c Fy(and)h(write)h Fq(\(funcall)e(#'fail\))
2745 g Fy(and)75 1179 y Fq(\(apply)h(#'fail)f(nil\))p Fy(.)31
2746 b(In)19 b(nondeterministic)f(con)o(texts,)i(the)f(expression)h
2747 Fq(\(fail\))d Fy(is)h(optimized)f(to)i(generate)75 1229
2748 y(inline)13 b(bac)o(ktrac)o(king)h(co)q(de.)75 1467 y
2749 Fq(local)21 b Fr(f)p Fu(expr)n(ession)p Fr(g)433 1452
2750 y Fi(\003)1813 1467 y Fy([)p Fu(Macr)n(o)p Fy(])75 1615
2751 y(Ev)n(aluates)14 b Fu(expr)n(essions)h Fy(in)f(the)h(same)f(fashion)g
2752 (as)g Fq(progn)g Fy(except)i(that)e(all)g Fq(setf)f Fy(and)i
2753 Fq(setq)f Fy(expressions)i Fu(lexic)n(al)r(ly)75 1665
2754 y(neste)n(d)e Fy(in)e(its)h(b)q(o)q(dy)h(result)g(in)e
2755 Fu(lo)n(c)n(al)h Fy(side)g(e\013ects)j(whic)o(h)d(are)g(undone)h(up)q
2756 (on)f(bac)o(ktrac)o(king.)18 b(Note)13 b(that)g(this)h(a\013ects)75
2757 1714 y(only)c(side)h(e\013ects)h(in)o(tro)q(duced)f(explicitly)f(via)f
2758 Fq(setf)h Fy(and)g Fq(setq)p Fy(.)16 b(Side)11 b(e\013ects)h(in)o(tro)q
2759 (duced)g(b)o(y)e Fv(Common)16 b(Lisp)11 b Fy(built-)75
2760 1764 y(in)g(functions)h(suc)o(h)g(as)g Fq(rplaca)e Fy(are)i(alw)o(a)o
2761 (ys)f(global.)k(F)m(urthermore,)d(it)f(a\013ects)i(only)e(o)q
2762 (ccurrences)k(of)c Fq(setf)f Fy(and)i Fq(setq)75 1814
2763 y Fy(whic)o(h)k(app)q(ear)h(textually)e(nested)j(in)d(the)i(b)q(o)q(dy)
2764 f(of)g(the)h Fq(local)e Fy(expression|not)h(those)h(app)q(earing)f(in)g
2765 (functions)75 1864 y(called)g(from)f(the)j(b)q(o)q(dy)m(.)25
2766 b Fq(Local)16 b Fy(and)g Fq(global)g Fy(expressions)i(ma)o(y)d(b)q(e)i
2767 (nested)h(inside)f(one)g(another.)26 b(The)18 b(nearest)75
2768 1914 y(surrounding)g(declaration)g(determines)g(whether)i(or)e(not)g(a)
2769 g(giv)o(en)f Fq(setf)g Fy(or)i Fq(setq)e Fy(results)i(in)f(a)f(lo)q
2770 (cal)h(or)g(global)75 1963 y(side)d(e\013ect.)23 b(Side)15
2771 b(e\013ects)j(default)c(to)h(b)q(e)h(global)d(when)i(there)i(is)e(no)f
2772 (surrounding)i Fq(local)e Fy(or)h Fq(global)e Fy(expression.)75
2773 2013 y(Lo)q(cal)g(side)g(e\013ects)i(can)e(app)q(ear)g(b)q(oth)g(in)g
2774 (deterministic)f(as)i(w)o(ell)e(as)h(nondeterministic)f(con)o(texts)i
2775 (though)f(di\013eren)o(t)75 2063 y(tec)o(hniques)19 b(are)f(used)h(to)f
2776 (implemen)o(t)d(the)k(trailing)d(of)h(prior)h(v)n(alues)g(for)f
2777 (restoration)h(up)q(on)g(bac)o(ktrac)o(king.)30 b(See)75
2778 2113 y(sections)20 b(14,)d(3)h(and)h(4)f(for)g(details.)32
2779 b(In)18 b(nondeterministic)g(con)o(texts,)i Fq(local)e
2780 Fy(as)g(w)o(ell)g(as)h Fq(setf)e Fy(are)i(treated)h(as)75
2781 2163 y(sp)q(ecial)14 b(forms)f(rather)h(than)g(macros.)j(This)d(should)
2782 g(b)q(e)g(completely)f(transparen)o(t)i(to)f(the)g(user.)75
2783 2401 y Fq(global)21 b Fr(f)p Fu(expr)n(ession)p Fr(g)455
2784 2386 y Fi(\003)1813 2401 y Fy([)p Fu(Macr)n(o)p Fy(])75
2785 2549 y(Ev)n(aluates)14 b Fu(expr)n(essions)h Fy(in)f(the)h(same)f
2786 (fashion)g(as)g Fq(progn)g Fy(except)i(that)e(all)g Fq(setf)f
2787 Fy(and)i Fq(setq)f Fy(expressions)i Fu(lexic)n(al)r(ly)75
2788 2599 y(neste)n(d)f Fy(in)g(its)g(b)q(o)q(dy)g(result)h(in)f
2789 Fu(glob)n(al)g Fy(side)g(e\013ects)i(whic)o(h)e(are)h
2790 Fu(not)f Fy(undone)h(up)q(on)f(bac)o(ktrac)o(king.)21
2791 b(Note)16 b(that)f(this)992 2723 y(11)p eop
2792 %%Page: 12 12
2793 12 11 bop 75 195 a Fy(a\013ects)11 b(only)d(side)i(e\013ects)h(in)o
2794 (tro)q(duced)f(explicitly)f(via)f Fq(setf)h Fy(and)g
2795 Fq(setq)p Fy(.)15 b(Side)10 b(e\013ects)h(in)o(tro)q(duced)f(b)o(y)f
2796 Fv(Common)17 b(Lisp)75 245 y Fy(built-in)c(functions)h(suc)o(h)h(as)f
2797 Fq(rplaca)f Fy(are)h(alw)o(a)o(ys)g(global)e(an)o(yw)o(a)o(y)m(.)17
2798 b(F)m(urthermore,)d(it)g(a\013ects)h(only)e(o)q(ccurrences)18
2799 b(of)75 295 y Fq(setf)10 b Fy(and)h Fq(setq)f Fy(whic)o(h)g(app)q(ear)i
2800 (textually)e(nested)i(in)f(the)g(b)q(o)q(dy)g(of)f(the)i
2801 Fq(global)d Fy(expression|not)j(those)f(app)q(earing)75
2802 345 y(in)17 b(functions)g(called)g(from)f(the)i(b)q(o)q(dy)m(.)28
2803 b Fq(Local)16 b Fy(and)h Fq(global)f Fy(expressions)j(ma)o(y)c(b)q(e)j
2804 (nested)h(inside)e(one)h(another.)75 394 y(The)d(nearest)h(surrounding)
2805 f(declaration)f(determines)h(whether)h(or)f(not)f(a)g(giv)o(en)h
2806 Fq(setf)e Fy(or)i Fq(setq)f Fy(results)h(in)g(a)f(lo)q(cal)75
2807 444 y(or)j(global)e(side)j(e\013ect.)29 b(Side)17 b(e\013ects)i
2808 (default)d(to)h(b)q(e)h(global)d(when)i(there)i(is)e(no)f(surrounding)h
2809 Fq(local)f Fy(or)h Fq(global)75 494 y Fy(expression.)28
2810 b(Global)15 b(side)i(e\013ects)h(can)f(app)q(ear)g(b)q(oth)g(in)f
2811 (deterministic)h(as)f(w)o(ell)g(as)h(nondeterministic)f(con)o(texts.)75
2812 544 y(See)d(sections)g(3)f(and)g(4)g(for)g(further)g(details.)18
2813 b(In)12 b(nondeterministic)f(con)o(texts,)i Fq(global)e
2814 Fy(as)h(w)o(ell)g(as)g Fq(setf)f Fy(are)i(treated)75
2815 594 y(as)h(sp)q(ecial)g(forms)f(rather)h(than)g(macros.)j(This)d
2816 (should)g(b)q(e)g(completely)f(transparen)o(t)i(to)f(the)g(user.)75
2817 831 y Fq(map-values)20 b Fu(function)i(expr)n(ession)882
2818 b Fy([)p Fu(Deterministic)13 b(Macr)n(o)p Fy(])75 979
2819 y Fu(F)m(unction)i Fy(m)o(ust)e(b)q(e)i(a)f(deterministic)g(function)g
2820 (ob)r(ject)h(whic)o(h)f(tak)o(es)h(one)f(argumen)o(t.)k(This)c
2821 (function)g(is)g(called)g(on)75 1029 y(eac)o(h)d(v)n(alue)e(returned)j
2822 (b)o(y)e(ev)n(aluating)f Fu(expr)n(ession)p Fy(,)h(bac)o(ktrac)o(king)g
2823 (after)g(calling)f Fu(function)i Fy(on)f(eac)o(h)g(v)n(alue)g(to)g(pro)
2824 q(duce)75 1079 y(another)k(v)n(alue)e(of)h Fu(expr)n(ession)g
2825 Fy(un)o(til)f(ev)n(aluating)g Fu(expr)n(ession)h Fy(fails)f(and)h(pro)q
2826 (duces)i(no)e(further)h(v)n(alues.)j(The)d(results)75
2827 1129 y(returned)h(b)o(y)e(calling)f Fu(function)i Fy(on)g(eac)o(h)g(v)n
2828 (alue)e(are)i(discarded.)19 b(Lo)q(cal)13 b(side)h(e\013ects)h(p)q
2829 (erformed)f(b)o(y)f Fu(expr)n(ession)h Fy(are)75 1178
2830 y(a)o(v)n(ailable)9 b(during)h(the)i(corresp)q(onding)g(call)e(to)h
2831 Fu(function)g Fy(but)g(are)g(undone)h(when)f(that)g(call)f(returns.)19
2832 b(Lik)o(ewise,)11 b(lo)q(cal)75 1228 y(side)h(e\013ects)h(p)q(erformed)
2833 f(b)o(y)f Fu(function)h Fy(are)g(undone)g(when)g(it)f(returns.)18
2834 b(Th)o(us)12 b(b)o(y)f(the)i(time)d Fq(map-values)f Fy(returns,)k(all)
2835 75 1278 y(lo)q(cal)f(side)h(e\013ects)i(p)q(erformed)e(either)h(b)o(y)e
2836 Fu(expr)n(ession)i Fy(or)e Fu(function)i Fy(are)f(undone.)18
2837 b(A)13 b Fq(map-values)e Fy(expression)j(itself)75 1328
2838 y(is)g(alw)o(a)o(ys)f(deterministic)g(and)h(alw)o(a)o(ys)f(returns)i
2839 Fq(nil)p Fy(.)j(In)c(nondeterministic)f(con)o(texts,)i
2840 Fq(map-values)d Fy(is)i(treated)h(as)75 1378 y(a)f(sp)q(ecial)g(form)e
2841 (rather)j(than)e(a)h(macro.)j(This)d(should)f(b)q(e)i(completely)e
2842 (transparen)o(t)i(to)e(the)i(user.)75 1615 y Fq(one-value)20
2843 b Fu(expr)n(ession)i Fy([)p Fu(default-expr)n(ession)p
2844 Fy(])968 b([)p Fu(Macr)n(o)p Fy(])75 1763 y(Returns)17
2845 b(the)f(\014rst)h(v)n(alue)e(of)g(a)h(nondeterministic)f(expression.)25
2846 b Fu(Expr)n(ession)16 b Fy(is)g(ev)n(aluated,)f(deterministically)f
2847 (re-)75 1813 y(turning)d(only)g(its)g(\014rst)h(nondeterministic)f(v)n
2848 (alue,)g(if)f(an)o(y)m(.)17 b(No)11 b(further)h(execution)g(of)f
2849 Fu(expr)n(ession)g Fy(is)h(attempted)f(after)75 1863
2850 y(it)i(successfully)i(returns)g(one)f(v)n(alue.)k(If)13
2851 b Fu(expr)n(ession)h Fy(do)q(es)g(not)g(return)h(an)o(y)e
2852 (nondeterministic)g(v)n(alues)g(\(i.e.)18 b(it)13 b(fails\))75
2853 1913 y(then)e Fu(default-expr)n(ession)g Fy(is)f(ev)n(aluated)g(and)h
2854 (its)f(v)n(alue)g(returned)i(instead.)18 b Fu(Default-expr)n(ession)10
2855 b Fy(defaults)h(to)f Fq(\(fail\))75 1962 y Fy(if)j(not)i(presen)o(t.)20
2856 b(Lo)q(cal)14 b(side)g(e\013ects)j(p)q(erformed)d(b)o(y)g
2857 Fu(expr)n(ession)g Fy(are)h(undone)f(when)h Fq(one-value)d
2858 Fy(returns.)21 b(On)14 b(the)75 2012 y(other)h(hand,)f(lo)q(cal)f(side)
2859 i(e\013ects)h(p)q(erformed)e(b)o(y)g Fu(default-expr)n(ession)g
2860 Fy(are)h(not)f(undone)h(when)g Fq(one-value)d Fy(returns.)75
2861 2062 y(A)k Fq(one-value)e Fy(expression)i(can)g(app)q(ear)g(in)g(b)q
2862 (oth)f(deterministic)h(and)f(nondeterministic)g(con)o(texts.)25
2863 b(Irresp)q(ectiv)o(e)75 2112 y(of)16 b(what)g(con)o(text)g(the)h
2864 Fq(one-value)d Fy(expression)k(app)q(ears)f(in,)e Fu(expr)n(ession)i
2865 Fy(is)f(alw)o(a)o(ys)f(in)h(a)f(nondeterministic)h(con-)75
2866 2162 y(text,)g(while)f Fu(default-expr)n(ession)h Fy(is)g(in)f(whatev)o
2867 (er)h(con)o(text)h(the)f Fq(one-value)e Fy(expression)j(app)q(ears.)24
2868 b(A)16 b Fq(one-value)75 2211 y Fy(expression)j(is)f(nondeterministic)g
2869 (if)g Fu(default-expr)n(ession)g Fy(is)g(presen)o(t)i(and)e(is)g
2870 (nondeterministic,)g(otherwise)h(it)f(is)75 2261 y(deterministic.)29
2871 b(If)17 b Fu(default-expr)n(ession)h Fy(is)f(presen)o(t)i(and)f
2872 (nondeterministic,)f(and)h(if)f Fu(expr)n(ession)h Fy(fails,)f(then)h
2873 (it)f(is)75 2311 y(p)q(ossible)e(to)g(bac)o(ktrac)o(k)h(in)o(to)e(the)i
2874 Fu(default-expr)n(ession)f Fy(and)g(for)f(the)i Fq(one-value)d
2875 Fy(expression)j(to)f(nondeterministi-)75 2361 y(cally)e(return)i(m)o
2876 (ultiple)d(times.)17 b Fq(One-value)12 b Fy(is)h(analogous)g(to)h(the)g
2877 (cut)h(primitiv)o(e)d(\()p Fq(!)p Fy(\))18 b(in)13 b
2878 Fv(Pr)o(olog)q Fy(.)75 2599 y Fq(all-values)20 b Fr(f)p
2879 Fu(expr)n(ession)p Fr(g)542 2584 y Fi(\003)1552 2599
2880 y Fy([)p Fu(Deterministic)13 b(Macr)n(o)p Fy(])992 2723
2881 y(12)p eop
2882 %%Page: 13 13
2883 13 12 bop 75 195 a Fy(Ev)n(aluates)16 b Fu(expr)n(essions)g
2884 Fy(\(wrapp)q(ed)h(in)f(an)g(implicit)d Fq(progn)p Fy(\))i(and)h
2885 (returns)i(a)d(list)h(of)g(all)e(of)i(the)h(nondeterministic)75
2886 245 y(v)n(alues)f(returned)j(b)o(y)d(the)h(last)f Fu(expr)n(ession)p
2887 Fy(.)27 b(These)17 b(v)n(alues)g(are)g(pro)q(duced)h(b)o(y)e(rep)q
2888 (eatedly)i(ev)n(aluating)d(the)i(b)q(o)q(dy)75 295 y(and)e(bac)o(ktrac)
2889 o(king)f(to)h(pro)q(duce)h(the)g(next)f(v)n(alue,)g(un)o(til)f(the)h(b)
2890 q(o)q(dy)g(fails)f(and)h(yields)g(no)f(further)i(v)n(alues.)21
2891 b(Accord-)75 345 y(ingly)m(,)11 b(lo)q(cal)g(side)i(e\013ects)i(p)q
2892 (erformed)d(b)o(y)g(the)i(b)q(o)q(dy)e(while)g(pro)q(ducing)h(eac)o(h)g
2893 (v)n(alue)f(are)h(undone)g(b)q(efore)g(attempting)75
2894 394 y(to)k(pro)q(duce)h(subsequen)o(t)h(v)n(alues,)e(and)g(all)f(lo)q
2895 (cal)g(side)i(e\013ects)h(p)q(erformed)e(b)o(y)g(the)h(b)q(o)q(dy)f
2896 (are)g(undone)h(up)q(on)f(exit)75 444 y(from)g Fq(all-values)p
2897 Fy(.)31 b(Returns)20 b(the)g(list)e(con)o(taining)g Fq(nil)h
2898 Fy(if)f(there)i(are)f(no)g Fu(expr)n(essions)p Fy(.)34
2899 b(An)19 b Fq(all-values)e Fy(ex-)75 494 y(pression)f(can)g(app)q(ear)f
2900 (in)g(b)q(oth)h(deterministic)f(and)g(nondeterministic)f(con)o(texts.)
2901 24 b(Irresp)q(ectiv)o(e)17 b(of)e(what)g(con)o(text)75
2902 544 y(the)j Fq(all-values)d Fy(expression)j(app)q(ears)g(in,)g(the)f
2903 Fu(expr)n(essions)h Fy(are)f(alw)o(a)o(ys)g(in)f(a)h(nondeterministic)g
2904 (con)o(text.)29 b(An)75 594 y Fq(all-values)14 b Fy(expression)j
2905 (itself)e(is)h(alw)o(a)o(ys)f(deterministic.)24 b Fq(All-values)14
2906 b Fy(is)h(analogous)g(to)h(the)g Fq(bagof)f Fy(primitiv)o(e)75
2907 643 y(in)e Fv(Pr)o(olog)q Fy(.)75 885 y Fq(ith-value)20
2908 b Fp(i)i Fu(expr)n(ession)g Fy([)p Fu(default-expr)n(ession)p
2909 Fy(])932 b([)p Fu(Macr)n(o)p Fy(])75 1041 y(Returns)12
2910 b(the)g Fp(i)313 1026 y Fo(th)359 1041 y Fy(v)n(alue)e(of)h(a)g
2911 (nondeterministic)g(expression.)19 b Fu(Expr)n(ession)12
2912 b Fy(is)f(ev)n(aluated,)g(deterministically)f(return-)75
2913 1090 y(ing)15 b(only)h(its)g Fp(i)314 1075 y Fo(th)363
2914 1090 y Fy(nondeterministic)g(v)n(alue,)g(if)f(an)o(y)m(.)23
2915 b Fp(I)d Fy(m)o(ust)15 b(b)q(e)i(an)f(in)o(teger.)25
2916 b(The)16 b(\014rst)h(nondeterministic)f(v)n(alue)75 1140
2917 y(returned)g(b)o(y)f Fu(expr)n(ession)g Fy(is)g(n)o(um)o(b)q(ered)f
2918 Fu(zer)n(o)p Fy(,)g(the)h(second)h Fu(one)p Fy(,)f(etc.)22
2919 b(The)15 b Fp(i)1321 1125 y Fo(th)1370 1140 y Fy(v)n(alue)f(is)g(pro)q
2920 (duced)i(b)o(y)f(rep)q(eatedly)75 1190 y(ev)n(aluating)g
2921 Fu(expr)n(ession)p Fy(,)i(bac)o(ktrac)o(king)f(through)g(and)g
2922 (discarding)h(the)g(\014rst)g Fp(i)f Fy(v)n(alues)h(and)f
2923 (deterministically)e(re-)75 1240 y(turning)i(the)g(next)g(v)n(alue)f
2924 (pro)q(duced.)25 b(No)16 b(further)h(execution)f(of)f
2925 Fu(expr)n(ession)h Fy(is)g(attempted)f(after)h(it)g(successfully)75
2926 1290 y(returns)g(the)g(desired)f(v)n(alue.)20 b(If)14
2927 b Fu(expr)n(ession)h Fy(fails)f(b)q(efore)h(returning)g(b)q(oth)g(the)g
2928 Fp(i)g Fy(v)n(alues)g(to)f(b)q(e)i(discarded,)f(as)g(w)o(ell)75
2929 1339 y(as)i(the)h(desired)h Fp(i)363 1324 y Fo(th)413
2930 1339 y Fy(v)n(alue,)e(then)h Fu(default-expr)n(ession)g
2931 Fy(is)f(ev)n(aluated)g(and)g(its)g(v)n(alue)g(returned)i(instead.)28
2932 b Fu(Default-)75 1389 y(expr)n(ession)19 b Fy(defaults)f(to)h
2933 Fq(\(fail\))e Fy(if)h(not)g(presen)o(t.)34 b(Lo)q(cal)18
2934 b(side)h(e\013ects)h(p)q(erformed)f(b)o(y)f Fu(expr)n(ession)h
2935 Fy(are)g(undone)75 1439 y(when)13 b Fq(ith-value)e Fy(returns.)19
2936 b(On)13 b(the)g(other)g(hand,)f(lo)q(cal)g(side)h(e\013ects)i(p)q
2937 (erformed)d(b)o(y)g Fu(default-expr)n(ession)h Fy(and)f(b)o(y)h
2938 Fp(i)75 1489 y Fy(are)k(not)f(undone)g(when)h Fq(ith-value)d
2939 Fy(returns.)27 b(An)16 b Fq(ith-value)f Fy(expression)i(can)g(app)q
2940 (ear)f(in)g(b)q(oth)g(deterministic)75 1539 y(and)g(nondeterministic)f
2941 (con)o(texts.)24 b(Irresp)q(ectiv)o(e)19 b(of)c(what)g(con)o(text)i
2942 (the)f Fq(ith-value)e Fy(expression)j(app)q(ears)f(in,)g
2943 Fu(ex-)75 1589 y(pr)n(ession)e Fy(is)f(alw)o(a)o(ys)g(in)h(a)f
2944 (nondeterministic)h(con)o(text,)g(while)f Fu(default-expr)n(ession)h
2945 Fy(and)g Fp(i)g Fy(are)g(in)g(whatev)o(er)g(con)o(text)75
2946 1638 y(the)j Fq(ith-value)d Fy(expression)k(app)q(ears.)26
2947 b(An)16 b Fq(ith-value)e Fy(expression)k(is)e(nondeterministic)g(if)f
2948 Fu(default-expr)n(ession)75 1688 y Fy(is)g(presen)o(t)i(and)e(is)g
2949 (nondeterministic,)f(or)h(if)g Fp(i)g Fy(is)g(nondeterministic.)22
2950 b(Otherwise)16 b(it)f(is)g(deterministic.)21 b(If)15
2951 b Fu(default-)75 1738 y(expr)n(ession)c Fy(is)f(presen)o(t)j(and)d
2952 (nondeterministic,)g(and)h(if)f Fu(expr)n(ession)g Fy(fails,)g(then)h
2953 (it)g(is)f(p)q(ossible)h(to)f(bac)o(ktrac)o(k)h(in)o(to)f(the)75
2954 1788 y Fq(default-expressio)o(n)i Fy(and)j(for)g(the)h
2955 Fq(ith-value)d Fy(expression)j(to)f(nondeterministically)e(return)k(m)o
2956 (ultiple)12 b(times.)75 1838 y(If)h Fp(i)h Fy(is)f(nondeterministic)g
2957 (then)h(the)g Fq(ith-value)d Fy(expression)k(op)q(erates)f
2958 (nondeterministically)e(on)h(eac)o(h)h(v)n(alue)e(of)h
2959 Fp(i)p Fy(.)75 1887 y(In)h(this)g(case,)g(bac)o(ktrac)o(king)f(for)h
2960 (eac)o(h)g(v)n(alue)f(of)g Fu(expr)n(ession)h Fy(and)g
2961 Fu(default-expr)n(ession)g Fy(is)f(nested)j(in,)d(and)g(restarted)75
2962 1937 y(for,)g(eac)o(h)h(bac)o(ktrac)o(k)h(of)e Fp(i)p
2963 Fy(.)75 2179 y Fq(print-values)19 b Fr(f)p Fu(expr)n(ession)p
2964 Fr(g)585 2163 y Fi(\003)1552 2179 y Fy([)p Fu(Deterministic)13
2965 b(Macr)n(o)p Fy(])75 2330 y(Ev)n(aluates)18 b Fu(expr)n(essions)f
2966 Fy(\(wrapp)q(ed)i(in)e(an)h(implicit)d Fq(progn)p Fy(\))h(and)i(prin)o
2967 (ts)g(eac)o(h)g(of)f(the)h(nondeterministic)f(v)n(alues)75
2968 2380 y(returned)11 b(b)o(y)f(the)g(last)g Fu(expr)n(ession)g
2969 Fy(in)f(succession)j(\(using)e Fq(print)p Fy(\).)15 b(After)c(eac)o(h)f
2970 (v)n(alue)f(is)h(prin)o(ted,)g(the)h(user)g(is)e(queried)75
2971 2430 y(as)k(to)g(whether)i(or)e(not)g(further)g(v)n(alues)g(are)h
2972 (desired.)19 b(These)14 b(v)n(alues)f(are)g(pro)q(duced)i(b)o(y)d(rep)q
2973 (eatedly)j(ev)n(aluating)c(the)75 2479 y(b)q(o)q(dy)j(and)g(bac)o
2974 (ktrac)o(king)g(to)h(pro)q(duce)g(the)g(next)g(v)n(alue,)e(un)o(til)h
2975 (either)h(the)g(user)g(indicates)g(that)f(no)g(further)h(v)n(alues)75
2976 2529 y(are)e(desired)i(or)e(un)o(til)f(the)i(b)q(o)q(dy)f(fails)e(and)i
2977 (yields)g(no)g(further)h(v)n(alues.)j(Accordingly)m(,)c(lo)q(cal)f
2978 (side)h(e\013ects)i(p)q(erformed)75 2579 y(b)o(y)k(the)g(b)q(o)q(dy)g
2979 (while)g(pro)q(ducing)g(eac)o(h)h(v)n(alue)e(are)h(undone)h(after)f
2980 (prin)o(ting)f(eac)o(h)i(v)n(alue,)f(b)q(efore)h(attempting)d(to)992
2981 2723 y(13)p eop
2982 %%Page: 14 14
2983 14 13 bop 75 195 a Fy(pro)q(duce)22 b(subsequen)o(t)g(v)n(alues,)g(and)
2984 e(all)g(lo)q(cal)g(side)h(e\013ects)h(p)q(erformed)f(b)o(y)f(the)h(b)q
2985 (o)q(dy)g(are)g(undone)g(up)q(on)g(exit)75 245 y(from)13
2986 b Fq(print-values)p Fy(,)e(either)16 b(b)q(ecause)g(there)f(are)g(no)g
2987 (further)g(v)n(alues)f(or)g(b)q(ecause)j(the)e(user)g(declines)g(to)g
2988 (pro)q(duce)75 295 y(further)21 b(v)n(alues.)37 b(A)20
2989 b Fq(print-values)e Fy(expression)j(can)g(app)q(ear)g(in)e(b)q(oth)i
2990 (deterministic)e(and)i(nondeterministic)75 345 y(con)o(texts.)34
2991 b(Irresp)q(ectiv)o(e)20 b(of)f(what)f(con)o(text)i(the)f
2992 Fq(print-values)d Fy(expression)k(app)q(ears)f(in,)g(the)h
2993 Fu(expr)n(essions)f Fy(are)75 394 y(alw)o(a)o(ys)f(in)g(a)g
2994 (nondeterministic)g(con)o(text.)34 b(A)18 b Fq(print-values)e
2995 Fy(expression)k(itself)f(is)f(alw)o(a)o(ys)g(deterministic)g(and)75
2996 444 y(alw)o(a)o(ys)13 b(returns)i Fq(nil)p Fy(.)j Fq(Print-values)11
2997 b Fy(is)j(analogous)e(to)i(the)h(standard)f(top-lev)o(el)f(user)i(in)o
2998 (terface)g(in)e Fv(Pr)o(olog)q Fy(.)75 681 y Fq(funcall-nondeterm)o
2999 (inist)o(ic)19 b Fu(function)j Fr(f)p Fu(ar)n(gument)p
3000 Fr(g)1000 666 y Fi(\003)1441 681 y Fy([)p Fu(Nondeterministic)14
3001 b(F)m(unction)p Fy(])75 827 y(Analogous)8 b(to)i(the)f
3002 Fv(Common)17 b(Lisp)9 b Fy(built-in)f(function)h Fq(funcall)f
3003 Fy(except)j(that)e(it)g(accepts)i(b)q(oth)e(ordinary)g
3004 Fv(Common)17 b(Lisp)75 877 y Fy(\(deterministic\))h(function)h(ob)r
3005 (jects)g(as)g(w)o(ell)f(as)g(nondeterministic)g(function)h(ob)r(jects)g
3006 (for)g Fu(function)p Fy(.)32 b(Y)m(ou)18 b(m)o(ust)75
3007 927 y(use)h Fq(funcall-nondetermi)o(nisti)o(c)d Fy(to)i(funcall)f(a)h
3008 (nondeterministic)g(function)g(ob)r(ject.)32 b(A)19 b(run)o(time)e
3009 (error)i(will)75 977 y(b)q(e)e(signalled)f(if)g(y)o(ou)h(attempt)f(to)h
3010 (funcall)f(a)g(nondeterministic)g(function)h(ob)r(ject)h(with)e
3011 Fq(funcall)p Fy(.)26 b(Y)m(ou)16 b(can)h(use)75 1027
3012 y Fq(funcall-nondeterm)o(inist)o(ic)8 b Fy(to)i(funcall)g(either)i(a)e
3013 (deterministic)g(or)h(nondeterministic)f(function)h(ob)r(ject)g(though)
3014 75 1076 y(ev)o(en)h(if)e(all)g(of)h(the)h(argumen)o(ts)e(to)h
3015 Fq(funcall-nondetermin)o(istic)c Fy(are)12 b(deterministic)f(and)g
3016 Fu(function)h Fy(is)f(a)g(determin-)75 1126 y(istic)j(function)g(ob)r
3017 (ject,)g(the)h(call)e(expression)j(will)c(still)h(b)q(e)i
3018 (nondeterministic)e(\(with)h(presumably)f(a)h(single)g(v)n(alue\),)75
3019 1176 y(since)g(it)e(is)h(imp)q(ossible)e(to)i(determine)g(at)f(compile)
3020 f(time)h(that)h(a)f(giv)o(en)h(call)f(to)h Fq(funcall-nondete)o(rmini)o
3021 (stic)c Fy(will)75 1226 y(b)q(e)15 b(passed)f(only)g(deterministic)f
3022 (function)h(ob)r(jects)h(for)e Fu(function)p Fy(.)75
3023 1462 y Fq(apply-nondetermin)o(istic)18 b Fu(function)23
3024 b Fr(f)p Fu(ar)n(gument)o Fr(g)956 1447 y Fo(+)1441 1462
3025 y Fy([)p Fu(Nondeterministic)14 b(F)m(unction)p Fy(])75
3026 1609 y(Analogous)8 b(to)i(the)f Fv(Common)17 b(Lisp)9
3027 b Fy(built-in)f(function)h Fq(apply)f Fy(except)j(that)e(it)g(accepts)i
3028 (b)q(oth)f(ordinary)e Fv(Common)17 b(Lisp)75 1659 y Fy
3029 (\(deterministic\))c(function)g(ob)r(jects)i(as)e(w)o(ell)g(as)g
3030 (nondeterministic)g(function)g(ob)r(jects)i(for)e Fu(function)p
3031 Fy(.)18 b(Y)m(ou)13 b(m)o(ust)f(use)75 1709 y Fq(apply-nondetermin)o
3032 (istic)7 b Fy(to)k(apply)f(a)h(nondeterministic)g(function)f(ob)r
3033 (ject.)18 b(A)11 b(run)o(time)f(error)i(will)d(b)q(e)j(signalled)75
3034 1758 y(if)c(y)o(ou)h(attempt)g(to)g(apply)f(a)h(nondeterministic)g
3035 (function)g(ob)r(ject)h(with)f Fq(apply)p Fy(.)15 b(Y)m(ou)9
3036 b(can)h(use)g Fq(apply-nondetermi)o(nisti)o(c)75 1808
3037 y Fy(to)15 b(apply)f(either)i(a)e(deterministic)h(or)f
3038 (nondeterministic)h(function)f(ob)r(ject)i(though)f(ev)o(en)g(if)f(all)
3039 g(of)g(the)i(argumen)o(ts)75 1858 y(to)f Fq(apply-nondeterm)o(inist)o
3040 (ic)d Fy(are)j(deterministic)f(and)g Fu(function)i Fy(is)e(a)h
3041 (deterministic)f(function)g(ob)r(ject,)h(the)h(call)75
3042 1908 y(expression)e(will)d(still)g(b)q(e)j(nondeterministic)d(\(with)i
3043 (presumably)e(a)i(single)f(v)n(alue\),)g(since)h(it)f(is)h(imp)q
3044 (ossible)d(to)j(deter-)75 1958 y(mine)i(at)g(compile)g(time)f(that)i(a)
3045 g(giv)o(en)g(call)f(to)h Fq(apply-nondetermi)o(nisti)o(c)d
3046 Fy(will)i(b)q(e)h(passed)h(only)e(deterministic)75 2008
3047 y(function)f(ob)r(jects)h(for)e Fu(function)p Fy(.)75
3048 2244 y Fq(purge)21 b Fu(function-name)1040 b Fy([)p Fu(Deterministic)14
3049 b(F)m(unction)p Fy(])75 2391 y(Remo)o(v)o(es)i(an)o(y)g(information)e
3050 (ab)q(out)j Fu(function-name)h Fy(from)d Fv(Screamer)q
3051 Fy('s)h(who-calls)h(database.)27 b(See)18 b(section)f(10)75
3052 2441 y(for)d(an)f(explanation)g(of)g(when)i(this)f(w)o(ould)f(b)q(e)h
3053 (used.)992 2723 y(14)p eop
3054 %%Page: 15 15
3055 15 14 bop 75 195 a Fq(unwedge-screamer)1079 b Fy([)p
3056 Fu(Deterministic)14 b(F)m(unction)p Fy(])75 333 y(Remo)o(v)o(es)i(an)o
3057 (y)g(information)e(ab)q(out)i(all)g(user)i(de\014ned)g(functions)f
3058 (from)e Fv(Screamer)p Fy('s)i(who-calls)f(database.)27
3059 b(See)75 382 y(section)15 b(10)e(for)g(an)h(explanation)f(of)g(when)i
3060 (this)f(w)o(ould)f(b)q(e)h(used.)75 610 y Fq(member-of)20
3061 b Fu(se)n(quenc)n(e)995 b Fy([)p Fu(Nondeterministic)14
3062 b(F)m(unction)p Fy(])75 748 y(Nondeterministically)f(returns)j(an)e
3063 (elemen)o(t)g(of)f Fu(se)n(quenc)n(e)p Fy(.)21 b(The)15
3064 b(elemen)o(ts)f(are)h(returned)h(in)e(the)h(order)g(that)f(they)75
3065 797 y(app)q(ear)g(in)g Fu(se)n(quenc)n(e)p Fy(.)19 b
3066 Fu(Se)n(quenc)n(e)c Fy(m)o(ust)d(b)q(e)j(either)g(a)e(list)h(or)g(a)f
3067 (v)o(ector.)75 1025 y Fq(integer-between)19 b Fu(low)i(high)862
3068 b Fy([)p Fu(Nondeterministic)14 b(F)m(unction)p Fy(])75
3069 1162 y(Nondeterministically)i(returns)j(an)f(in)o(teger)g(in)g(the)g
3070 (closed)g(in)o(terv)n(al)f([)p Fu(low)o Fp(;)7 b Fu(high)p
3071 Fy(].)29 b(The)19 b(results)g(are)f(returned)h(in)75
3072 1212 y(ascending)14 b(order.)19 b Fu(L)n(ow)14 b Fy(and)f
3073 Fu(high)h Fy(m)o(ust)f(b)q(e)i(in)o(tegers.)k(F)m(ails)12
3074 b(if)h(the)i(in)o(terv)n(al)e(do)q(es)i(not)e(con)o(tain)h(an)o(y)f(in)
3075 o(tegers.)75 1440 y Fq(make-variable)19 b Fy([)p Fu(name)p
3076 Fy(])1005 b([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
3077 1577 y(Creates)k(and)e(returns)h(a)f(new)h(v)n(ariable.)24
3078 b(V)m(ariables)15 b(are)i(assigned)f(a)g(name)f(whic)o(h)h(is)g(only)g
3079 (used)h(to)f(iden)o(tify)f(the)75 1627 y(v)n(ariable)10
3080 b(when)i(it)e(is)h(prin)o(ted.)18 b(If)11 b(the)g(parameter)g
3081 Fu(name)h Fy(is)f(giv)o(en)f(then)i(it)f(is)g(assigned)g(as)h(the)f
3082 (name)f(of)h(the)h(v)n(ariable.)75 1677 y(Otherwise,)j(a)e(unique)h
3083 (name)f(is)h(assigned.)k(The)d(parameter)e Fu(name)i
3084 Fy(can)f(b)q(e)g(an)o(y)g Fv(Lisp)f Fy(ob)r(ject.)75
3085 1904 y Fq(numberv)20 b Fp(x)1233 b Fy([)p Fu(Deterministic)14
3086 b(F)m(unction)p Fy(])75 2042 y(If)j(when)g Fq(numberv)f
3087 Fy(is)h(called,)g Fp(x)g Fy(is)g(kno)o(wn)g(to)g(b)q(e)h(n)o(umeric)e
3088 (then)i Fq(numberv)d Fy(returns)k Fq(t)p Fy(.)28 b(Alternativ)o(ely)m
3089 (,)16 b(if)g(when)75 2092 y Fq(numberv)10 b Fy(is)h(called,)g
3090 Fp(x)g Fy(is)h(kno)o(wn)f(to)g(b)q(e)h(non-n)o(umeric)e(then)i
3091 Fq(numberv)e Fy(returns)j Fq(nil)p Fy(.)k(If)11 b(it)g(is)g(not)g(kno)o
3092 (wn)g(whether)i(or)75 2142 y(not)e Fp(x)g Fy(is)g(n)o(umeric)f(when)i
3093 Fq(numberv)e Fy(is)h(called)f(then)i Fq(numberv)e Fy(creates)j(and)e
3094 (returns)i(a)d(new)i(b)q(o)q(olean)f(v)n(ariable)f Fp(v)q
3095 Fy(.)18 b(The)75 2191 y(v)n(alues)12 b(of)f Fp(x)g Fy(and)h
3096 Fp(v)i Fy(are)e(m)o(utually)d(constrained)k(via)e(noticers)i(so)f(that)
3097 g Fp(v)h Fy(is)f(equal)f(to)h Fq(t)g Fy(if)f(and)g(only)g(if)g
3098 Fp(x)h Fy(is)g(kno)o(wn)f(to)75 2241 y(b)q(e)j(n)o(umeric)e(and)h
3099 Fp(v)i Fy(is)e(equal)f(to)h Fq(nil)g Fy(if)f(and)h(only)f(if)h
3100 Fp(x)f Fy(is)h(kno)o(wn)g(to)g(b)q(e)h(non-n)o(umeric.)i(If)d
3101 Fp(x)g Fy(later)g(b)q(ecomes)g(kno)o(wn)75 2291 y(to)i(b)q(e)g(n)o
3102 (umeric,)f(a)g(noticer)h(attac)o(hed)h(to)e Fp(x)h Fy(restricts)h
3103 Fp(v)h Fy(to)d(equal)h Fq(t)p Fy(.)20 b(Lik)o(ewise,)14
3104 b(if)g Fp(x)h Fy(later)f(b)q(ecomes)h(kno)o(wn)g(to)f(b)q(e)75
3105 2341 y(non-n)o(umeric,)e(a)h(noticer)i(attac)o(hed)f(to)f
3106 Fp(x)h Fy(restricts)h Fp(v)g Fy(to)f(equal)f Fq(nil)p
3107 Fy(.)k(F)m(urthermore,)d(if)e Fp(v)k Fy(ev)o(er)e(b)q(ecomes)g(kno)o
3108 (wn)f(to)75 2391 y(equal)j Fq(t)g Fy(then)h(a)g(noticer)g(attac)o(hed)g
3109 (to)f Fp(v)i Fy(restricts)g Fp(x)f Fy(to)f(b)q(e)h(n)o(umeric.)25
3110 b(Lik)o(ewise,)16 b(if)g Fp(v)i Fy(ev)o(er)f(b)q(ecomes)g(kno)o(wn)f
3111 (to)75 2441 y(equal)e Fq(nil)f Fy(then)h(a)g(noticer)g(attac)o(hed)h
3112 (to)f Fp(v)h Fy(restricts)h Fp(x)d Fy(to)h(b)q(e)h(non-n)o(umeric.)992
3113 2723 y(15)p eop
3114 %%Page: 16 16
3115 16 15 bop 75 195 a Fq(realv)21 b Fp(x)1276 b Fy([)p Fu(Deterministic)14
3116 b(F)m(unction)p Fy(])75 346 y(If)i(when)i Fq(realv)e
3117 Fy(is)g(called,)h Fp(x)g Fy(is)f(kno)o(wn)h(to)f(b)q(e)i(real)f(then)g
3118 Fq(realv)f Fy(returns)i Fq(t)p Fy(.)27 b(Alternativ)o(ely)m(,)16
3119 b(if)g(when)h Fq(realv)f Fy(is)75 396 y(called,)g Fp(x)g
3120 Fy(is)f(kno)o(wn)h(to)g(b)q(e)h(non-real)e(then)i Fq(realv)e
3121 Fy(returns)j Fq(nil)p Fy(.)23 b(If)16 b(it)g(is)g(not)f(kno)o(wn)h
3122 (whether)h(or)f(not)g Fp(x)g Fy(is)g(real)75 446 y(when)g
3123 Fq(realv)e Fy(is)h(called)g(then)g Fq(realv)f Fy(creates)j(and)e
3124 (returns)i(a)e(new)g(b)q(o)q(olean)g(v)n(ariable)f Fp(v)q
3125 Fy(.)23 b(The)15 b(v)n(alues)g(of)g Fp(x)f Fy(and)h Fp(v)75
3126 496 y Fy(are)g(m)o(utually)e(constrained)i(via)f(noticers)i(so)f(that)g
3127 Fp(v)h Fy(is)f(equal)g(to)f Fq(t)h Fy(if)f(and)h(only)f(if)g
3128 Fp(x)g Fy(is)h(kno)o(wn)g(to)f(b)q(e)i(real)f(and)f Fp(v)75
3129 546 y Fy(is)g(equal)f(to)h Fq(nil)g Fy(if)f(and)h(only)f(if)g
3130 Fp(x)h Fy(is)f(kno)o(wn)h(to)g(b)q(e)g(non-real.)k(If)c
3131 Fp(x)g Fy(later)g(b)q(ecomes)g(kno)o(wn)f(to)h(b)q(e)h(real,)e(a)h
3132 (noticers)75 595 y(attac)o(hed)e(to)f Fp(x)g Fy(restricts)i
3133 Fp(v)g Fy(to)e(equal)g Fq(t)p Fy(.)17 b(Lik)o(ewise,)11
3134 b(if)g Fp(x)g Fy(later)g(b)q(ecomes)h(kno)o(wn)e(to)i(b)q(e)f
3135 (non-real,)g(a)g(noticer)h(attac)o(hed)75 645 y(to)i
3136 Fp(x)g Fy(restricts)i Fp(v)g Fy(to)e(equal)g Fq(nil)p
3137 Fy(.)k(F)m(urthermore,)c(if)f Fp(v)j Fy(ev)o(er)f(b)q(ecomes)f(kno)o
3138 (wn)g(to)g(equal)g Fq(t)g Fy(then)h(a)f(noticer)g(attac)o(hed)75
3139 695 y(to)g Fp(v)h Fy(restricts)h Fp(x)e Fy(to)g(b)q(e)g(real.)19
3140 b(Lik)o(ewise,)13 b(if)g Fp(v)j Fy(ev)o(er)f(b)q(ecomes)f(kno)o(wn)f
3141 (to)h(equal)g Fq(nil)f Fy(then)i(a)e(noticer)i(attac)o(hed)g(to)e
3142 Fp(v)75 745 y Fy(restricts)j Fp(x)d Fy(to)h(b)q(e)h(non-real.)75
3143 986 y Fq(integerv)20 b Fp(x)1211 b Fy([)p Fu(Deterministic)14
3144 b(F)m(unction)p Fy(])75 1138 y(If)g(when)i Fq(integerv)d
3145 Fy(is)i(called,)f Fp(x)h Fy(is)f(kno)o(wn)h(to)f(b)q(e)i(in)o(teger)f
3146 (v)n(alued)f(then)i Fq(integerv)d Fy(returns)j Fq(t)p
3147 Fy(.)21 b(Alternativ)o(ely)m(,)14 b(if)75 1187 y(when)i
3148 Fq(integerv)e Fy(is)h(called,)h Fp(x)f Fy(is)h(kno)o(wn)f(to)g(b)q(e)h
3149 (non-in)o(teger)g(v)n(alued)f(then)h Fq(integerv)e Fy(returns)k
3150 Fq(nil)p Fy(.)k(If)15 b(it)h(is)f(not)75 1237 y(kno)o(wn)e(whether)i
3151 (or)e(not)g Fp(x)g Fy(is)g(in)o(teger)h(v)n(alued)f(when)h
3152 Fq(integerv)d Fy(is)i(called)g(then)h Fq(integerv)e Fy(creates)j(and)e
3153 (returns)i(a)75 1287 y(new)g(b)q(o)q(olean)f(v)n(ariable)g
3154 Fp(v)q Fy(.)20 b(The)15 b(v)n(alues)g(of)f Fp(x)g Fy(and)g
3155 Fp(v)j Fy(are)e(m)o(utually)d(constrained)j(via)f(noticers)h(so)g(that)
3156 g Fp(v)h Fy(is)e(equal)75 1337 y(to)g Fq(t)g Fy(if)f(and)h(only)f(if)h
3157 Fp(x)f Fy(is)h(kno)o(wn)g(to)g(b)q(e)h(in)o(teger)f(v)n(alued)g(and)g
3158 Fp(v)h Fy(is)f(equal)g(to)g Fq(nil)f Fy(if)h(and)f(only)h(if)f
3159 Fp(x)h Fy(is)g(kno)o(wn)f(to)h(b)q(e)75 1387 y(non-in)o(teger)f(v)n
3160 (alued.)18 b(If)12 b Fp(x)h Fy(later)h(b)q(ecomes)f(kno)o(wn)g(to)g(b)q
3161 (e)h(in)o(teger)f(v)n(alued,)g(a)g(noticer)g(attac)o(hed)h(to)f
3162 Fp(x)g Fy(restricts)i Fp(v)g Fy(to)75 1436 y(equal)e
3163 Fq(t)p Fy(.)k(Lik)o(ewise,)c(if)f Fp(x)h Fy(later)g(b)q(ecomes)h(kno)o
3164 (wn)e(to)h(b)q(e)h(non-in)o(teger)f(v)n(alued,)f(a)h(noticer)h(attac)o
3165 (hed)g(to)f Fp(x)f Fy(restricts)j Fp(v)75 1486 y Fy(to)c(equal)h
3166 Fq(nil)p Fy(.)k(F)m(urthermore,)c(if)e Fp(v)k Fy(ev)o(er)e(b)q(ecomes)g
3167 (kno)o(wn)f(to)g(equal)h Fq(t)f Fy(then)h(a)f(noticer)i(attac)o(hed)f
3168 (to)f Fp(v)i Fy(restricts)h Fp(x)d Fy(to)75 1536 y(b)q(e)h(in)o(teger)g
3169 (v)n(alued.)k(Lik)o(ewise,)11 b(if)g Fp(v)i Fy(ev)o(er)f(b)q(ecomes)f
3170 (kno)o(wn)g(to)g(equal)g Fq(nil)g Fy(then)h(a)e(noticer)i(attac)o(hed)g
3171 (to)f Fp(v)i Fy(restricts)g Fp(x)75 1586 y Fy(to)h(b)q(e)g(non-in)o
3172 (teger)g(v)n(alued.)75 1827 y Fq(memberv)20 b Fp(x)i(y)1191
3173 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
3174 1979 y(The)g(curren)o(t)h(implem)o(en)o(tation)c(imp)q(oses)h(t)o(w)o
3175 (o)h(constrain)o(ts)h(on)f(the)h(parameter)f Fp(y)q Fy(.)19
3176 b(First,)13 b Fp(y)j Fy(m)o(ust)c(b)q(e)i(b)q(ound)f(when)75
3177 2028 y Fq(memberv)d Fy(is)i(called.)17 b(Second,)c Fp(y)g
3178 Fy(m)o(ust)e(not)h(con)o(tain)f(an)o(y)g(un)o(b)q(ound)h(v)n(ariables)f
3179 (when)h Fq(memberv)f Fy(is)g(called.)17 b(The)c(v)n(alue)75
3180 2078 y(of)h(parameter)g Fp(y)j Fy(m)o(ust)c(b)q(e)i(a)g(sequence,)h
3181 (i.e.)e(either)h(a)g(list)f(or)g(a)h(v)o(ector.)21 b(If)14
3182 b(when)h Fq(memberv)e Fy(is)i(called,)f Fp(x)g Fy(is)g(kno)o(wn)75
3183 2128 y(to)f(b)q(e)h(a)e(mem)o(b)q(er)g(of)g Fp(y)j Fy(\(using)e(the)g
3184 Fv(Common)k(Lisp)c Fy(function)g Fq(eql)f Fy(as)h(a)g(test)h
3185 (function\))f(then)h Fq(memberv)d Fy(returns)k Fq(t)p
3186 Fy(.)75 2178 y(Alternativ)o(ely)m(,)d(if)g(when)h Fq(memberv)f
3187 Fy(is)g(called,)h Fp(x)f Fy(is)h(kno)o(wn)g(not)f(to)h(b)q(e)h(a)e(mem)
3188 o(b)q(er)g(of)g Fp(y)j Fy(then)e Fq(memberv)f Fy(returns)i
3189 Fq(nil)p Fy(.)75 2228 y(If)g(it)f(is)h(not)g(kno)o(wn)g(whether)h(or)g
3190 (not)f Fp(x)f Fy(is)h(a)g(mem)o(b)q(er)f(of)g Fp(y)j
3191 Fy(when)e Fq(memberv)f Fy(is)h(called)g(then)h Fq(memberv)d
3192 Fy(creates)k(and)75 2277 y(returns)f(a)e(new)g(b)q(o)q(olean)g(v)n
3193 (ariable)f Fp(v)q Fy(.)19 b(The)13 b(v)n(alues)g(of)g
3194 Fp(x)g Fy(and)g Fp(v)i Fy(are)e(m)o(utually)e(constrained)j(via)f
3195 (noticers)h(so)f(that)g Fp(v)75 2327 y Fy(is)k(equal)f(to)h
3196 Fq(t)g Fy(if)f(and)g(only)g(if)h Fp(x)f Fy(is)h(kno)o(wn)f(to)h(b)q(e)g
3197 (a)g(mem)o(b)q(er)e(of)i Fp(y)h Fy(and)f Fp(v)h Fy(is)f(equal)g(to)f
3198 Fq(nil)h Fy(if)f(and)g(only)g(if)h Fp(x)f Fy(is)75 2377
3199 y(kno)o(wn)d(not)g(to)g(b)q(e)h(a)f(mem)o(b)q(er)e(of)i
3200 Fp(y)q Fy(.)18 b(If)13 b Fp(x)g Fy(later)g(b)q(ecomes)h(kno)o(wn)e(to)h
3201 (b)q(e)h(a)f(mem)o(b)q(er)f(of)g Fp(y)q Fy(,)i(a)f(noticer)g(attac)o
3202 (hed)h(to)f Fp(x)75 2427 y Fy(restricts)k Fp(v)f Fy(to)f(equal)f
3203 Fq(t)p Fy(.)21 b(Lik)o(ewise,)15 b(if)f Fp(x)g Fy(later)h(b)q(ecomes)g
3204 (kno)o(wn)g(not)g(to)f(b)q(e)i(a)e(mem)o(b)q(er)g(of)g
3205 Fp(y)q Fy(,)h(a)g(noticer)g(attac)o(hed)75 2477 y(to)f
3206 Fp(x)g Fy(restricts)i Fp(v)g Fy(to)e(equal)g Fq(nil)p
3207 Fy(.)k(F)m(urthermore,)c(if)f Fp(v)j Fy(ev)o(er)f(b)q(ecomes)f(kno)o
3208 (wn)g(to)g(equal)g Fq(t)g Fy(then)h(a)f(noticer)g(attac)o(hed)75
3209 2526 y(to)i Fp(v)i Fy(restricts)h Fp(x)d Fy(to)h(b)q(e)g(a)f(mem)o(b)q
3210 (er)f(of)h Fp(y)q Fy(.)27 b(Lik)o(ewise,)16 b(if)g Fp(v)i
3211 Fy(ev)o(er)g(b)q(ecomes)e(kno)o(wn)g(to)h(equal)f Fq(nil)g
3212 Fy(then)h(a)f(noticer)75 2576 y(attac)o(hed)f(to)e Fp(v)j
3213 Fy(restricts)g Fp(x)d Fy(not)h(to)g(b)q(e)g(a)g(mem)o(b)q(er)e(of)h
3214 Fp(y)q Fy(.)992 2723 y(16)p eop
3215 %%Page: 17 17
3216 17 16 bop 75 195 a Fq(booleanv)20 b Fp(x)1211 b Fy([)p
3217 Fu(Deterministic)14 b(F)m(unction)p Fy(])75 343 y(The)g(expression)h
3218 Fq(\(booleanv)20 b Fp(x)p Fq(\))14 b Fy(is)f(an)h(abbreviation)f(for)h
3219 Fq(\(memberv)20 b Fp(x)h Fq('\(t)h(nil\)\))p Fy(.)75
3220 581 y Fq(assert!)e Fp(x)1279 b Fy([)p Fu(Deterministic)13
3221 b(Macr)n(o)p Fy(])75 729 y(The)i(argumen)o(t)e Fp(x)i
3222 Fy(can)g(b)q(e)g(either)g(a)f(v)n(ariable)g(or)g(a)h(non-v)n(ariable.)j
3223 (The)d(expression)h Fq(\(assert!)k Fp(x)p Fq(\))14 b
3224 Fy(restricts)j Fp(x)d Fy(to)75 779 y(equal)g Fq(t)p Fy(.)19
3225 b(This)c(assertion)g(ma)o(y)d(cause)k(other)f(assertions)g(to)g(b)q(e)g
3226 (made)e(due)i(to)f(noticers)h(attac)o(hed)g(to)g Fp(x)p
3227 Fy(.)k(A)14 b(call)g(to)75 829 y Fq(assert!)h Fy(fails)g(if)g
3228 Fp(x)h Fy(is)g(kno)o(wn)f(not)i(to)f(equal)f Fq(t)h Fy(prior)g(to)g
3229 (the)h(assertion)g(or)f(if)f(an)o(y)h(of)f(the)i(assertions)g(p)q
3230 (erformed)75 879 y(b)o(y)d(the)i(noticers)f(result)h(in)e(failure.)20
3231 b(No)14 b(meaningful)e(result)k(is)e(returned.)22 b(Except)16
3232 b(for)e(the)i(fact)e(that)h(one)g(cannot)75 928 y(write)k
3233 Fq(#'assert!)p Fy(,)e Fq(assert!)g Fy(b)q(eha)o(v)o(es)i(lik)o(e)f(a)g
3234 (function,)h(ev)o(en)g(though)f(it)g(is)g(implemen)o(ted)e(as)j(a)f
3235 (macro.)31 b(The)75 978 y(reason)12 b(it)g(is)f(implemen)o(ted)e(as)j
3236 (a)g(macro)e(is)i(to)f(allo)o(w)f(a)h(n)o(um)o(b)q(er)g(of)g(compile)f
3237 (time)h(optimizations.)k(Expressions)e(lik)o(e)75 1028
3238 y Fq(\(assert!)20 b(\(notv)h Fp(x)p Fq(\)\))p Fy(,)11
3239 b Fq(\(assert!)20 b(\(numberv)g Fp(x)p Fq(\)\))10 b Fy(and)h
3240 Fq(\(assert!)21 b(\(notv)f(\(numberv)h Fp(x)p Fq(\)\)\))10
3241 b Fy(are)i(transformed)75 1078 y(in)o(to)h(calls)f(to)i(functions)f(in)
3242 o(ternal)g(to)g Fv(Screamer)h Fy(whic)o(h)f(eliminate)e(the)j(need)h
3243 (to)e(create)i(the)e(b)q(o)q(olean)g(v)n(ariable\(s\))75
3244 1128 y(normally)8 b(returned)j(b)o(y)f(functions)h(lik)o(e)e
3245 Fq(notv)g Fy(and)h Fq(numberv)p Fy(.)16 b(Calls)9 b(to)h(the)h
3246 (functions)f Fq(numberv)p Fy(,)f Fq(realv)p Fy(,)g Fq(integerv)p
3247 Fy(,)75 1177 y Fq(memberv)p Fy(,)f Fq(booleanv)p Fy(,)h
3248 Fq(=v)p Fy(,)g Fq(<v)p Fy(,)g Fq(<=v)p Fy(,)h Fq(>v)p
3249 Fy(,)f Fq(>=v)p Fy(,)g Fq(/=v)p Fy(,)h Fq(notv)p Fy(,)f
3250 Fq(funcallv)p Fy(,)f Fq(applyv)g Fy(and)h Fq(equalv)f
3251 Fy(whic)o(h)i(app)q(ear)g(directly)75 1227 y(nested)15
3252 b(in)e(a)g(call)f(to)i Fq(assert!)p Fy(,)d(or)i(directly)h(nested)h(in)
3253 e(a)g(call)f(to)i Fq(notv)e Fy(whic)o(h)h(is)h(in)e(turn)i(directly)g
3254 (nested)h(in)e(a)g(call)75 1277 y(to)h Fq(assert!)p Fy(,)e(are)i
3255 (similarly)d(transformed.)75 1515 y Fq(known?)21 b Fp(x)1300
3256 b Fy([)p Fu(Deterministic)13 b(Macr)n(o)p Fy(])75 1663
3257 y(The)19 b(argumen)o(t)f Fp(x)h Fy(can)g(b)q(e)g(either)h(a)f(v)n
3258 (ariable)e(or)i(a)g(non-v)n(ariable.)31 b(The)20 b(expression)g
3259 Fq(\(known?)g Fp(x)p Fq(\))e Fy(restricts)j Fp(x)75 1713
3260 y Fy(to)d(b)q(e)g(b)q(o)q(olean.)29 b(This)17 b(assertion)i(ma)o(y)d
3261 (cause)i(other)h(assertions)f(to)g(b)q(e)g(made)f(due)h(to)f(noticers)i
3262 (attac)o(hed)f(to)g Fp(x)p Fy(.)75 1763 y(A)h(call)e(to)i
3263 Fq(known?)e Fy(fails)g(if)h Fp(x)g Fy(is)h(kno)o(wn)f(not)g(to)g(b)q(e)
3264 i(b)q(o)q(olean)e(prior)g(to)g(the)i(assertion)f(or)f(if)g(an)o(y)g(of)
3265 g(the)h(asser-)75 1813 y(tions)d(p)q(erformed)h(b)o(y)f(the)i(noticers)
3266 f(result)h(in)e(failure.)25 b(Restricting)17 b Fp(x)g
3267 Fy(to)f(b)q(e)h(b)q(o)q(olean)g(attac)o(hes)g(a)g(noticer)g(on)f
3268 Fp(x)75 1862 y Fy(so)i(that)g(an)o(y)f(subsequen)o(t)j(assertion)e
3269 (whic)o(h)g(restricts)h Fp(x)f Fy(to)g(b)q(e)g(non-b)q(o)q(olean)f
3270 (will)f(fail.)29 b(If)17 b Fp(x)g Fy(is)h(equal)g(to)f
3271 Fq(t)h Fy(af-)75 1912 y(ter)g(b)q(eing)f(restricted)i(to)e(b)q(e)h(b)q
3272 (o)q(olean)e(then)i Fq(known?)e Fy(returns)j Fq(t)p Fy(.)27
3273 b(If)17 b Fp(x)f Fy(is)h(equal)g(to)g Fq(nil)f Fy(or)h(if)g(the)g(v)n
3274 (alue)g(of)f Fp(x)h Fy(is)75 1962 y(unkno)o(wn)g(then)g
3275 Fq(known?)f Fy(returns)j Fq(nil)p Fy(.)26 b(Except)18
3276 b(for)f(the)h(fact)f(that)g(one)g(cannot)g(write)g Fq(#'known?)p
3277 Fy(,)f Fq(known?)f Fy(b)q(e-)75 2012 y(ha)o(v)o(es)20
3278 b(lik)o(e)e(a)h(function,)h(ev)o(en)h(though)e(it)g(is)g(implemen)o
3279 (ted)e(as)j(a)f(macro.)33 b(The)20 b(reason)g(it)f(is)h(implem)o(en)o
3280 (ted)e(as)75 2062 y(a)h(macro)e(is)i(to)g(allo)o(w)e(a)i(n)o(um)o(b)q
3281 (er)f(of)g(compile)f(time)h(optimizations.)31 b(Expressions)20
3282 b(lik)o(e)e Fq(\(known?)i(\(notv)h Fp(x)p Fq(\)\))p Fy(,)75
3283 2111 y Fq(\(known?)f(\(numberv)g Fp(x)p Fq(\)\))12 b
3284 Fy(and)f Fq(\(known?)21 b(\(notv)f(\(numberv)h Fp(x)p
3285 Fq(\)\)\))11 b Fy(are)h(transformed)f(in)o(to)g(calls)h(to)g(functions)
3286 g(in-)75 2161 y(ternal)k(to)g Fv(Screamer)h Fy(whic)o(h)f(eliminate)e
3287 (the)j(need)g(to)e(create)j(the)f(b)q(o)q(olean)e(v)n(ariable\(s\))h
3288 (normally)d(returned)18 b(b)o(y)75 2211 y(functions)12
3289 b(lik)o(e)f Fq(notv)f Fy(and)i Fq(numberv)p Fy(.)k(Calls)11
3290 b(to)g(the)h(functions)g Fq(numberv)p Fy(,)e Fq(realv)p
3291 Fy(,)h Fq(integerv)p Fy(,)f Fq(memberv)p Fy(,)g Fq(booleanv)p
3292 Fy(,)75 2261 y Fq(=v)p Fy(,)15 b Fq(<v)p Fy(,)g Fq(<=v)p
3293 Fy(,)g Fq(>v)p Fy(,)g Fq(>=v)p Fy(,)g Fq(/=v)p Fy(,)g
3294 Fq(notv)p Fy(,)f Fq(funcallv)p Fy(,)g Fq(applyv)g Fy(and)i
3295 Fq(equalv)e Fy(whic)o(h)h(app)q(ear)h(directly)g(nested)h(in)e(a)h
3296 (call)75 2311 y(to)f Fq(known?)p Fy(,)e(or)i(directly)g(nested)i(in)d
3297 (a)h(call)f(to)h Fq(notv)f Fy(whic)o(h)h(is)f(in)h(turn)g(directly)h
3298 (nested)g(in)f(a)f(call)g(to)h Fq(known?)p Fy(,)f(are)75
3299 2361 y(similarly)d(transformed.)75 2599 y Fq(decide)21
3300 b Fp(x)1235 b Fy([)p Fu(Nondeterministic)13 b(Macr)n(o)p
3301 Fy(])992 2723 y(17)p eop
3302 %%Page: 18 18
3303 18 17 bop 75 195 a Fy(The)13 b(argumen)o(t)e Fp(x)i Fy(can)f(b)q(e)h
3304 (either)h(a)e(v)n(ariable)f(or)i(a)f(non-v)n(ariable.)k(The)d
3305 (expression)h Fq(\(decide)20 b Fp(x)p Fq(\))12 b Fy(restricts)j
3306 Fp(x)d Fy(to)g(b)q(e)75 245 y(b)q(o)q(olean.)18 b(This)c(assertion)h
3307 (ma)o(y)d(cause)j(other)f(assertions)h(to)f(b)q(e)h(made)e(due)h(to)g
3308 (noticers)h(attac)o(hed)g(to)f Fp(x)p Fy(.)k(A)c(call)f(to)75
3309 295 y Fq(decide)e Fy(imm)o(ediately)e(fails)i(if)g Fp(x)h
3310 Fy(is)g(kno)o(wn)g(not)g(to)g(b)q(e)g(b)q(o)q(olean)g(prior)g(to)g(the)
3311 g(assertion)h(or)f(if)f(an)o(y)h(of)f(the)i(assertions)75
3312 345 y(p)q(erformed)h(b)o(y)h(the)g(noticers)g(result)h(in)e(failure.)19
3313 b(Restricting)c Fp(x)f Fy(to)g(b)q(e)i(b)q(o)q(olean)e(attac)o(hes)h(a)
3314 g(noticer)g(on)f Fp(x)g Fy(so)h(that)75 394 y(an)o(y)c(subsequen)o(t)j
3315 (assertion)e(whic)o(h)g(restricts)i Fp(x)d Fy(to)h(b)q(e)g(non-b)q(o)q
3316 (olean)g(will)e(fail.)16 b(After)c Fp(x)g Fy(is)f(restricted)j(to)e(b)q
3317 (e)g(b)q(o)q(olean)75 444 y(a)h(nondeterministic)g(c)o(hoice)h(is)f
3318 (made.)k(F)m(or)c(one)h(branc)o(h,)f Fp(x)g Fy(is)h(restricted)h(to)e
3319 (equal)g Fq(t)h Fy(and)f Fq(\(decide)20 b Fp(x)p Fq(\))13
3320 b Fy(returns)i Fq(t)75 494 y Fy(as)g(a)f(result.)21 b(F)m(or)14
3321 b(the)h(other)g(branc)o(h,)g Fp(x)f Fy(is)h(restricted)h(to)f(equal)f
3322 Fq(nil)g Fy(and)g Fq(\(decide)21 b Fp(x)p Fq(\))14 b
3323 Fy(returns)i Fq(nil)e Fy(as)g(a)h(result.)75 544 y(Except)g(for)f
3324 (implem)o(en)o(tation)d(optimizations)g Fq(\(decide)21
3325 b Fp(x)p Fq(\))13 b Fy(is)h(equiv)n(alen)o(t)f(to:)179
3326 625 y Fq(\(either)20 b(\(progn)h(\(assert!)f Fp(x)p Fq(\))h(t\))h
3327 (\(progn)e(\(assert!)g(\(notv)h Fp(x)p Fq(\)\))g(nil\)\))p
3328 Fy(.)75 705 y(The)11 b(implemen)o(tation)c(guaran)o(tees)12
3329 b(that)e Fp(x)h Fy(is)f(ev)n(aluated)h(only)e(once)j(so)e(it)h(ma)o(y)d
3330 (safely)j(con)o(tain)f(side)h(e\013ects.)19 b(Except)75
3331 755 y(for)d(the)g(fact)g(that)g(one)g(cannot)g(write)g
3332 Fq(#'decide)p Fy(,)e Fq(decide)h Fy(b)q(eha)o(v)o(es)h(lik)o(e)g(a)f
3333 (function,)h(ev)o(en)g(though)g(it)f(is)h(imple-)75 805
3334 y(men)o(ted)d(as)g(a)f(macro.)17 b(The)c(reason)h(it)f(is)g(implem)o
3335 (en)o(ted)e(as)i(a)g(macro)f(is)h(to)g(allo)o(w)e(a)i(n)o(um)o(b)q(er)f
3336 (of)h(compile)e(time)h(opti-)75 855 y(mizations.)j(Expressions)10
3337 b(lik)o(e)f Fq(\(decide)20 b(\(notv)h Fp(x)p Fq(\)\))p
3338 Fy(,)9 b Fq(\(decide)20 b(\(numberv)g Fp(x)p Fq(\)\))9
3339 b Fy(and)g Fq(\(decide)20 b(\(notv)h(\(numberv)f Fp(x)p
3340 Fq(\)\)\))75 905 y Fy(are)e(transformed)e(in)o(to)g(calls)h(to)g
3341 (functions)g(in)o(ternal)g(to)g Fv(Screamer)h Fy(whic)o(h)f(eliminate)e
3342 (the)j(need)g(to)f(create)h(the)75 954 y(b)q(o)q(olean)j(v)n
3343 (ariable\(s\))f(normally)e(returned)23 b(b)o(y)d(functions)h(lik)o(e)f
3344 Fq(notv)g Fy(and)h Fq(numberv)p Fy(.)38 b(Calls)20 b(to)g(the)i
3345 (functions)75 1004 y Fq(numberv)p Fy(,)17 b Fq(realv)p
3346 Fy(,)g Fq(integerv)p Fy(,)g Fq(memberv)p Fy(,)f Fq(booleanv)p
3347 Fy(,)h Fq(=v)p Fy(,)h Fq(<v)p Fy(,)g Fq(<=v)p Fy(,)f
3348 Fq(>v)p Fy(,)h Fq(>=v)p Fy(,)g Fq(/=v)p Fy(,)f Fq(notv)p
3349 Fy(,)h Fq(funcallv)p Fy(,)e Fq(applyv)75 1054 y Fy(and)e
3350 Fq(equalv)e Fy(whic)o(h)i(app)q(ear)g(directly)h(nested)g(in)e(a)h
3351 (call)f(to)h Fq(decide)p Fy(,)e(or)i(directly)g(nested)h(in)f(a)f(call)
3352 g(to)h Fq(notv)f Fy(whic)o(h)75 1104 y(is)h(in)f(turn)i(directly)f
3353 (nested)h(in)f(a)f(call)g(to)h Fq(decide)p Fy(,)e(are)i(similarly)d
3354 (transformed.)75 1342 y Fq(=v)21 b Fp(x)164 1327 y Fo(+)1506
3355 1342 y Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
3356 1491 y(Returns)h(a)f(b)q(o)q(olean)g(v)n(alue)g(whic)o(h)h(is)f
3357 (constrained)h(to)f(b)q(e)h Fq(t)g Fy(if)e(all)g(of)h(the)h(argumen)o
3358 (ts)f(are)h(n)o(umerically)d(equal)i(and)75 1540 y(constrained)j(to)g
3359 (b)q(e)g Fq(nil)f Fy(if)g(t)o(w)o(o)g(or)g(more)g(of)g(the)h(argumen)o
3360 (ts)f(n)o(umerically)e(di\013er.)27 b(This)16 b(function)g(tak)o(es)h
3361 (one)g(or)75 1590 y(more)f(argumen)o(ts.)28 b(All)16
3362 b(of)h(the)h(argumen)o(ts)e(are)i(restricted)h(to)e(b)q(e)h(n)o(umeric)
3363 f(\(see)h(section)g(8\).)28 b(Returns)18 b Fq(t)f Fy(when)75
3364 1640 y(called)c(with)g(one)g(argumen)o(t.)j(A)e(call)e(suc)o(h)i(as)f
3365 Fq(\(=v)21 b Fp(x)936 1646 y Fo(1)976 1640 y Fp(x)1000
3366 1646 y Fo(2)1025 1640 y Fp(:)7 b(:)g(:)f(x)1105 1646
3367 y Fh(n)1127 1640 y Fq(\))13 b Fy(with)g(more)f(than)h(t)o(w)o(o)f
3368 (argumen)o(ts)h(b)q(eha)o(v)o(es)h(lik)o(e)75 1690 y(a)g(conjunction)f
3369 (of)h(t)o(w)o(o)f(argumen)o(t)g(calls:)179 1771 y Fq(\(andv)21
3370 b(\(=v)g Fp(x)421 1777 y Fo(1)461 1771 y Fp(x)485 1777
3371 y Fo(2)503 1771 y Fq(\))p Fp(:)7 b(:)g(:)n Fq(\(=v)22
3372 b Fp(x)685 1777 y Fh(i)720 1771 y Fp(x)744 1777 y Fh(i)p
3373 Fo(+1)800 1771 y Fq(\))p Fp(:)7 b(:)g(:)n Fq(\(=v)21
3374 b Fp(x)981 1777 y Fh(n)p Fi(\000)p Fo(1)1068 1771 y Fp(x)1092
3375 1777 y Fh(n)1114 1771 y Fq(\)\))75 1851 y Fy(Beha)o(v)o(es)16
3376 b(as)f(follo)o(ws)e(when)i(called)f(with)h(t)o(w)o(o)f(argumen)o(ts.)19
3377 b(Returns)d Fq(t)e Fy(if)g Fp(x)1305 1857 y Fo(1)1338
3378 1851 y Fy(is)h(kno)o(wn)f(to)h(b)q(e)g(equal)f(to)h Fp(x)1808
3379 1857 y Fo(2)1841 1851 y Fy(at)f(the)75 1901 y(time)j(of)g(call.)30
3380 b(Tw)o(o)18 b(n)o(umeric)f(v)n(alues)h(are)g(kno)o(wn)g(to)g(b)q(e)g
3381 (equal)g(only)f(when)i(they)g(are)f(b)q(oth)g(b)q(ound)g(and)g(equal)75
3382 1951 y(according)12 b(to)g(the)g Fv(Common)17 b(Lisp)12
3383 b Fy(function)f Fq(=)p Fy(.)17 b(Returns)c Fq(nil)e Fy(if)g
3384 Fp(x)1166 1957 y Fo(1)1196 1951 y Fy(is)h(kno)o(wn)g(not)f(to)h(b)q(e)h
3385 (equal)e(to)h Fp(x)1721 1957 y Fo(2)1751 1951 y Fy(at)g(the)g(time)75
3386 2001 y(of)i(call.)19 b(Tw)o(o)13 b(n)o(umeric)h(v)n(alues)g(are)h(kno)o
3387 (wn)f(not)g(to)g(b)q(e)h(equal)f(when)h(their)g(domains)e(are)h
3388 (disjoin)o(t)g(\(see)h(section)h(6\).)75 2051 y(F)m(urthermore)h(t)o(w)
3389 o(o)f(real)h(v)n(alues)f(are)i(kno)o(wn)e(not)h(to)f(b)q(e)i(equal)e
3390 (when)i(their)f(ranges)g(are)h(disjoin)o(t,)e(i.e.)g(the)h(upp)q(er)75
3391 2100 y(b)q(ound)f(of)f(one)h(is)g(greater)h(than)f(the)h(lo)o(w)o(er)e
3392 (b)q(ound)h(of)f(the)i(other)g(\(see)g(section)f(6\).)24
3393 b(If)16 b(it)g(is)f(not)h(kno)o(wn)g(whether)75 2150
3394 y(or)g(not)f Fp(x)227 2156 y Fo(1)261 2150 y Fy(is)h(equal)f(to)h
3395 Fp(x)493 2156 y Fo(2)527 2150 y Fy(when)g Fq(=v)g Fy(is)f(called)h
3396 (then)g Fq(=v)f Fy(creates)j(and)d(returns)j(a)d(new)h(b)q(o)q(olean)g
3397 (v)n(ariable)e Fp(v)q Fy(.)25 b(The)75 2200 y(v)n(alues)15
3398 b(of)f Fp(x)272 2206 y Fo(1)291 2200 y Fy(,)g Fp(x)341
3399 2206 y Fo(2)375 2200 y Fy(and)h Fp(v)h Fy(are)g(m)o(utually)d
3400 (constrained)j(via)e(noticers)i(so)f(that)g Fp(v)i Fy(is)e(equal)g(to)g
3401 Fq(t)g Fy(if)f(and)h(only)f(if)h Fp(x)1889 2206 y Fo(1)1922
3402 2200 y Fy(is)75 2250 y(kno)o(wn)d(to)h(b)q(e)g(equal)f(to)g
3403 Fp(x)491 2256 y Fo(2)522 2250 y Fy(and)h Fp(v)h Fy(is)e(equal)g(to)h
3404 Fq(nil)f Fy(if)g(and)g(only)g(if)f Fp(x)1178 2256 y Fo(1)1209
3405 2250 y Fy(is)i(kno)o(wn)f(not)g(to)h(b)q(e)g(equal)f(to)h
3406 Fp(x)1739 2256 y Fo(2)1757 2250 y Fy(.)k(If)c(it)f(later)75
3407 2300 y(b)q(ecomes)i(kno)o(wn)g(that)g Fp(x)486 2306 y
3408 Fo(1)518 2300 y Fy(is)g(equal)f(to)h Fp(x)744 2306 y
3409 Fo(2)762 2300 y Fy(,)g(noticers)h(attac)o(hed)f(to)g
3410 Fp(x)1187 2306 y Fo(1)1219 2300 y Fy(and)g Fp(x)1324
3411 2306 y Fo(2)1356 2300 y Fy(restrict)i Fp(v)f Fy(to)f(equal)f
3412 Fq(t)p Fy(.)18 b(Lik)o(ewise,)c(if)75 2350 y(it)e(later)g(b)q(ecomes)h
3413 (kno)o(wn)f(that)g Fp(x)616 2356 y Fo(1)646 2350 y Fy(is)g(not)h(equal)
3414 f(to)g Fp(x)940 2356 y Fo(2)958 2350 y Fy(,)g(noticers)h(attac)o(hed)g
3415 (to)f Fp(x)1376 2356 y Fo(1)1407 2350 y Fy(and)g Fp(x)1510
3416 2356 y Fo(2)1540 2350 y Fy(restrict)i Fp(v)g Fy(to)e(equal)g
3417 Fq(nil)p Fy(.)75 2399 y(F)m(urthermore,)j(if)f Fp(v)j
3418 Fy(ev)o(er)f(b)q(ecomes)g(kno)o(wn)f(to)g(equal)g Fq(t)g
3419 Fy(then)h(a)f(noticer)h(attac)o(hed)g(to)f Fp(v)i Fy(restricts)g
3420 Fp(x)1711 2405 y Fo(1)1744 2399 y Fy(to)e(b)q(e)h(equal)75
3421 2449 y(to)h Fp(x)153 2455 y Fo(2)172 2449 y Fy(.)29 b(Lik)o(ewise,)17
3422 b(if)g Fp(v)i Fy(ev)o(er)g(b)q(ecomes)e(kno)o(wn)g(to)h(equal)f
3423 Fq(nil)g Fy(then)h(a)f(noticer)h(attac)o(hed)g(to)g Fp(v)h
3424 Fy(restricts)g Fp(x)1854 2455 y Fo(1)1890 2449 y Fy(not)75
3425 2499 y(to)f(b)q(e)h(equal)f(to)g Fp(x)384 2505 y Fo(2)402
3426 2499 y Fy(.)32 b(Restricting)18 b(t)o(w)o(o)g(v)n(alues)g
3427 Fp(x)898 2505 y Fo(1)934 2499 y Fy(and)h Fp(x)1044 2505
3428 y Fo(2)1080 2499 y Fy(to)f(b)q(e)h(equal)f(is)g(p)q(erformed)g(b)o(y)g
3429 (attac)o(hing)g(noticers)75 2549 y(to)c Fp(x)150 2555
3430 y Fo(1)183 2549 y Fy(and)g Fp(x)288 2555 y Fo(2)307 2549
3431 y Fy(.)19 b(These)d(noticers)f(con)o(tin)o(ually)e(restrict)j(the)f
3432 (domains)e(of)h Fp(x)1281 2555 y Fo(1)1313 2549 y Fy(and)h
3433 Fp(x)1419 2555 y Fo(2)1451 2549 y Fy(to)g(b)q(e)g(equiv)n(alen)o(t)e
3434 (sets)j(\(using)75 2599 y(the)f Fv(Common)i(Lisp)e Fy(function)f
3435 Fq(=)h Fy(as)f(a)h(test)h(function\))e(as)h(their)g(domains)e(are)i
3436 (restricted.)23 b(F)m(urthermore,)14 b(if)g Fp(x)1889
3437 2605 y Fo(1)1922 2599 y Fy(is)992 2723 y(18)p eop
3438 %%Page: 19 19
3439 19 18 bop 75 195 a Fy(kno)o(wn)16 b(to)g(b)q(e)h(real)f(then)h(the)g
3440 (noticer)g(attac)o(hed)f(to)h Fp(x)965 201 y Fo(2)999
3441 195 y Fy(con)o(tin)o(ually)e(restrict)j(the)e(upp)q(er)i(b)q(ound)e(of)
3442 g Fp(x)1760 201 y Fo(1)1794 195 y Fy(to)g(b)q(e)h(no)75
3443 245 y(higher)h(than)f(the)h(upp)q(er)h(b)q(ound)e(of)g
3444 Fp(x)710 251 y Fo(2)746 245 y Fy(and)g(the)i(lo)o(w)o(er)e(b)q(ound)g
3445 (of)g Fp(x)1224 251 y Fo(1)1260 245 y Fy(to)g(b)q(e)i(no)e(lo)o(w)o(er)
3446 g(than)h(the)g(lo)o(w)o(er)f(b)q(ound)75 295 y(of)h Fp(x)151
3447 301 y Fo(2)169 295 y Fy(.)31 b(The)19 b(noticer)g(of)e
3448 Fp(x)520 301 y Fo(2)557 295 y Fy(p)q(erforms)h(a)g(symmetric)e
3449 (restriction)j(on)f(the)h(b)q(ounds)g(of)e Fp(x)1545
3450 301 y Fo(1)1582 295 y Fy(if)g(it)h(is)g(kno)o(wn)g(to)g(b)q(e)75
3451 345 y(real.)28 b(Restricting)17 b(t)o(w)o(o)g(v)n(alues)g
3452 Fp(x)631 351 y Fo(1)667 345 y Fy(and)g Fp(x)775 351 y
3453 Fo(2)810 345 y Fy(to)g(not)g(b)q(e)h(equal)f(is)g(also)g(p)q(erformed)g
3454 (b)o(y)g(attac)o(hing)f(noticers)j(to)e Fp(x)1932 351
3455 y Fo(1)75 394 y Fy(and)12 b Fp(x)178 400 y Fo(2)197 394
3456 y Fy(.)17 b(These)d(noticers)f(ho)o(w)o(ev)o(er,)g(do)f(not)g(restrict)
3457 i(the)f(domains)e(or)h(ranges)h(of)f Fp(x)1418 400 y
3458 Fo(1)1449 394 y Fy(or)g Fp(x)1522 400 y Fo(2)1540 394
3459 y Fy(.)18 b(They)13 b(simply)d(monitor)75 444 y(their)15
3460 b(con)o(tin)o(ually)e(restrictions)j(and)e(fail)f(when)i(an)o(y)f
3461 (assertion)i(causes)g Fp(x)1272 450 y Fo(1)1305 444 y
3462 Fy(to)e(b)q(e)h(kno)o(wn)f(to)h(b)q(e)g(equal)f(to)h
3463 Fp(x)1840 450 y Fo(2)1858 444 y Fy(.)20 b(See)75 494
3464 y(section)15 b(6)e(for)h(a)f(discussion)i(of)e(v)n(ariable)g(upp)q(er)i
3465 (and)e(lo)o(w)o(er)h(b)q(ounds,)g(and)g(domains.)75 735
3466 y Fq(<v)21 b Fp(x)164 720 y Fo(+)1506 735 y Fy([)p Fu(Deterministic)14
3467 b(F)m(unction)p Fy(])75 887 y(Returns)19 b(a)f(b)q(o)q(olean)g(v)n
3468 (alue)g(whic)o(h)g(is)g(constrained)h(to)f(b)q(e)h Fq(t)f
3469 Fy(if)g(eac)o(h)g(argumen)o(t)g Fp(x)1453 893 y Fh(i)1484
3470 887 y Fy(is)g(less)h(than)g(the)g(follo)o(wing)75 936
3471 y(argumen)o(t)13 b Fp(x)285 942 y Fh(i)p Fo(+1)355 936
3472 y Fy(and)h(constrained)h(to)f(b)q(e)g Fq(nil)g Fy(if)f(some)g(argumen)o
3473 (t)g Fp(x)1197 942 y Fh(i)1225 936 y Fy(is)h(greater)h(than)f(or)g
3474 (equal)g(to)g(the)h(follo)o(wing)75 986 y(argumen)o(t)f
3475 Fp(x)286 992 y Fh(i)p Fo(+1)342 986 y Fy(.)22 b(This)16
3476 b(function)f(tak)o(es)h(one)f(or)h(more)e(argumen)o(ts.)22
3477 b(All)14 b(of)h(the)h(argumen)o(ts)f(are)h(restricted)h(to)e(b)q(e)75
3478 1036 y(real)g(\(see)i(section)f(8\).)22 b(Returns)17
3479 b Fq(t)e Fy(when)g(called)h(with)f(one)g(argumen)o(t.)21
3480 b(A)16 b(call)e(suc)o(h)j(as)e Fq(\(<v)21 b Fp(x)1641
3481 1042 y Fo(1)1681 1036 y Fp(x)1705 1042 y Fo(2)1731 1036
3482 y Fp(:)7 b(:)g(:)e(x)1810 1042 y Fh(n)1832 1036 y Fq(\))15
3483 b Fy(with)75 1086 y(more)e(than)h(t)o(w)o(o)f(argumen)o(ts)g(b)q(eha)o
3484 (v)o(es)i(lik)o(e)e(a)h(conjunction)g(of)f(t)o(w)o(o)g(argumen)o(t)g
3485 (calls:)179 1169 y Fq(\(andv)21 b(\(<v)g Fp(x)421 1175
3486 y Fo(1)461 1169 y Fp(x)485 1175 y Fo(2)503 1169 y Fq(\))p
3487 Fp(:)7 b(:)g(:)n Fq(\(<v)22 b Fp(x)685 1175 y Fh(i)720
3488 1169 y Fp(x)744 1175 y Fh(i)p Fo(+1)800 1169 y Fq(\))p
3489 Fp(:)7 b(:)g(:)n Fq(\(<v)21 b Fp(x)981 1175 y Fh(n)p
3490 Fi(\000)p Fo(1)1068 1169 y Fp(x)1092 1175 y Fh(n)1114
3491 1169 y Fq(\)\))75 1252 y Fy(Beha)o(v)o(es)15 b(as)f(follo)o(ws)f(when)h
3492 (called)g(with)g(t)o(w)o(o)g(argumen)o(ts.)j(Returns)e
3493 Fq(t)f Fy(if)g Fp(x)1298 1258 y Fo(1)1330 1252 y Fy(is)g(kno)o(wn)g(to)
3494 f(b)q(e)i(less)g(than)f Fp(x)1809 1258 y Fo(2)1841 1252
3495 y Fy(at)g(the)75 1302 y(time)e(of)g(call.)18 b(A)13 b(real)g(v)n(alue)g
3496 Fp(x)563 1308 y Fo(1)594 1302 y Fy(is)g(kno)o(wn)g(to)g(b)q(e)h(less)g
3497 (than)f(a)g(real)g(v)n(alue)f Fp(x)1288 1308 y Fo(2)1320
3498 1302 y Fy(if)g Fp(x)1381 1308 y Fo(1)1413 1302 y Fy(has)h(an)g(upp)q
3499 (er)h(b)q(ound,)f Fp(x)1824 1308 y Fo(2)1856 1302 y Fy(has)g(a)75
3500 1352 y(lo)o(w)o(er)g(b)q(ound)h(and)g(the)g(upp)q(er)h(b)q(ound)f(of)f
3501 Fp(x)781 1358 y Fo(1)813 1352 y Fy(is)h(less)g(than)g(the)g(lo)o(w)o
3502 (er)g(b)q(ound)f(of)h Fp(x)1407 1358 y Fo(2)1439 1352
3503 y Fy(\(see)h(section)f(6\).)k(Returns)d Fq(nil)75 1401
3504 y Fy(if)h Fp(x)140 1407 y Fo(1)176 1401 y Fy(is)h(kno)o(wn)f(to)h(b)q
3505 (e)h(greater)g(than)f(or)g(equal)g(to)g Fp(x)958 1407
3506 y Fo(2)993 1401 y Fy(at)g(the)h(time)d(of)i(call.)27
3507 b(A)17 b(real)g(v)n(alue)f Fp(x)1638 1407 y Fo(1)1674
3508 1401 y Fy(is)h(kno)o(wn)f(to)h(b)q(e)75 1451 y(greater)f(than)e(or)h
3509 (equal)f(to)g(a)g(real)h(v)n(alue)f Fp(x)776 1457 y Fo(2)809
3510 1451 y Fy(if)f Fp(x)871 1457 y Fo(1)904 1451 y Fy(has)i(a)f(lo)o(w)o
3511 (er)g(b)q(ound,)h Fp(x)1288 1457 y Fo(2)1321 1451 y Fy(has)f(an)h(upp)q
3512 (er)g(b)q(ound)g(and)f(the)h(lo)o(w)o(er)75 1501 y(b)q(ound)d(of)g
3513 Fp(x)271 1507 y Fo(1)302 1501 y Fy(is)g(greater)h(than)g(or)f(equal)g
3514 (to)g(the)h(upp)q(er)g(b)q(ound)g(of)f Fp(x)1167 1507
3515 y Fo(2)1197 1501 y Fy(\(see)i(section)f(6\).)k(If)12
3516 b(it)g(is)g(not)h(kno)o(wn)f(whether)75 1551 y(or)j(not)g
3517 Fp(x)226 1557 y Fo(1)260 1551 y Fy(is)g(less)h(than)f
3518 Fp(x)503 1557 y Fo(2)536 1551 y Fy(when)h Fq(<v)f Fy(is)g(called)f
3519 (then)i Fq(>v)f Fy(creates)i(and)e(returns)i(a)e(new)g(b)q(o)q(olean)g
3520 (v)n(ariable)f Fp(v)q Fy(.)23 b(The)75 1601 y(v)n(alues)15
3521 b(of)f Fp(x)272 1607 y Fo(1)291 1601 y Fy(,)g Fp(x)341
3522 1607 y Fo(2)375 1601 y Fy(and)h Fp(v)h Fy(are)g(m)o(utually)d
3523 (constrained)j(via)e(noticers)i(so)f(that)g Fp(v)i Fy(is)e(equal)g(to)g
3524 Fq(t)g Fy(if)f(and)h(only)f(if)h Fp(x)1889 1607 y Fo(1)1922
3525 1601 y Fy(is)75 1650 y(kno)o(wn)g(to)h(b)q(e)g(less)g(than)g
3526 Fp(x)520 1656 y Fo(2)553 1650 y Fy(and)g Fp(v)h Fy(is)e(equal)h(to)f
3527 Fq(nil)g Fy(if)g(and)g(only)g(if)g Fp(x)1240 1656 y Fo(1)1273
3528 1650 y Fy(is)h(kno)o(wn)f(to)g(b)q(e)i(greater)f(than)g(or)f(equal)75
3529 1700 y(to)h Fp(x)152 1706 y Fo(2)171 1700 y Fy(.)26 b(If)16
3530 b(it)g(later)h(b)q(ecomes)g(kno)o(wn)f(that)g Fp(x)815
3531 1706 y Fo(1)850 1700 y Fy(is)h(less)g(than)f Fp(x)1097
3532 1706 y Fo(2)1116 1700 y Fy(,)h(noticers)g(attac)o(hed)g(to)g
3533 Fp(x)1552 1706 y Fo(1)1587 1700 y Fy(and)f Fp(x)1694
3534 1706 y Fo(2)1729 1700 y Fy(restrict)i Fp(v)g Fy(to)75
3535 1750 y(equal)e Fq(t)p Fy(.)25 b(Lik)o(ewise,)16 b(if)f(it)h(later)g(b)q
3536 (ecomes)h(kno)o(wn)e(that)i Fp(x)1028 1756 y Fo(1)1062
3537 1750 y Fy(is)f(greater)h(than)g(or)f(equal)g(to)g Fp(x)1591
3538 1756 y Fo(2)1609 1750 y Fy(,)g(noticers)h(attac)o(hed)75
3539 1800 y(to)e Fp(x)151 1806 y Fo(1)185 1800 y Fy(and)h
3540 Fp(x)292 1806 y Fo(2)325 1800 y Fy(restrict)i Fp(v)f
3541 Fy(to)e(equal)g Fq(nil)p Fy(.)23 b(F)m(urthermore,)15
3542 b(if)g Fp(v)i Fy(ev)o(er)f(b)q(ecomes)g(kno)o(wn)f(to)g(equal)h
3543 Fq(t)f Fy(then)h(a)f(noticer)75 1850 y(attac)o(hed)i(to)g
3544 Fp(v)h Fy(restricts)g Fp(x)525 1856 y Fo(1)560 1850 y
3545 Fy(to)e(b)q(e)i(less)f(than)f Fp(x)875 1856 y Fo(2)894
3546 1850 y Fy(.)26 b(Lik)o(ewise,)16 b(if)g Fp(v)i Fy(ev)o(er)g(b)q(ecomes)
3547 e(kno)o(wn)h(to)f(equal)g Fq(nil)g Fy(then)h(a)75 1899
3548 y(noticer)g(attac)o(hed)g(to)f Fp(v)h Fy(restricts)i
3549 Fp(x)665 1905 y Fo(1)699 1899 y Fy(to)d(b)q(e)h(greater)g(than)f(or)h
3550 (equal)e(to)h Fp(x)1295 1905 y Fo(2)1314 1899 y Fy(.)25
3551 b(Restricting)16 b(a)g(real)g(v)n(alue)g Fp(x)1820 1905
3552 y Fo(1)1854 1899 y Fy(to)g(b)q(e)75 1949 y(less)g(than)g(a)g(real)g(v)n
3553 (alue)f Fp(x)505 1955 y Fo(2)539 1949 y Fy(is)g(p)q(erformed)h(b)o(y)f
3554 (attac)o(hing)h(noticers)g(to)g Fp(x)1261 1955 y Fo(1)1295
3555 1949 y Fy(and)g Fp(x)1402 1955 y Fo(2)1420 1949 y Fy(.)24
3556 b(The)16 b(noticer)h(attac)o(hed)f(to)g Fp(x)1932 1955
3557 y Fo(1)75 1999 y Fy(con)o(tin)o(ually)11 b(restricts)j(the)f(lo)o(w)o
3558 (er)f(b)q(ound)g(of)g Fp(x)818 2005 y Fo(2)849 1999 y
3559 Fy(to)g(b)q(e)h(no)f(lo)o(w)o(er)g(than)g(the)h(upp)q(er)g(b)q(ound)g
3560 (of)f Fp(x)1595 2005 y Fo(1)1625 1999 y Fy(if)g Fp(x)1686
3561 2005 y Fo(1)1716 1999 y Fy(has)h(an)f(upp)q(er)75 2049
3562 y(b)q(ound.)18 b(The)c(noticer)g(attac)o(hed)f(to)h Fp(x)685
3563 2055 y Fo(2)716 2049 y Fy(con)o(tin)o(ually)e(restricts)j(the)f(upp)q
3564 (er)g(b)q(ound)g(of)e Fp(x)1475 2055 y Fo(1)1507 2049
3565 y Fy(to)h(b)q(e)h(no)f(higher)g(than)g(the)75 2099 y(lo)o(w)o(er)h(b)q
3566 (ound)g(of)g Fp(x)384 2105 y Fo(2)416 2099 y Fy(if)f
3567 Fp(x)478 2105 y Fo(2)511 2099 y Fy(has)h(a)g(lo)o(w)o(er)g(b)q(ound.)19
3568 b(Since)c(these)g(restrictions)h(only)d(guaran)o(tee)i(that)f
3569 Fp(x)1701 2105 y Fo(1)1733 2099 y Fy(b)q(e)h(less)g(than)75
3570 2149 y(or)d(equal)g(to)g Fp(x)305 2155 y Fo(2)323 2149
3571 y Fy(,)g(the)h(constrain)o(t)f(that)h Fp(x)723 2155 y
3572 Fo(1)753 2149 y Fy(b)q(e)g(strictly)f(less)h(than)f Fp(x)1142
3573 2155 y Fo(2)1173 2149 y Fy(is)g(enforced)h(b)o(y)f(ha)o(ving)f(the)i
3574 (noticers)g(fail)d(when)75 2198 y(b)q(oth)k Fp(x)197
3575 2204 y Fo(1)229 2198 y Fy(and)g Fp(x)334 2204 y Fo(2)366
3576 2198 y Fy(b)q(ecome)g(kno)o(wn)g(to)g(b)q(e)g(equal.)k(Restricting)c(a)
3577 g(real)g(v)n(alue)f Fp(x)1340 2204 y Fo(1)1373 2198 y
3578 Fy(to)g(b)q(e)i(greater)g(than)f(or)g(equal)f(to)h(a)75
3579 2248 y(real)f(v)n(alue)f Fp(x)285 2254 y Fo(2)316 2248
3580 y Fy(is)h(p)q(erformed)g(b)o(y)f(an)h(analogous)f(set)i(of)e(noticers)i
3581 (without)e(this)h(last)g(equalit)o(y)f(c)o(hec)o(k.)19
3582 b(See)14 b(section)f(6)75 2298 y(for)h(a)f(discussion)i(of)e(v)n
3583 (ariable)g(upp)q(er)h(and)g(lo)o(w)o(er)g(b)q(ounds,)g(and)f(domains.)
3584 75 2539 y Fq(<=v)21 b Fp(x)186 2524 y Fo(+)1506 2539
3585 y Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])992
3586 2723 y(19)p eop
3587 %%Page: 20 20
3588 20 19 bop 75 195 a Fy(Returns)17 b(a)f(b)q(o)q(olean)f(v)n(alue)h(whic)
3589 o(h)g(is)g(constrained)g(to)g(b)q(e)h Fq(t)f Fy(if)f(eac)o(h)i(argumen)
3590 o(t)e Fp(x)1424 201 y Fh(i)1453 195 y Fy(is)h(less)h(than)f(or)g(equal)
3591 f(to)h(the)75 245 y(follo)o(wing)e(argumen)o(t)h Fp(x)465
3592 251 y Fh(i)p Fo(+1)537 245 y Fy(and)h(constrained)h(to)g(b)q(e)g
3593 Fq(nil)e Fy(if)h(some)f(argumen)o(t)h Fp(x)1398 251 y
3594 Fh(i)1428 245 y Fy(is)g(greater)h(than)g(the)g(follo)o(wing)75
3595 295 y(argumen)o(t)d Fp(x)286 301 y Fh(i)p Fo(+1)342 295
3596 y Fy(.)22 b(This)16 b(function)f(tak)o(es)h(one)f(or)h(more)e(argumen)o
3597 (ts.)22 b(All)14 b(of)h(the)h(argumen)o(ts)f(are)h(restricted)h(to)e(b)
3598 q(e)75 345 y(real)f(\(see)i(section)f(8\).)k(Returns)c
3599 Fq(t)f Fy(when)h(called)f(with)g(one)g(argumen)o(t.)k(A)c(call)g(suc)o
3600 (h)h(as)f Fq(\(<=v)21 b Fp(x)1642 351 y Fo(1)1682 345
3601 y Fp(x)1706 351 y Fo(2)1732 345 y Fp(:)7 b(:)g(:)e(x)1811
3602 351 y Fh(n)1833 345 y Fq(\))14 b Fy(with)75 394 y(more)f(than)h(t)o(w)o
3603 (o)f(argumen)o(ts)g(b)q(eha)o(v)o(es)i(lik)o(e)e(a)h(conjunction)g(of)f
3604 (t)o(w)o(o)g(argumen)o(t)g(calls:)179 475 y Fq(\(andv)21
3605 b(\(<=v)g Fp(x)443 481 y Fo(1)483 475 y Fp(x)507 481
3606 y Fo(2)525 475 y Fq(\))p Fp(:)7 b(:)g(:)n Fq(\(<=v)21
3607 b Fp(x)728 481 y Fh(i)764 475 y Fp(x)788 481 y Fh(i)p
3608 Fo(+1)843 475 y Fq(\))p Fp(:)7 b(:)g(:)n Fq(\(<=v)21
3609 b Fp(x)1046 481 y Fh(n)p Fi(\000)p Fo(1)1133 475 y Fp(x)1157
3610 481 y Fh(n)1179 475 y Fq(\)\))75 556 y Fy(Beha)o(v)o(es)16
3611 b(as)f(follo)o(ws)e(when)j(called)f(with)f(t)o(w)o(o)h(argumen)o(ts.)20
3612 b(Returns)c Fq(t)f Fy(if)f Fp(x)1309 562 y Fo(1)1342
3613 556 y Fy(is)h(kno)o(wn)f(to)h(b)q(e)h(less)f(than)g(or)g(equal)75
3614 606 y(to)g Fp(x)151 612 y Fo(2)184 606 y Fy(at)f(the)i(time)d(of)h
3615 (call.)20 b(A)15 b(real)g(v)n(alue)f Fp(x)806 612 y Fo(1)839
3616 606 y Fy(is)g(kno)o(wn)h(to)f(b)q(e)i(less)f(than)g(or)g(equal)f(to)h
3617 (a)f(real)h(v)n(alue)f Fp(x)1761 612 y Fo(2)1794 606
3618 y Fy(if)g Fp(x)1857 612 y Fo(1)1890 606 y Fy(has)75 655
3619 y(an)j(upp)q(er)g(b)q(ound,)h Fp(x)425 661 y Fo(2)460
3620 655 y Fy(has)f(a)f(lo)o(w)o(er)h(b)q(ound)g(and)f(the)i(upp)q(er)g(b)q
3621 (ound)f(of)f Fp(x)1302 661 y Fo(1)1337 655 y Fy(is)h(less)g(than)g(or)g
3622 (equal)f(to)h(the)g(lo)o(w)o(er)75 705 y(b)q(ound)c(of)g
3623 Fp(x)273 711 y Fo(2)304 705 y Fy(\(see)h(section)g(6\).)k(Returns)13
3624 b Fq(nil)g Fy(if)f Fp(x)887 711 y Fo(1)918 705 y Fy(is)h(kno)o(wn)g(to)
3625 f(b)q(e)i(greater)g(than)f Fp(x)1455 711 y Fo(2)1486
3626 705 y Fy(at)g(the)h(time)e(of)g(call.)17 b(A)c(real)75
3627 755 y(v)n(alue)f Fp(x)205 761 y Fo(1)235 755 y Fy(is)g(kno)o(wn)g(to)g
3628 (b)q(e)h(greater)g(than)f(a)g(real)g(v)n(alue)g Fp(x)985
3629 761 y Fo(2)1015 755 y Fy(if)g Fp(x)1076 761 y Fo(1)1106
3630 755 y Fy(has)h(a)f(lo)o(w)o(er)g(b)q(ound,)g Fp(x)1481
3631 761 y Fo(2)1511 755 y Fy(has)h(an)f(upp)q(er)h(b)q(ound)f(and)75
3632 805 y(the)i(lo)o(w)o(er)g(b)q(ound)g(of)f Fp(x)454 811
3633 y Fo(1)486 805 y Fy(is)h(greater)g(than)g(the)h(upp)q(er)f(b)q(ound)g
3634 (of)f Fp(x)1154 811 y Fo(2)1187 805 y Fy(\(see)i(section)f(6\).)k(If)13
3635 b(it)h(is)g(not)f(kno)o(wn)h(whether)75 855 y(or)j(not)g
3636 Fp(x)230 861 y Fo(1)265 855 y Fy(is)g(less)h(than)f(or)g(equal)g(to)g
3637 Fp(x)735 861 y Fo(2)770 855 y Fy(when)h Fq(>=v)e Fy(is)h(called)g(then)
3638 h Fq(>=v)e Fy(creates)j(and)e(returns)i(a)e(new)g(b)q(o)q(olean)75
3639 905 y(v)n(ariable)e Fp(v)q Fy(.)24 b(The)16 b(v)n(alues)g(of)f
3640 Fp(x)576 911 y Fo(1)594 905 y Fy(,)h Fp(x)646 911 y Fo(2)680
3641 905 y Fy(and)f Fp(v)j Fy(are)e(m)o(utually)d(constrained)k(via)e
3642 (noticers)h(so)g(that)g Fp(v)h Fy(is)f(equal)g(to)f Fq(t)h
3643 Fy(if)75 954 y(and)d(only)f(if)g Fp(x)306 960 y Fo(1)338
3644 954 y Fy(is)g(kno)o(wn)h(to)g(b)q(e)g(less)h(than)f(or)g(equal)g(to)g
3645 Fp(x)1019 960 y Fo(2)1050 954 y Fy(and)g Fp(v)h Fy(is)f(equal)g(to)g
3646 Fq(nil)f Fy(if)g(and)h(only)f(if)g Fp(x)1710 960 y Fo(1)1742
3647 954 y Fy(is)h(kno)o(wn)f(to)75 1004 y(b)q(e)h(greater)h(than)e
3648 Fp(x)389 1010 y Fo(2)408 1004 y Fy(.)17 b(If)c(it)f(later)g(b)q(ecomes)
3649 h(kno)o(wn)g(that)f Fp(x)1020 1010 y Fo(1)1051 1004 y
3650 Fy(is)h(less)g(than)f(or)h(equal)f(to)h Fp(x)1494 1010
3651 y Fo(2)1512 1004 y Fy(,)f(noticers)i(attac)o(hed)f(to)g
3652 Fp(x)1932 1010 y Fo(1)75 1054 y Fy(and)k Fp(x)183 1060
3653 y Fo(2)218 1054 y Fy(restrict)h Fp(v)g Fy(to)f(equal)f
3654 Fq(t)p Fy(.)27 b(Lik)o(ewise,)16 b(if)g(it)h(later)g(b)q(ecomes)g(kno)o
3655 (wn)f(that)h Fp(x)1415 1060 y Fo(1)1450 1054 y Fy(is)f(greater)i(than)f
3656 Fp(x)1762 1060 y Fo(2)1780 1054 y Fy(,)g(noticers)75
3657 1104 y(attac)o(hed)f(to)g Fp(x)323 1110 y Fo(1)357 1104
3658 y Fy(and)g Fp(x)464 1110 y Fo(2)498 1104 y Fy(restrict)h
3659 Fp(v)h Fy(to)d(equal)h Fq(nil)p Fy(.)23 b(F)m(urthermore,)15
3660 b(if)g Fp(v)j Fy(ev)o(er)e(b)q(ecomes)g(kno)o(wn)g(to)f(equal)h
3661 Fq(t)f Fy(then)75 1154 y(a)h(noticer)g(attac)o(hed)g(to)g
3662 Fp(v)i Fy(restricts)f Fp(x)699 1160 y Fo(1)734 1154 y
3663 Fy(to)e(b)q(e)i(less)f(than)g(or)g(equal)f(to)h Fp(x)1263
3664 1160 y Fo(2)1281 1154 y Fy(.)24 b(Lik)o(ewise,)16 b(if)f
3665 Fp(v)j Fy(ev)o(er)e(b)q(ecomes)g(kno)o(wn)75 1203 y(to)e(equal)f
3666 Fq(nil)h Fy(then)g(a)g(noticer)g(attac)o(hed)h(to)f Fp(v)h
3667 Fy(restricts)h Fp(x)1022 1209 y Fo(1)1054 1203 y Fy(to)e(b)q(e)g
3668 (greater)h(than)f Fp(x)1423 1209 y Fo(2)1442 1203 y Fy(.)k(Restricting)
3669 c(a)g(real)f(v)n(alue)h Fp(x)1932 1209 y Fo(1)75 1253
3670 y Fy(to)g(b)q(e)g(less)h(than)e(or)h(equal)g(to)f(a)h(real)f(v)n(alue)h
3671 Fp(x)813 1259 y Fo(2)845 1253 y Fy(is)f(p)q(erformed)h(b)o(y)f(attac)o
3672 (hing)h(noticers)g(to)g Fp(x)1555 1259 y Fo(1)1587 1253
3673 y Fy(and)g Fp(x)1692 1259 y Fo(2)1710 1253 y Fy(.)k(The)c(noticer)75
3674 1303 y(attac)o(hed)i(to)g Fp(x)323 1309 y Fo(1)357 1303
3675 y Fy(con)o(tin)o(ually)e(restricts)k(the)e(lo)o(w)o(er)g(b)q(ound)g(of)
3676 f Fp(x)1121 1309 y Fo(2)1155 1303 y Fy(to)g(b)q(e)i(no)e(lo)o(w)o(er)h
3677 (than)f(the)i(upp)q(er)g(b)q(ound)e(of)h Fp(x)1932 1309
3678 y Fo(1)75 1353 y Fy(if)d Fp(x)137 1359 y Fo(1)169 1353
3679 y Fy(has)h(an)f(upp)q(er)i(b)q(ound.)j(The)c(noticer)h(attac)o(hed)f
3680 (to)g Fp(x)1031 1359 y Fo(2)1063 1353 y Fy(con)o(tin)o(ually)e
3681 (restricts)k(the)e(upp)q(er)h(b)q(ound)f(of)f Fp(x)1825
3682 1359 y Fo(1)1857 1353 y Fy(to)g(b)q(e)75 1403 y(no)h(higher)g(than)g
3683 (the)g(lo)o(w)o(er)g(b)q(ound)g(of)f Fp(x)736 1409 y
3684 Fo(2)768 1403 y Fy(if)g Fp(x)830 1409 y Fo(2)862 1403
3685 y Fy(has)h(a)g(lo)o(w)o(er)f(b)q(ound.)19 b(Restricting)14
3686 b(a)f(real)h(v)n(alue)f Fp(x)1683 1409 y Fo(1)1716 1403
3687 y Fy(to)g(b)q(e)i(greater)75 1452 y(than)d(a)g(real)g(v)n(alue)g
3688 Fp(x)412 1458 y Fo(2)442 1452 y Fy(is)g(p)q(erformed)g(b)o(y)g(an)g
3689 (analogous)e(set)k(of)d(noticers.)18 b(Since)13 b(these)h(restrictions)
3690 f(only)e(guaran)o(tee)75 1502 y(that)j Fp(x)189 1508
3691 y Fo(1)221 1502 y Fy(b)q(e)h(greater)f(than)g(or)g(equal)g(to)f
3692 Fp(x)750 1508 y Fo(2)769 1502 y Fy(,)g(the)i(constrain)o(t)f(that)g
3693 Fp(x)1175 1508 y Fo(1)1207 1502 y Fy(b)q(e)g(strictly)h(greater)f(than)
3694 g Fp(x)1667 1508 y Fo(2)1699 1502 y Fy(is)g(enforced)h(b)o(y)75
3695 1552 y(ha)o(ving)e(the)i(noticers)g(fail)e(when)h(b)q(oth)h
3696 Fp(x)738 1558 y Fo(1)770 1552 y Fy(and)f Fp(x)875 1558
3697 y Fo(2)908 1552 y Fy(b)q(ecome)g(kno)o(wn)f(to)h(b)q(e)h(equal.)k(See)c
3698 (section)g(6)f(for)g(a)f(discussion)75 1602 y(of)g(v)n(ariable)g(upp)q
3699 (er)i(and)f(lo)o(w)o(er)f(b)q(ounds,)h(and)g(domains.)75
3700 1840 y Fq(>v)21 b Fp(x)164 1825 y Fo(+)1506 1840 y Fy([)p
3701 Fu(Deterministic)14 b(F)m(unction)p Fy(])75 1989 y(Returns)i(a)e(b)q(o)
3702 q(olean)g(v)n(alue)g(whic)o(h)h(is)g(constrained)g(to)g(b)q(e)g
3703 Fq(t)f Fy(if)g(eac)o(h)i(argumen)o(t)d Fp(x)1406 1995
3704 y Fh(i)1434 1989 y Fy(is)i(greater)h(than)e(the)i(follo)o(wing)75
3705 2039 y(argumen)o(t)h Fp(x)289 2045 y Fh(i)p Fo(+1)362
3706 2039 y Fy(and)g(constrained)i(to)e(b)q(e)i Fq(nil)e Fy(if)g(some)f
3707 (argumen)o(t)h Fp(x)1233 2045 y Fh(i)1264 2039 y Fy(is)h(less)g(than)g
3708 (or)f(equal)h(to)f(the)i(follo)o(wing)75 2088 y(argumen)o(t)14
3709 b Fp(x)286 2094 y Fh(i)p Fo(+1)342 2088 y Fy(.)22 b(This)16
3710 b(function)f(tak)o(es)h(one)f(or)h(more)e(argumen)o(ts.)22
3711 b(All)14 b(of)h(the)h(argumen)o(ts)f(are)h(restricted)h(to)e(b)q(e)75
3712 2138 y(real)g(\(see)i(section)f(8\).)22 b(Returns)17
3713 b Fq(t)e Fy(when)g(called)h(with)f(one)g(argumen)o(t.)21
3714 b(A)16 b(call)e(suc)o(h)j(as)e Fq(\(>v)21 b Fp(x)1641
3715 2144 y Fo(1)1681 2138 y Fp(x)1705 2144 y Fo(2)1731 2138
3716 y Fp(:)7 b(:)g(:)e(x)1810 2144 y Fh(n)1832 2138 y Fq(\))15
3717 b Fy(with)75 2188 y(more)e(than)h(t)o(w)o(o)f(argumen)o(ts)g(b)q(eha)o
3718 (v)o(es)i(lik)o(e)e(a)h(conjunction)g(of)f(t)o(w)o(o)g(argumen)o(t)g
3719 (calls:)179 2269 y Fq(\(andv)21 b(\(>v)g Fp(x)421 2275
3720 y Fo(1)461 2269 y Fp(x)485 2275 y Fo(2)503 2269 y Fq(\))p
3721 Fp(:)7 b(:)g(:)n Fq(\(>v)22 b Fp(x)685 2275 y Fh(i)720
3722 2269 y Fp(x)744 2275 y Fh(i)p Fo(+1)800 2269 y Fq(\))p
3723 Fp(:)7 b(:)g(:)n Fq(\(>v)21 b Fp(x)981 2275 y Fh(n)p
3724 Fi(\000)p Fo(1)1068 2269 y Fp(x)1092 2275 y Fh(n)1114
3725 2269 y Fq(\)\))75 2350 y Fy(Beha)o(v)o(es)15 b(as)g(follo)o(ws)e(when)i
3726 (called)f(with)g(t)o(w)o(o)g(argumen)o(ts.)19 b(Returns)c
3727 Fq(t)f Fy(if)g Fp(x)1302 2356 y Fo(1)1335 2350 y Fy(is)g(kno)o(wn)g(to)
3728 g(b)q(e)h(greater)h(than)e Fp(x)1880 2356 y Fo(2)1913
3729 2350 y Fy(at)75 2399 y(the)i(time)f(of)g(call.)23 b(A)15
3730 b(real)h(v)n(alue)f Fp(x)654 2405 y Fo(1)688 2399 y Fy(is)h(kno)o(wn)f
3731 (to)h(b)q(e)g(greater)h(than)f(a)f(real)h(v)n(alue)f
3732 Fp(x)1470 2405 y Fo(2)1504 2399 y Fy(if)g Fp(x)1568 2405
3733 y Fo(1)1602 2399 y Fy(has)h(a)f(lo)o(w)o(er)g(b)q(ound,)75
3734 2449 y Fp(x)99 2455 y Fo(2)130 2449 y Fy(has)e(an)g(upp)q(er)g(b)q
3735 (ound)g(and)g(the)g(lo)o(w)o(er)f(b)q(ound)h(of)g Fp(x)959
3736 2455 y Fo(1)990 2449 y Fy(is)f(greater)i(than)f(the)g(upp)q(er)h(b)q
3737 (ound)f(of)f Fp(x)1651 2455 y Fo(2)1682 2449 y Fy(\(see)i(section)g
3738 (6\).)75 2499 y(Returns)f Fq(nil)f Fy(if)g Fp(x)370 2505
3739 y Fo(1)401 2499 y Fy(is)g(kno)o(wn)g(to)h(b)q(e)g(less)g(than)f(or)h
3740 (equal)f(to)h Fp(x)1078 2505 y Fo(2)1108 2499 y Fy(at)g(the)g(time)e
3741 (of)h(call.)17 b(A)12 b(real)h(v)n(alue)f Fp(x)1712 2505
3742 y Fo(1)1743 2499 y Fy(is)g(kno)o(wn)g(to)75 2549 y(b)q(e)j(less)g(than)
3743 g(or)f(equal)g(to)g(a)g(real)h(v)n(alue)e Fp(x)767 2555
3744 y Fo(2)800 2549 y Fy(if)h Fp(x)863 2555 y Fo(1)895 2549
3745 y Fy(has)h(an)f(upp)q(er)i(b)q(ound,)e Fp(x)1312 2555
3746 y Fo(2)1344 2549 y Fy(has)h(a)f(lo)o(w)o(er)g(b)q(ound)h(and)f(the)h
3747 (upp)q(er)75 2599 y(b)q(ound)f(of)e Fp(x)273 2605 y Fo(1)305
3748 2599 y Fy(is)i(less)g(than)f(or)h(equal)f(to)g(the)h(lo)o(w)o(er)f(b)q
3749 (ound)h(of)f Fp(x)1107 2605 y Fo(2)1138 2599 y Fy(\(see)i(section)f
3750 (6\).)k(If)13 b(it)g(is)h(not)f(kno)o(wn)g(whether)i(or)992
3751 2723 y(20)p eop
3752 %%Page: 21 21
3753 21 20 bop 75 195 a Fy(not)15 b Fp(x)174 201 y Fo(1)206
3754 195 y Fy(is)g(greater)h(than)e Fp(x)512 201 y Fo(2)545
3755 195 y Fy(when)h Fq(>v)f Fy(is)h(called)f(then)h Fq(>v)g
3756 Fy(creates)h(and)e(returns)j(a)d(new)h(b)q(o)q(olean)f(v)n(ariable)g
3757 Fp(v)q Fy(.)21 b(The)75 245 y(v)n(alues)15 b(of)f Fp(x)272
3758 251 y Fo(1)291 245 y Fy(,)g Fp(x)341 251 y Fo(2)375 245
3759 y Fy(and)h Fp(v)h Fy(are)g(m)o(utually)d(constrained)j(via)e(noticers)i
3760 (so)f(that)g Fp(v)i Fy(is)e(equal)g(to)g Fq(t)g Fy(if)f(and)h(only)f
3761 (if)h Fp(x)1889 251 y Fo(1)1922 245 y Fy(is)75 295 y(kno)o(wn)g(to)h(b)
3762 q(e)g(greater)g(than)g Fp(x)584 301 y Fo(2)618 295 y
3763 Fy(and)f Fp(v)i Fy(is)f(equal)f(to)g Fq(nil)g Fy(if)g(and)g(only)g(if)g
3764 Fp(x)1304 301 y Fo(1)1338 295 y Fy(is)g(kno)o(wn)g(to)h(b)q(e)g(less)g
3765 (than)g(or)f(equal)75 345 y(to)f Fp(x)150 351 y Fo(2)168
3766 345 y Fy(.)k(If)13 b(it)h(later)g(b)q(ecomes)g(kno)o(wn)f(that)h
3767 Fp(x)788 351 y Fo(1)820 345 y Fy(is)g(greater)g(than)g
3768 Fp(x)1123 351 y Fo(2)1142 345 y Fy(,)f(noticers)i(attac)o(hed)f(to)g
3769 Fp(x)1566 351 y Fo(1)1598 345 y Fy(and)f Fp(x)1702 351
3770 y Fo(2)1734 345 y Fy(restrict)j Fp(v)f Fy(to)75 394 y(equal)f
3771 Fq(t)p Fy(.)k(Lik)o(ewise,)c(if)f(it)h(later)g(b)q(ecomes)g(kno)o(wn)g
3772 (that)g Fp(x)1004 400 y Fo(1)1036 394 y Fy(is)g(less)h(than)f(or)g
3773 (equal)g(to)g Fp(x)1488 400 y Fo(2)1506 394 y Fy(,)g(noticers)h(attac)o
3774 (hed)g(to)f Fp(x)1932 400 y Fo(1)75 444 y Fy(and)e Fp(x)178
3775 450 y Fo(2)209 444 y Fy(restrict)i Fp(v)g Fy(to)e(equal)h
3776 Fq(nil)p Fy(.)j(F)m(urthermore,)d(if)e Fp(v)j Fy(ev)o(er)g(b)q(ecomes)e
3777 (kno)o(wn)g(to)h(equal)f Fq(t)g Fy(then)h(a)f(noticer)h(attac)o(hed)75
3778 494 y(to)i Fp(v)i Fy(restricts)g Fp(x)349 500 y Fo(1)382
3779 494 y Fy(to)e(b)q(e)g(greater)i(than)e Fp(x)756 500 y
3780 Fo(2)774 494 y Fy(.)21 b(Lik)o(ewise,)15 b(if)f Fp(v)j
3781 Fy(ev)o(er)f(b)q(ecomes)f(kno)o(wn)g(to)g(equal)f Fq(nil)h
3782 Fy(then)h(a)e(noticer)75 544 y(attac)o(hed)h(to)g Fp(v)h
3783 Fy(restricts)g Fp(x)517 550 y Fo(1)550 544 y Fy(to)f(b)q(e)g(less)g
3784 (than)g(or)f(equal)g(to)h Fp(x)1071 550 y Fo(2)1089 544
3785 y Fy(.)20 b(Restricting)15 b(a)f(real)h(v)n(alue)f Fp(x)1584
3786 550 y Fo(1)1617 544 y Fy(to)g(b)q(e)h(greater)h(than)75
3787 594 y(a)e(real)f(v)n(alue)h Fp(x)322 600 y Fo(2)354 594
3788 y Fy(is)g(p)q(erformed)f(b)o(y)h(attac)o(hing)f(noticers)i(to)f
3789 Fp(x)1065 600 y Fo(1)1097 594 y Fy(and)g Fp(x)1202 600
3790 y Fo(2)1220 594 y Fy(.)k(The)d(noticer)f(attac)o(hed)h(to)e
3791 Fp(x)1718 600 y Fo(1)1751 594 y Fy(con)o(tin)o(ually)75
3792 643 y(restricts)18 b(the)g(upp)q(er)f(b)q(ound)g(of)f
3793 Fp(x)638 649 y Fo(2)673 643 y Fy(to)g(b)q(e)h(no)g(higher)f(than)h(the)
3794 g(lo)o(w)o(er)f(b)q(ound)h(of)f Fp(x)1465 649 y Fo(1)1500
3795 643 y Fy(if)f Fp(x)1564 649 y Fo(1)1599 643 y Fy(has)i(a)f(lo)o(w)o(er)
3796 g(b)q(ound.)75 693 y(The)h(noticer)g(attac)o(hed)g(to)f
3797 Fp(x)553 699 y Fo(2)587 693 y Fy(con)o(tin)o(ually)f(restricts)j(the)f
3798 (lo)o(w)o(er)f(b)q(ound)g(of)g Fp(x)1354 699 y Fo(1)1389
3799 693 y Fy(to)g(b)q(e)h(no)f(lo)o(w)o(er)g(than)g(the)h(upp)q(er)75
3800 743 y(b)q(ound)e(of)f Fp(x)276 749 y Fo(2)309 743 y Fy(if)g
3801 Fp(x)372 749 y Fo(2)405 743 y Fy(has)h(an)f(upp)q(er)i(b)q(ound.)21
3802 b(Since)15 b(these)h(restrictions)g(only)e(guaran)o(tee)h(that)g
3803 Fp(x)1635 749 y Fo(1)1668 743 y Fy(b)q(e)g(greater)h(than)75
3804 793 y(or)e(equal)g(to)h Fp(x)312 799 y Fo(2)330 793 y
3805 Fy(,)f(the)h(constrain)o(t)g(that)f Fp(x)738 799 y Fo(1)771
3806 793 y Fy(b)q(e)h(strictly)g(greater)g(than)f Fp(x)1233
3807 799 y Fo(2)1266 793 y Fy(is)g(enforced)i(b)o(y)e(ha)o(ving)f(the)i
3808 (noticers)g(fail)75 843 y(when)d(b)q(oth)g Fp(x)301 849
3809 y Fo(1)332 843 y Fy(and)f Fp(x)434 849 y Fo(2)465 843
3810 y Fy(b)q(ecome)g(kno)o(wn)h(to)g(b)q(e)g(equal.)17 b(Restricting)12
3811 b(a)g(real)g(v)n(alue)f Fp(x)1421 849 y Fo(1)1451 843
3812 y Fy(to)h(b)q(e)h(less)f(than)g(or)g(equal)f(to)h(a)75
3813 892 y(real)h(v)n(alue)f Fp(x)285 898 y Fo(2)316 892 y
3814 Fy(is)h(p)q(erformed)g(b)o(y)f(an)h(analogous)f(set)i(of)e(noticers)i
3815 (without)e(this)h(last)g(equalit)o(y)f(c)o(hec)o(k.)19
3816 b(See)14 b(section)f(6)75 942 y(for)h(a)f(discussion)i(of)e(v)n
3817 (ariable)g(upp)q(er)h(and)g(lo)o(w)o(er)g(b)q(ounds,)g(and)f(domains.)
3818 75 1184 y Fq(>=v)21 b Fp(x)186 1169 y Fo(+)1506 1184
3819 y Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
3820 1335 y(Returns)j(a)g(b)q(o)q(olean)f(v)n(alue)g(whic)o(h)g(is)h
3821 (constrained)g(to)f(b)q(e)h Fq(t)g Fy(if)e(eac)o(h)i(argumen)o(t)f
3822 Fp(x)1430 1341 y Fh(i)1460 1335 y Fy(is)g(greater)i(than)e(or)h(equal)f
3823 (to)75 1385 y(the)g(follo)o(wing)e(argumen)o(t)g Fp(x)537
3824 1391 y Fh(i)p Fo(+1)609 1385 y Fy(and)h(constrained)i(to)f(b)q(e)g
3825 Fq(nil)f Fy(if)g(some)g(argumen)o(t)g Fp(x)1465 1391
3826 y Fh(i)1494 1385 y Fy(is)h(less)g(than)g(the)h(follo)o(wing)75
3827 1435 y(argumen)o(t)d Fp(x)286 1441 y Fh(i)p Fo(+1)342
3828 1435 y Fy(.)22 b(This)16 b(function)f(tak)o(es)h(one)f(or)h(more)e
3829 (argumen)o(ts.)22 b(All)14 b(of)h(the)h(argumen)o(ts)f(are)h
3830 (restricted)h(to)e(b)q(e)75 1484 y(real)f(\(see)i(section)f(8\).)k
3831 (Returns)c Fq(t)f Fy(when)h(called)f(with)g(one)g(argumen)o(t.)k(A)c
3832 (call)g(suc)o(h)h(as)f Fq(\(>=v)21 b Fp(x)1642 1490 y
3833 Fo(1)1682 1484 y Fp(x)1706 1490 y Fo(2)1732 1484 y Fp(:)7
3834 b(:)g(:)e(x)1811 1490 y Fh(n)1833 1484 y Fq(\))14 b Fy(with)75
3835 1534 y(more)f(than)h(t)o(w)o(o)f(argumen)o(ts)g(b)q(eha)o(v)o(es)i(lik)
3836 o(e)e(a)h(conjunction)g(of)f(t)o(w)o(o)g(argumen)o(t)g(calls:)179
3837 1617 y Fq(\(andv)21 b(\(>=v)g Fp(x)443 1623 y Fo(1)483
3838 1617 y Fp(x)507 1623 y Fo(2)525 1617 y Fq(\))p Fp(:)7
3839 b(:)g(:)n Fq(\(>=v)21 b Fp(x)728 1623 y Fh(i)764 1617
3840 y Fp(x)788 1623 y Fh(i)p Fo(+1)843 1617 y Fq(\))p Fp(:)7
3841 b(:)g(:)n Fq(\(>=v)21 b Fp(x)1046 1623 y Fh(n)p Fi(\000)p
3842 Fo(1)1133 1617 y Fp(x)1157 1623 y Fh(n)1179 1617 y Fq(\)\))75
3843 1700 y Fy(Beha)o(v)o(es)13 b(as)e(follo)o(ws)f(when)i(called)g(with)f
3844 (t)o(w)o(o)g(argumen)o(ts.)17 b(Returns)12 b Fq(t)g Fy(if)e
3845 Fp(x)1271 1706 y Fo(1)1301 1700 y Fy(is)i(kno)o(wn)f(to)g(b)q(e)i
3846 (greater)f(than)g(or)f(equal)75 1750 y(to)h Fp(x)148
3847 1756 y Fo(2)179 1750 y Fy(at)g(the)h(time)e(of)g(call.)17
3848 b(A)c(real)f(v)n(alue)g Fp(x)781 1756 y Fo(1)811 1750
3849 y Fy(is)g(kno)o(wn)g(to)g(b)q(e)h(greater)h(than)e(or)g(equal)g(to)g(a)
3850 g(real)g(v)n(alue)g Fp(x)1768 1756 y Fo(2)1799 1750 y
3851 Fy(if)f Fp(x)1859 1756 y Fo(1)1890 1750 y Fy(has)75 1800
3852 y(a)j(lo)o(w)o(er)f(b)q(ound,)g Fp(x)381 1806 y Fo(2)413
3853 1800 y Fy(has)h(an)g(upp)q(er)h(b)q(ound)f(and)f(the)i(lo)o(w)o(er)e(b)
3854 q(ound)h(of)f Fp(x)1251 1806 y Fo(1)1283 1800 y Fy(is)h(greater)h(than)
3855 f(or)f(equal)h(to)g(the)g(upp)q(er)75 1850 y(b)q(ound)i(of)f
3856 Fp(x)278 1856 y Fo(2)311 1850 y Fy(\(see)i(section)g(6\).)23
3857 b(Returns)16 b Fq(nil)f Fy(if)g Fp(x)913 1856 y Fo(1)947
3858 1850 y Fy(is)g(kno)o(wn)g(to)g(b)q(e)i(less)f(than)f
3859 Fp(x)1434 1856 y Fo(2)1468 1850 y Fy(at)h(the)g(time)e(of)h(call.)22
3860 b(A)16 b(real)75 1899 y(v)n(alue)11 b Fp(x)204 1905 y
3861 Fo(1)235 1899 y Fy(is)g(kno)o(wn)h(to)g(b)q(e)g(less)h(than)f(a)g(real)
3862 g(v)n(alue)f Fp(x)918 1905 y Fo(2)948 1899 y Fy(if)h
3863 Fp(x)1009 1905 y Fo(1)1039 1899 y Fy(has)g(an)g(upp)q(er)h(b)q(ound,)f
3864 Fp(x)1446 1905 y Fo(2)1476 1899 y Fy(has)g(a)g(lo)o(w)o(er)f(b)q(ound)i
3865 (and)e(the)75 1949 y(upp)q(er)i(b)q(ound)f(of)f Fp(x)387
3866 1955 y Fo(1)417 1949 y Fy(is)h(less)g(than)g(the)g(lo)o(w)o(er)g(b)q
3867 (ound)f(of)h Fp(x)997 1955 y Fo(2)1027 1949 y Fy(\(see)h(section)f
3868 (6\).)18 b(If)11 b(it)g(is)h(not)g(kno)o(wn)f(whether)i(or)f(not)g
3869 Fp(x)1932 1955 y Fo(1)75 1999 y Fy(is)h(greater)h(than)f(or)g(equal)f
3870 (to)h Fp(x)584 2005 y Fo(2)615 1999 y Fy(when)h Fq(>=v)e
3871 Fy(is)h(called)f(then)i Fq(>=v)e Fy(creates)j(and)e(returns)h(a)f(new)g
3872 (b)q(o)q(olean)g(v)n(ariable)f Fp(v)q Fy(.)75 2049 y(The)i(v)n(alues)f
3873 (of)f Fp(x)353 2055 y Fo(1)372 2049 y Fy(,)g Fp(x)420
3874 2055 y Fo(2)452 2049 y Fy(and)h Fp(v)i Fy(are)e(m)o(utually)e
3875 (constrained)j(via)f(noticers)h(so)f(that)g Fp(v)i Fy(is)e(equal)g(to)g
3876 Fq(t)g Fy(if)g(and)g(only)f(if)h Fp(x)1932 2055 y Fo(1)75
3877 2099 y Fy(is)j(kno)o(wn)f(to)g(b)q(e)i(greater)f(than)g(or)g(equal)f
3878 (to)g Fp(x)844 2105 y Fo(2)878 2099 y Fy(and)h Fp(v)h
3879 Fy(is)f(equal)f(to)h Fq(nil)f Fy(if)f(and)i(only)f(if)g
3880 Fp(x)1566 2105 y Fo(1)1600 2099 y Fy(is)g(kno)o(wn)g(to)h(b)q(e)g(less)
3881 75 2149 y(than)c Fp(x)194 2155 y Fo(2)213 2149 y Fy(.)17
3882 b(If)12 b(it)g(later)h(b)q(ecomes)f(kno)o(wn)g(that)h
3883 Fp(x)824 2155 y Fo(1)855 2149 y Fy(is)f(greater)h(than)g(or)f(equal)g
3884 (to)g Fp(x)1360 2155 y Fo(2)1379 2149 y Fy(,)g(noticers)h(attac)o(hed)g
3885 (to)g Fp(x)1798 2155 y Fo(1)1828 2149 y Fy(and)g Fp(x)1932
3886 2155 y Fo(2)75 2198 y Fy(restrict)i Fp(v)f Fy(to)f(equal)g
3887 Fq(t)p Fy(.)18 b(Lik)o(ewise,)13 b(if)f(it)h(later)g(b)q(ecomes)g(kno)o
3888 (wn)g(that)g Fp(x)1223 2204 y Fo(1)1255 2198 y Fy(is)g(less)h(than)f
3889 Fp(x)1492 2204 y Fo(2)1510 2198 y Fy(,)g(noticers)h(attac)o(hed)g(to)f
3890 Fp(x)1932 2204 y Fo(1)75 2248 y Fy(and)f Fp(x)178 2254
3891 y Fo(2)209 2248 y Fy(restrict)i Fp(v)g Fy(to)e(equal)h
3892 Fq(nil)p Fy(.)j(F)m(urthermore,)d(if)e Fp(v)j Fy(ev)o(er)g(b)q(ecomes)e
3893 (kno)o(wn)g(to)h(equal)f Fq(t)g Fy(then)h(a)f(noticer)h(attac)o(hed)75
3894 2298 y(to)g Fp(v)i Fy(restricts)g Fp(x)343 2304 y Fo(1)375
3895 2298 y Fy(to)e(b)q(e)h(greater)g(than)f(or)h(equal)f(to)g
3896 Fp(x)951 2304 y Fo(2)969 2298 y Fy(.)18 b(Lik)o(ewise,)13
3897 b(if)f Fp(v)j Fy(ev)o(er)f(b)q(ecomes)g(kno)o(wn)f(to)g(equal)g
3898 Fq(nil)f Fy(then)75 2348 y(a)k(noticer)h(attac)o(hed)g(to)f
3899 Fp(v)i Fy(restricts)g Fp(x)702 2354 y Fo(1)737 2348 y
3900 Fy(to)e(b)q(e)h(less)g(than)f Fp(x)1051 2354 y Fo(2)1070
3901 2348 y Fy(.)25 b(Restricting)17 b(a)f(real)g(v)n(alue)g
3902 Fp(x)1577 2354 y Fo(1)1611 2348 y Fy(to)h(b)q(e)g(greater)g(than)75
3903 2398 y(or)d(equal)g(to)f(a)h(real)g(v)n(alue)f Fp(x)533
3904 2404 y Fo(2)566 2398 y Fy(is)h(p)q(erformed)f(b)o(y)h(attac)o(hing)g
3905 (noticers)g(to)g Fp(x)1277 2404 y Fo(1)1310 2398 y Fy(and)f
3906 Fp(x)1414 2404 y Fo(2)1433 2398 y Fy(.)18 b(The)d(noticer)f(attac)o
3907 (hed)h(to)f Fp(x)1932 2404 y Fo(1)75 2447 y Fy(con)o(tin)o(ually)d
3908 (restricts)k(the)f(upp)q(er)g(b)q(ound)f(of)g Fp(x)833
3909 2453 y Fo(2)864 2447 y Fy(to)g(b)q(e)h(no)e(higher)i(than)f(the)g(lo)o
3910 (w)o(er)g(b)q(ound)g(of)f Fp(x)1624 2453 y Fo(1)1656
3911 2447 y Fy(if)g Fp(x)1717 2453 y Fo(1)1748 2447 y Fy(has)i(a)e(lo)o(w)o
3912 (er)75 2497 y(b)q(ound.)21 b(The)15 b(noticer)g(attac)o(hed)h(to)f
3913 Fp(x)694 2503 y Fo(2)727 2497 y Fy(con)o(tin)o(ually)e(restricts)k(the)
3914 e(lo)o(w)o(er)f(b)q(ound)h(of)f Fp(x)1484 2503 y Fo(1)1518
3915 2497 y Fy(to)g(b)q(e)i(no)e(lo)o(w)o(er)h(than)f(the)75
3916 2547 y(upp)q(er)h(b)q(ound)f(of)f Fp(x)393 2553 y Fo(2)425
3917 2547 y Fy(if)g Fp(x)487 2553 y Fo(2)519 2547 y Fy(has)h(an)g(upp)q(er)g
3918 (b)q(ound.)k(Restricting)c(a)g(real)g(v)n(alue)f Fp(x)1373
3919 2553 y Fo(1)1405 2547 y Fy(to)h(b)q(e)g(less)g(than)g(a)g(real)g(v)n
3920 (alue)f Fp(x)1932 2553 y Fo(2)75 2597 y Fy(is)f(p)q(erformed)g(b)o(y)g
3921 (an)g(analogous)e(set)j(of)f(noticers.)18 b(Since)13
3922 b(these)h(restrictions)f(only)e(guaran)o(tee)i(that)f
3923 Fp(x)1707 2603 y Fo(1)1737 2597 y Fy(b)q(e)h(less)g(than)992
3924 2723 y(21)p eop
3925 %%Page: 22 22
3926 22 21 bop 75 195 a Fy(or)12 b(equal)g(to)g Fp(x)305 201
3927 y Fo(2)323 195 y Fy(,)g(the)h(constrain)o(t)f(that)h
3928 Fp(x)723 201 y Fo(1)753 195 y Fy(b)q(e)g(strictly)f(less)h(than)f
3929 Fp(x)1142 201 y Fo(2)1173 195 y Fy(is)g(enforced)h(b)o(y)f(ha)o(ving)f
3930 (the)i(noticers)g(fail)d(when)75 245 y(b)q(oth)16 b Fp(x)199
3931 251 y Fo(1)232 245 y Fy(and)g Fp(x)339 251 y Fo(2)373
3932 245 y Fy(b)q(ecome)f(kno)o(wn)g(to)g(b)q(e)h(equal.)23
3933 b(See)16 b(section)h(6)e(for)g(a)g(discussion)h(of)f(v)n(ariable)g(upp)
3934 q(er)h(and)f(lo)o(w)o(er)75 295 y(b)q(ounds,)f(and)g(domains.)75
3935 533 y Fq(/=v)21 b Fp(x)186 518 y Fo(+)1506 533 y Fy([)p
3936 Fu(Deterministic)14 b(F)m(unction)p Fy(])75 682 y(Returns)g(a)f(b)q(o)q
3937 (olean)g(v)n(alue)f(whic)o(h)h(is)g(constrained)h(to)f(b)q(e)h
3938 Fq(t)f Fy(if)f(t)o(w)o(o)h(or)g(more)f(of)g(the)i(argumen)o(ts)e(n)o
3939 (umerically)f(di\013er)75 732 y(and)j(constrained)h(to)f(b)q(e)h
3940 Fq(nil)f Fy(all)f(of)h(the)h(argumen)o(ts)e(are)i(n)o(umerically)d
3941 (equal.)19 b(This)14 b(function)g(tak)o(es)h(one)g(or)f(more)75
3942 782 y(argumen)o(ts.)19 b(All)13 b(of)h(the)h(argumen)o(ts)f(are)h
3943 (restricted)h(to)e(b)q(e)h(n)o(umeric)f(\(see)i(section)f(8\).)k
3944 (Returns)d Fq(nil)d Fy(when)i(called)75 832 y(with)h(one)h(argumen)o
3945 (t.)26 b(A)17 b(call)f(suc)o(h)i(as)f Fq(\(/=v)j Fp(x)872
3946 838 y Fo(1)913 832 y Fp(x)937 838 y Fo(2)962 832 y Fp(:)7
3947 b(:)g(:)e(x)1041 838 y Fh(n)1064 832 y Fq(\))16 b Fy(with)h(more)e
3948 (than)i(t)o(w)o(o)f(argumen)o(ts)h(b)q(eha)o(v)o(es)g(lik)o(e)f(a)75
3949 881 y(conjunction)e(of)f(t)o(w)o(o)h(argumen)o(t)e(calls:)204
3950 960 y Fq(\(andv)20 b(\(/=v)h Fp(x)467 966 y Fo(1)508
3951 960 y Fp(x)532 966 y Fo(2)550 960 y Fq(\))g Fp(:)7 b(:)g(:)21
3952 b Fq(\(/=v)g Fp(x)797 966 y Fo(1)837 960 y Fp(x)861 966
3953 y Fh(n)883 960 y Fq(\))334 1009 y(\(/=v)g Fp(x)467 1015
3954 y Fo(2)508 1009 y Fp(x)532 1015 y Fo(3)550 1009 y Fq(\))g
3955 Fp(:)7 b(:)g(:)21 b Fq(\(/=v)g Fp(x)797 1015 y Fo(2)837
3956 1009 y Fp(x)861 1015 y Fh(n)883 1009 y Fq(\))334 1054
3957 y(.)334 1071 y(.)334 1088 y(.)334 1138 y(\(/=v)g Fp(x)467
3958 1144 y Fh(i)503 1138 y Fp(x)527 1144 y Fh(i)p Fo(+1)604
3959 1138 y Fp(:)7 b(:)g(:)20 b Fq(\(/=v)h Fp(x)807 1144 y
3960 Fh(i)843 1138 y Fp(x)867 1144 y Fh(n)889 1138 y Fq(\))334
3961 1183 y(.)334 1199 y(.)334 1216 y(.)334 1266 y(\(/=v)g
3962 Fp(x)467 1272 y Fh(n)p Fi(\000)p Fo(1)554 1266 y Fp(x)578
3963 1272 y Fh(n)600 1266 y Fq(\)\))75 1345 y Fy(Beha)o(v)o(es)16
3964 b(as)e(follo)o(ws)f(when)i(called)g(with)f(t)o(w)o(o)g(argumen)o(ts.)19
3965 b(Returns)d Fq(t)e Fy(if)g Fp(x)1304 1351 y Fo(1)1337
3966 1345 y Fy(is)g(kno)o(wn)g(not)h(to)f(b)q(e)i(equal)e(to)g
3967 Fp(x)1880 1351 y Fo(2)1913 1345 y Fy(at)75 1394 y(the)j(time)e(of)g
3968 (call.)24 b(Tw)o(o)16 b(n)o(umeric)f(v)n(alues)h(are)g(kno)o(wn)g(not)g
3969 (to)g(b)q(e)h(equal)f(when)g(their)h(domains)d(are)j(disjoin)o(t)e
3970 (\(see)75 1444 y(section)h(6\).)24 b(F)m(urthermore)16
3971 b(t)o(w)o(o)f(real)g(v)n(alues)h(are)g(kno)o(wn)f(not)h(to)g(b)q(e)g
3972 (equal)f(when)i(their)f(ranges)g(are)g(disjoin)o(t,)f(i.e.)75
3973 1494 y(the)g(upp)q(er)h(b)q(ound)e(of)g(one)h(is)f(greater)h(than)g
3974 (the)g(lo)o(w)o(er)f(b)q(ound)g(of)g(the)h(other)g(\(see)h(section)f
3975 (6\).)20 b(Returns)15 b Fq(nil)f Fy(if)g Fp(x)1932 1500
3976 y Fo(1)75 1544 y Fy(is)i(kno)o(wn)f(to)h(b)q(e)g(equal)f(to)h
3977 Fp(x)551 1550 y Fo(2)585 1544 y Fy(at)g(the)g(time)f(of)g(call.)23
3978 b(Tw)o(o)15 b(n)o(umeric)g(v)n(alues)g(are)i(kno)o(wn)e(to)h(b)q(e)g
3979 (equal)f(only)g(when)75 1594 y(they)g(are)g(b)q(oth)g(b)q(ound)f(and)g
3980 (equal)h(according)f(to)h(the)g Fv(Common)h(Lisp)f Fy(function)f
3981 Fq(=)p Fy(.)20 b(If)14 b(it)g(is)g(not)h(kno)o(wn)f(whether)75
3982 1644 y(or)g(not)g Fp(x)224 1650 y Fo(1)256 1644 y Fy(is)f(equal)h(to)g
3983 Fp(x)482 1650 y Fo(2)514 1644 y Fy(when)g Fq(/=v)f Fy(is)h(called)f
3984 (then)i Fq(/=v)e Fy(creates)j(and)e(returns)h(a)e(new)i(b)q(o)q(olean)e
3985 (v)n(ariable)g Fp(v)q Fy(.)19 b(The)75 1693 y(v)n(alues)c(of)f
3986 Fp(x)272 1699 y Fo(1)291 1693 y Fy(,)g Fp(x)341 1699
3987 y Fo(2)375 1693 y Fy(and)h Fp(v)h Fy(are)g(m)o(utually)d(constrained)j
3988 (via)e(noticers)i(so)f(that)g Fp(v)i Fy(is)e(equal)g(to)g
3989 Fq(t)g Fy(if)f(and)h(only)f(if)h Fp(x)1889 1699 y Fo(1)1922
3990 1693 y Fy(is)75 1743 y(kno)o(wn)h(not)g(to)g(b)q(e)g(equal)g(to)g
3991 Fp(x)585 1749 y Fo(2)620 1743 y Fy(and)f Fp(v)j Fy(is)e(equal)g(to)g
3992 Fq(nil)f Fy(if)h(and)g(only)f(if)g Fp(x)1311 1749 y Fo(1)1346
3993 1743 y Fy(is)g(kno)o(wn)h(to)g(b)q(e)h(equal)f(to)g Fp(x)1824
3994 1749 y Fo(2)1842 1743 y Fy(.)25 b(If)15 b(it)75 1793
3995 y(later)h(b)q(ecomes)h(kno)o(wn)f(that)h Fp(x)593 1799
3996 y Fo(1)627 1793 y Fy(is)g(not)f(equal)g(to)g Fp(x)937
3997 1799 y Fo(2)956 1793 y Fy(,)g(noticers)h(attac)o(hed)g(to)g
3998 Fp(x)1391 1799 y Fo(1)1425 1793 y Fy(and)g Fp(x)1533
3999 1799 y Fo(2)1567 1793 y Fy(restrict)h Fp(v)g Fy(to)f(equal)f
4000 Fq(t)p Fy(.)75 1843 y(Lik)o(ewise,)f(if)f(it)h(later)g(b)q(ecomes)g
4001 (kno)o(wn)g(that)g Fp(x)849 1849 y Fo(1)882 1843 y Fy(is)g(equal)g(to)g
4002 Fp(x)1112 1849 y Fo(2)1130 1843 y Fy(,)g(noticers)h(attac)o(hed)f(to)g
4003 Fp(x)1559 1849 y Fo(1)1593 1843 y Fy(and)g Fp(x)1699
4004 1849 y Fo(2)1732 1843 y Fy(restrict)h Fp(v)h Fy(to)75
4005 1893 y(equal)e Fq(nil)p Fy(.)24 b(F)m(urthermore,)15
4006 b(if)g Fp(v)j Fy(ev)o(er)e(b)q(ecomes)g(kno)o(wn)g(to)f(equal)h
4007 Fq(t)f Fy(then)i(a)e(noticer)i(attac)o(hed)f(to)g Fp(v)h
4008 Fy(restricts)h Fp(x)1932 1899 y Fo(1)75 1942 y Fy(to)f(not)g(b)q(e)h
4009 (equal)f(to)g Fp(x)457 1948 y Fo(2)476 1942 y Fy(.)28
4010 b(Lik)o(ewise,)18 b(if)e Fp(v)j Fy(ev)o(er)f(b)q(ecomes)g(kno)o(wn)f
4011 (to)g(equal)g Fq(nil)f Fy(then)i(a)f(noticer)h(attac)o(hed)g(to)f
4012 Fp(v)75 1992 y Fy(restricts)g Fp(x)260 1998 y Fo(1)294
4013 1992 y Fy(to)e(b)q(e)g(equal)g(to)g Fp(x)590 1998 y Fo(2)608
4014 1992 y Fy(.)22 b(Restricting)16 b(t)o(w)o(o)e(v)n(alues)h
4015 Fp(x)1085 1998 y Fo(1)1119 1992 y Fy(and)g Fp(x)1225
4016 1998 y Fo(2)1258 1992 y Fy(to)g(b)q(e)h(equal)f(is)g(p)q(erformed)g(b)o
4017 (y)f(attac)o(hing)75 2042 y(noticers)g(to)e Fp(x)302
4018 2048 y Fo(1)333 2042 y Fy(and)h Fp(x)437 2048 y Fo(2)455
4019 2042 y Fy(.)18 b(These)c(noticers)g(con)o(tin)o(ually)d(restrict)j(the)
4020 g(domains)d(of)h Fp(x)1416 2048 y Fo(1)1447 2042 y Fy(and)g
4021 Fp(x)1550 2048 y Fo(2)1582 2042 y Fy(to)g(b)q(e)i(equiv)n(alen)o(t)e
4022 (sets)75 2092 y(\(using)j(the)i Fv(Common)f(Lisp)g Fy(function)f
4023 Fq(=)g Fy(as)h(a)f(test)i(function\))e(as)h(their)g(domains)d(are)j
4024 (restricted.)26 b(F)m(urthermore,)75 2142 y(if)17 b Fp(x)141
4025 2148 y Fo(1)177 2142 y Fy(is)h(kno)o(wn)f(to)h(b)q(e)g(real)g(then)g
4026 (the)g(noticer)h(attac)o(hed)f(to)g Fp(x)1126 2148 y
4027 Fo(2)1162 2142 y Fy(con)o(tin)o(ually)e(restrict)j(the)g(upp)q(er)g(b)q
4028 (ound)e(of)h Fp(x)1932 2148 y Fo(1)75 2191 y Fy(to)d(b)q(e)h(no)g
4029 (higher)f(than)h(the)g(upp)q(er)g(b)q(ound)g(of)f Fp(x)868
4030 2197 y Fo(2)902 2191 y Fy(and)g(the)h(lo)o(w)o(er)f(b)q(ound)h(of)f
4031 Fp(x)1370 2197 y Fo(1)1404 2191 y Fy(to)g(b)q(e)h(no)g(lo)o(w)o(er)f
4032 (than)g(the)h(lo)o(w)o(er)75 2241 y(b)q(ound)f(of)g Fp(x)277
4033 2247 y Fo(2)295 2241 y Fy(.)21 b(The)16 b(noticer)f(of)g
4034 Fp(x)627 2247 y Fo(2)660 2241 y Fy(p)q(erforms)f(a)h(symmetric)e
4035 (restriction)j(on)f(the)h(b)q(ounds)f(of)g Fp(x)1623
4036 2247 y Fo(1)1656 2241 y Fy(if)f(it)h(is)g(kno)o(wn)f(to)75
4037 2291 y(b)q(e)h(real.)k(Restricting)c(t)o(w)o(o)f(v)n(alues)g
4038 Fp(x)671 2297 y Fo(1)704 2291 y Fy(and)g Fp(x)809 2297
4039 y Fo(2)842 2291 y Fy(to)g(not)g(b)q(e)h(equal)f(is)g(also)g(p)q
4040 (erformed)g(b)o(y)g(attac)o(hing)g(noticers)h(to)g Fp(x)1932
4041 2297 y Fo(1)75 2341 y Fy(and)d Fp(x)178 2347 y Fo(2)197
4042 2341 y Fy(.)17 b(These)d(noticers)f(ho)o(w)o(ev)o(er,)g(do)f(not)g
4043 (restrict)i(the)f(domains)e(or)h(ranges)h(of)f Fp(x)1418
4044 2347 y Fo(1)1449 2341 y Fy(or)g Fp(x)1522 2347 y Fo(2)1540
4045 2341 y Fy(.)18 b(They)13 b(simply)d(monitor)75 2391 y(their)15
4046 b(con)o(tin)o(ually)e(restrictions)j(and)e(fail)f(when)i(an)o(y)f
4047 (assertion)i(causes)g Fp(x)1272 2397 y Fo(1)1305 2391
4048 y Fy(to)e(b)q(e)h(kno)o(wn)f(to)h(b)q(e)g(equal)f(to)h
4049 Fp(x)1840 2397 y Fo(2)1858 2391 y Fy(.)20 b(See)75 2441
4050 y(section)15 b(6)e(for)h(a)f(discussion)i(of)e(v)n(ariable)g(upp)q(er)i
4051 (and)e(lo)o(w)o(er)h(b)q(ounds,)g(and)g(domains.)992
4052 2723 y(22)p eop
4053 %%Page: 23 23
4054 23 22 bop 75 195 a Fq(real-abovev)20 b Fu(low)1109 b
4055 Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75 342
4056 y(Returns)j(a)e(real)h(v)n(ariable)e(whose)j(v)n(alue)e(is)h
4057 (constrained)g(to)g(b)q(e)g(greater)h(than)f(or)f(equal)h(to)g
4058 Fu(low)p Fy(.)23 b(The)16 b(expression)75 392 y Fq(\(real-above)k
4059 Fu(low)p Fq(\))13 b Fy(is)g(an)h(abbreviation)f(for:)204
4060 464 y Fq(\(let)21 b(\(\()p Fp(v)i Fq(\(make-variable\)\))o(\))225
4061 514 y(\(assert!)e(\(realv)f Fp(v)q Fq(\)\))225 564 y(\(assert!)h(\(>=v)
4062 g Fp(v)i Fu(low)p Fq(\)\))225 614 y Fp(v)q Fq(\))75 880
4063 y(real-belowv)d Fu(high)1095 b Fy([)p Fu(Deterministic)14
4064 b(F)m(unction)p Fy(])75 1027 y(Returns)19 b(a)f(real)h(v)n(ariable)e
4065 (whose)i(v)n(alue)f(is)g(constrained)h(to)f(b)q(e)h(less)g(than)g(or)f
4066 (equal)g(to)g Fu(high)p Fy(.)32 b(The)19 b(expression)75
4067 1077 y Fq(\(real-belowv)g Fu(high)p Fq(\))14 b Fy(is)g(an)g
4068 (abbreviation)f(for:)204 1154 y Fq(\(let)21 b(\(\()p
4069 Fp(v)i Fq(\(make-variable\)\))o(\))225 1204 y(\(assert!)e(\(realv)f
4070 Fp(v)q Fq(\)\))225 1254 y(\(assert!)h(\(<=v)g Fp(v)i
4071 Fu(high)p Fq(\)\))225 1304 y Fp(v)q Fq(\))75 1570 y(real-betweenv)c
4072 Fu(low)i(high)971 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p
4073 Fy(])75 1717 y(Returns)19 b(a)g(real)f(v)n(ariable)f(whose)j(v)n(alue)d
4074 (is)i(constrained)g(to)f(b)q(e)i(greater)f(than)g(or)f(equal)g(to)h
4075 Fu(low)e Fy(and)i(less)g(than)75 1767 y(or)g(equal)g(to)f
4076 Fu(high)p Fy(.)34 b(If)18 b(the)i(resulting)f(real)g(v)n(ariable)f(is)h
4077 (b)q(ound,)g(its)g(v)n(alue)g(is)f(returned)j(instead.)34
4078 b(F)m(ails)17 b(if)i(it)f(is)75 1817 y(kno)o(wn)d(that)g
4079 Fu(low)g Fy(is)g(greater)i(than)e Fu(high)h Fy(at)f(the)h(time)e(of)h
4080 (call.)21 b(The)16 b(expression)h Fq(\(real-betweenv)i
4081 Fu(low)i(high)p Fq(\))15 b Fy(is)75 1867 y(an)f(abbreviation)f(for:)204
4082 1936 y Fq(\(let)21 b(\(\()p Fp(v)i Fq(\(make-variable\)\))o(\))225
4083 1985 y(\(assert!)e(\(realv)f Fp(v)q Fq(\)\))225 2035
4084 y(\(assert!)h(\(>=v)g Fp(v)i Fu(low)p Fq(\)\))225 2085
4085 y(\(assert!)e(\(<=v)g Fp(v)i Fu(high)p Fq(\)\))225 2135
4086 y(\(value-of)d Fp(v)q Fq(\)\))75 2402 y(integer-abovev)f
4087 Fu(low)1044 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p
4088 Fy(])75 2549 y(Returns)e(an)f(in)o(teger)h(v)n(ariable)e(whose)i(v)n
4089 (alue)e(is)h(constrained)h(to)f(b)q(e)h(greater)g(than)g(or)f(equal)g
4090 (to)g Fu(low)p Fy(.)16 b(The)c(expression)75 2599 y Fq(\(integer-above)
4091 19 b Fu(low)p Fq(\))13 b Fy(is)h(an)f(abbreviation)g(for:)992
4092 2723 y(23)p eop
4093 %%Page: 24 24
4094 24 23 bop 204 188 a Fq(\(let)21 b(\(\()p Fp(v)i Fq(\(make-variable\)\))
4095 o(\))225 238 y(\(assert!)e(\(integerv)f Fp(v)q Fq(\)\))225
4096 288 y(\(assert!)h(\(>=v)g Fp(v)i Fu(low)p Fq(\)\))225
4097 338 y Fp(v)q Fq(\))75 611 y(integer-belowv)c Fu(high)1030
4098 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
4099 762 y(Returns)h(an)f(in)o(teger)h(v)n(ariable)e(whose)h(v)n(alue)g(is)g
4100 (constrained)h(to)f(b)q(e)h(less)g(than)f(or)g(equal)g(to)g
4101 Fu(high)p Fy(.)19 b(The)c(expression)75 812 y Fq(\(integer-belowv)k
4102 Fu(high)p Fq(\))14 b Fy(is)f(an)h(abbreviation)f(for:)204
4103 893 y Fq(\(let)21 b(\(\()p Fp(v)i Fq(\(make-variable\)\))o(\))225
4104 943 y(\(assert!)e(\(integerv)f Fp(v)q Fq(\)\))225 993
4105 y(\(assert!)h(\(<=v)g Fp(v)i Fu(high)p Fq(\)\))225 1043
4106 y Fp(v)q Fq(\))75 1316 y(integer-betweenv)18 b Fu(low)k(high)905
4107 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
4108 1467 y(Returns)21 b(an)e(in)o(teger)h(v)n(ariable)f(whose)i(v)n(alue)e
4109 (is)g(constrained)i(to)f(b)q(e)g(greater)h(than)f(or)f(equal)h(to)f
4110 Fu(low)h Fy(and)f(less)75 1517 y(than)f(or)g(equal)f(to)h
4111 Fu(high)p Fy(.)30 b(If)18 b(the)h(resulting)f(in)o(teger)g(v)n(ariable)
4112 f(is)h(b)q(ound,)g(its)g(v)n(alue)f(is)h(returned)i(instead.)30
4113 b(F)m(ails)75 1567 y(if)21 b(it)g(is)g(kno)o(wn)g(that)h(there)g(is)g
4114 (no)f(in)o(teger)h(b)q(et)o(w)o(een)h Fu(low)e Fy(and)g
4115 Fu(high)h Fy(at)f(the)h(time)e(of)h(call.)40 b(The)22
4116 b(expression)75 1616 y Fq(\(integer-betweenv)c Fu(low)j(high)p
4117 Fq(\))14 b Fy(is)g(an)g(abbreviation)f(for:)204 1697
4118 y Fq(\(let)21 b(\(\()p Fp(v)i Fq(\(make-variable\)\))o(\))225
4119 1747 y(\(assert!)e(\(integerv)f Fp(v)q Fq(\)\))225 1797
4120 y(\(assert!)h(\(>=v)g Fp(v)i Fu(low)p Fq(\)\))225 1847
4121 y(\(assert!)e(\(<=v)g Fp(v)i Fu(high)p Fq(\)\))225 1897
4122 y(\(value-of)d Fp(v)q Fq(\)\))75 2170 y(member-ofv)g
4123 Fu(se)n(quenc)n(e)1038 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p
4124 Fy(])75 2321 y(Returns)h(a)f(v)n(ariable)g(whose)h(v)n(alue)e(is)i
4125 (restricted)h(to)e(b)q(e)h(a)g(mem)o(b)q(er)d(of)i Fu(se)n(quenc)n(e)p
4126 Fy(.)21 b(If)14 b Fu(se)n(quenc)n(e)h Fy(is)f(a)g(singleton)g(and)75
4127 2371 y(the)k(resulting)f(v)n(ariable)f(w)o(ould)h(b)q(e)h(b)q(ound,)g
4128 (its)f(v)n(alue)f(is)i(returned)h(instead.)28 b(F)m(ails)16
4129 b(if)h Fu(se)n(quenc)n(e)h Fy(is)f(empt)o(y)m(.)27 b(The)75
4130 2421 y(expression)15 b Fq(\(member-ofv)20 b Fu(se)n(quenc)n(e)p
4131 Fq(\))14 b Fy(is)g(an)f(abbreviation)h(for:)204 2501
4132 y Fq(\(let)21 b(\(\()p Fp(v)i Fq(\(make-variable\)\))o(\))225
4133 2550 y(\(assert!)e(\(memberv)f Fp(v)j Fu(se)n(quenc)n(e)p
4134 Fq(\)\))225 2600 y(\(value-of)d Fp(v)q Fq(\)\))992 2723
4135 y Fy(24)p eop
4136 %%Page: 25 25
4137 25 24 bop 75 195 a Fq(notv)21 b Fp(x)1298 b Fy([)p Fu(Deterministic)14
4138 b(F)m(unction)p Fy(])75 346 y(Restricts)k Fp(x)e Fy(to)g(b)q(e)i(b)q(o)
4139 q(olean)e(\(see)i(section)f(8\).)26 b(Returns)17 b Fq(nil)f
4140 Fy(if)g Fp(x)g Fy(is)g(kno)o(wn)g(to)h(equal)f Fq(t)g
4141 Fy(after)h(this)g(restriction.)75 396 y(Returns)d Fq(t)g
4142 Fy(if)f Fp(x)g Fy(is)g(kno)o(wn)h(to)f(equal)g Fq(nil)g
4143 Fy(after)h(this)g(restriction.)19 b(If)13 b(it)g(is)h(not)f(kno)o(wn)h
4144 (whether)h Fp(x)e Fy(equals)h Fq(t)f Fy(or)h Fq(nil)75
4145 446 y Fy(then)f Fq(notv)e Fy(creates)j(and)f(returns)g(a)f(new)h(b)q(o)
4146 q(olean)f(v)n(ariable)f Fp(v)q Fy(.)18 b(The)13 b(v)n(alues)f(of)g
4147 Fp(x)g Fy(and)g Fp(v)i Fy(are)e(m)o(utually)e(constrained)75
4148 496 y(via)h(noticers)i(so)f(that)g Fp(v)h Fy(is)f(equal)g(to)f
4149 Fq(t)h Fy(if)f(and)h(only)f(if)g Fp(x)h Fy(is)f(kno)o(wn)h(to)g(equal)f
4150 Fq(nil)g Fy(and)h Fp(v)i Fy(is)d(equal)h(to)g Fq(nil)f
4151 Fy(if)g(and)h(only)75 546 y(if)j Fp(x)g Fy(is)g(kno)o(wn)g(to)h(equal)f
4152 Fq(t)p Fy(.)22 b(If)16 b Fp(x)f Fy(later)g(b)q(ecomes)h(kno)o(wn)f(to)g
4153 (equal)h Fq(t)f Fy(then)h(a)f(noticer)h(attac)o(hed)g(to)g
4154 Fp(x)f Fy(restricts)i Fp(v)75 595 y Fy(to)e(equal)g Fq(nil)p
4155 Fy(.)21 b(Lik)o(ewise,)15 b(if)f Fp(x)h Fy(later)g(b)q(ecomes)g(kno)o
4156 (wn)g(to)g(equal)f Fq(nil)h Fy(then)h(a)e(noticer)i(attac)o(hed)g(to)f
4157 Fp(x)f Fy(restricts)j Fp(v)75 645 y Fy(to)f(equal)f Fq(t)p
4158 Fy(.)24 b(F)m(urthermore,)15 b(if)g Fp(v)j Fy(later)e(b)q(ecomes)g(kno)
4159 o(wn)f(to)h(equal)f Fq(t)h Fy(then)g(a)g(noticer)g(attac)o(hed)h(to)e
4160 Fp(v)j Fy(restricts)f Fp(x)75 695 y Fy(to)e(equal)g Fq(nil)p
4161 Fy(.)21 b(Lik)o(ewise,)15 b(if)f Fp(v)j Fy(later)e(b)q(ecomes)h(kno)o
4162 (wn)f(to)g(equal)g Fq(nil)f Fy(then)i(a)f(noticer)h(attac)o(hed)f(to)g
4163 Fp(v)i Fy(restricts)g Fp(x)75 745 y Fy(to)d(equal)f Fq(t)p
4164 Fy(.)18 b(Note)c(that)g Fq(notv)f Fy(di\013ers)i(from)d(the)j
4165 Fv(Common)h(Lisp)e Fy(primitiv)o(e)e Fq(not)h Fy(in)g(that)h(while)g
4166 Fq(not)f Fy(accepts)i(an)o(y)75 795 y Fv(Common)i(Lisp)e
4167 Fy(ob)r(ject)h(as)f(input,)g(treating)g(an)o(y)g(non-)p
4168 Fq(nil)f Fy(v)n(alue)h(as)g(true,)h Fq(notv)e Fy(restricts)j(is)e
4169 (argumen)o(t)f(to)h(b)q(e)h(a)75 845 y(b)q(o)q(olean)e(v)n(alue,)e
4170 (failing)g(if)h(its)h(argumen)o(t)f(cannot)h(b)q(e)g(restricted)i(to)e
4171 (b)q(e)g(b)q(o)q(olean.)75 1086 y Fq(andv)21 b Fp(x)208
4172 1071 y Fi(\003)1506 1086 y Fy([)p Fu(Deterministic)14
4173 b(F)m(unction)p Fy(])75 1237 y(T)m(ak)o(es)k(zero)g(or)g(more)e
4174 (argumen)o(ts.)29 b(Restricts)19 b(eac)o(h)f(argumen)o(t)f(to)g(b)q(e)i
4175 (b)q(o)q(olean)e(\(see)i(section)f(8\).)30 b(Returns)18
4176 b Fq(t)g Fy(if)75 1287 y(called)f(with)g(no)g(argumen)o(ts.)27
4177 b(Returns)18 b Fq(nil)e Fy(if)h(an)o(y)g(argumen)o(t)f(is)h(kno)o(wn)f
4178 (to)h(equal)g Fq(nil)g Fy(after)g(this)h(restriction.)75
4179 1337 y(Returns)c Fq(t)f Fy(if)g(all)f(argumen)o(ts)g(are)i(kno)o(wn)f
4180 (to)g(equal)g Fq(t)g Fy(after)g(this)h(restriction.)19
4181 b(If)12 b(neither)j(of)d(the)i(ab)q(o)o(v)o(e)f(conditions)75
4182 1387 y(hold)g(then)h Fq(andv)e Fy(creates)j(and)e(returns)i(a)e(new)h
4183 (b)q(o)q(olean)f(v)n(ariable)f Fp(v)q Fy(.)19 b(The)13
4184 b(v)n(alues)g(of)g(the)h(argumen)o(ts)f Fp(x)1753 1393
4185 y Fh(i)1780 1387 y Fy(and)g Fp(v)i Fy(are)75 1436 y(m)o(utually)10
4186 b(constrained)k(via)e(noticers)h(so)g(that)g Fp(v)h Fy(is)f(equal)f(to)
4187 h Fq(t)g Fy(if)e(and)i(only)f(if)g(all)f(of)i(the)g(argumen)o(ts)f
4188 Fp(x)1738 1442 y Fh(i)1764 1436 y Fy(are)h(kno)o(wn)75
4189 1486 y(to)j(equal)g Fq(t)g Fy(and)g Fp(v)i Fy(is)e(equal)f(to)h
4190 Fq(nil)g Fy(if)f(and)h(only)g(if)f(some)g(argumen)o(t)g
4191 Fp(x)1264 1492 y Fh(i)1294 1486 y Fy(is)h(kno)o(wn)g(to)g(equal)g
4192 Fq(nil)p Fy(.)24 b(If)16 b(all)f(of)g(the)75 1536 y(argumen)o(ts)f
4193 Fp(x)302 1542 y Fh(i)331 1536 y Fy(later)h(b)q(ecomes)h(kno)o(wn)e(to)h
4194 (equal)g Fq(t)g Fy(then)h(noticers)g(attac)o(hed)g(to)f(the)h(argumen)o
4195 (ts)e Fp(x)1703 1542 y Fh(i)1732 1536 y Fy(restrict)i
4196 Fp(v)h Fy(to)75 1586 y(equal)c Fq(t)p Fy(.)18 b(Lik)o(ewise,)13
4197 b(if)g(some)g(argumen)o(t)g Fp(x)766 1592 y Fh(i)793
4198 1586 y Fy(later)h(b)q(ecomes)g(kno)o(wn)f(to)h(equal)f
4199 Fq(nil)g Fy(then)i(a)e(noticer)h(attac)o(hed)h(to)e Fp(x)1936
4200 1592 y Fh(i)75 1636 y Fy(restricts)18 b Fp(v)g Fy(to)e(equal)f
4201 Fq(nil)p Fy(.)24 b(F)m(urthermore,)16 b(if)f Fp(v)j Fy(later)e(b)q
4202 (ecomes)g(kno)o(wn)g(to)g(equal)g Fq(nil)f Fy(then)i(a)f(noticer)g
4203 (attac)o(hed)75 1686 y(to)e Fp(v)i Fy(restricts)g(all)d(of)g(the)i
4204 (argumen)o(ts)e Fp(x)725 1692 y Fh(i)753 1686 y Fy(to)h(equal)g
4205 Fq(nil)p Fy(.)k Fv(Screamer)c Fy(implemen)o(ts)e(one)i(further)h
4206 (optimization.)h(If)75 1735 y(when)c Fq(andv)f Fy(is)g(called,)g(all)f
4207 (of)h(the)h(argumen)o(ts)f(except)i(for)e(one,)h(sa)o(y)f
4208 Fp(x)1183 1741 y Fh(i)1196 1735 y Fy(,)h(are)g(kno)o(wn)f(to)g(equal)g
4209 Fq(t)g Fy(and)h(it)f(is)g(not)g(kno)o(wn)75 1785 y(whether)17
4210 b Fp(x)260 1791 y Fh(i)290 1785 y Fy(equals)f Fq(t)g
4211 Fy(or)g Fq(nil)f Fy(then)i Fq(andv)e Fy(returns)i(the)g(argumen)o(t)e
4212 Fp(x)1221 1791 y Fh(i)1250 1785 y Fy(directly)i(as)f(the)g(result.)25
4213 b(Note)17 b(that)f Fq(andv)75 1835 y Fy(di\013ers)g(from)e(the)j
4214 Fv(Common)f(Lisp)g Fy(primitiv)o(e)d Fq(and)i Fy(in)g(t)o(w)o(o)g(imp)q
4215 (ortan)o(t)f(w)o(a)o(ys.)23 b(First,)16 b(while)f Fq(and)g
4216 Fy(is)g(a)h(macro)e(and)75 1885 y(ev)n(aluates)i(its)f(argumen)o(ts)g
4217 (from)f(left)h(to)h(righ)o(t)f(halting)f(that)i(ev)n(aluation)e(when)i
4218 (an)g(argumen)o(t)e(ev)n(aluates)i(to)f Fq(nil)p Fy(,)75
4219 1935 y Fq(andv)e Fy(is)h(a)f(function)h(whic)o(h)g(alw)o(a)o(ys)f(ev)n
4220 (aluates)h(all)e(of)i(its)g(argumen)o(ts.)j(Since)d Fq(andv)f
4221 Fy(is)h(a)g(function)f(ho)o(w)o(ev)o(er,)h(it)g(can)75
4222 1984 y(b)q(e)h(funcalled)e(and)h(mapp)q(ed,)f(something)f(whic)o(h)i
4223 (cannot)g(b)q(e)h(done)f(with)g Fq(and)f Fy(since)i(it)e(is)h(a)g
4224 (macro.)j(Second,)d(while)75 2034 y Fq(and)h Fy(accepts)j(an)o(y)d
4225 Fv(Common)h(Lisp)g Fy(ob)r(ject)h(as)f(input,)f(treating)h(an)o(y)g
4226 (non-)p Fq(nil)f Fy(v)n(alue)g(as)h(true,)g Fq(andv)f
4227 Fy(restricts)j(its)75 2084 y(argumen)o(ts)13 b(to)h(b)q(e)g(b)q(o)q
4228 (olean)g(v)n(alues,)f(failing)f(if)h(an)o(y)g(argumen)o(t)g(cannot)h(b)
4229 q(e)h(restricted)g(to)f(b)q(e)h(b)q(o)q(olean.)75 2325
4230 y Fq(orv)21 b Fp(x)186 2310 y Fi(\003)1506 2325 y Fy([)p
4231 Fu(Deterministic)14 b(F)m(unction)p Fy(])75 2477 y(T)m(ak)o(es)j(zero)i
4232 (or)e(more)g(argumen)o(ts.)28 b(Restricts)19 b(eac)o(h)f(argumen)o(t)f
4233 (to)g(b)q(e)i(b)q(o)q(olean)e(\(see)i(section)f(8\).)29
4234 b(Returns)19 b Fq(nil)75 2526 y Fy(if)g(called)g(with)g(no)h(argumen)o
4235 (ts.)34 b(Returns)21 b Fq(t)e Fy(if)g(an)o(y)g(argumen)o(t)f(is)i(kno)o
4236 (wn)f(to)g(equal)h Fq(t)f Fy(after)h(this)g(restriction.)75
4237 2576 y(Returns)g Fq(nil)f Fy(if)f(all)g(argumen)o(ts)g(are)i(kno)o(wn)f
4238 (to)g(equal)g Fq(nil)f Fy(after)i(this)f(restriction.)35
4239 b(If)19 b(neither)h(of)e(the)i(ab)q(o)o(v)o(e)992 2723
4240 y(25)p eop
4241 %%Page: 26 26
4242 26 25 bop 75 195 a Fy(conditions)13 b(hold)h(then)g Fq(orv)f
4243 Fy(creates)j(and)d(returns)j(a)d(new)h(b)q(o)q(olean)g(v)n(ariable)f
4244 Fp(v)q Fy(.)18 b(The)c(v)n(alues)g(of)f(the)h(argumen)o(ts)f
4245 Fp(x)1936 201 y Fh(i)75 245 y Fy(and)e Fp(v)i Fy(are)f(m)o(utually)d
4246 (constrained)k(via)d(noticers)j(so)e(that)h Fp(v)h Fy(is)e(equal)h(to)f
4247 Fq(nil)g Fy(if)g(and)g(only)g(if)f(all)h(of)g(the)h(argumen)o(ts)e
4248 Fp(x)1936 251 y Fh(i)75 295 y Fy(are)j(kno)o(wn)g(to)f(equal)h
4249 Fq(nil)f Fy(and)h Fp(v)h Fy(is)f(equal)f(to)h Fq(t)f
4250 Fy(if)g(and)h(only)f(if)g(some)g(argumen)o(t)g Fp(x)1413
4251 301 y Fh(i)1439 295 y Fy(is)h(kno)o(wn)f(to)h(equal)f
4252 Fq(t)p Fy(.)18 b(If)12 b(all)g(of)75 345 y(the)g(argumen)o(ts)f
4253 Fp(x)368 351 y Fh(i)392 345 y Fy(later)h(b)q(ecomes)g(kno)o(wn)e(to)i
4254 (equal)f Fq(nil)f Fy(then)i(noticers)h(attac)o(hed)f(to)f(the)h
4255 (argumen)o(ts)f Fp(x)1763 351 y Fh(i)1787 345 y Fy(restrict)i
4256 Fp(v)75 394 y Fy(to)e(equal)f Fq(nil)p Fy(.)17 b(Lik)o(ewise,)11
4257 b(if)f(some)g(argumen)o(t)g Fp(x)843 400 y Fh(i)867 394
4258 y Fy(later)h(b)q(ecomes)h(kno)o(wn)e(to)h(equal)g Fq(t)f
4259 Fy(then)i(a)f(noticer)g(attac)o(hed)h(to)e Fp(x)1936
4260 400 y Fh(i)75 444 y Fy(restricts)18 b Fp(v)f Fy(to)f(equal)g
4261 Fq(t)p Fy(.)23 b(F)m(urthermore,)16 b(if)f Fp(v)j Fy(later)e(b)q
4262 (ecomes)g(kno)o(wn)f(to)h(equal)g Fq(t)f Fy(then)i(a)f(noticer)g(attac)
4263 o(hed)h(to)e Fp(v)75 494 y Fy(restricts)i(all)d(of)h(the)h(argumen)o
4264 (ts)e Fp(x)644 500 y Fh(i)673 494 y Fy(to)h(equal)g Fq(t)p
4265 Fy(.)22 b Fv(Screamer)16 b Fy(implem)o(en)o(ts)e(one)h(further)h
4266 (optimization.)k(If)14 b(when)75 544 y Fq(orv)h Fy(is)g(called,)g(all)g
4267 (of)f(the)i(argumen)o(ts)f(except)i(for)e(one,)h(sa)o(y)f
4268 Fp(x)1099 550 y Fh(i)1113 544 y Fy(,)g(are)h(kno)o(wn)f(to)g(equal)g
4269 Fq(nil)g Fy(and)h(it)f(is)g(not)g(kno)o(wn)75 594 y(whether)e
4270 Fp(x)256 600 y Fh(i)281 594 y Fy(equals)f Fq(t)g Fy(or)g
4271 Fq(nil)f Fy(then)h Fq(orv)f Fy(returns)j(the)e(argumen)o(t)f
4272 Fp(x)1153 600 y Fh(i)1178 594 y Fy(directly)h(as)g(the)h(result.)18
4273 b(Note)12 b(that)g Fq(orv)f Fy(di\013ers)75 643 y(from)f(the)i
4274 Fv(Common)k(Lisp)c Fy(primitiv)o(e)d Fq(or)i Fy(in)g(t)o(w)o(o)g(imp)q
4275 (ortan)o(t)f(w)o(a)o(ys.)17 b(First,)12 b(while)f Fq(or)g
4276 Fy(is)g(a)h(macro)e(and)h(ev)n(aluates)h(its)75 693 y(argumen)o(ts)g
4277 (from)g(left)h(to)g(righ)o(t)f(halting)g(that)i(ev)n(aluation)d(when)j
4278 (an)f(argumen)o(t)f(ev)n(aluates)h(to)g Fq(t)p Fy(,)g
4279 Fq(orv)f Fy(is)h(a)g(function)75 743 y(whic)o(h)j(alw)o(a)o(ys)g(ev)n
4280 (aluates)g(all)f(of)h(its)h(argumen)o(ts.)24 b(Since)17
4281 b Fq(orv)f Fy(is)g(a)g(function)h(ho)o(w)o(ev)o(er,)f(it)h(can)f(b)q(e)
4282 h(funcalled)f(and)75 793 y(mapp)q(ed,)g(something)g(whic)o(h)g(cannot)h
4283 (b)q(e)g(done)h(with)e Fq(or)g Fy(since)i(it)e(is)h(a)f(macro.)26
4284 b(Second,)17 b(while)g Fq(or)f Fy(accepts)i(an)o(y)75
4285 843 y Fv(Common)f(Lisp)f Fy(ob)r(ject)i(as)f(input,)g(treating)g(an)o
4286 (y)f(non-)p Fq(nil)g Fy(v)n(alue)g(as)h(true,)h Fq(orv)e
4287 Fy(restricts)j(its)e(argumen)o(ts)f(to)g(b)q(e)75 892
4288 y(b)q(o)q(olean)e(v)n(alues,)f(failing)e(if)i(an)o(y)h(argumen)o(t)f
4289 (cannot)h(b)q(e)g(restricted)i(to)e(b)q(e)g(b)q(o)q(olean.)75
4290 1134 y Fq(+v)21 b Fp(x)164 1119 y Fi(\003)1506 1134 y
4291 Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75 1477
4292 y Fq(-v)21 b Fp(x)164 1462 y Fo(+)1506 1477 y Fy([)p
4293 Fu(Deterministic)14 b(F)m(unction)p Fy(])75 1819 y Fq(*v)21
4294 b Fp(x)164 1804 y Fi(\003)1506 1819 y Fy([)p Fu(Deterministic)14
4295 b(F)m(unction)p Fy(])75 2162 y Fq(/v)21 b Fp(x)164 2147
4296 y Fo(+)1506 2162 y Fy([)p Fu(Deterministic)14 b(F)m(unction)p
4297 Fy(])75 2505 y Fq(minv)21 b Fp(x)208 2490 y Fo(+)1506
4298 2505 y Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])992
4299 2723 y(26)p eop
4300 %%Page: 27 27
4301 27 26 bop 75 195 a Fq(maxv)21 b Fp(x)208 180 y Fo(+)1506
4302 195 y Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
4303 538 y Fq(funcallv)20 b Fu(function)i Fp(x)465 523 y Fi(\003)1506
4304 538 y Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
4305 689 y(The)h(argumen)o(t)f Fu(function)h Fy(m)o(ust)f(b)q(e)i(b)q(ound)e
4306 (to)h(a)g(deterministic)f Fv(Common)j(Lisp)d Fy(function)h(ob)r(ject.)
4307 22 b(Returns)15 b(the)75 739 y(result)c(of)f(funcalling)f
4308 Fu(function)i Fy(on)g(the)g(dereferenced)j(v)n(alues)c(of)g(the)h
4309 (argumen)o(ts)f Fp(x)1391 745 y Fh(i)1415 739 y Fy(if)g(all)f(of)h(the)
4310 i Fp(x)1641 745 y Fh(i)1665 739 y Fy(are)f(b)q(ound)f(when)75
4311 789 y Fq(funcallv)i Fy(is)i(called.)j(If)d(some)f(of)g(the)h(argumen)o
4312 (ts)f Fp(x)928 795 y Fh(i)955 789 y Fy(are)h(not)g(b)q(ound)g(when)g
4313 Fq(funcallv)e Fy(is)i(called)f(then)i Fq(funcallv)75
4314 839 y Fy(creates)d(and)d(returns)j(a)d(v)n(ariable)g
4315 Fp(v)q Fy(.)17 b(The)10 b(argumen)o(ts)f Fp(x)961 845
4316 y Fh(i)985 839 y Fy(and)g Fp(v)j Fy(are)e(m)o(utually)d(constrained)k
4317 (via)e(noticers)i(so)f(that)f(if)g Fp(v)75 889 y Fy(and)i(the)h
4318 (argumen)o(ts)f Fp(x)446 895 y Fh(i)471 889 y Fy(ev)o(er)i(all)d(b)q
4319 (ecome)h(b)q(ound)h(then)g Fp(v)h Fy(is)e(restricted)j(to)d(equal)g
4320 (the)h(result)h(of)e(funcalling)e Fu(function)75 938
4321 y Fy(on)14 b(the)h(dereferenced)i(v)n(alues)d(of)f(the)i(argumen)o(ts)e
4322 Fp(x)913 944 y Fh(i)927 938 y Fy(.)18 b(The)d(noticers)g(furthermore)f
4323 (implemen)o(t)d(forw)o(ard)j(c)o(hec)o(king,)75 988 y(i.e.)i(if)f(the)j
4324 (collection)e Fp(v)i Fy(com)o(bined)d(with)h(the)i(argumen)o(ts)d
4325 Fp(x)1073 994 y Fh(i)1104 988 y Fy(all)g(b)q(ecome)h(b)q(ound,)h(sa)o
4326 (v)o(e)g(one)g(v)n(ariable,)e(and)i(this)75 1038 y(one)d(v)n(ariable)e
4327 (has)h(a)g(\014nite)h(domain)d(then)j(this)f(domain)e(is)i(restricted)j
4328 (to)d(con)o(tain)g(only)f(those)i(elemen)o(ts)f(whic)o(h)h(are)75
4329 1088 y(consisten)o(t)h(with)f(the)h(v)n(alues)f(of)g(the)h(remaining)d
4330 (b)q(ound)j(v)n(ariables.)j(The)d(follo)o(wing)c(is)k(a)f(standard)g
4331 (clic)o(h)o(\023)-20 b(e)15 b(used)g(to)75 1138 y(constrain)f(the)h(v)n
4332 (ariables)e Fp(x)523 1144 y Fo(1)548 1138 y Fp(:)7 b(:)g(:)e(x)627
4333 1144 y Fh(n)664 1138 y Fy(to)13 b(ob)q(ey)i(a)e(giv)o(en)h(predicate:)
4334 179 1221 y Fq(\(assert!)20 b(\(funcallv)g(#'\(lambda)g(\()p
4335 Fp(x)857 1227 y Fo(1)882 1221 y Fp(:)7 b(:)g(:)e(x)961
4336 1227 y Fh(n)984 1221 y Fq(\))21 b Fu(pr)n(e)n(dic)n(ate)p
4337 Fq(\))g Fp(x)1253 1227 y Fo(1)1279 1221 y Fp(:)7 b(:)g(:)e(x)1358
4338 1227 y Fh(n)1380 1221 y Fq(\)\))75 1495 y(applyv)21 b
4339 Fu(function)h Fp(x)422 1480 y Fo(+)1506 1495 y Fy([)p
4340 Fu(Deterministic)14 b(F)m(unction)p Fy(])75 1646 y(The)h(argumen)o(t)f
4341 Fu(function)h Fy(m)o(ust)f(b)q(e)i(b)q(ound)e(to)h(a)g(deterministic)f
4342 Fv(Common)j(Lisp)d Fy(function)h(ob)r(ject.)22 b(Returns)15
4343 b(the)75 1696 y(result)d(of)g(applying)e Fu(function)i
4344 Fy(on)g(the)g(dereferenced)j(v)n(alues)c(of)g(the)h(argumen)o(ts)f
4345 Fp(x)1382 1702 y Fh(i)1408 1696 y Fy(if)f(all)h(of)g(the)h
4346 Fp(x)1637 1702 y Fh(i)1663 1696 y Fy(are)g(b)q(ound)f(when)75
4347 1746 y Fq(applyv)h Fy(is)h(called.)18 b(If)13 b(some)f(of)h(the)h
4348 (argumen)o(ts)e Fp(x)881 1752 y Fh(i)908 1746 y Fy(are)i(not)f(b)q
4349 (ound)g(when)h Fq(applyv)e Fy(is)h(called)g(then)h Fq(applyv)e
4350 Fy(creates)75 1796 y(and)17 b(returns)i(a)d(v)n(ariable)g
4351 Fp(v)q Fy(.)29 b(The)17 b(argumen)o(ts)f Fp(x)881 1802
4352 y Fh(i)912 1796 y Fy(and)h Fp(v)i Fy(are)e(m)o(utually)e(constrained)j
4353 (via)e(noticers)i(so)f(that)g(if)f Fp(v)75 1846 y Fy(and)c(the)i
4354 (argumen)o(ts)e Fp(x)450 1852 y Fh(i)476 1846 y Fy(ev)o(er)h(all)f(b)q
4355 (ecome)g(b)q(ound)h(then)g Fp(v)h Fy(is)f(restricted)i(to)d(equal)h
4356 (the)g(result)g(of)f(applying)f Fu(function)75 1896 y
4357 Fy(on)j(the)h(dereferenced)i(v)n(alues)d(of)f(the)i(argumen)o(ts)e
4358 Fp(x)913 1902 y Fh(i)927 1896 y Fy(.)18 b(The)d(noticers)g(furthermore)
4359 f(implemen)o(t)d(forw)o(ard)j(c)o(hec)o(king,)75 1945
4360 y(i.e.)i(if)f(the)j(collection)e Fp(v)i Fy(com)o(bined)d(with)h(the)i
4361 (argumen)o(ts)d Fp(x)1073 1951 y Fh(i)1104 1945 y Fy(all)g(b)q(ecome)h
4362 (b)q(ound,)h(sa)o(v)o(e)g(one)g(v)n(ariable,)e(and)i(this)75
4363 1995 y(one)d(v)n(ariable)e(has)h(a)g(\014nite)h(domain)d(then)j(this)f
4364 (domain)e(is)i(restricted)j(to)d(con)o(tain)g(only)f(those)i(elemen)o
4365 (ts)f(whic)o(h)h(are)75 2045 y(consisten)o(t)h(with)f(the)g(v)n(alues)g
4366 (of)f(the)h(remaining)e(b)q(ound)i(v)n(ariables.)75 2286
4367 y Fq(equalv)21 b Fp(x)g(y)1213 b Fy([)p Fu(Deterministic)14
4368 b(F)m(unction)p Fy(])75 2438 y(Returns)k Fq(t)f Fy(if)f(the)i
4369 (aggregate)f(ob)r(ject)h Fp(x)f Fy(is)g(kno)o(wn)g(to)g(equal)f(the)i
4370 (aggregate)f(ob)r(ject)h Fp(y)h Fy(when)f Fq(equalv)e
4371 Fy(is)h(called.)75 2487 y(Returns)i Fq(nil)e Fy(if)g(the)h(aggregate)g
4372 (ob)r(ject)h Fp(x)e Fy(is)h(kno)o(wn)f(not)h(to)f(equal)h(the)g
4373 (aggregate)g(ob)r(ject)h Fp(y)g Fy(when)g Fq(equalv)d
4374 Fy(is)75 2537 y(called.)28 b(If)17 b(it)g(is)g(not)g(kno)o(wn)g
4375 (whether)h(or)g(not)f Fp(x)g Fy(equals)g Fp(y)i Fy(when)f
4376 Fq(equalv)e Fy(is)h(called)g(then)h Fq(equalv)e Fy(creates)j(and)75
4377 2587 y(returns)e(a)e(b)q(o)q(olean)h(v)n(ariable)e Fp(v)q
4378 Fy(.)24 b(The)16 b(v)n(alues)f(of)g Fp(x)p Fy(,)g Fp(y)j
4379 Fy(and)d Fp(v)i Fy(are)f(m)o(utually)d(constrain)o(ts)k(via)d(noticers)
4380 j(so)f(that)f Fp(v)992 2723 y Fy(27)p eop
4381 %%Page: 28 28
4382 28 27 bop 75 195 a Fy(equals)14 b Fq(t)g Fy(if)g(and)g(only)g(if)f
4383 Fp(x)h Fy(is)g(kno)o(wn)g(to)g(equal)g Fp(y)i Fy(and)f
4384 Fp(v)g Fy(equals)g Fq(nil)e Fy(if)h(and)g(only)g(if)f
4385 Fp(x)h Fy(is)g(kno)o(wn)g(not)g(to)h(equal)f Fp(y)q Fy(.)75
4386 245 y(Noticers)19 b(are)g(attac)o(hed)f(to)g Fp(v)i Fy(as)e(w)o(ell)f
4387 (as)i(to)f(all)e(v)n(ariables)i(nested)h(in)f(b)q(oth)g(in)g
4388 Fp(x)g Fy(and)g Fp(y)q Fy(.)31 b(When)18 b(the)h(noticers)75
4389 295 y(attac)o(hed)f(to)e(v)n(ariables)h(nested)h(in)e
4390 Fp(x)h Fy(and)g Fp(y)h Fy(detect)h(that)e Fp(x)g Fy(is)f(kno)o(wn)h(to)
4391 g(equal)f Fp(y)j Fy(they)e(restrict)i Fp(v)f Fy(to)f(equal)g
4392 Fq(t)p Fy(.)75 345 y(Lik)o(ewise,)12 b(when)g(the)g(noticers)h(attac)o
4393 (hed)f(to)g(v)n(ariables)f(nested)i(in)e Fp(x)g Fy(and)h
4394 Fp(y)h Fy(detect)h(that)d Fp(x)h Fy(is)f(kno)o(wn)h(not)f(to)h(equal)f
4395 Fp(y)75 394 y Fy(they)i(restrict)i Fp(v)f Fy(to)f(equal)f
4396 Fq(nil)p Fy(.)17 b(F)m(urthermore,)c(if)f Fp(v)i Fy(later)f(b)q(ecomes)
4397 g(kno)o(wn)g(to)f(equal)h Fq(t)g Fy(then)g Fp(x)g Fy(and)f
4398 Fp(y)j Fy(are)e(uni\014ed.)75 444 y(Lik)o(ewise,)k(if)e
4399 Fp(v)j Fy(later)f(b)q(ecomes)g(kno)o(wn)f(to)g(equal)g
4400 Fq(nil)g Fy(then)h Fp(x)f Fy(and)h Fp(y)h Fy(are)f(restricted)h(to)f
4401 (not)f(b)q(e)h(equal.)26 b(This)16 b(is)75 494 y(accomplished)h(b)o(y)g
4402 (attac)o(hing)g(noticers)h(to)g(the)g(v)n(ariables)f(nested)i(in)e
4403 Fp(x)g Fy(and)g Fp(y)j Fy(whic)o(h)d(detect)i(when)f
4404 Fp(x)g Fy(b)q(ecomes)75 544 y(equal)13 b(to)g Fp(y)j
4405 Fy(and)d(fail.)j(The)e(expression)h Fq(\(known?)20 b(\(equalv)h
4406 Fp(x)g(y)q Fq(\)\))14 b Fy(is)f(analogous)f(to)i(the)g(extra-logical)e
4407 (predicate)75 594 y Fq(==)g Fy(t)o(ypically)g(a)o(v)n(ailable)f(in)h
4408 Fv(Pr)o(olog)q Fy(.)17 b(The)d(expression)g Fq(\(known?)20
4409 b(\(notv)h(\(equalv)f Fp(x)i(y)q Fq(\)\)\))13 b Fy(is)g(analogous)f(to)
4410 g(the)75 643 y(extra-logical)i(predicate)j Fq(\\=)e Fy(t)o(ypically)f
4411 (a)o(v)n(ailable)f(in)i Fv(Pr)o(olog)p Fy(.)23 b(The)16
4412 b(expression)g Fq(\(assert!)k(\(equalv)h Fp(x)g(y)q Fq(\)\))16
4413 b Fy(is)75 693 y(analogous)g(to)h Fv(Pr)o(olog)h Fy(uni\014cation.)28
4414 b(The)18 b(expression)g Fq(\(assert!)j(\(notv)f(\(equalv)h
4415 Fp(x)g(y)q Fq(\)\)\))d Fy(is)f(analogous)f(to)75 743
4416 y(the)e(disuni\014cation)f(op)q(erator)h(a)o(v)n(ailable)d(in)i
4417 Fv(Pr)o(olog-I)q(I)p Fy(.)k(See)e(section)f(9)f(for)g(a)g(discussion)h
4418 (of)f(aggregate)g(ob)r(jects.)75 984 y Fq(bound?)21 b
4419 Fp(x)1254 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p
4420 Fy(])75 1136 y(Returns)e Fq(t)f Fy(if)f Fp(x)h Fy(is)g(not)g(a)g(v)n
4421 (ariable)f(or)i(if)e Fp(x)h Fy(is)g(a)g(b)q(ound)g(v)n(ariable.)16
4422 b(Otherwise)d(returns)g Fq(nil)p Fy(.)j Fq(Bound?)10
4423 b Fy(is)h(analogous)f(to)75 1186 y(the)i(extra-logical)e(predicates)j
4424 Fq(var)e Fy(and)h Fq(nonvar)e Fy(t)o(ypically)g(a)o(v)n(ailable)f(in)i
4425 Fv(Pr)o(olog)q Fy(.)17 b(See)c(section)f(7)f(for)g(a)g(discussion)75
4426 1235 y(of)i(ho)o(w)h Fv(Screamer)g Fy(determines)g(whether)i(or)e(not)f
4427 (a)h(v)n(ariable)f(is)g(b)q(ound.)75 1477 y Fq(value-of)20
4428 b Fp(x)1211 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p
4429 Fy(])75 1628 y(Returns)21 b Fp(x)f Fy(if)g Fp(x)g Fy(is)g(not)g(a)h(v)n
4430 (ariable.)36 b(If)20 b Fp(x)g Fy(is)g(a)g(v)n(ariable)g(then)h
4431 Fq(value-of)d Fy(dereferences)24 b Fp(x)c Fy(and)g(returns)i(the)75
4432 1678 y(dereferenced)c(v)n(alue.)k(If)15 b Fp(x)g Fy(is)g(b)q(ound)g
4433 (then)h(the)g(v)n(alue)f(returned)i(will)d(not)h(b)q(e)h(a)f(v)n
4434 (ariable.)21 b(If)15 b Fp(x)g Fy(is)g(un)o(b)q(ound)g(then)75
4435 1728 y(the)g(v)n(alue)g(returned)h(will)e(b)q(e)h(a)g(v)n(ariable)e
4436 (whic)o(h)i(ma)o(y)e(b)q(e)i Fp(x)g Fy(itself)f(or)h(another)g(v)n
4437 (ariable)f(whic)o(h)h(is)f(shared)i(with)f Fp(x)p Fy(.)75
4438 1777 y(See)f(section)f(7)f(for)h(a)f(discussion)h(of)f(ho)o(w)g
4439 Fv(Screamer)i Fy(determines)f(whether)h(or)e(not)h(a)f(v)n(ariable)g
4440 (is)g(b)q(ound)h(and)f(ho)o(w)75 1827 y Fv(Screamer)j
4441 Fy(dereferences)i(v)n(ariables.)75 2069 y Fq(ground?)j
4442 Fp(x)1233 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p
4443 Fy(])75 2220 y(The)f(primitiv)o(e)d Fq(ground?)h Fy(is)i(an)f
4444 (extension)h(of)f(the)h(primitiv)o(e)d Fq(bound?)i Fy(whic)o(h)g(can)h
4445 (recursiv)o(ely)g(determine)g(whether)75 2270 y(an)g(en)o(tire)h
4446 (aggregate)f(ob)r(ject)g(is)g(b)q(ound.)18 b(Returns)c
4447 Fq(t)f Fy(if)f Fp(x)h Fy(is)g(b)q(ound)g(and)g(either)h(the)f(v)n(alue)
4448 g(of)f Fp(x)h Fy(is)g(atomic)e(or)i(all)f(of)75 2319
4449 y(the)j(slots)f(in)g(the)g(v)n(alue)g(of)f Fp(x)h Fy(are)h(also)e(b)q
4450 (ound.)19 b(Otherwise)c(returns)h Fq(nil)p Fy(.)i(See)d(section)g(7)f
4451 (for)f(a)h(discussion)h(of)e(ho)o(w)75 2369 y Fv(Screamer)j
4452 Fy(determines)g(whether)h(or)e(not)g(a)h(v)n(ariable)e(is)h(b)q(ound.)
4453 23 b(See)16 b(section)h(9)e(for)g(a)g(discussion)h(of)f(aggregate)75
4454 2419 y(ob)r(jects.)992 2723 y(28)p eop
4455 %%Page: 29 29
4456 29 28 bop 75 195 a Fq(apply-substitutio)o(n)19 b Fp(x)993
4457 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
4458 346 y(The)19 b(primitiv)o(e)c Fq(apply-substitution)g
4459 Fy(is)j(an)g(extension)g(of)g(the)g(primitiv)o(e)e Fq(value-of)h
4460 Fy(whic)o(h)h(can)g(recursiv)o(ely)75 396 y(dereference)f(an)d(en)o
4461 (tire)i(aggregate)e(ob)r(ject.)20 b(If)14 b Fp(x)g Fy(is)h(an)f(un)o(b)
4462 q(ound)g(v)n(ariable)f(then)i Fq(apply-substitution)c
4463 Fy(b)q(eha)o(v)o(es)75 446 y(lik)o(e)f Fq(value-of)e
4464 Fy(dereferencing)13 b Fp(x)d Fy(and)g(returning)h(the)g(dereferenced)j
4465 (v)n(alue.)i(The)11 b(v)n(alue)f(returned)i(will)d(b)q(e)i(a)f(v)n
4466 (ariable)75 496 y(whic)o(h)j(ma)o(y)d(b)q(e)j Fp(x)g
4467 Fy(itself)f(or)h(another)g(v)n(ariable)e(whic)o(h)i(is)f(shared)i(with)
4468 e Fp(x)p Fy(.)17 b(Otherwise,)d(returns)g(a)f(cop)o(y)f(of)g(the)i(v)n
4469 (alue)75 546 y(of)e Fp(x)p Fy(.)17 b(Eac)o(h)12 b(slot)g(of)g
4470 Fp(x)g Fy(that)g(con)o(tains)g(a)g(b)q(ound)h(v)n(ariable)e(is)h
4471 (replaced)h(in)f(the)h(cop)o(y)f(with)g(the)h(dereferenced)i(v)n(alue)d
4472 (of)75 595 y(that)g(v)n(ariable)f(pro)q(duced)i(b)o(y)e(a)h(recursiv)o
4473 (e)h(application)e(of)g Fq(apply-substitutio)o(n)p Fy(.)k(See)d
4474 (section)h(7)e(for)h(a)f(discussion)75 645 y(of)18 b(ho)o(w)h
4475 Fv(Screamer)g Fy(determines)g(whether)h(or)f(not)g(a)f(v)n(ariable)g
4476 (is)g(b)q(ound)h(and)g(ho)o(w)f Fv(Screamer)i Fy(dereferences)75
4477 695 y(v)n(ariables.)d(See)e(section)g(9)e(for)h(a)f(discussion)i(of)e
4478 (aggregate)h(ob)r(jects.)75 936 y Fq(linear-force)19
4479 b Fp(x)1059 b Fy([)p Fu(Nondeterministic)14 b(F)m(unction)p
4480 Fy(])75 1088 y(Returns)19 b Fp(x)f Fy(if)f Fp(x)h Fy(is)g(not)g(a)g(v)n
4481 (ariable.)29 b(If)18 b Fp(x)g Fy(is)g(a)g(b)q(ound)g(v)n(ariable)f
4482 (then)i(b)q(eha)o(v)o(es)g(lik)o(e)e Fq(value-of)g Fy(returning)h(the)
4483 75 1138 y(dereferenced)g(v)n(alue)d(of)f Fp(x)p Fy(.)21
4484 b(If)15 b Fp(x)g Fy(is)g(an)g(un)o(b)q(ound)g(v)n(ariable)f(then)i(it)e
4485 (m)o(ust)g(b)q(e)i(kno)o(wn)f(to)g(ha)o(v)o(e)g(a)f(coun)o(table)i(set)
4486 g(of)75 1187 y(p)q(oten)o(tial)d(v)n(alues.)k(In)d(this)f(case)i
4487 Fp(x)e Fy(is)g(nondeterministically)e(restricted)16 b(to)d(b)q(e)h
4488 (equal)f(to)g(one)h(of)f(the)h(v)n(alues)f(in)g(this)75
4489 1237 y(coun)o(table)i(set,)h(th)o(us)g(forcing)f Fp(x)g
4490 Fy(to)g(b)q(e)h(b)q(ound.)22 b(The)15 b(dereferenced)k(v)n(alue)14
4491 b(of)h Fp(x)g Fy(is)g(then)h(returned.)23 b(An)16 b(un)o(b)q(ound)75
4492 1287 y(v)n(ariable)c(is)g(kno)o(wn)g(to)h(ha)o(v)o(e)f(a)g(coun)o
4493 (table)h(set)h(of)e(p)q(oten)o(tial)g(v)n(alues)g(either)h(if)f(it)h
4494 (is)f(kno)o(wn)g(to)h(ha)o(v)o(e)f(a)g(\014nite)h(domain)75
4495 1337 y(or)g(if)f(it)g(is)g(kno)o(wn)h(to)f(b)q(e)i(in)o(teger)f(v)n
4496 (alued.)k(An)c(error)g(is)g(signalled)f(if)f Fp(x)i Fy(is)f(not)h(kno)o
4497 (wn)f(to)h(ha)o(v)o(e)f(a)h(\014nite)g(domain)d(and)75
4498 1387 y(is)k(not)h(kno)o(wn)f(to)g(b)q(e)i(in)o(teger)f(v)n(alued.)k(Up)
4499 q(on)c(bac)o(ktrac)o(king)f Fp(x)g Fy(will)g(b)q(e)h(b)q(ound)f(to)h
4500 (eac)o(h)g(p)q(oten)o(tial)f(v)n(alue)g(in)g(turn,)75
4501 1436 y(failing)c(when)j(there)h(remain)c(no)j(un)o(tried)f(alternativ)o
4502 (es.)18 b(Since)13 b(the)g(set)g(of)f(p)q(oten)o(tial)f(v)n(alues)h(is)
4503 g(required)i(only)d(to)h(b)q(e)75 1486 y(coun)o(table,)j(not)f
4504 (\014nite,)h(the)g(set)h(of)e(un)o(tried)i(alternativ)o(e)e(ma)o(y)f
4505 (nev)o(er)j(b)q(e)f(exhausted)h(and)f(bac)o(ktrac)o(king)f(need)i(not)
4506 75 1536 y(terminate.)21 b(This)15 b(can)g(happ)q(en,)h(for)e(instance,)
4507 i(when)g Fp(x)e Fy(is)h(kno)o(wn)g(to)g(b)q(e)h(an)e(in)o(teger)i(but)f
4508 (lac)o(ks)g(either)h(an)f(upp)q(er)75 1586 y(of)d(lo)o(w)o(er)h(b)q
4509 (ound.)k(The)d(order)f(in)g(whic)o(h)f(the)i(nondeterministic)e
4510 (alternativ)o(es)h(are)g(tried)g(is)g(left)f(unsp)q(eci\014ed)j(to)e
4511 (giv)o(e)75 1636 y(future)j(implemen)o(tations)d(leew)o(a)o(y)i(in)h
4512 (incorp)q(orating)f(heuristics)i(in)e(the)i(pro)q(cess)g(of)e
4513 (determining)g(a)g(go)q(o)q(d)h(searc)o(h)75 1686 y(order.)j(See)c
4514 (section)g(6)e(for)h(a)g(discussion)g(of)g(restriction)g(to)g(\014nite)
4515 g(domains)f(and)g(to)h(in)o(teger)h(v)n(alues.)j(See)d(section)f(7)75
4516 1735 y(for)g(a)g(discussion)h(of)f(ho)o(w)g Fv(Screamer)h
4517 Fy(determines)g(whether)g(or)g(not)f(a)g(v)n(ariable)f(is)i(b)q(ound)f
4518 (and)g(ho)o(w)g Fv(Screamer)75 1785 y Fy(dereferences)j(v)n(ariables.)
4519 75 2026 y Fq(divide-and-conque)o(r-for)o(ce)i Fp(x)797
4520 b Fy([)p Fu(Nondeterministic)14 b(F)m(unction)p Fy(])75
4521 2178 y(Returns)19 b Fp(x)f Fy(if)f Fp(x)h Fy(is)g(not)g(a)g(v)n
4522 (ariable.)29 b(If)18 b Fp(x)g Fy(is)g(a)g(b)q(ound)g(v)n(ariable)f
4523 (then)i(b)q(eha)o(v)o(es)g(lik)o(e)e Fq(value-of)g Fy(returning)h(the)
4524 75 2228 y(dereferenced)k(v)n(alue)c(of)g Fp(x)p Fy(.)32
4525 b(If)19 b Fp(x)f Fy(is)h(an)g(un)o(b)q(ound)f(v)n(ariable)g(then)i(it)e
4526 (m)o(ust)g(b)q(e)h(kno)o(wn)f(either)i(to)f(ha)o(v)o(e)f(a)h(\014nite)
4527 75 2277 y(domain)d(or)j(to)g(b)q(e)g(real)g(and)g(ha)o(v)o(e)f(a)h(lo)o
4528 (w)o(er)f(and)h(upp)q(er)h(b)q(ound.)32 b(If)19 b(it)f(is)h(kno)o(wn)f
4529 (to)h(ha)o(v)o(e)f(a)h(\014nite)g(domain)d Fp(d)75 2327
4530 y Fy(then)h(this)g(domain)d(is)j(split)f(in)o(to)g(t)o(w)o(o)g(halv)o
4531 (es)h(and)f(the)h(v)n(alue)f(of)g Fp(x)h Fy(is)f(nondeterministically)f
4532 (restricted)k(to)d(b)q(e)h(a)75 2377 y(mem)o(b)q(er)10
4533 b(one)i(of)f(the)h(halv)o(es.)17 b(If)12 b Fp(x)f Fy(b)q(ecomes)h(b)q
4534 (ound)g(b)o(y)f(this)h(restriction)g(then)h(its)e(dereferenced)k(v)n
4535 (alue)c(is)h(returned.)75 2427 y(Otherwise,)17 b Fp(x)f
4536 Fy(itself)f(is)h(returned.)25 b(The)16 b(metho)q(d)f(of)g(splitting)g
4537 (the)i(domain)c(in)o(to)i(t)o(w)o(o)g(halv)o(es)h(is)g(left)f(unsp)q
4538 (eci\014ed)75 2477 y(to)g(giv)o(e)f(future)i(implem)o(en)o(tations)c
4539 (leew)o(a)o(y)j(in)f(incorp)q(orating)h(heuristics)h(in)e(the)i(pro)q
4540 (cess)h(of)d(determining)g(a)g(go)q(o)q(d)75 2526 y(searc)o(h)k(order.)
4541 30 b(All)16 b(that)i(is)f(sp)q(eci\014ed)i(is)e(that)g(if)g(the)h
4542 (domain)d(size)j(is)f(ev)o(en)h(prior)f(to)h(splitting,)e(the)i(halv)o
4543 (es)g(are)75 2576 y(of)h(equal)g(size,)i(while)e(if)f(the)i(domain)d
4544 (size)k(is)e(o)q(dd,)h(the)g(halv)o(es)f(di\013er)h(in)f(size)h(b)o(y)f
4545 (at)h(most)e(one.)35 b(If)19 b Fp(x)g Fy(is)g(not)992
4546 2723 y(29)p eop
4547 %%Page: 30 30
4548 30 29 bop 75 195 a Fy(kno)o(wn)14 b(to)g(ha)o(v)o(e)h(a)f(\014nite)h
4549 (domain)d(but)j(is)f(kno)o(wn)g(to)h(b)q(e)g(real)f(and)h(to)f(ha)o(v)o
4550 (e)h(b)q(oth)f(lo)o(w)o(er)g(and)h(upp)q(er)g(b)q(ounds)g(then)75
4551 245 y(nondeterministically)10 b(either)i(the)g(lo)o(w)o(er)f(or)h(upp)q
4552 (er)g(b)q(ound)g(is)f(restricted)i(to)f(the)g(midp)q(oin)o(t)d(b)q(et)o
4553 (w)o(een)k(the)f(lo)o(w)o(er)f(and)75 295 y(upp)q(er)g(b)q(ound.)17
4554 b(This)11 b(restriction)g(will)e(cause)i Fp(x)f Fy(to)g(b)q(ecome)h(b)q
4555 (ound)f(if)g(the)h(di\013erence)h(b)q(et)o(w)o(een)g(the)f(lo)o(w)o(er)
4556 f(and)g(upp)q(er)75 345 y(b)q(ounds)i(b)q(ecomes)g(smaller)f(than)g
4557 Fq(*fuzz*)p Fy(.)16 b(If)c Fp(x)f Fy(b)q(ecomes)h(b)q(ound)g(b)o(y)g
4558 (this)g(restriction)g(then)h(its)f(dereferenced)j(v)n(alue)75
4559 394 y(is)f(returned.)21 b(Otherwise,)15 b Fp(x)f Fy(itself)g(is)g
4560 (returned.)20 b(An)15 b(error)g(is)f(signalled)f(if)g
4561 Fp(x)h Fy(is)g(not)g(kno)o(wn)g(to)g(b)q(e)h(restricted)h(to)e(a)75
4562 444 y(\014nite)f(domain)e(and)h(either)i(is)e(not)h(kno)o(wn)f(to)h(b)q
4563 (e)h(real)e(or)h(is)g(not)f(kno)o(wn)h(to)f(ha)o(v)o(e)h(b)q(oth)g(a)f
4564 (lo)o(w)o(er)h(and)g(upp)q(er)g(b)q(ound.)75 494 y Fq
4565 (Divide-and-conque)o(r-for)o(ce)e Fy(implemen)o(ts)h(a)i(single)g
4566 (binary-branc)o(hing)f(step)i(of)f(a)g(divide-and-conquer)g(searc)o(h)
4567 75 544 y(algorithm.)23 b(There)18 b(are)f(alw)o(a)o(ys)e(t)o(w)o(o)h
4568 (alternativ)o(es,)h(the)g(second)h(of)e(whic)o(h)g(is)h(tried)g(up)q
4569 (on)f(bac)o(ktrac)o(king.)26 b(While)75 594 y(a)14 b(single)g
4570 (application)f(of)h Fq(divide-and-conq)o(uer-f)o(orce)d
4571 Fy(ma)o(y)h(not)i(cause)i(its)e(argumen)o(t)f(to)h(b)q(e)h(b)q(ound,)f
4572 (rep)q(eated)75 643 y(application)g(is)h(guaran)o(teed)g(to)g(ev)o(en)o
4573 (tually)g(bind)g(its)g(argumen)o(t)f(so)h(long)f(as)h
4574 Fq(*fuzz*)f Fy(is)h(non-zero.)22 b(See)16 b(section)g(6)75
4575 693 y(for)e(a)g(discussion)g(of)g(restriction)h(to)f(\014nite)g
4576 (domains)e(and)i(to)g(real)g(v)n(alues.)k(See)d(section)g(7)f(for)f(a)h
4577 (discussion)h(of)e(ho)o(w)75 743 y Fv(Screamer)i Fy(determines)f
4578 (whether)h(or)f(not)g(a)f(v)n(ariable)g(is)h(b)q(ound)g(and)f(ho)o(w)h
4579 Fv(Screamer)g Fy(dereferences)k(v)n(ariables.)75 984
4580 y Fq(static-ordering)h Fu(for)n(c)n(e-function)833 b
4581 Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75 1136
4582 y(This)k(function)f(is)h(a)f(higher-order)i(function)e(whic)o(h)h(tak)o
4583 (es)g(a)g Fu(for)n(c)n(e-function)f Fy(as)h(an)g(argumen)o(t)e(and)i
4584 (returns)h(an)75 1186 y(ordering)d(force)h(function)f(as)g(its)h
4585 (result.)26 b(The)16 b Fu(for)n(c)n(e-function)g Fy(is)g(an)o(y)g(\(p)q
4586 (oten)o(tially)f(nondeterministic\))h(function)75 1235
4587 y(whic)o(h)j(can)g(b)q(e)g(applied)g(to)f(a)h(v)n(ariable)f(as)h(its)g
4588 (single)f(argumen)o(t)g(with)h(the)g(stipulation)f(that)h(a)g(\014nite)
4589 g(n)o(um)o(b)q(er)75 1285 y(of)e(rep)q(eated)i(applications)d(will)g
4590 (force)i(the)g(v)n(ariable)e(to)i(b)q(e)g(b)q(ound.)28
4591 b(The)18 b Fu(for)n(c)n(e-function)f Fy(need)i(not)e(return)h(an)o(y)75
4592 1335 y(useful)h(v)n(alue.)30 b Fv(Screamer)19 b Fy(curren)o(tly)h(pro)o
4593 (vides)e(t)o(w)o(o)g(con)o(v)o(enien)o(t)h Fu(for)n(c)n(e-function)p
4594 Fy(s,)g(namely)e Fq(#'linear-force)75 1385 y Fy(and)f
4595 Fq(#'divide-and-conq)o(uer-)o(force)c Fy(though)k(future)h(implemen)o
4596 (tati)o(ons)d(ma)o(y)g(pro)o(vide)h(additional)g(ones.)25
4597 b(The)75 1435 y(de\014ned)15 b Fv(Screamer)g Fy(proto)q(col)e(do)q(es)i
4598 (not)f(pro)o(vide)g(su\016cien)o(t)g(ho)q(oks)g(for)g(the)g(user)h(to)f
4599 (de\014ne)h(her)g(o)o(wn)e Fu(for)n(c)n(e)i(func-)75
4600 1484 y(tion)p Fy(s.)j(The)d(ordering)f(force)g(function)g(whic)o(h)f
4601 (is)h(returned)i(is)d(a)h(nondeterministic)f(function)h(whic)o(h)f(tak)
4602 o(es)i(a)e(single)75 1534 y(argumen)o(t)k Fp(x)p Fy(.)32
4603 b(This)19 b(argumen)o(t)e Fp(x)h Fy(can)h(b)q(e)g(a)f(list)g(of)g(v)n
4604 (alues)h(where)g(eac)o(h)g(v)n(alue)f(ma)o(y)f(b)q(e)i(either)g(a)g(v)n
4605 (ariable)e(or)75 1584 y(a)f(non-v)n(ariable.)24 b(The)17
4606 b(ordering)f(force)h(function)f(applies)g(the)h Fu(for)n(c)n
4607 (e-function)f Fy(in)f(turn)i(to)f(eac)o(h)h(of)f(the)h(v)n(ariables)75
4608 1634 y(in)e Fp(x)p Fy(,)h(in)f(the)i(order)g(that)e(they)i(app)q(ear,)f
4609 (rep)q(eatedly)h(applying)e(the)h Fu(for)n(c)n(e-function)g
4610 Fy(to)g(a)f(giv)o(en)h(v)n(ariable)e(un)o(til)h(it)75
4611 1684 y(b)q(ecomes)e(b)q(ound)h(b)q(efore)g(pro)q(ceeding)g(to)f(the)g
4612 (next)h(v)n(ariable.)j(The)c(ordering)h(force)f(function)g(do)q(es)h
4613 (not)f(return)h(an)o(y)75 1733 y(meaningful)d(result.)75
4614 1975 y Fq(domain-size)20 b Fp(x)1145 b Fy([)p Fu(Deterministic)14
4615 b(F)m(unction)p Fy(])75 2126 y(Returns)d(the)h(domain)c(size)j(of)f
4616 Fp(x)p Fy(.)17 b(This)10 b(is)h(the)g(n)o(um)o(b)q(er)f(of)g(p)q
4617 (ossible)h(ground)f(v)n(alues)g(whic)o(h)h Fp(x)f Fy(ma)o(y)f
4618 (consisten)o(tly)i(tak)o(e)75 2176 y(on.)26 b(This)17
4619 b(function)f(recursiv)o(ely)i(tra)o(v)o(erses)g(aggregate)e(ob)r(jects)
4620 i(when)f(computing)e(domain)g(sizes.)27 b(The)17 b(domain)75
4621 2226 y(size)d(of)g(an)f(aggregate)h(ob)r(ject)g(is)g(the)g(pro)q(duct)h
4622 (of)e(the)h(domain)e(sizes)i(of)g(its)f(slots.)18 b(An)c(atomic)e
4623 (non-v)n(ariable)g(has)i(a)75 2276 y(domain)d(size)k(of)e(one.)18
4624 b(The)c(domain)e(size)i(of)g(a)f(b)q(ound)h(v)n(ariable)e(is)i(the)g
4625 (domain)e(size)i(of)f(its)h(dereferenced)j(v)n(alue.)g(If)75
4626 2325 y(an)c(un)o(b)q(ound)g(v)n(ariable)f(is)g(kno)o(wn)h(to)g(ha)o(v)o
4627 (e)f(a)h(\014nite)g(domain)e(then)i(its)g(domain)e(size)j(is)e(the)i
4628 (size)g(of)e(that)h(domain.)i(If)75 2375 y(an)d(un)o(b)q(ound)h(v)n
4629 (ariable)e(is)h(not)g(kno)o(wn)g(to)g(ha)o(v)o(e)h(a)f(\014nite)g
4630 (domain)e(but)j(is)f(kno)o(wn)g(to)g(b)q(e)h(in)o(teger)g(v)n(alued)f
4631 (and)g(to)g(ha)o(v)o(e)75 2425 y(upp)q(er)i(and)f(lo)o(w)o(er)f(b)q
4632 (ounds)i(then)f(its)g(domain)e(size)j(is)f(the)g(one)g(plus)g(the)h
4633 (di\013erence)h(b)q(et)o(w)o(een)f(the)g(upp)q(er)g(and)e(lo)o(w)o(er)
4634 75 2475 y(b)q(ounds)i(Otherwise,)g(the)g(domain)d(size)k(of)d(an)h(un)o
4635 (b)q(ound)h(v)n(ariable)e(is)h(in\014nite.)18 b Fq(Domain-size)11
4636 b Fy(returns)k Fq(nil)e Fy(if)f Fp(x)p Fy(,)h(or)75 2525
4637 y(an)o(y)g(slot)h(nested)h(in)f Fp(x)p Fy(,)f(has)h(an)g(in\014nite)f
4638 (domain)f(size.)19 b(See)14 b(section)h(9)f(for)f(a)h(discussion)g(of)f
4639 (aggregate)h(ob)r(jects.)992 2723 y(30)p eop
4640 %%Page: 31 31
4641 31 30 bop 75 195 a Fq(reorder)20 b Fu(for)n(c)n(e-function)1008
4642 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])75
4643 342 y(This)k(function)f(is)h(a)f(higher-order)i(function)e(whic)o(h)h
4644 (tak)o(es)g(a)g Fu(for)n(c)n(e-function)f Fy(as)h(an)g(argumen)o(t)e
4645 (and)i(returns)h(an)75 392 y(ordering)d(force)h(function)f(as)g(its)h
4646 (result.)26 b(The)16 b Fu(for)n(c)n(e-function)g Fy(is)g(an)o(y)g(\(p)q
4647 (oten)o(tially)f(nondeterministic\))h(function)75 442
4648 y(whic)o(h)j(can)g(b)q(e)g(applied)g(to)f(a)h(v)n(ariable)f(as)h(its)g
4649 (single)f(argumen)o(t)g(with)h(the)g(stipulation)f(that)h(a)g(\014nite)
4650 g(n)o(um)o(b)q(er)75 492 y(of)e(rep)q(eated)i(applications)d(will)g
4651 (force)i(the)g(v)n(ariable)e(to)i(b)q(e)g(b)q(ound.)28
4652 b(The)18 b Fu(for)n(c)n(e-function)f Fy(need)i(not)e(return)h(an)o(y)75
4653 542 y(useful)h(v)n(alue.)30 b Fv(Screamer)19 b Fy(curren)o(tly)h(pro)o
4654 (vides)e(t)o(w)o(o)g(con)o(v)o(enien)o(t)h Fu(for)n(c)n(e-function)p
4655 Fy(s,)g(namely)e Fq(#'linear-force)75 591 y Fy(and)f
4656 Fq(#'divide-and-conq)o(uer-)o(force)c Fy(though)k(future)h(implemen)o
4657 (tati)o(ons)d(ma)o(y)g(pro)o(vide)h(additional)g(ones.)25
4658 b(The)75 641 y(de\014ned)15 b Fv(Screamer)g Fy(proto)q(col)e(do)q(es)i
4659 (not)f(pro)o(vide)g(su\016cien)o(t)g(ho)q(oks)g(for)g(the)g(user)h(to)f
4660 (de\014ne)h(her)g(o)o(wn)e Fu(for)n(c)n(e)i(func-)75
4661 691 y(tion)p Fy(s.)j(The)d(ordering)f(force)g(function)g(whic)o(h)f(is)
4662 h(returned)i(is)d(a)h(nondeterministic)f(function)h(whic)o(h)f(tak)o
4663 (es)i(a)e(single)75 741 y(argumen)o(t)j Fp(x)p Fy(.)26
4664 b(This)17 b(argumen)o(t)e Fp(x)i Fy(can)g(b)q(e)g(a)f(list)h(of)f(v)n
4665 (alues)g(where)i(eac)o(h)g(v)n(alue)e(ma)o(y)e(b)q(e)k(either)f(a)g(v)n
4666 (ariable)f(or)g(a)75 791 y(non-v)n(ariable.)g(The)e(ordering)f(force)h
4667 (function)f(rep)q(eatedly)h(applies)f(the)g Fu(for)n(c)n(e-function)g
4668 Fy(to)g(the)h(v)n(ariable)e(in)h Fp(x)f Fy(with)75 840
4669 y(the)i(smallest)f(domain)e(size)k(un)o(til)e(all)f(v)n(ariables)h(in)g
4670 Fp(x)h Fy(are)g(b)q(ound.)k(The)c(ordering)g(force)g(function)g(do)q
4671 (es)g(not)g(return)75 890 y(an)o(y)f(meaningful)f(result.)75
4672 1127 y Fq(solution)20 b Fu(list)h(or)n(dering-for)n(c)n(e-function)680
4673 b Fy([)p Fu(Nondeterministic)14 b(F)m(unction)p Fy(])75
4674 1275 y(The)19 b(argumen)o(t)e Fu(list)g Fy(is)h(a)g(list)g(of)f(v)n
4675 (alues.)31 b(T)o(ypically)17 b(it)h(is)g(a)g(list)f(of)h(v)n(ariables)f
4676 (but)i(it)f(ma)o(y)e(also)i(con)o(tain)f(non-)75 1324
4677 y(v)n(ariables.)g(The)c(sp)q(eci\014ed)i Fu(or)n(dering-for)n(c)n
4678 (e-function)d Fy(is)h(used)h(to)e(force)i(eac)o(h)f(of)g(the)g(v)n
4679 (ariables)f(in)h Fu(list)f Fy(to)h(b)q(e)g(b)q(ound.)75
4680 1374 y(Returns)h(a)f(list)f(of)h(the)h(dereference)i(v)n(alues)c(of)h
4681 (the)h(elemen)o(ts)e(of)h Fu(list)f Fy(in)h(the)g(same)g(order)g(that)h
4682 (they)f(app)q(ear)h(in)e Fu(list)p Fy(,)75 1424 y(irresp)q(ectiv)o(e)i
4683 (of)d(the)i(forcing)e(order)i(imp)q(osed)e(b)o(y)g(the)i
4684 Fu(or)n(dering-for)n(c)n(e-function)p Fy(.)j(The)d Fu(or)n(dering-for)n
4685 (c)n(e-function)e Fy(can)75 1474 y(b)q(e)h(an)o(y)f(function)g(whic)o
4686 (h)h(tak)o(es)g(a)f(list)g(of)g(v)n(alues)g(as)h(its)f(single)h
4687 (argumen)o(t)e(that)h(is)h(guaran)o(teed)g(to)f(force)h(all)f(v)n
4688 (ariables)75 1524 y(in)k(that)h(list)f(to)h(b)q(e)g(b)q(ound)g(up)q(on)
4689 f(its)h(return.)25 b(The)16 b(returned)h(v)n(alue)e(of)g(the)h
4690 Fu(or)n(dering-for)n(c)n(e-function)f Fy(is)h(ignored.)75
4691 1573 y(The)j(user)h(can)f(construct)h(her)g(o)o(wn)e
4692 Fu(or)n(dering-for)n(c)n(e-function)g Fy(or)h(use)h(one)f(of)f(the)h
4693 (follo)o(wing)d(four)j(alternativ)o(es)75 1623 y(pro)o(vided)14
4694 b(with)f Fv(Screamer)q Fy(.)137 1703 y Fr(\017)21 b Fq
4695 (\(static-ordering)d(#'linear-force\))p Fy(,)137 1784
4696 y Fr(\017)j Fq(\(static-ordering)d(#'divide-and-conque)o(r-for)o(ce\))p
4697 Fy(,)137 1866 y Fr(\017)j Fq(\(reorder)f(#'linear-force\))11
4698 b Fy(and)137 1947 y Fr(\017)21 b Fq(\(reorder)f(#'divide-and-conq)o
4699 (uer-f)o(orce\))o Fy(.)75 2027 y(F)m(uture)14 b(implemen)o(tation)d(of)
4700 i Fv(Screamer)i Fy(ma)o(y)d(pro)o(vide)h(additional)f(forcing)i(and)f
4701 (ordering)h(functions.)75 2264 y Fq(best-value)20 b Fu(obje)n
4702 (ctive-function)i(expr)n(ession)648 b Fy([)p Fu(Nondeterministic)13
4703 b(Macr)n(o)p Fy(])75 2599 y Fq(template)20 b Fp(x)1211
4704 b Fy([)p Fu(Deterministic)14 b(F)m(unction)p Fy(])992
4705 2723 y(31)p eop
4706 %%Page: 32 32
4707 32 31 bop 75 195 a Fy(Copies)13 b(an)g(aggregate)g(ob)r(ject,)h
4708 (replacing)f(an)o(y)g(sym)o(b)q(ol)e(b)q(eginning)i(with)g(a)g
4709 (question)g(mark)f(with)g(a)h(newly)g(created)75 245
4710 y(v)n(ariable.)k(If)c(the)h(same)f(sym)o(b)q(ol)f(app)q(ears)i(more)e
4711 (than)i(once)g(in)f Fp(x)p Fy(,)g(only)g(one)h(v)n(ariable)e(is)h
4712 (created)i(for)f(that)f(sym)o(b)q(ol,)75 295 y(the)i(same)f(v)n
4713 (ariable)g(replacing)g(an)o(y)h(o)q(ccurrences)j(of)c(that)g(sym)o(b)q
4714 (ol.)19 b(Th)o(us)c Fq(\(template)20 b('\(a)h(b)h(\(?c)f(d)h(?e\))f
4715 (?e\)\))75 345 y Fy(has)14 b(the)h(same)e(e\013ect)i(as:)204
4716 414 y Fq(\(let)21 b(\(\(?c)g(\(make-variable\)\))334
4717 463 y(\(?e)h(\(make-variable\)\))o(\))225 513 y(\(list)f('a)h('b)f
4718 (\(list)g(c)g('d)h(e\))f(e\)\).)75 591 y Fy(This)14 b(is)g(useful)g
4719 (for)g(creating)g(patterns)h(to)f(b)q(e)h(uni\014ed)f(with)g(other)g
4720 (structures.)21 b(See)15 b(section)g(9)f(for)f(a)h(discussion)h(of)75
4721 641 y(aggregate)f(ob)r(jects.)75 879 y Fq(*fuzz*)1571
4722 b Fy([)p Fu(V)m(ariable)p Fy(])75 1026 y(The)18 b(v)n(ariable)f
4723 Fq(*fuzz*)g Fy(is)h(used)h(to)f(determine)g(whether)h(a)f(real)g(v)n
4724 (ariable)f(is)g(b)q(ound)i(when)f(it)g(is)g(not)g(kno)o(wn)f(to)75
4725 1076 y(ha)o(v)o(e)e(a)f(\014nite)h(domain.)k(If)c(a)f(real)h(v)n(alue)f
4726 (has)h(lo)o(w)o(er)g(and)f(upp)q(er)i(b)q(ounds)g(and)e(the)i
4727 (di\013erence)h(b)q(et)o(w)o(een)f(the)f(lo)o(w)o(er)75
4728 1126 y(and)g(upp)q(er)h(b)q(ounds)g(is)f(less)h(than)g
4729 Fq(*fuzz*)e Fy(then)i(the)g(v)n(ariable)e(is)h(considered)i(b)q(ound.)
4730 22 b(When)16 b(suc)o(h)g(a)f(v)n(ariable)f(is)75 1176
4731 y(dereferenced,)i(the)f(lo)o(w)o(er)e(b)q(ound)h(is)g(arbitrarily)f
4732 (tak)o(en)h(as)g(its)g(v)n(alue.)j(See)e(section)g(6)e(for)h(further)h
4733 (discussion.)75 1312 y Fw(12)69 b(Examples)75 1403 y
4734 Fy(In)12 b(this)f(section)i(I)e(will)g(presen)o(t)i(a)e(n)o(um)o(b)q
4735 (er)g(of)g(examples)g(of)g Fv(Screamer)h Fy(programs)f(to)g(illustrate)
4736 h(t)o(ypical)f(program-)75 1453 y(ming)i(st)o(yles)i(and)g(clic)o(h)o
4737 (\023)-20 b(es.)21 b(Figure)15 b(1)g(con)o(tains)g(a)f(program)g(for)g
4738 (computing)f(all)h(Pythagorean)h(triples)g(of)f(p)q(ositiv)o(e)75
4739 1503 y(in)o(tegers)g(less)g(than)f(or)g(equal)f(to)h
4740 Fp(n)p Fy(.)18 b(It)13 b(illustrates)g(a)g(simple)f(generate-and-test)j
4741 (paradigm.)g(The)f Fq(let)e Fy(bindings)h(of)75 1553
4742 y(the)f(function)f Fq(pythagorean-trip)o(les)d Fy(constitute)k(the)g
4743 (generator)g(while)f(the)g Fq(unless)f Fy(expression)j(constitutes)f
4744 (the)75 1602 y(test.)24 b(The)16 b(function)g Fq(integer-between)c
4745 Fy(nondeterministically)i(returns)j(an)e(in)o(teger)h(in)f(the)i(range)
4746 e(giv)o(en)h(b)o(y)f(its)75 1652 y(argumen)o(ts.)k(This)14
4747 b(function)g(is)h(so)f(useful)h(that)f(it)g(is)g(built)g(in)o(to)g
4748 Fv(Screamer)p Fy(,)g(though)h(it)f(could)g(easily)g(b)q(e)h(de\014ned)
4749 75 1702 y(as)f(in)f(\014gure)i(1.)137 1752 y(Figure)i(1)g(also)g(con)o
4750 (tains)g(a)g(second)h(program)d(for)i(\014nding)g(p)o(ythagorean)g
4751 (triples.)28 b(While)16 b(the)i(\014rst)f(one)h(uses)75
4752 1802 y(pure)f(bac)o(ktrac)o(king)f(searc)o(h,)h(the)g(second)g
4753 (function)f Fq(pythagorean-tripl)o(esv)d Fy(uses)k(the)g
4754 Fv(Screamer)g Fy(constrain)o(t)75 1851 y(pac)o(k)n(age.)25
4755 b(While)15 b(for)h(this)h(problem,)e(the)h(constrain)o(t)h(based)g(v)o
4756 (ersion)f(do)q(es)h(not)g(o\013er)f(m)o(uc)o(h)g(computational)d(ad-)75
4757 1901 y(v)n(an)o(tage)i(o)o(v)o(er)g(the)i(bac)o(ktrac)o(king)e(v)o
4758 (ersion,)h(this)f(example)f(do)q(es)j(illustrate)e(a)g(standard)h(clic)
4759 o(h)o(\023)-20 b(e)16 b(for)f(reform)o(ulating)75 1951
4760 y(generate-and-test)20 b(algorithms)c(in)o(to)h(constrain)o(t)h
4761 (propagation)f(ones.)31 b(Note)18 b(the)g(in)o(ten)o(tional)f
4762 (similarit)o(y)e(in)i(the)75 2001 y(names)f(of)g(the)i(primitiv)o(es)d
4763 Fq(integer-between)f Fy(and)i Fq(integer-betweenv)p Fy(.)24
4764 b(A)17 b(similar)e(analogy)g(exists)j(b)q(et)o(w)o(een)75
4765 2051 y(the)c(primitiv)o(es)f Fq(member-of)f Fy(and)h
4766 Fq(member-ofv)p Fy(.)137 2100 y(Figure)i(2)g(con)o(tains)g(a)f(program)
4767 f(for)i(solving)e(the)j Fp(N)5 b Fy(-Queens)16 b(problem.)k(The)15
4768 b(function)f Fq(attacks)g Fy(returns)i Fq(t)f Fy(if)75
4769 2150 y(a)e(queen)h(on)f(ro)o(w)g Fp(q)382 2156 y Fh(i)409
4770 2150 y Fy(attac)o(ks)g(a)g(queen)h(on)f(ro)o(w)g Fp(q)858
4771 2156 y Fh(j)889 2150 y Fy(when)g(the)h(queens)h(are)e
4772 Fu(distanc)n(e)h Fy(columns)e(apart.)18 b(The)13 b(function)75
4773 2200 y Fq(check-queens)h Fy(c)o(hec)o(ks)j(whether)h(a)e(new)g(queen)h
4774 (can)g(b)q(e)f(placed)h(on)f(the)g(b)q(oard)h(without)e(attac)o(king)h
4775 (the)h(queens)75 2250 y(already)g(placed.)27 b(It)17
4776 b(recursiv)o(ely)h(c)o(hec)o(ks)h(the)e(new)h(queen)f(against)g(eac)o
4777 (h)g(previously)g(placed)g(queen)h(and)f(fails)f(if)75
4778 2300 y(it)f(detects)i(an)e(attac)o(k.)23 b(The)15 b(parameter)g
4779 Fu(que)n(en)h Fy(giv)o(es)g(the)f(ro)o(w)h(of)e(the)i(new)g(queen)g(to)
4780 f(b)q(e)h(placed)g(in)f(the)h(column)75 2350 y(adjacen)o(t)f(to)g
4781 (columns)e(of)h(the)i(previously)e(placed)h(queens.)22
4782 b(The)15 b(parameter)g Fu(que)n(ens)g Fy(is)g(a)f(list)h(of)f(the)h(ro)
4783 o(ws)g(of)f(the)75 2399 y(previously)h(placed)h(queens.)24
4784 b(Note)16 b(that)g(the)g(functions)g Fq(attacks)e Fy(and)h
4785 Fq(check-queens)e Fy(are)j(deterministic.)23 b(The)75
4786 2449 y(function)14 b Fq(n-queens)f Fy(nondeterministically)g(recursiv)o
4787 (ely)i(places)g(queens)h(on)e(the)h(b)q(oard,)f(c)o(hec)o(king)h(for)f
4788 (attac)o(ks)h(as)75 2499 y(eac)o(h)f(queen)h(is)f(placed.)137
4789 2549 y(This)f(example)e(illustrates)i(the)g(clic)o(h)o(\023)-20
4790 b(e)13 b(of)f(in)o(terlea)o(ving)g(the)h(generate)h(and)f(test)g(pro)q
4791 (cesses)j(to)c(implemen)o(t)e(early)75 2599 y(failure)k(detection.)23
4792 b(Rather)15 b(than)g(w)o(ait)g(un)o(til)f(all)g(queens)i(are)g(placed)f
4793 (b)q(efore)h(c)o(hec)o(king)f(for)g(attac)o(ks,)g(consistency)992
4794 2723 y(32)p eop
4795 %%Page: 33 33
4796 33 32 bop 134 197 1757 2 v 134 1068 2 872 v 173 244 a
4797 Fq(\(defun)21 b(integer-between)e(\(low)i(high\))195
4798 294 y(\(if)g(\(>)h(low)f(high\))g(\(fail\))f(\(either)h(low)g
4799 (\(integer-between)d(\(1+)j(low\))g(high\)\)\)\))173
4800 394 y(\(defun)g(pythagorean-triple)o(s)e(\(n\))195 443
4801 y(\(all-values)217 493 y(\(let)i(\(\(a)g(\(integer-between)e(1)i(n\)\))
4802 348 543 y(\(b)g(\(integer-between)e(1)i(n\)\))348 593
4803 y(\(c)g(\(integer-between)e(1)i(n\)\)\))239 643 y(\(unless)f(\(=)i(\(+)
4804 f(\(*)g(a)h(a\))f(\(*)h(b)f(b\)\))g(\(*)h(c)f(c\)\))h(\(fail\)\))239
4805 692 y(\(list)f(a)g(b)h(c\)\)\)\))173 792 y(\(defun)f
4806 (pythagorean-triple)o(sv)e(\(n\))195 842 y(\(let)i(\(\(a)g
4807 (\(integer-betweenv)e(1)i(n\)\))326 892 y(\(b)g(\(integer-betweenv)e(1)
4808 i(n\)\))326 941 y(\(c)g(\(integer-betweenv)e(1)i(n\)\)\))217
4809 991 y(\(assert!)f(\(=v)h(\(+v)h(\(*v)f(a)g(a\))h(\(*v)f(b)g(b\)\))h
4810 (\(*v)f(c)g(c\)\)\))217 1041 y(\(all-values)f(\(solution)g(\(list)g(a)i
4811 (b)f(c\))h(\(reorder)e(#'divide-and-conq)o(uer-f)o(orce\))o(\)\)\)\))p
4812 1889 1068 V 134 1070 1757 2 v 193 1183 a FA(Figure)e(1:)24
4813 b(Tw)o(o)16 b Fz(Screamer)h FA(programs)h(for)e(\014nding)j(p)o
4814 (ythagorean)g(triples.)30 b(The)16 b(\014rst)h(uses)h(bac)o(ktrac)o
4815 (king)193 1229 y(searc)o(h)13 b(while)h(the)g(second)g(uses)f(the)g
4816 (constrain)o(t)i(pac)o(k)n(age.)75 1361 y Fy(is)e(c)o(hec)o(k)o(ed)i
4817 (after)f(making)d(eac)o(h)j(nondeterministic)f(c)o(hoice.)19
4818 b(This)13 b(example)g(also)g(illustrates)g(ho)o(w)g Fv(Common)k(Lisp)75
4819 1411 y Fy(features)e(suc)o(h)g(as)f Fq(&optional)e Fy(argumen)o(ts)h
4820 (are)h(a)o(v)n(ailable)e(in)h Fv(Screamer)q Fy(.)137
4821 1460 y(Figure)j(3)f(con)o(tains)g(a)g(program)f(for)h(\014nding)g(all)f
4822 (simple)g(paths)i(in)f(a)g(directed)h(graph.)23 b(A)15
4823 b(simple)f(path)h(is)h(one)75 1510 y(whic)o(h)e(do)q(es)g(not)f(visit)g
4824 (a)h(v)o(ertex)g(more)f(than)h(once.)k(The)c(graph)g(is)f(represen)o
4825 (ted)k(via)12 b(the)j Fq(defstruct)20 b(node)p Fy(.)d(Eac)o(h)75
4826 1560 y(no)q(de)c(con)o(tains)g(t)o(w)o(o)f(slots.)17
4827 b(The)d Fq(marked?)d Fy(slot)h(is)h(used)g(to)g(record)g(when)g(a)g(no)
4828 q(de)g(has)g(already)f(b)q(een)i(visited)e(in)g(the)75
4829 1610 y(path)j(b)q(eing)f(constructed.)22 b(The)15 b Fq(next-nodes)e
4830 Fy(slot)h(con)o(tains)g(a)h(list)f(of)g(all)f(of)h(the)h(no)q(des)g
4831 (reac)o(hable)g(from)e(a)h(giv)o(en)75 1660 y(no)q(de)g(via)f
4832 (out-edges.)19 b(The)c(function)e Fq(member-of)f Fy(is)i(used)h(to)f
4833 (nondeterministically)e(c)o(ho)q(ose)j(one)f(of)f(the)i(no)q(des)f(in)
4834 75 1709 y(the)f Fq(next-nodes)e Fy(slot)i(as)f(the)i(next)f(no)q(de)g
4835 (in)g(the)g(path)g(b)q(eing)g(constructed.)19 b(This)13
4836 b(function)f(is)h(so)g(useful)g(that)g(it)f(is)75 1759
4837 y(built)g(in)o(to)g Fv(Screamer)p Fy(,)h(though)f(it)g(could)h(easily)f
4838 (b)q(e)h(de\014ned)h(as)e(in)g(\014gure)i(3.)j(The)c(v)o(ersion)g
4839 (built)e(in)o(to)h Fv(Screamer)75 1809 y Fy(is)i(sligh)o(tly)e(more)h
4840 (complex)g(as)h(it)f(accepts)j(either)e(a)g(v)o(ector)h(or)f(a)f(list)h
4841 (as)g(its)f(argumen)o(t.)137 1859 y(This)g(example)e(illustrates)i(the)
4842 h(utilit)o(y)d(of)h(lo)q(cal)g(side)h(e\013ects.)20 b(Lo)q(cal)12
4843 b(side)i(e\013ects)g(are)g(used)f(to)g(mark)e(a)i(no)q(de)g(as)75
4844 1909 y(b)q(eing)f(visited)h(so)f(that)h(they)g(are)f(not)h(included)f
4845 (t)o(wice)h(in)f(the)h(path.)18 b(The)12 b(marking)f(is)h(undone)h(up)q
4846 (on)f(bac)o(ktrac)o(king)75 1958 y(as)i(di\013eren)o(t)h(paths)f(are)g
4847 (considered.)137 2008 y(The)k(function)f Fq(simple-path)e
4848 Fy(nev)o(er)j(o)o(v)o(erwrites)g(a)f(lo)q(cal)f(side)h(e\013ect.)30
4849 b(As)18 b(suc)o(h,)g(its)f(side)h(e\013ects)h(are)e(single)75
4850 2058 y(assignmen)o(t,)11 b(m)o(uc)o(h)g(lik)o(e)h Fv(Pr)o(olog)p
4851 Fy('s)g(binding)g(of)g(logic)f(v)n(ariables.)17 b Fv(Screamer)c
4852 Fy(allo)o(ws)e(m)o(ultiple)f(assignmen)o(t)h(lo)q(cal)75
4853 2108 y(side)j(e\013ects,)i(something)d(whic)o(h)g(is)h(not)g(p)q
4854 (ossible)g(in)g Fv(Pr)o(olog)p Fy(.)k(The)d(second)g(example)e(in)g
4855 (\014gure)i(3)e(illustrates)h(the)75 2158 y(utilit)o(y)i(of)g(m)o
4856 (ultiple)e(assignmen)o(t)i(lo)q(cal)g(side)i(e\013ects.)29
4857 b(Let)17 b(us)h(extend)f(the)h(de\014nition)f(of)f(simple)f(path)i(to)g
4858 (de\014ne)75 2208 y(the)h(notion)e(of)h(a)g Fp(k)q Fy(-simple)e(path.)
4859 28 b(A)17 b Fp(k)q Fy(-simple)f(path)h(is)g(one)g(whic)o(h)g(nev)o(er)h
4860 (visits)f(a)g(no)q(de)h(more)e(than)h Fp(k)h Fy(times.)75
4861 2257 y(A)d(program)e(for)h(\014nding)g(simple)f(paths)i(can)g(b)q(e)g
4862 (con)o(v)o(erted)h(in)o(to)e(one)h(whic)o(h)f(\014nds)h
4863 Fp(k)q Fy(-simple)e(paths)i(b)o(y)g(k)o(eeping)f(a)75
4864 2307 y Fq(visits)d Fy(coun)o(t)i(for)e(eac)o(h)i(no)q(de)g(instead)g
4865 (of)e(a)h Fq(marked?)f Fy(\015ag.)17 b(Incremen)o(ting)12
4866 b(this)g Fq(visits)f Fy(coun)o(t)i(requires)g(m)o(ultiple)75
4867 2357 y(assignmen)o(t)j(lo)q(cal)g(side)i(e\013ects.)29
4868 b(This)17 b(example)f(also)h(illustrates)g(ho)o(w)f(lo)q(cal)h(side)g
4869 (e\013ects)i(can)f(b)q(e)f(done)h(on)e(an)o(y)75 2407
4870 y Fv(Common)h(Lisp)c Fy(generalized)i(v)n(ariable)e(\(suc)o(h)i(as)f
4871 Fq(defstruct)e Fy(slots\))i(via)f(the)h Fq(setf)f Fy(primitiv)o(e.)137
4872 2457 y(The)i Fv(Screamer)g Fy(constrain)o(t)g(pac)o(k)n(age)f(is)g
4873 (implemen)o(ted)e(using)i(the)h(basic)g(nondeterministic)f(primitiv)o
4874 (es)e(pro-)75 2506 y(vided)d(b)o(y)g Fv(Screamer)q Fy(.)17
4875 b(No)9 b(in)o(ternals)g(of)g Fv(Screamer)h Fy(needed)h(to)e(b)q(e)h(mo)
4876 q(di\014ed)e(to)h(supp)q(ort)h(the)g(constrain)o(t)g(pac)o(k)n(age.)75
4877 2556 y(Had)k(the)h(constrain)o(t)f(pac)o(k)n(age)g(not)g(b)q(een)h(pro)
4878 o(vided)f(with)f Fv(Screamer)q Fy(,)h(a)f(user)j(could)d(ha)o(v)o(e)h
4879 (constructed)j(her)d(o)o(wn)992 2723 y(33)p eop
4880 %%Page: 34 34
4881 34 33 bop 124 654 1778 2 v 124 1974 2 1321 v 163 701
4882 a Fq(\(defun)20 b(attacks)g(\(qi)i(qj)f(distance\))184
4883 751 y(\(or)h(\(=)f(qi)g(qj\))272 801 y(\(=)g(qi)g(\(+)h(qj)f
4884 (distance\)\))272 851 y(\(=)g(qi)g(\(-)h(qj)f(distance\)\)\)\))163
4885 950 y(\(defun)f(check-queens)f(\(queen)i(queens)g(&optional)e
4886 (\(distance)h(1\)\))184 1000 y(\(unless)h(\(null)f(queens\))206
4887 1050 y(\(if)h(\(attacks)f(queen)h(\(first)g(queens\))f(distance\))g
4888 (\(fail\)\))206 1100 y(\(check-queens)f(queen)i(\(rest)g(queens\))f
4889 (\(1+)h(distance\)\)\)\))163 1199 y(\(defun)f(n-queens)g(\(n)i
4890 (&optional)e(queens\))184 1249 y(\(if)i(\(=)f(\(length)f(queens\))h
4891 (n\))272 1299 y(queens)272 1349 y(\(let)g(\(\(queen)f
4892 (\(integer-between)e(1)k(n\)\)\))293 1399 y(\(check-queens)d(queen)i
4893 (queens\))293 1448 y(\(n-queens)f(n)i(\(cons)f(queen)f
4894 (queens\)\)\)\)\))163 1548 y(\(defun)g(n-queensv)g(\(n\))184
4895 1598 y(\(let)h(\(\(q)h(\(make-array)d(n\)\)\))206 1648
4896 y(\(dotimes)h(\(i)i(n\))228 1697 y(\(setf)f(\(aref)f(q)i(i\))f
4897 (\(member-ofv)f(\(all-values)f(\(integer-between)g(1)j(n\)\)\)\)\))206
4898 1747 y(\(dotimes)e(\(i)i(n\))228 1797 y(\(dotimes)e(\(j)h(n\))250
4899 1847 y(\(if)g(\(>)g(j)h(i\))337 1897 y(\(assert!)e(\(notv)h(\(funcallv)
4900 f(#'attacks)g(\(aref)g(q)i(i\))f(\(aref)g(q)h(j\))f(\(-)g(j)h
4901 (i\)\)\)\)\)\)\))206 1946 y(\(all-values)e(\(solution)g(\(coerce)g(q)i
4902 ('list\))e(\(reorder)g(#'linear-force\)\)\)\))o(\))p
4903 1900 1974 V 124 1976 1778 2 v 193 2089 a FA(Figure)13
4904 b(2:)k(Tw)o(o)12 b Fz(Screamer)h FA(programs)g(for)g(solving)i(the)d
4905 Fg(N)t FA(-Queens)h(problem.)18 b(The)13 b(\014rst)g(uses)g(bac)o
4906 (ktrac)o(king)193 2134 y(searc)o(h)g(while)h(the)g(second)g(uses)f(the)
4907 g(constrain)o(t)i(pac)o(k)n(age.)992 2723 y Fy(34)p eop
4908 %%Page: 35 35
4909 35 34 bop 200 801 1626 2 v 200 1872 2 1071 v 239 848
4910 a Fq(\(defun)20 b(member-of)g(\(list\))261 898 y(\(if)h(\(null)g
4911 (list\))f(\(fail\))h(\(either)f(\(first)h(list\))g(\(member-of)e
4912 (\(rest)i(list\)\)\)\)\))239 998 y(\(defstruct)f(\(node)g(\(:conc-name)
4913 g(nil\))h(\(:print-function)d(print-node\)\))282 1048
4914 y(name)j(next-nodes)f(\(marked?)g(nil\))h(\(visits)g(0\)\))239
4915 1147 y(\(defun)f(print-node)g(\(node)h(stream)f(print-level\))261
4916 1197 y(\(declare)g(\(ignore)g(print-level\)\))261 1247
4917 y(\(princ)g(\(name)h(node\))g(stream\)\))239 1347 y(\(defun)f
4918 (simple-path)g(\(u)h(v\))261 1396 y(\(if)g(\(marked?)f(u\))h
4919 (\(fail\)\))261 1446 y(\(local)f(\(setf)h(\(marked?)f(u\))h(t\)\))261
4920 1496 y(\(either)f(\(progn)h(\(unless)f(\(eq)h(u)h(v\))f(\(fail\)\))f
4921 (\(list)h(u\)\))435 1546 y(\(cons)g(u)g(\(simple-path)f(\(member-of)f
4922 (\(next-nodes)h(u\)\))h(v\)\)\)\))239 1645 y(\(defun)f(k-simple-path)g
4923 (\(u)h(v)g(k\))261 1695 y(\(if)g(\(=)g(\(visits)g(u\))g(k\))g
4924 (\(fail\)\))261 1745 y(\(local)f(\(setf)h(\(visits)f(u\))i(\(1+)f
4925 (\(visits)f(u\)\)\)\))261 1795 y(\(either)g(\(progn)h(\(unless)f(\(eq)h
4926 (u)h(v\))f(\(fail\)\))f(\(list)h(u\)\))435 1845 y(\(cons)g(u)g
4927 (\(k-simple-path)e(\(member-of)h(\(next-nodes)f(u\)\))j(v)f(k\)\)\)\))p
4928 1824 1872 V 200 1874 1626 2 v 450 1987 a FA(Figure)14
4929 b(3:)j(A)12 b Fz(Screamer)i FA(program)f(for)g(\014nding)i(simple)g
4930 (paths)e(in)h(a)f(graph.)992 2723 y Fy(35)p eop
4931 %%Page: 36 36
4932 36 35 bop 75 195 a Fy(using)13 b(nothing)g(more)f(than)i(the)g
4933 (facilities)e(already)h(pro)o(vided)h(b)o(y)f Fv(Common)j(Lisp)e
4934 Fy(and)f(the)h(non)f(constrain)o(t)h(pac)o(k-)75 245
4935 y(age)d(p)q(ortions)h(of)f Fv(Screamer)p Fy(.)18 b(This)11
4936 b(is)g(in)g(striking)g(con)o(trast)i(to)e(constrain)o(t)h(logic)e
4937 (programming)e(languages)j(whic)o(h)75 295 y(cannot)17
4938 b(b)q(e)h(implemen)o(ted)d(e\016cien)o(tly)i(on)h(top)f(of)f(existing)h
4939 Fv(Pr)o(olog)h Fy(implemen)o(tations)c(but)k(rather)g(necessitate)75
4940 345 y(creating)c(a)g(new)g(language)f(implemen)o(tation.)137
4941 394 y(T)m(o)f(illustrate)g(the)g(essen)o(tial)h(organization)e(of)g
4942 (the)i(constrain)o(t)g(pac)o(k)n(age)e(and)h(ho)o(w)g(it)g(is)g(implem)
4943 o(en)o(ted)f(on)h(top)g(of)75 444 y(nondeterministic)h
4944 Fv(Common)j(Lisp)p Fy(,)d(\014gure)h(4)f(con)o(tains)g(a)g(greatly)g
4945 (simpli\014ed)e(v)o(ersion)i(of)g(the)h(constrain)o(t)f(pac)o(k)n(age)
4946 75 494 y(whic)o(h)k(supp)q(orts)h(only)f(b)q(o)q(olean)g(constrain)o
4947 (ts.)28 b(This)17 b(v)o(ersion)h(is)f(th)o(us)g(analogous)f(to)h(what)g
4948 (is)g(commonly)d(called)75 544 y(a)20 b(truth)h(main)o(tenance)e
4949 (system)h(or)g(TMS.)36 b(V)m(ariables)20 b(ha)o(v)o(e)g(t)o(w)o(o)g
4950 (slots,)h(a)f Fq(value)f Fy(whic)o(h)h(is)g(either)h
4951 Fq(t)p Fy(,)g Fq(nil)e Fy(or)75 594 y Fq(:unassigned)p
4952 Fy(,)12 b(and)j(a)g(list)f(of)h Fq(noticers)p Fy(,)e(pro)q(cedures)k
4953 (to)e(b)q(e)h(called)e(to)h(p)q(erform)f(constrain)o(t)i(propagation)d
4954 (when)75 643 y(a)g(v)n(ariable)f(is)h(assigned)h(a)e(v)n(alue.)18
4955 b(The)13 b(functions)g Fq(notv)g Fy(and)g Fq(andv)f Fy(tak)o(e)h(v)n
4956 (ariables)g(as)g(argumen)o(ts)f(and)h(create)i(and)75
4957 693 y(return)j(a)f(new)h(v)n(ariable)e(constrained)i(b)o(y)f(the)g
4958 (appropriate)h(relation)e(to)h(the)h(argumen)o(ts.)27
4959 b(The)18 b(constrain)o(ts)g(are)75 743 y(implemen)o(ted)9
4960 b(via)h(noticers)i(attac)o(hed)f(b)q(oth)g(to)g(the)h(argumen)o(t)d
4961 (and)i(result)h(v)n(ariables.)k(The)11 b(function)g Fq(set-value)e
4962 Fy(is)75 793 y(used)i(to)f(set)i(the)f(v)n(alue)e(of)h(a)g(v)n
4963 (ariable.)16 b(It)10 b(\014rst)h(c)o(hec)o(ks)h(whether)f(the)g(v)n
4964 (ariable)f(can)g(b)q(e)h(set)g(to)f(the)h(giv)o(en)f(v)n(alue,)g
4965 (failing)75 843 y(if)i(it)g(cannot.)18 b(If)13 b(the)g(v)n(ariable)f(w)
4966 o(as)g(not)h(previously)f(b)q(ound,)h Fq(set-value)e
4967 Fy(calls)h(its)h(noticers)h(after)f(setting)g(its)g(v)n(alue)75
4968 892 y(in)h(order)h(to)g(p)q(erform)e(constrain)o(t)i(propagation.)k
4969 (Note)14 b(that)h(the)g(functions)g Fq(notv)p Fy(,)e
4970 Fq(andv)g Fy(and)i Fq(set-value)d Fy(are)j(all)75 942
4971 y(deterministic.)k(This)14 b(is)g(in)g(k)o(eeping)h(with)f(the)h
4972 (requiremen)o(t)f(that)g(constrain)o(t)h(propagation)e(b)q(e)i(a)f
4973 (fast)h(op)q(eration.)75 992 y(Nonetheless,)20 b(it)e(is)f(an)h
4974 (incomplete)f(metho)q(d)g(for)g(\014nding)g(solutions)h(to)g(prop)q
4975 (ositional)e(satis\014abilit)o(y)g(problems.)75 1042
4976 y(Man)o(y)10 b(truth)h(main)o(tenance)f(systems)h(rely)f(solely)h(on)f
4977 (constrain)o(t)h(propagation)e(and)i(are)g(th)o(us)g(incomplete.)16
4978 b(Figure)10 b(4)75 1092 y(sho)o(ws)h(ho)o(w)e(a)h(TMS)h(built)e(in)h
4979 Fv(Screamer)h Fy(can)f(circum)o(v)o(en)o(t)g(this)g(problem)f(b)o(y)h
4980 (pro)o(viding)f(a)h(ho)q(ok)g(in)o(to)f(bac)o(ktrac)o(king)75
4981 1142 y(searc)o(h.)22 b(The)15 b(function)g Fq(solution)e
4982 Fy(is)i(suc)o(h)g(a)g(ho)q(ok)f(whic)o(h)h(nondeterministically)e
4983 (assigns)i(v)n(alues)g(to)g(unassigned)75 1191 y(v)n(ariables,)j(in)o
4984 (terlea)o(ving)f(constrain)o(t)i(propagation)e(with)g(eac)o(h)i
4985 (assignmen)o(t.)30 b(The)18 b(\014nal)g(expression)h(in)f(\014gure)g(4)
4986 75 1241 y(sho)o(ws)c(ho)o(w)g(this)g(TMS)g(can)g(b)q(e)g(used)h(to)f
4987 (\014nd)g(all)e(solutions)i(to)g(an)o(y)f(prop)q(ositional)g
4988 (satis\014abilit)o(y)f(problem.)137 1291 y(Figure)j(5)g(con)o(tains)f
4989 (a)h(program)e(for)i(learning)f(the)h(syn)o(tactic)h(categories)f(of)f
4990 (w)o(ords)h(app)q(earing)g(in)f(a)h(corpus)h(of)75 1341
4991 y(sen)o(tences.)21 b(It)14 b(is)f(a)h(problem)f(\014rst)h(prop)q(osed)h
4992 (and)f(solv)o(ed)g(b)o(y)f(Ra)o(yner)h(et)h(al.)d(\(1988\).)18
4993 b(The)c(basic)g(idea)g(is)f(that)h(y)o(ou)75 1391 y(are)f(presen)o(ted)
4994 h(with)e(a)h(con)o(text)g(free)g(grammar)c(and)j(a)h(corpus)g(of)f(sen)
4995 o(tences)j(generated)f(b)o(y)e(that)g(grammar)e(but)i(do)75
4996 1440 y(not)g(kno)o(w)g(the)i(syn)o(tactic)f(categories)g(of)f(the)h(w)o
4997 (ords)g(app)q(earing)f(in)g(the)i(corpus.)k(One)13 b(can)g(\014nd)g(a)f
4998 (lexicon)g(mapping)75 1490 y(w)o(ords)g(to)g(categories)h(b)o(y)f
4999 (nondeterministically)e(en)o(umerating)g(all)h(p)q(ossible)h(mappings)e
5000 (and)i(\014ltering)g(out)g(the)g(ones)75 1540 y(whic)o(h)i(do)g(not)h
5001 (allo)o(w)d(the)j(sen)o(tences)i(to)e(b)q(e)f(parsed)i(b)o(y)e(the)h
5002 (grammar.)h(The)f(k)o(ey)f(to)h(making)d(this)i(tractable)h(is)f(to)75
5003 1590 y(order)i(the)f(searc)o(h)h(so)f(as)g(to)g(dela)o(y)f(the)i(pro)q
5004 (cess)g(of)e(making)f(nondeterministic)h(c)o(hoices)i(for)e(lexical)g
5005 (en)o(tries)i(for)f(as)75 1640 y(long)e(as)h(p)q(ossible.)137
5006 1689 y(Figure)20 b(5)f(sho)o(ws)i(a)e Fv(Screamer)h Fy(v)o(ersion)g(of)
5007 f(the)h(original)e Fv(Pr)o(olog)i Fy(solution.)35 b(The)20
5008 b(v)n(ariable)f Fq(*grammar*)75 1739 y Fy(con)o(tains)d(a)g(list)g(of)g
5009 (con)o(text)h(free)g(rules.)26 b(The)17 b(function)f
5010 Fq(lhs)g Fy(returns)i(the)f(category)f(on)g(the)h(left)g(hand)f(side)h
5011 (of)e(a)75 1789 y(rule)j(while)g(the)g(function)g Fq(rhs)f
5012 Fy(returns)j(the)e(list)g(of)f(categories)i(forming)d(the)i(righ)o(t)g
5013 (hand)g(side)g(of)f(a)h(rule.)31 b(The)75 1839 y(function)20
5014 b Fq(parse)e Fy(returns)k Fq(t)d Fy(if)g(a)h(list)f(of)g
5015 Fu(wor)n(ds)g Fy(can)h(b)q(e)h(parsed)g(as)e(a)h(phrase)h(of)e(a)g(giv)
5016 o(en)h Fu(c)n(ate)n(gory)f Fy(and)h(fails)75 1889 y(otherwise.)g(It)14
5017 b(is)g(essen)o(tially)g(a)g(simple)f(top-do)o(wn)g(left-to-righ)o(t)g
5018 (nondeterministic)h(parser.)20 b(It)14 b(calls)g Fq(parse-rule)75
5019 1939 y Fy(whic)o(h)i(nondeterministically)e(tries)j(to)e(parse)i(the)g
5020 Fu(wor)n(ds)e Fy(using)h(ev)o(ery)g(grammar)d(rule)j(whic)o(h)g(con)o
5021 (tains)g Fu(c)n(ate)n(gory)75 1988 y Fy(as)e(its)g(left)g(hand)g(side.)
5022 20 b(The)14 b(core)h(of)f(the)g(parser)i(is)e(the)g(function)g
5023 Fq(parse-categories)p Fy(.)i(It)e(tak)o(es)h(the)f(righ)o(t)g(hand)75
5024 2038 y(side)h(of)e(a)h(rule)g(and)g(nondeterministically)f(splits)h(a)g
5025 (list)g(of)f(w)o(ords)i(in)o(to)e(sub-phrases)j(to)e(assign)g(to)g(eac)
5026 o(h)h(category)75 2088 y(in)e(the)i(righ)o(t)e(hand)h(side,)g(in)f(ev)o
5027 (ery)i(p)q(ossible)f(w)o(a)o(y)m(,)e(and)i(attempts)g(to)f(recursiv)o
5028 (ely)i(parse)g(eac)o(h)f(sub-phrase.)137 2138 y(So)k(far)f(this)g(is)h
5029 (a)f(straigh)o(tforw)o(ard)g(parser.)30 b(Nothing)17
5030 b(ab)q(out)g(this)h(parser)g(is)g(particular)f(to)g(the)h(problem)f(of)
5031 75 2188 y(category)j(acquisition.)33 b(The)19 b(\014rst)h(de\014nition)
5032 f(for)g(the)g(function)g Fq(category)f Fy(completes)h(the)h
5033 (de\014nition)e(of)h(this)75 2237 y(parser.)35 b(By)19
5034 b(replacing)g(this)g(de\014nition)g(with)g(the)g(second)h(one,)g(the)g
5035 (parser)g(is)f(transformed)g(in)o(to)f(a)h(language)75
5036 2287 y(acquisition)13 b(device.)18 b(While)13 b(the)h(\014rst)h
5037 (de\014nition)e(returns)i(the)f(categories)g(asso)q(ciated)h(with)e(a)g
5038 (w)o(ord)h(deriv)o(ed)g(from)75 2337 y(a)i(pre-existing)h(lexicon,)f
5039 (the)g(second)i(de\014nition)e(creates)i(that)e(lexicon)g(on)g(the)h
5040 (\015y)m(.)25 b(It)16 b(enforces)i(the)f(monosem)o(y)75
5041 2387 y(constrain)o(t)i(b)o(y)g(returning)h(the)f(category)h(of)e(a)h(w)
5042 o(ord)g(whic)o(h)g(is)g(already)g(in)f(the)i(lexicon.)33
5043 b(New)20 b(lexical)e(en)o(tries)75 2437 y(are)f(added)g(as)f(new)h(w)o
5044 (ords)g(are)f(encoun)o(tered,)j(nondeterministically)c(assigning)g
5045 (categories)i(to)g(eac)o(h)g(new)g(w)o(ord.)75 2487 y(Notice)11
5046 b(ho)o(w)f(lexical)f(en)o(tries)j(are)f(added)f(b)o(y)h(p)q(erforming)d
5047 (lo)q(cal)i(side)h(e\013ects)h(to)e(a)h(hash)f(table,)h(something)e(p)q
5048 (ossible)h(in)75 2536 y Fv(Screamer)k Fy(but)f(not)g(in)f
5049 Fv(Pr)o(olog)q Fy(.)17 b(The)d(last)e(expression)j(in)d(\014gure)i(5)e
5050 (illustrates)h(ho)o(w)g(to)g(solv)o(e)f(a)h(giv)o(en)g(category)75
5051 2586 y(acquisition)j(puzzle)i(b)o(y)e(forming)f(a)h(series)j(of)d
5052 (calls)g(to)h(the)h(parser,)g(one)f(for)g(eac)o(h)g(sen)o(tence)i(in)e
5053 (the)g(corpus,)h(and)992 2723 y(36)p eop
5054 %%Page: 37 37
5055 37 36 bop 186 197 1654 2 v 186 2642 2 2445 v 238 241
5056 a Ff(\(defstruc)o(t)17 b(\(boolean)o(-va)o(ri)o(abl)o(e)g(\(:conc-n)o
5057 (ame)f(nil\)\))i(\(value)f(:unassign)o(ed\))f(noticers\))238
5058 333 y(\(defun)h(notb)h(\(x\))257 378 y(\(let)g(\(\(z)h(\(make-boo)o
5059 (lea)o(n-)o(var)o(iab)o(le)o(\)\)\))277 424 y(\(local)e(\(push)h
5060 (#'\(lambda)e(\(\))j(\(set-valu)o(e)e(x)i(\(not)f(\(value)f(z\)\)\)\))h
5061 (\(noticers)e(z\)\))414 469 y(\(push)i(#'\(lambda)e(\(\))j(\(set-valu)o
5062 (e)e(z)i(\(not)f(\(value)f(x\)\)\)\))h(\(noticers)e(x\)\)\))277
5063 515 y(z\)\))238 606 y(\(defun)h(andb)h(\(x)h(y\))257
5064 652 y(\(let)f(\(\(z)h(\(make-boo)o(lea)o(n-)o(var)o(iab)o(le)o(\)\)\))
5065 277 698 y(\(local)297 743 y(\(push)e(#'\(lambda)f(\(\))473
5066 789 y(\(cond)i(\(\(value)f(x\))610 835 y(\(unless)g(\(eq)i(\(value)e
5067 (y\))i(:unassign)o(ed\))d(\(set-valu)o(e)h(z)i(\(value)e(y\)\)\))610
5068 880 y(\(unless)g(\(eq)i(\(value)e(z\))i(:unassign)o(ed\))d(\(set-valu)o
5069 (e)h(y)i(\(value)e(z\)\)\)\))591 926 y(\(t)i(\(set-valu)o(e)d(z)k
5070 (nil\)\)\)\))414 972 y(\(noticers)c(x\)\))297 1017 y(\(push)h
5071 (#'\(lambda)f(\(\))473 1063 y(\(cond)i(\(\(value)f(y\))610
5072 1109 y(\(unless)g(\(eq)i(\(value)e(x\))i(:unassign)o(ed\))d(\(set-valu)
5073 o(e)h(z)i(\(value)e(x\)\)\))610 1154 y(\(unless)g(\(eq)i(\(value)e(z\))
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5102 1837 2642 V 186 2644 1654 2 v 193 2757 a FA(Figure)11
5103 b(4:)16 b(A)10 b Fz(Screamer)g FA(program)i(for)e(solving)i(prop)q
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5106 (ktrac)o(king)h(searc)o(h.)992 2723 y Fy(37)p eop
5107 %%Page: 38 38
5108 38 37 bop 233 197 1560 2 v 233 3361 2 3165 v 272 244
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5153 3363 1560 2 v 365 3476 a FA(Figure)14 b(5:)j(A)c Fz(Screamer)g
5154 FA(program)h(for)f(learning)i(the)e(syn)o(tactic)h(categories)h(of)d(w)
5155 o(ords.)992 2723 y Fy(38)p eop
5156 %%Page: 39 39
5157 39 38 bop 75 195 a Fy(bac)o(ktrac)o(king)14 b(un)o(til)f(a)g(solution)g
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5161 y(extension)14 b(w)o(as)f(using)g(a)g(constrain)o(t)h(propagation)e
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5175 b(In)14 b(the)h(deriv)o(ed)f(program,)f(the)h(functions)h
5176 Fq(parse-categories)o Fy(,)c Fq(parse-rule)p Fy(,)h Fq(parse)h
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5178 b(They)c(read)g(in)f(a)g(corpus)i(and)e(construct)i(a)e(large)g
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5181 h(in)f(\014gure)h(6)e(triggers)i(the)f(constrain)o(t)h(solving)e(pro)q
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5193 (es)g(a)g Fv(Screamer)h Fy(program)d(for)75 942 y(solving)f(crossw)o
5194 (ord)j(puzzles.)19 b(A)13 b(v)n(ariable)e(is)h(created)i(for)f(eac)o(h)
5195 g(across)g(and)g(do)o(wn)f(en)o(try)h(whic)o(h)f(w)o(e)h(will)e(call)h
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5198 (of)g(the)h(requisite)g(length.)k(A)c(constrain)o(t)75
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5202 (tain)f(the)h(same)f(letter)h(at)f(their)h(in)o(tersection)h(p)q(oin)o
5203 (t.)i(The)d(function)f Fq(crossword-variabl)o(es)75 1142
5204 y Fy(creates)21 b(the)e(v)n(ariables)g(and)f(asserts)j(the)e(constrain)
5205 o(ts)h(b)q(et)o(w)o(een)g(them.)33 b(It)19 b(is)g(a)f(deterministic)h
5206 (function.)33 b(The)75 1191 y(function)14 b Fq(crosswordv)d
5207 Fy(is)j(a)g(nondeterministic)f(function)h(whic)o(h)f(initiates)h(the)g
5208 (searc)o(h)h(for)f(a)f(solution.)137 1241 y(The)i(arithmetic)e
5209 (constrain)o(t)i(primitiv)o(es)d(of)i(the)h Fv(Screamer)g
5210 Fy(constrain)o(t)f(pac)o(k)n(age)g(can)h(b)q(e)g(used)g(to)f(\014nd)g
5211 (solu-)75 1291 y(tions)9 b(to)h(complex)e(systems)i(of)f(nonlinear)g
5212 (equations)h(and)f(inequalities)g(o)o(v)o(er)h(the)g(reals,)g(as)g(w)o
5213 (ell)f(as)h(in)o(teger)g(program-)75 1341 y(ming)e(problems.)16
5214 b(Figures)11 b(10)f(illustrates)h(ho)o(w)f(this)h(can)g(b)q(e)g(done.)
5215 17 b(Problems)10 b(o)o(v)o(er)g(the)h(reals)g(m)o(ust)f(b)q(e)h(solv)o
5216 (ed)f(using)75 1391 y Fq(static-ordering)i Fy(and)j Fq
5217 (divide-and-conquer)o(-forc)o(e)p Fy(.)k(In)o(teger)d(programming)c
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5219 Fq(static-ordering)8 b Fy(or)k Fq(reorder)e Fy(as)i(w)o(ell)f(as)h
5220 (either)h Fq(linear-force)c Fy(or)j Fq(divide-and-conque)o(r-for)o(ce)
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5222 i(p)q(erformance.)137 1540 y(Our)22 b(\014nal)e(example)f(is)h(an)h
5223 (illustration)e(of)h(a)h(standard)g(clic)o(h)o(\023)-20
5224 b(e)21 b(for)f(translating)g Fv(Pr)o(olog)h Fy(programs)f(in)o(to)75
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5228 Fv(Pr)o(olog)g Fy(program)e(in)o(to)h Fv(Screamer)p Fy(.)33
5229 b(Automation)16 b(of)i(this)h(translation)f(is)g(quite)h(straigh)o
5230 (tforw)o(ard.)32 b(A)75 1689 y(future)13 b(release)i(of)d
5231 Fv(Screamer)h Fy(will)f(ha)o(v)o(e)g(a)h(facilit)o(y)e(for)i(doing)f
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5234 Fv(Pr)o(olog)q Fy(.)75 1877 y Fw(13)69 b(Using)23 b(Screamer)75
5235 1968 y Fy(Y)m(ou)13 b(m)o(ust)g(include)h(the)h(follo)o(wing)c(three)k
5236 (expressions)h(at)d(the)i(top)f(of)f(ev)o(ery)i(\014le)e(whic)o(h)h
5237 (uses)h Fv(Screamer)q Fy(.)p 570 2015 885 2 v 570 2189
5238 2 175 v 609 2062 a Fq(\(in-package)20 b(:my-package\))609
5239 2112 y(\(use-package)g('\(:lisp)g(:screamer\)\))609 2162
5240 y(\(shadowing-import)f('\(screamer::def)o(un\)\))p 1453
5241 2189 V 570 2191 885 2 v 75 2257 a Fy(Y)m(ou)c(ma)o(y)f(replace)j
5242 Fq(:my-package)c Fy(with)i(the)i(desired)f(pac)o(k)n(age)g(name)e(for)i
5243 (y)o(our)f(\014le)h(and)f(ha)o(v)o(e)h(that)g(pac)o(k)n(age)f(use)75
5244 2307 y(an)o(y)h(other)h(pac)o(k)n(ages)g(that)g(y)o(ou)f(wish.)26
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5253 f(including)f(a)i(new)o(er)g(program)e(whic)o(h)i(is)g(written)f(in)h
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5255 y(nondetermi)o(nisti)o(c)d Fm(Lisp)i Fs(and)g(not)f(the)h(constrain)o
5256 (t)e(pac)o(k)n(age.)992 2723 y Fy(39)p eop
5257 %%Page: 40 40
5258 40 39 bop 167 228 1691 2 v 167 2446 2 2219 v 206 275
5259 a Fq(\(defun)21 b(parse-categories)o(v)e(\(categories)g(words1)i
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5261 375 y(\(if)g(\(and)g(\(null)g(words1\))f(\(null)h(words2\)\))f(t)i
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5268 873 y(\(defun)h(parse-rulev)e(\(category)h(words)h(rules\))228
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5270 y(\(ORV)g(\(if)g(\(eq)g(\(lhs)g(\(first)g(rules\)\))f(category\))511
5271 1072 y(\(parse-categoriesv)e(\(rhs)j(\(first)g(rules\)\))f(words\))511
5272 1122 y(NIL\))424 1172 y(\(parse-rulev)f(category)i(words)f(\(rest)h
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5274 1321 y(\(if)h(\(null)g(\(rest)g(words\)\))315 1371 y(\(EQUALV)f
5275 (CATEGORY)h(\(CATEGORYV)e(\(FIRST)i(WORDS\)\)\))315 1421
5276 y(\(parse-rulev)e(category)i(words)f(*grammar*\)\)\))206
5277 1520 y(\(defun)h(categoryv)f(\(word\))228 1570 y(\(declare)g(\(special)
5278 g(lexicon\)\))228 1620 y(\(let)h(\(\(category)f(\(gethash)g(word)h
5279 (lexicon\)\)\))250 1670 y(\(if)g(category)337 1719 y(category)337
5280 1769 y(\(setf)g(\(gethash)f(word)h(lexicon\))f(\(MEMBER-OFV)f
5281 (\(categories)h(*grammar*\)\)\)\)\)\))206 1869 y(\(defun)h(grow-upv)f
5282 (\(\))228 1919 y(\(let)h(\(\(lexicon)f(\(make-hash-table)e(:test)j
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5284 2018 y(\(ASSERT!)g(\(ANDV)h(\(parsev)f('s)h('\(the)g(cup)g(slid)g(from)
5285 g(john)g(to)h(mary\)\))577 2068 y(\(parsev)e('s)h('\(john)g(walked)f
5286 (to)i(the)f(table\)\)\)\))250 2118 y(\(all-values)272
5287 2168 y(\(FUNCALL)f(\(REORDER)g(#'LINEAR-FORCE\))468 2218
5288 y(\(ITERATE)g(\(FOR)h(\(WORD)g(CATEGORY\))e(IN-HASHTABLE)h(LEXICON\))
5289 664 2267 y(\(DECLARE)g(\(IGNORE)g(WORD\)\))664 2317 y(\(COLLECT)g
5290 (CATEGORY\)\)\))272 2367 y(\(iterate)g(\(for)h(\(word)f(category\))g
5291 (in-hashtable)g(lexicon\))468 2418 y(\(format)g(t)i(")708
5292 2407 y(~)708 2418 y(\045)730 2411 y(~)730 2418 y(S:)816
5293 2411 y(~)816 2418 y(S")g(word)f(category\)\)\)\)\))p
5294 1856 2446 V 167 2448 1691 2 v 221 2561 a FA(Figure)15
5295 b(6:)i(A)12 b(constrain)o(t-based)k Fz(Screamer)d FA(program)h(for)e
5296 (learning)k(the)d(syn)o(tactic)h(categories)g(of)f(w)o(ords.)992
5297 2723 y Fy(40)p eop
5298 %%Page: 41 41
5299 41 40 bop 539 1730 a Fy(ad)122 b(al)137 b(alas)111 b(aloha)52
5300 b(art)122 b(at)539 1780 y(atl)117 b(bags)89 b(bang)k(base)72
5301 b(b)q(ore)96 b(coat)539 1830 y(dad)j(dart)94 b(dime)e(dine)74
5302 b(div)o(e)101 b(do)539 1879 y(eh)125 b(elf)i(er)147 b(ev)n(ade)50
5303 b(ev)o(en)95 b(fan)539 1929 y(fee)117 b(\014ne)106 b(gate)f(goat)71
5304 b(happ)o(y)64 b(hares)539 1979 y(hem)89 b(hide)94 b(hire)112
5305 b(hiv)o(e)76 b(ho)q(e)112 b(hone)539 2029 y(inn)c(largest)50
5306 b(learned)g(lee)102 b(lemons)49 b(lid)539 2079 y(lilac)91
5307 b(lip)123 b(lo)148 b(load)73 b(mates)68 b(mile)539 2128
5308 y(mirror)49 b(mist)90 b(mo)q(on)79 b(more)59 b(oak)111
5309 b(oliv)o(e)539 2178 y(ore)g(pans)87 b(paris)93 b(pa)o(y)85
5310 b(p)q(ea)112 b(p)q(edal)539 2228 y(p)q(enn)o(y)57 b(pier)101
5311 b(pile)116 b(pins)76 b(pits)108 b(raise)539 2278 y(rips)99
5312 b(ro)q(e)114 b(rop)q(es)86 b(ro)o(y)92 b(salads)66 b(see)539
5313 2328 y(slam)81 b(slat)105 b(some)90 b(sp)q(ot)73 b(steer)91
5314 b(stew)539 2378 y(tag)108 b(tame)79 b(tan)121 b(tank)68
5315 b(tea)120 b(tee)539 2427 y(tie)g(tigers)71 b(tire)119
5316 b(to)113 b(to)q(e)119 b(w)o(ager)539 2477 y(w)o(a)o(v)o(e)78
5317 b(wider)71 b(win)116 b(wires)276 2605 y FA(Figure)14
5318 b(7:)j(A)c(sample)h(crossw)o(ord)g(puzzle)g(whic)o(h)g(can)f(b)q(e)g
5319 (solv)o(ed)i(b)o(y)e(the)g(the)g(program)h(in)g(\014gure)g(8.)992
5320 2723 y Fy(41)p eop
5321 %%Page: 42 42
5322 42 41 bop 145 197 1735 2 v 145 3659 2 3463 v 184 244
5323 a Fq(\(defun)21 b(row)g(\(placement\))f(\(first)g(placement\)\))184
5324 344 y(\(defun)h(column)f(\(placement\))g(\(second)g(placement\)\))184
5325 443 y(\(defun)h(direction)f(\(placement\))f(\(third)i(placement\)\))184
5326 543 y(\(defun)g(placement-length)d(\(placement\))i(\(fourth)g
5327 (placement\)\))184 643 y(\(defun)h(intersect?)f(\(placement1)f
5328 (placement2\))206 692 y(\(and)228 742 y(\(not)i(\(eq)g(\(direction)f
5329 (placement1\))f(\(direction)h(placement2\)\)\))228 792
5330 y(\(if)h(\(eq)g(\(direction)f(placement1\))g('across\))315
5331 842 y(\(and)h(\(>=)g(\(row)g(placement1\))f(\(row)h(placement2\)\))424
5332 892 y(\(<=)g(\(row)g(placement1\))511 941 y(\(+)h(\(row)f(placement2\))
5333 e(\(placement-length)f(placement2\))i(-1\)\))424 991
5334 y(\(>=)h(\(column)g(placement2\))e(\(column)h(placement1\)\))424
5335 1041 y(\(<=)h(\(column)g(placement2\))511 1091 y(\(+)h(\(column)e
5336 (placement1\))f(\(placement-length)g(placement1\))g(-1\)\)\))315
5337 1141 y(\(and)i(\(>=)g(\(row)g(placement2\))f(\(row)h(placement1\)\))424
5338 1191 y(\(<=)g(\(row)g(placement2\))511 1240 y(\(+)h(\(row)f
5339 (placement1\))e(\(placement-length)f(placement1\))i(-1\)\))424
5340 1290 y(\(>=)h(\(column)g(placement1\))e(\(column)h(placement2\)\))424
5341 1340 y(\(<=)h(\(column)g(placement1\))511 1390 y(\(+)h(\(column)e
5342 (placement2\))f(\(placement-length)g(placement2\))g(-1\)\)\)\)\)\))184
5343 1489 y(\(defun)i(consistent-placem)o(ents?)272 1539 y(\(placement1)e
5344 (placement2)h(placement1-word)e(placement2-word\))206
5345 1589 y(\(or)j(\(not)g(\(intersect?)f(placement1)g(placement2\)\))293
5346 1639 y(\(if)i(\(eq)f(\(direction)e(placement1\))h('across\))381
5347 1689 y(\(char=)g(\(aref)h(placement1-word)664 1738 y(\(-)g(\(column)g
5348 (placement2\))e(\(column)h(placement1\)\)\))533 1788
5349 y(\(aref)h(placement2-word)664 1838 y(\(-)g(\(row)g(placement1\))f
5350 (\(row)h(placement2\)\)\)\))381 1888 y(\(char=)f(\(aref)h
5351 (placement2-word)664 1938 y(\(-)g(\(column)g(placement1\))e(\(column)h
5352 (placement2\)\)\))533 1988 y(\(aref)h(placement1-word)664
5353 2037 y(\(-)g(\(row)g(placement2\))f(\(row)h(placement1\)\)\)\)\)\))o
5354 (\))184 2137 y(\(defun)g(word-of-length)e(\(n)i(dictionary\))206
5355 2187 y(\(if)g(\(null)g(dictionary\))293 2237 y(\(fail\))293
5356 2286 y(\(if)h(\(=)f(\(length)f(\(first)h(dictionary\)\))e(n\))381
5357 2336 y(\(either)h(\(first)g(dictionary\))g(\(word-of-length)f(n)i
5358 (\(rest)g(dictionary\)\)\))381 2386 y(\(word-of-length)d(n)k(\(rest)f
5359 (dictionary\)\)\)\)\))184 2486 y(\(defun)g(check-placement)e
5360 (\(placement)g(word)i(solution\))206 2535 y(\(dolist)g
5361 (\(placement-word)d(solution\))228 2585 y(\(if)j(\(not)g
5362 (\(consistent-placem)o(ents?)446 2635 y(\(first)f(placement-word\))f
5363 (placement)h(\(second)g(placement-word\))f(word\)\))315
5364 2685 y(\(fail\)\)\)\))184 2785 y(\(defun)i(choose-placement)d
5365 (\(placements)i(solution\))206 2834 y(\(block)h(exit)228
5366 2884 y(\(dolist)f(\(placement)g(placements\))250 2934
5367 y(\(if)h(\(some)g(#'\(lambda)f(\(placement-word)o(\))533
5368 2984 y(\(intersect?)g(\(first)g(placement-word\))f(placement\)\))468
5369 3034 y(solution\))337 3083 y(\(return-from)g(exit)i(placement\)\)\))228
5370 3133 y(\(return-from)e(exit)i(\(first)g(placements\)\)\)\))184
5371 3233 y(\(defun)g(crossword)f(\(placements)f(dictionary)h(&optional)g
5372 (solution\))206 3283 y(\(if)h(\(null)g(placements\))293
5373 3333 y(solution)293 3382 y(\(let*)g(\(\(placement)f(\(choose-placeme)o
5374 (nt)f(placements)h(solution\)\))446 3432 y(\(word)h(\(word-of-length)d
5375 (\(placement-length)h(placement\))g(dictionary\)\)\))315
5376 3482 y(\(check-placement)g(placement)h(word)g(solution\))315
5377 3532 y(\(crossword)g(\(remove)g(placement)g(placements\))555
5378 3582 y(dictionary)555 3631 y(\(cons)h(\(list)f(placement)g(word\))h
5379 (solution\)\)\)\)\))p 1878 3659 V 145 3661 1735 2 v 386
5380 3774 a FA(Figure)15 b(8:)i(A)12 b(bac)o(ktrac)o(king)j
5381 Fz(Screamer)f FA(program)f(for)g(solving)i(crossw)o(ord)f(puzzles.)992
5382 2723 y Fy(42)p eop
5383 %%Page: 43 43
5384 43 42 bop 298 477 1430 2 v 298 2196 2 1719 v 337 525
5385 a Fq(\(defun)20 b(crossword-variables)e(\(placements)i(dictionary\))359
5386 575 y(\(iterate)381 624 y(\(with)g(variables)g(=)511
5387 674 y(\(iterate)533 724 y(\(for)h(placement)f(in)h(placements\))533
5388 774 y(\(collect)555 824 y(\(member-ofv)577 873 y(\(all-values)598
5389 923 y(\(let)g(\(\(word)g(\(member-of)f(dictionary\)\)\))620
5390 973 y(\(unless)h(\(=)g(\(length)f(word\))860 1023 y(\(placement-length)
5391 e(placement\)\))642 1073 y(\(fail\)\))620 1122 y(word\)\)\)\)\)\))381
5392 1172 y(\(for)i(\(variable1)g(.)44 b(remaining-varia)o(bles\))18
5393 b(on)k(variables\))381 1222 y(\(for)e(\(placement1)g(.)43
5394 b(remaining-placement)o(s\))19 b(on)i(placements\))381
5395 1272 y(\(iterate)402 1322 y(\(for)g(variable2)f(in)i(remaining-varia)o
5396 (bles\))402 1372 y(\(for)f(placement2)f(in)h(remaining-placement)o(s\))
5397 402 1421 y(\(if)g(\(intersect?)f(placement1)g(placement2\))489
5398 1471 y(\(let)h(\(\(placement1)f(placement1\))620 1521
5399 y(\(placement2)g(placement2\)\))511 1571 y(\(assert!)533
5400 1621 y(\(funcallv)g(#'\(lambda)g(\(word1)g(word2\))816
5401 1670 y(\(consistent-placeme)o(nts?)838 1720 y(placement1)g(placement2)g
5402 (word1)g(word2\)\))751 1770 y(variable1)751 1820 y(variable2\)\)\)\)\))
5403 381 1870 y(\(finally)g(\(return)g(variables\)\)\)\))337
5404 1969 y(\(defun)g(crosswordv)g(\(placements)g(dictionary\))359
5405 2019 y(\(mapcar)g(#'list)533 2069 y(placements)533 2119
5406 y(\(solution)g(\(crossword-variab)o(les)f(placements)g(dictionary\))751
5407 2169 y(\(reorder)h(#'linear-force\)\)\)\))p 1725 2196
5408 V 298 2198 1430 2 v 370 2311 a FA(Figure)14 b(9:)j(A)c(constrain)o
5409 (t-based)i(Screamer)f(program)g(for)e(solving)k(crossw)o(ord)d
5410 (puzzles.)992 2723 y Fy(43)p eop
5411 %%Page: 44 44
5412 44 43 bop 200 269 1626 2 v 200 991 2 723 v 239 316 a
5413 Fq(\(one-value)261 366 y(\(let)21 b(\(\(x)g(\(real-betweenv)e(-1e40)h
5414 (1e40\)\))391 416 y(\(y)i(\(real-betweenv)d(-1e40)h(1e40\)\))391
5415 466 y(\(z)i(\(real-betweenv)d(-1e40)h(1e40\)\)\))282
5416 515 y(\(assert!)h(\(andv)f(\(orv)h(\(=v)g(\(+v)h(\(*v)f(4)g(x)h(x)g
5417 (y\))893 565 y(\(*v)f(7)g(y)h(z)g(z\))893 615 y(\(*)f(6)h(x)f(x)h(z)f
5418 (z\)\))805 665 y(2\))718 715 y(\(=v)g(\(+v)h(\(*v)f(3)g(x)h(y\))893
5419 764 y(\(*v)f(2)g(y)h(y\))893 814 y(\(*v)f(5)g(x)h(y)g(z\)\))805
5420 864 y(-4\)\))609 914 y(\(>=v)f(\(*v)g(\(+v)h(x)f(y\))h(\(+v)f(y)g
5421 (z\)\))h(-5\)\)\)\))282 964 y(\(solution)e(\(list)h(x)h(y)f(z\))h
5422 (\(static-ordering)c(#'divide-and-conqu)o(er-fo)o(rce\)\))o(\))p
5423 1824 991 V 200 993 1626 2 v 459 1106 a FA(Figure)c(10:)k(A)12
5424 b Fz(Screamer)h FA(program)h(for)f(solving)i(nonlinear)h(inequaliti)q
5425 (es.)p 516 1334 994 2 v 516 2405 2 1071 v 555 1381 a
5426 Fq(append\([],x,x\).)555 1431 y(append\([a|x],y,[a)o(|z]\))o(:-app)o
5427 (end\(x)o(,y,z\))o(.)555 1530 y(\(defun)k(prolog-append)f(\(x)j(y)f
5428 (z\))577 1580 y(\(either)f(\(progn)h(\(assert!)f(\(equalv)g(x)i
5429 (nil\)\))904 1630 y(\(assert!)e(\(equalv)g(y)i(z\)\)\))751
5430 1680 y(\(let)f(\(\(x1)g(\(make-variable\)\))882 1730
5431 y(\(y1)g(\(make-variable\)\))882 1779 y(\(z1)g(\(make-variable\)\))882
5432 1829 y(\(a)g(\(make-variable\)\)\))773 1879 y(\(assert!)f(\(equalv)g(x)
5433 i(\(cons)f(a)g(x1\)\)\))773 1929 y(\(assert!)f(\(equalv)g(y)i(y1\)\))
5434 773 1979 y(\(assert!)e(\(equalv)g(z)i(\(cons)f(a)g(z1\)\)\))773
5435 2028 y(\(prolog-append)e(x1)i(y1)g(z1\)\)\)\))555 2128
5436 y(\(defun)f(split-list)g(\(\))577 2178 y(\(all-values)598
5437 2228 y(\(let)h(\(\(x)h(\(make-variable\))o(\))729 2278
5438 y(\(y)g(\(make-variable\))o(\)\))620 2327 y(\(prolog-append)d(x)j(y)f
5439 ('\(a)g(b)h(c)g(d\)\))620 2377 y(\(print)f(\(list)g(x)g(y\)\)\)\)\))p
5440 1508 2405 V 516 2407 994 2 v 424 2519 a FA(Figure)15
5441 b(11:)i(A)12 b(metho)q(d)i(for)f(translating)i Fz(Pr)o(olog)e
5442 FA(programs)h(in)o(to)g Fz(Screamer)992 2723 y Fy(44)p
5443 eop
5444 %%Page: 45 45
5445 45 44 bop 466 245 a Fy([)o(\()p Fq(either)o Fy(\)])652
5446 257 y Fo(c)710 245 y Fe(;)41 b Fy(\()p Fq(throw)11 b('fail)g(nil)o
5447 Fy(\))916 b(\(1\))435 307 y([\()p Fq(either)10 b Fp(e)p
5448 Fy(\)])652 320 y Fo(c)710 307 y Fe(;)41 b Fy([)p Fp(e)p
5449 Fy(])836 320 y Fo(c)2048 307 y Fy(\(2\))312 369 y([\()p
5450 Fq(either)10 b Fp(e)501 375 y Fo(1)527 369 y Fp(:)d(:)g(:)e(e)601
5451 375 y Fh(n)624 369 y Fy(\)])652 382 y Fo(c)710 369 y
5452 Fe(;)62 b Fy(\()p Fq(let)p Fy(\(\()p Fp(a)11 b(c)p Fy(\)\))826
5453 419 y(\()p Fq(catch)f('fail)18 b Fy([)o Fp(e)1120 425
5454 y Fo(1)1139 419 y Fy(])1151 432 y Fo(a)1169 419 y Fy(\))826
5455 463 y(.)826 480 y(.)826 497 y(.)826 547 y(\()p Fq(catch)10
5456 b('fail)18 b Fy([)o Fp(e)1120 553 y Fh(n)p Fi(\000)p
5457 Fo(1)1186 547 y Fy(])1197 559 y Fo(a)1216 547 y Fy(\))826
5458 596 y([)o Fp(e)856 602 y Fh(n)879 596 y Fy(])891 609
5459 y Fo(a)909 596 y Fy(\))2048 369 y(\(3\))509 659 y([\()p
5460 Fq(fail)o Fy(\)])652 671 y Fo(c)710 659 y Fe(;)41 b Fy(\()p
5461 Fq(throw)11 b('fail)g(nil)o Fy(\))916 b(\(4\))75 721
5462 y([\()p Fq(nondeterministic)o(-setf)8 b Fp(v)13 b(e)p
5463 Fy(\)])652 734 y Fo(c)710 721 y Fe(;)41 b Fy([)p Fp(e)p
5464 Fy(])857 742 y(\()p Fp(\025)p Fy(\()p Fp(d)p Fy(\))868
5465 792 y(\()p Fq(let)p Fy(\(\()p Fp(b)11 b(v)q Fy(\)\))880
5466 841 y(\()p Fq(unwind-protect)903 891 y Fy(\()p Fq(progn)f
5467 Fy(\()p Fq(setf)h Fp(v)i(d)p Fy(\))f(\()p Fq(funcall)e(c)h
5468 Fp(d)p Fy(\)\))891 941 y(\()p Fq(setq)g Fp(v)i(b)p Fy(\)\)\)\))2048
5469 721 y(\(5\))452 1004 y([\()p Fq(quote)e Fp(x)p Fy(\)])652
5470 1016 y Fo(c)710 1004 y Fe(;)41 b Fy(\()p Fq(funcall)11
5471 b Fp(c)g Fy(\()p Fq(quote)g Fp(x)p Fy(\)\))852 b(\(6\))387
5472 1066 y([\()p Fq(function)10 b Fp(x)p Fy(\)])652 1079
5473 y Fo(c)710 1066 y Fe(;)41 b Fy(\()p Fq(funcall)11 b Fp(c)g
5474 Fy(\()p Fq(function)f Fp(x)p Fy(\)\))787 b(\(7\))488
5475 1128 y([)o(\()p Fq(progn)o Fy(\)])652 1141 y Fo(c)710
5476 1128 y Fe(;)41 b Fy(\()p Fq(funcall)11 b Fp(c)g Fq(nil)o
5477 Fy(\))964 b(\(8\))438 1191 y([\()p Fq(progn)10 b Fp(e)605
5478 1197 y Fo(1)624 1191 y Fy(\)])652 1203 y Fo(c)710 1191
5479 y Fe(;)41 b Fy([)p Fp(e)824 1197 y Fo(1)843 1191 y Fy(])854
5480 1203 y Fo(c)2048 1191 y Fy(\(9\))334 1253 y([\()p Fq(progn)10
5481 b Fp(e)501 1259 y Fo(1)527 1253 y Fp(:)d(:)g(:)e(e)601
5482 1259 y Fh(n)624 1253 y Fy(\)])652 1265 y Fo(c)710 1253
5483 y Fe(;)41 b Fy([)p Fp(e)824 1259 y Fo(1)843 1253 y Fy(])854
5484 1265 y Fo(\()p Fh(\025)p Fo(\()p Fh(d)917 1269 y Fd(1)933
5485 1265 y Fo(\))p Fh(:::)p Fo([)p Fh(e)1001 1269 y Fc(n)1022
5486 1265 y Fo(])1031 1275 y Fd(c)1046 1265 y Fh(:::)o Fo(\))2028
5487 1253 y Fy(\(10\))445 1322 y([\()p Fq(setq)11 b Fp(v)i(e)p
5488 Fy(\)])652 1335 y Fo(c)710 1322 y Fe(;)41 b Fy([)p Fp(e)p
5489 Fy(])836 1335 y Fo(\()p Fh(\025)p Fo(\()p Fh(d)p Fo(\))9
5490 b(\()p Fq(setq)g Fh(v)h(d)p Fo(\))f(\()p Fq(funcall)f
5491 Fh(c)i(d)p Fo(\)\))2028 1322 y Fy(\(11\))405 1392 y([)o(\()p
5492 Fq(if)h Fp(e)506 1398 y Fo(1)537 1392 y Fp(e)556 1398
5493 y Fo(2)586 1392 y Fp(e)605 1398 y Fo(3)624 1392 y Fy(\)])652
5494 1404 y Fo(c)710 1392 y Fe(;)41 b Fy(\()p Fq(let)p Fy(\(\()p
5495 Fp(a)12 b(c)p Fy(\)\))18 b([)p Fp(e)1040 1398 y Fo(1)1059
5496 1392 y Fy(])1070 1404 y Fo(\()p Fh(\025)p Fo(\(d\))10
5497 b(\()p Fq(if)f Fo(d)h([e)1275 1408 y Fd(2)1291 1404 y
5498 Fo(])1300 1414 y Fd(a)1326 1404 y Fo([e)1350 1408 y Fd(3)1366
5499 1404 y Fo(])1376 1414 y Fd(a)1392 1404 y Fo(\)\))1420
5500 1392 y Fy(\))592 b(\(12\))418 1461 y([\()p Fp(f)16 b(e)501
5501 1467 y Fo(1)527 1461 y Fp(:)7 b(:)g(:)e(e)601 1467 y
5502 Fh(n)624 1461 y Fy(\)])652 1474 y Fo(c)710 1461 y Fe(;)41
5503 b Fy([)p Fp(e)824 1467 y Fo(1)843 1461 y Fy(])875 1482
5504 y(\()p Fp(\025)p Fy(\()p Fp(d)953 1488 y Fo(1)972 1482
5505 y Fy(\))18 b Fp(:)7 b(:)g(:)f Fy([)o Fp(e)1092 1488 y
5506 Fh(n)1115 1482 y Fy(])1127 1494 y Fo(\()p Fh(\025)p Fo(\(d)1191
5507 1498 y Fd(n)1208 1494 y Fo(\))k(\(f)i(c)d(d)1308 1498
5508 y Fd(1)1325 1494 y Fh(:::)o Fo(d)1372 1498 y Fd(n)1390
5509 1494 y Fo(\)\))p Fh(:::)1448 1482 y Fy(\))1494 1461 y(when)j
5510 Fp(f)k Fy(is)e(nondeterministic)47 b(\(13\))418 1549
5511 y([\()p Fp(f)16 b(e)501 1555 y Fo(1)527 1549 y Fp(:)7
5512 b(:)g(:)e(e)601 1555 y Fh(n)624 1549 y Fy(\)])652 1562
5513 y Fo(c)710 1549 y Fe(;)41 b Fy([)p Fp(e)824 1555 y Fo(1)843
5514 1549 y Fy(])875 1570 y(\()p Fp(\025)p Fy(\()p Fp(d)953
5515 1576 y Fo(1)972 1570 y Fy(\))18 b Fp(:)7 b(:)g(:)f Fy([)o
5516 Fp(e)1092 1576 y Fh(n)1115 1570 y Fy(])1127 1582 y Fo(\()p
5517 Fh(\025)p Fo(\(d)1191 1586 y Fd(n)1208 1582 y Fo(\))k(\()p
5518 Fq(funcall)e Fo(c)h(\(f)j(d)1483 1586 y Fd(1)1500 1582
5519 y Fh(:::)o Fo(d)1547 1586 y Fd(n)1565 1582 y Fo(\)\)\))p
5520 Fh(:::)1636 1570 y Fy(\))1682 1549 y(when)g Fp(f)k Fy(is)e
5521 (deterministic)-74 b(\(14\))605 1637 y([)p Fp(x)p Fy(])652
5522 1650 y Fo(c)710 1637 y Fe(;)41 b Fy(\()p Fq(funcall)11
5523 b Fp(c)g(x)p Fy(\)when)q Fp(x)p Fy(is)i(a)h(v)n(ariable)e(or)i(is)g
5524 (self)g(ev)n(aluating)282 b(\(15\))493 1763 y FA(T)m(able)14
5525 b(1:)j(Some)c(of)g(the)g(CPS)g(con)o(v)o(ersion)i(rules)f(used)g(b)o(y)
5526 f Fz(Screamer)q FA(.)75 1895 y Fw(14)69 b(Implemen)n(tation)75
5527 1986 y Fv(Screamer)19 b Fy(implemen)o(ts)d(bac)o(ktrac)o(king)i(b)o(y)g
5528 (p)q(erforming)f(CPS)i(\(Con)o(tin)o(uation)e(P)o(assing)h(St)o(yle\))h
5529 (con)o(v)o(ersion)f(on)75 2035 y(expressions)j(in)e(nondeterministic)g
5530 (con)o(texts.)36 b(Without)19 b(CPS)g(con)o(v)o(ersion,)i(returning)f
5531 (v)n(alues)f(from)f(functions)75 2085 y(is)g(handled)g(b)o(y)h(the)f
5532 (underlying)g Fv(Lisp)h Fy(function)f(return)h(mec)o(hanism.)29
5533 b(A)19 b(CPS)f(con)o(v)o(erted)i(expression)f(returns)75
5534 2135 y(its)f(v)n(alue)e(b)o(y)i(calling)e(a)h(con)o(tin)o(uation)g
5535 (with)g(the)h(returned)h(v)n(alue)e(as)h(its)f(single)h(argumen)o(t.)28
5536 b(This)17 b(frees)i(up)e(the)75 2185 y(underlying)c Fv(Lisp)g
5537 Fy(function)g(return)h(mec)o(hanism)d(to)h(b)q(e)i(usurp)q(ed)h(to)d
5538 (handle)h(bac)o(ktrac)o(king.)18 b(Th)o(us)13 b(in)g
5539 Fv(Screamer)p Fy(,)75 2235 y(a)h(nondeterministic)f(function)g(fails)g
5540 (b)o(y)h(returning)g(and)g(returns)h(b)o(y)f(calling)f(its)g(con)o(tin)
5541 o(uation.)137 2285 y(If)h Fp(e)h Fy(and)f Fp(c)h Fy(are)g(non-CPS-con)o
5542 (v)o(erted)g(expressions)h(expressions,)g(w)o(e)e(denote)i(b)o(y)e([)o
5543 Fp(e)p Fy(])1503 2297 y Fo(c)1520 2285 y Fy(,)g(the)h(CPS)g(con)o(v)o
5544 (ersion)g(of)75 2334 y Fp(e)i Fy(so)f(that)g(it)g(calls)g(the)h(con)o
5545 (tin)o(uation)e(denoted)i(b)o(y)f Fp(c)g Fy(with)g(its)g(result.)26
5546 b(Some)15 b(of)h(the)h(transformations)d(rules)j(for)75
5547 2384 y(p)q(erforming)12 b(CPS)j(con)o(v)o(ersion)f(of)f(expressions)i
5548 (allo)o(w)o(ed)e(in)g(nondeterministic)h(con)o(texts)h(is)e(giv)o(en)h
5549 (in)f(table)h(1.)137 2434 y(Some)k(commen)o(ts)f(p)q(ertaining)h(to)h
5550 (these)h(CPS)f(con)o(v)o(ersion)g(rules)g(are)h(w)o(orth)o(while.)32
5551 b(First,)19 b(an)o(y)g(v)n(ariable)e(in)75 2484 y(italics)e(app)q
5552 (earing)g(on)g(the)h(righ)o(t)f(hand)h(side)f(of)g(a)g(rule)h(and)f
5553 (not)h(the)g(left)f(hand)g(side)h(denotes)h(a)e(new)h(unin)o(terned)75
5554 2534 y(sym)o(b)q(ol)c(created)k(b)o(y)d Fq(gensym)p Fy(.)k(Second,)e
5555 (rules)f(3)g(and)g(12)f(in)o(tro)q(duce)i(new)f(v)n(ariables)g
5556 Fp(a)g Fy(to)f(factor)h(out)g(the)h(common)75 2583 y(con)o(tin)o
5557 (uation)i(sub)q(expression)j(and)d(a)o(v)o(oid)g(the)h(p)q(oten)o(tial)
5558 g(exp)q(onen)o(tial)f(gro)o(wth)h(in)f(expression)i(size)g(that)f(w)o
5559 (ould)992 2723 y(45)p eop
5560 %%Page: 46 46
5561 46 45 bop 75 195 a Fy(o)q(ccur)16 b(if)d(suc)o(h)i(common)d(sub)q
5562 (expression)k(factoring)e(w)o(ere)i(not)e(p)q(erformed.)19
5563 b(As)c(an)f(optimization,)e(if)i(this)g(v)n(ariable)75
5564 245 y Fp(a)g Fy(w)o(ould)f(only)h(rename)f(another)i(created)h(v)n
5565 (ariable,)c(then)j(the)g Fq(let)e Fy(in)o(tro)q(ducing)h
5566 Fp(a)g Fy(is)g Fp(\014)r Fy(-con)o(v)o(erted.)21 b(Third,)13
5567 b(while)75 295 y(bac)o(ktrac)o(king)i(could)h(ha)o(v)o(e)g(b)q(een)h
5568 (implem)o(en)o(ted)d(as)i(simple)e(function)i(return,)h(instead)f(c)o
5569 (hoice)g(p)q(oin)o(ts)g(are)g(set)h(up)75 345 y(as)g
5570 Fq(catch)g Fy(frames)f(with)h(the)h(tag)f Fq(fail)f Fy(and)h(bac)o
5571 (ktrac)o(king)g(is)g(implemen)o(ted)e(via)i(a)g Fq(throw)f
5572 Fy(to)h(the)h(most)e(recen)o(t)75 394 y(catc)o(h)i(frame)d(named)h
5573 Fq(fail)p Fy(.)26 b(Presumably)m(,)16 b(un)o(winding)g(a)h(stac)o(k)g
5574 (via)f Fq(throw)g Fy(is)h(faster)h(than)e(returning)i(through)75
5575 444 y(all)h(of)g(the)i(in)o(termediate)e(frames.)35 b(F)m(ourth,)21
5576 b(the)f(dumm)o(y)d(v)n(ariables)i Fp(d)1273 450 y Fo(1)1298
5577 444 y Fp(:)7 b(:)g(:)f(d)1376 450 y Fh(n)p Fi(\000)p
5578 Fo(1)1460 444 y Fy(in)20 b(rule)g(10)f(are)i(nev)o(er)g(used.)75
5579 494 y(T)m(o)15 b(a)o(v)o(oid)g(b)q(eing)h(\015agged)g(with)g(w)o
5580 (arnings)f(b)o(y)h(some)f Fv(Common)i(Lisp)f Fy(compilers,)f(they)i
5581 (are)f(declared)h(as)f Fq(ignore)75 544 y Fy(v)n(ariables.)25
5582 b(Fifth,)16 b(all)f(of)h(the)h(closures)g(created)h(b)o(y)e(the)h(lam)o
5583 (b)q(da)d(expressions)k(created)g(b)o(y)e(the)h(CPS)g(con)o(v)o(ersion)
5584 75 594 y(can)e(b)q(e)h(stac)o(k)f(allo)q(cated)g(b)o(y)g
5585 Fv(Common)h(Lisp)f Fy(compilers)g(whic)o(h)f(pro)o(vide)h(suc)o(h)h(a)f
5586 (capabilit)o(y)m(.)20 b(As)15 b(the)h(Sym)o(b)q(olics)75
5587 643 y(compiler)g(supp)q(orts)i(stac)o(k)g(allo)q(cated)f(closures)i
5588 (only)d(when)i(lam)o(b)q(da)d(expression)j(are)g(declared)g(as)g(suc)o
5589 (h)g(via)e(the)75 693 y(declaration)g Fq(sys:downward-fun)o(ctio)o(n)p
5590 Fy(,)d(suc)o(h)k(a)e(declaration)h(is)g(added)g(to)g(all)f(lam)o(b)q
5591 (da)e(expressions)18 b(generated)75 743 y(b)o(y)c(CPS)g(con)o(v)o
5592 (ersion.)428 728 y Fo(9)137 793 y Fy(The)d(CPS)f(con)o(v)o(erter)i(p)q
5593 (erforms)e(one)g(additional)f(optimization.)14 b(Stated)c(in)g(their)h
5594 (simple)e(form)f(giv)o(en)i(in)g(table)g(1,)75 843 y(the)19
5595 b(CPS)g(con)o(v)o(ersion)g(rules)g(generate)g(a)g(great)f(deal)h(of)f
5596 (redundan)o(t)h(lam)o(b)q(da)d(expressions)k(whic)o(h)e(immediately)75
5597 892 y(get)i(funcalled.)33 b(T)m(o)19 b(remo)o(v)o(e)f(suc)o(h)i
5598 (redundan)o(t)g(lam)o(b)q(da)d(expressions,)22 b(the)e(CPS)g(con)o(v)o
5599 (erter)g(incorp)q(orates)g(a)f Fp(\014)r Fy(-)75 942
5600 y(con)o(v)o(ersion)e(rule.)25 b(The)17 b Fq(let)e Fy(bindings)h(for)g
5601 (the)h(v)n(ariable)e Fp(a)h Fy(created)i(b)o(y)e(rules)h(3)f(and)g(12)g
5602 (can)g(sometimes)f(th)o(w)o(art)75 992 y(the)j Fp(\014)r
5603 Fy(-con)o(v)o(ersion)g(optimization.)24 b(The)18 b(aforemen)o(tioned)e
5604 (optimization)e(whereb)o(y)k Fq(let)f Fy(bindings)f(whic)o(h)h(simply)
5605 75 1042 y(bind)12 b Fp(a)g Fy(to)g(a)g(previously)g(created)i(v)n
5606 (ariable)d(are)i Fp(\014)r Fy(-con)o(v)o(erted)h(ma)o(y)d(circum)o(v)o
5607 (en)o(t)g(this)i(th)o(w)o(arting)e(and)h(allo)o(w)f(further)75
5608 1092 y Fp(\014)r Fy(-con)o(v)o(ersion)k(b)o(y)e(the)i(curren)o(t)g
5609 (rule.)137 1142 y(The)20 b(actual)e(implemen)o(tatio)o(n)e(uses)k(a)f
5610 (more)f(e\016cien)o(t)h(CPS)g(con)o(v)o(ersion)g(algorithm.)30
5611 b(First,)20 b(it)f(p)q(erforms)f(a)75 1191 y(more)c(e\016cien)o(t)h
5612 (CPS)g(con)o(v)o(ersion)g(on)f(sp)q(ecial)h(forms)e(whic)o(h)i(ha)o(v)o
5613 (e)f(only)g(deterministic)g(sub-expressions.)23 b(Second,)75
5614 1241 y(it)16 b(p)q(erforms)g(a)g(more)f(e\016cien)o(t)i(CPS)f(con)o(v)o
5615 (ersion)h(for)f(the)h(sp)q(ecial)f(forms)f Fq(if)p Fy(,)h
5616 Fq(progn)g Fy(and)g Fq(setq)f Fy(when)i(it)f(can)g(b)q(e)75
5617 1291 y(sho)o(wn)e(that)g(their)g(v)n(alues)g(are)g(not)g(b)q(eing)g
5618 (used)g(and)g(they)h(are)f(only)f(b)q(eing)h(called)f(for)h(side)g
5619 (e\013ect.)75 1428 y Fw(15)69 b(In)n(tellectual)20 b(Heritage)75
5620 1519 y Fy(Nondeterministic)f Fv(Lisp)g Fy(is)h(not)f(new.)36
5621 b(The)20 b(addition)e(of)h(a)g(nondeterministic)g(c)o(hoice)h(op)q
5622 (erator)g(\(once)g(called)75 1569 y Fq(amb)p Fy(\))h(to)g
5623 Fv(Lisp)g Fy(dates)h(bac)o(k)f(to)g(McCarth)o(y)h(\(1963\).)39
5624 b(Clinger)21 b(\(1982\))g(discusses)i(the)f(di\016culties)e(in)o(v)o
5625 (olv)o(ed)g(in)75 1619 y(giving)e(a)i(formal)d(seman)o(tics)i(to)h(a)f
5626 (nondeterministic)g(c)o(hoice)h(op)q(erator)g(in)g Fv(Lisp)p
5627 Fy(.)35 b Fv(Dependency)24 b(Directed)75 1669 y(Lisp)18
5628 b Fy(\(also)f(kno)o(wn)g(as)h Fv(ddl)p Fy(\))g(\(Chapman,)e
5629 (unpublished\))i(w)o(as)g(an)f(implemen)o(tation)e(of)i
5630 (nondeterministic)g Fv(Lisp)75 1718 y Fy(used)h(to)g(implem)o(en)o(t)d
5631 Fv(Tweak)j Fy(\(Chapman,)d(1985\),)i(a)h(non-linear)e(constrain)o(t-p)q
5632 (osting)i(planner.)29 b Fv(ddl)17 b Fy(recorded)75 1768
5633 y(dep)q(endency)j(information)15 b(during)i(execution)i(to)e(supp)q
5634 (ort)i(selectiv)o(e)g(bac)o(ktrac)o(king.)29 b Fv(Schemer)18
5635 b Fy(\(Zabih,)f(1987;)75 1818 y(Zabih,)f(McAllester)j(and)e(Chapman,)e
5636 (1987;)i(Zabih,)g(McAllester)h(and)f(Chapman,)e(forthcoming\))h(w)o(as)
5637 h(an)g(in)o(ter-)75 1868 y(preter)j(for)e(nondeterministic)g
5638 Fv(Scheme)h Fy(that)g(recorded)h(and)e(analyzed)g(dep)q(endency)j
5639 (information)15 b(to)k(p)q(erform)75 1918 y(b)q(oth)c(selectiv)o(e)i
5640 (bac)o(ktrac)o(king)e(and)g(lateral)g(pruning.)21 b Fv(Schemer)16
5641 b Fy(and)f Fv(ddl)h Fy(w)o(ere)g(b)q(oth)f(in)o(terpreters)j(to)d(supp)
5642 q(ort)75 1968 y(retaining)k(the)i(dep)q(endency)h(information)17
5643 b(needed)k(for)e(in)o(telligen)o(t)g(bac)o(ktrac)o(king.)36
5644 b(Because)21 b Fv(Screamer)g Fy(uses)75 2017 y(c)o(hronological)15
5645 b(bac)o(ktrac)o(king,)h(it)g(can)h(macro-expand)e(in)o(to)h(ordinary)g
5646 Fv(Common)g(Lisp)h Fy(whic)o(h)f(is)g(then)i(compiled)75
5647 2067 y(in)o(to)d(e\016cien)o(t)h(co)q(de.)24 b Fv(Lambex)17
5648 b Fy(\(McAllester,)g(unpublished\))f(and)f(new)h Fv(Ontic)f
5649 Fy(\(McAllester,)i(unpublished\))f(are)75 2117 y(dialects)h(of)g
5650 Fv(Lisp)g Fy(whic)o(h)f(incorp)q(orate)i(a)f(nondeterministic)f(c)o
5651 (hoice)i(op)q(erator.)27 b(They)18 b(are)f(in)o(tended)h(to)e(b)q(e)i
5652 (used)75 2167 y(as)e(a)g(declarativ)o(e)h(input)f(language)f(for)h
5653 (stating)g(theorems)h(to)f(a)g(pro)q(of)g(c)o(hec)o(k)o(er)i(and)e(no)g
5654 (op)q(erational)f(ev)n(aluators)75 2217 y(ha)o(v)o(e)h(b)q(een)h
5655 (constructed)h(for)d(them.)24 b(Ha)o(ynes)16 b(\(1987\))f(describ)q(es)
5656 j(ho)o(w)e(a)g(nondeterministic)f(c)o(hoice)h(op)q(erator)h(can)75
5657 2266 y(b)q(e)e(added)f(to)f Fv(Scheme)i Fy(using)f(the)g
5658 Fq(call/cc)e Fy(function.)137 2316 y(The)i(tec)o(hniques)g(used)g(for)e
5659 (implemen)o(ting)e(bac)o(ktrac)o(king)i(in)h Fv(Screamer)g
5660 Fy(are)h(analogous)d(to)i(those)h(used)f(when)75 2366
5661 y(compiling)e Fv(Pr)o(olog)k Fy(in)o(to)e Fv(Lisp)i Fy(\(Kahn,)f(1982;)
5662 e(Kahn,)i(1983;)f(Kahn)h(and)g(Carrlson,)g(1984;)f(Siskind,)g(1989\).)
5663 18 b(CPS)75 2416 y(con)o(v)o(ersion)c(w)o(as)g(used)h(in)e(the)i
5664 Fv(Rabbit)e Fy(compiler)g(for)g Fv(Scheme)i Fy(\(Steele)g(and)f
5665 (Sussman,)e(1976;)h(Steele,)h(1977\).)p 75 2453 750 2
5666 v 121 2480 a Fn(9)139 2491 y Fs(Since)d(e\016cien)o(t)i(CPS)g(con)o(v)o
5667 (ersion)e(relies)h(on)h(b)q(eing)f(able)g(to)h(stac)o(k)f(allo)q(cate)g
5668 (closures)f(to)i(a)o(v)o(oid)f(needing)f(to)i(garbage)e(collect)h(the)
5669 75 2531 y(man)o(y)e(closures)g(created)g(during)f(the)i(execution)e(of)
5670 i(nondetermini)o(stic)d(functions,)h(in)j(w)o(ould)f(b)q(e)g(nice)f(if)
5671 i Fm(Common)h(Lisp)e Fs(incorp)q(orate)o(d)75 2570 y(the)g(option)f(of)
5672 h(a)g Fl(sys:downwar)o(d-)o(fun)o(cti)o(on)d Fs(declaration)h(as)i(a)g
5673 (standard)f(feature.)992 2723 y Fy(46)p eop
5674 %%Page: 47 47
5675 47 46 bop 137 195 a Fy(Constrain)o(t)17 b(solv)o(ers)h(based)g(on)f
5676 (forw)o(ard)g(c)o(hec)o(king)g(\(sometimes)f(called)h(constrain)o(t)g
5677 (propagation\))g(also)f(ha)o(v)o(e)75 245 y(a)10 b(long)g(history)m(.)
5678 16 b(Some)9 b(of)h(the)h(earliest)g(and)f(b)q(est)i(kno)o(wn)e(of)g
5679 (suc)o(h)h(systems)g(w)o(ere)g Fv(Sketchp)m(ad)h Fy(\(Sutherland,)e
5680 (1963\),)75 295 y Fv(Thinglab)g Fy(\(Borning,)f(1979\),)f
5681 Fv(Consys)j Fy(\(Steele,)e(1980;)h(Sussman)e(and)h(Steele,)h(1980\))f
5682 (and)g Fv(Ma)o(gritte)f Fy(\(Gosling,)f(1983\).)75 345
5683 y(Since)13 b(constrain)o(t)g(propagation)e(is)i(an)f(incomplete)g(tec)o
5684 (hnique)h(for)f(solving)g(systems)g(of)g(constrain)o(ts,)h(systems)g
5685 (suc)o(h)75 394 y(as)f(these)h(whic)o(h)f(rely)g(primarily)e(on)i
5686 (constrain)o(t)g(propagation)f(are)h(incapable)g(of)f(solving)g(man)o
5687 (y)f(problems)h(they)i(are)75 444 y(giv)o(en.)k(The)d(constrain)o(t)f
5688 (handling)f(mec)o(hanism)f(used)j(in)e Fv(Screamer)i
5689 Fy(w)o(as)f(adapted)g(from)f(the)h(one)h(used)g(in)e
5690 Fv(CHiP)75 494 y Fy(\(V)m(an)f(Hen)o(tenryc)o(k,)h(1989\).)k(The)c(no)o
5691 (v)o(el)e(approac)o(h)h(tak)o(en)h(b)o(y)f Fv(CHiP)f
5692 Fy(and)h Fv(Screamer)g Fy(is)g(to)g(com)o(bine)f(bac)o(ktrac)o(king)75
5693 544 y(searc)o(h)j(with)f(constrain)o(t)g(propagation)f(to)h(yield)g(a)g
5694 (complete)f(constrain)o(t)h(solv)o(er.)18 b(Unlik)o(e)11
5695 b Fv(CHiP)g Fy(whic)o(h)h(uses)h(linear)75 594 y(programming)7
5696 b(tec)o(hniques)13 b(to)d(solv)o(e)h(systems)g(of)g(n)o(umeric)f
5697 (constrain)o(ts,)h Fv(Screamer)h Fy(uses)g(range)f(propagation)f(and)75
5698 643 y(supp)q(orts)k(a)e(divide)g(and)g(conquer)i(approac)o(h)e(to)h
5699 (solving)e(nonlinear)h(n)o(umeric)g(constrain)o(t)g(problems.)17
5700 b(V)m(an)12 b(Hen)o(ten-)75 693 y(ryc)o(k's)f(b)q(o)q(ok)g(giv)o(es)g
5701 (an)f(excellen)o(t)i(historical)f(o)o(v)o(erview)f(of)h(the)g(dev)o
5702 (elopmen)o(t)f(of)h(constrain)o(t)g(satisfaction)g(tec)o(hniques)75
5703 743 y(and)j(languages)f(and)h(con)o(tains)g(an)f(extensiv)o(e)i
5704 (bibliograph)o(y)d(of)h(that)h(\014eld.)75 879 y Fw(16)69
5705 b(Obtaining)22 b(Screamer)75 970 y Fv(Screamer)13 b Fy(is)e(in)o
5706 (tended)i(to)f(b)q(e)h(p)q(ortable)f(and)f(should)h(run)h(under)f(an)o
5707 (y)g Fv(Common)k(Lisp)c Fy(implemen)o(tation.)i(A)o(t)e(the)75
5708 1020 y(M.)h(I.)h(T.)f(Arti\014cial)g(In)o(telligence)h(lab)q(oratory)m
5709 (,)f(the)h(source)h(co)q(de)g(for)f Fv(Screamer)g Fy(is)g(a)o(v)n
5710 (ailable)e(from)g(the)i(\014le:)204 1099 y Fq(/src/local/lispl)o(ib/sr)
5711 o(c/scr)o(eame)o(r/scr)o(eamer)o(.lisp)75 1178 y Fy(Compiled)d(co)q(de)
5712 j(for)e(v)n(arious)h(com)o(binations)e(of)h(mac)o(hines)g(and)h
5713 Fv(Common)j(Lisp)d Fy(compilers)f(is)h(a)o(v)n(ailable)e(from)g(the)75
5714 1228 y(\014les:)204 1307 y Fq(/src/local/lispl)o(ib/)p
5715 Fu(machine)p Fq(/scre)o(amer.)o Fu(binary)75 1386 y Fy(where)17
5716 b Fu(machine)g Fy(is)g(the)g(directory)g(for)f(storing)g(compiled)f
5717 Fv(Lisp)h Fy(co)q(de)h(for)f(that)g(arc)o(hitecture)j(and)d
5718 Fu(binary)g Fy(is)g(the)75 1436 y(standard)f(extension)g(for)f(that)h
5719 (arc)o(hitecture.)21 b(The)15 b(follo)o(wing)d(\014le)j(is)f(useful)h
5720 (if)e(y)o(ou)h(attempt)g(to)h(p)q(ort)f Fv(Screamer)75
5721 1485 y Fy(to)g(a)f(new)i(mac)o(hine)d(or)i Fv(Common)j(Lisp)d
5722 Fy(implem)o(en)o(tation:)204 1564 y Fq(/src/local/lispl)o(ib/sr)o
5723 (c/scr)o(eame)o(r/pri)o(mordi)o(al.li)o(sp)75 1643 y
5724 Fy(It)h(con)o(tains)h(a)f(series)h(of)f(examples)g(designed)h(to)f
5725 (exercise)i Fv(Screamer)q Fy(.)22 b(Simply)13 b(compile)h(that)h
5726 (\014le)g(and)h(run)f(the)75 1693 y(function)h Fq(\(prime-ordeal\))p
5727 Fy(.)22 b(It)17 b(should)f(return)h Fq(t)f Fy(if)g(the)g
5728 Fv(Screamer)h Fy(p)q(ort)g(w)o(as)f(successful)i(and)e(giv)o(e)g(an)g
5729 (error)75 1743 y(message)e(if)f(not.)18 b(Additionally)m(,)10
5730 b(a)k(\014le)g(con)o(taining)f(all)f(of)i(the)g(examples)f(from)f(this)
5731 i(man)o(ual)e(is)h(a)o(v)n(ailable)f(as:)204 1822 y Fq
5732 (/src/local/lispl)o(ib/sr)o(c/scr)o(eame)o(r/scr)o(eams.)o(lisp)75
5733 1901 y Fy(Finally)m(,)f(a)j(p)q(ostscript)h(\014le)f(con)o(taining)f
5734 (this)h(man)o(ual)d(is)j(a)o(v)n(ailable)e(from)g(the)i(\014le:)204
5735 1980 y Fq(/src/local/lispl)o(ib/do)o(c/scr)o(eame)o(r.ps)137
5736 2059 y Fy(F)m(rom)e(outside)j(M.)e(I.)g(T.,)g Fv(Screamer)i
5737 Fy(is)e(a)o(v)n(ailable)f(b)o(y)i(public)f(FTP)h(from)f(the)h(host:)204
5738 2138 y Fq(ftp.ai.mit.edu)75 2217 y Fy(in)f(the)i(directory:)204
5739 2296 y Fq(/com/ftp/pub/scr)o(eamer)o(/)75 2375 y Fy(In)f(that)g
5740 (directory)g(y)o(ou)g(will)e(\014nd)i(the)h(\014les:)204
5741 2451 y Fq(screamer.lisp)204 2501 y(primordial.lisp)204
5742 2550 y(screams.lisp)204 2600 y(screamer.ps)992 2723 y
5743 Fy(47)p eop
5744 %%Page: 48 48
5745 48 47 bop 75 195 a Fy(Y)m(ou)11 b(will)g(ha)o(v)o(e)g(to)h(compile)e
5746 Fv(Screamer)i Fy(y)o(ourself)g(for)f(whic)o(hev)o(er)i(mac)o(hine)e
5747 (and)g Fv(Common)17 b(Lisp)11 b Fy(implemen)o(tation)75
5748 245 y(y)o(ou)i(use.)137 295 y(W)m(e)k(main)o(tain)e(sev)o(eral)j
5749 (mailing)c(lists)j(p)q(ertaining)g(to)g Fv(Screamer)q
5750 Fy(.)29 b(The)17 b(mailing)d(list)j Fq(Info-Screamer)e
5751 Fy(is)i(a)75 345 y(c)o(hannel)f(from)e(the)i(dev)o(elop)q(ers)h(to)e
5752 (the)h(users)h(and)f(con)o(tains)f(announcemen)o(ts)h(of)f(enhancemen)o
5753 (ts)h(and)f(bug)h(\014xes.)75 394 y(T)m(o)d(b)q(e)i(added)f(to)g(that)g
5754 (maili)o(ng)d(list,)i(send)i(mail)c(to:)204 471 y Fq(Info-Screamer-Re)o
5755 (quest)o(@AI.M)o(IT.E)o(DU)75 547 y Fy(If)j(y)o(ou)f(detect)i(a)f(bug)g
5756 (in)f Fv(Screamer)i Fy(please)f(send)h(mail)c(to:)204
5757 624 y Fq(Bug-Screamer@AI.)o(MIT.E)o(DU)75 700 y Fy(Please)i(do)e(not)h
5758 (send)h(mail)c(directly)j(to)g(the)g(author)g(as)g(the)h
5759 Fq(Bug-Screamer)c Fy(mailing)g(list)i(is)h(arc)o(hiv)o(ed)g(separately)
5760 g(to)75 750 y(aid)f(in)h(main)o(taining)c Fv(Screamer)q
5761 Fy(.)17 b(W)m(e)12 b(also)f(ask)h(that)g(y)o(ou)f(rep)q(ort)i
5762 Fu(al)r(l)f Fy(bugs)g(whether)h(or)f(not)g(y)o(ou)f(need)i(them)f
5763 (\014xed)75 800 y(and)d(whether)i(or)e(not)h(y)o(ou)f(\014x)g(them)g(y)
5764 o(ourself.)16 b(This)9 b(will)f(assist)i(us)g(in)f(helping)g(the)h(en)o
5765 (tire)g(user)h(comm)o(unit)o(y)l(.)j(Finally)m(,)75 850
5766 y(w)o(e)j(ask)g(that)g(y)o(ou)f(send)i(mail)c(to)j Fq(Bug-Screamer)d
5767 Fy(whenev)o(er)k(y)o(ou)f(attempt)f(to)g(p)q(ort)i Fv(Screamer)f
5768 Fy(to)g(a)f(mac)o(hine)75 900 y(or)d Fv(Common)k(Lisp)c
5769 Fy(implemen)o(tation)d(not)j(listed)h(at)f(the)h(b)q(eginning)e(of)h
5770 (the)h(\014le)f Fq(screamer.lisp)e Fy(whether)k(or)e(not)75
5771 950 y(that)h(p)q(ort)g(is)g(successful.)137 999 y Fv(Screamer)i
5772 Fy(is)g(a)o(v)n(ailable)d(free)j(of)f(c)o(harge)h(and)g(without)f(an)o
5773 (y)g(restriction.)24 b(All)15 b(w)o(e)g(ask)h(is)f(that)h(y)o(ou)f
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5775 (sending)g(bug)h(rep)q(orts)g(and)f(also)g(send)h(mail)d(to)i
5776 Fq(Info-Screamer-Reque)o(st)d Fy(if)j(y)o(ou)g(obtain)75
5777 1099 y(a)h(cop)o(y)f(in)h(an)o(y)f(w)o(a)o(y)g(so)h(that)g(w)o(e)g(ma)o
5778 (y)e(k)o(eep)j(trac)o(k)f(of)f(who)h(has)g(obtained)f(a)h(cop)o(y)g
5779 (and)f(k)o(eep)i(users)g(informed)e(of)75 1149 y(enhancemen)o(ts)g(and)
5780 e(bug)h(\014xes)h(b)o(y)e(w)o(a)o(y)g(of)h(the)g Fq(Info-Screamer)d
5781 Fy(mailing)g(list.)825 1232 y Fb(Ac)o(kno)o(wledgmen)o(ts)137
5782 1315 y Fy(Bug-DDL@AI.MIT.EDU)75 1451 y Fw(References)96
5783 1542 y Fy([1])19 b(Alan)d(Hamilton)e(Borning.)25 b Fv(Thinglab)q
5784 Fu(|A)17 b(Constr)n(aint-Oriente)n(d)f(Simulation)h(L)n(ab)n(or)n
5785 (atory)p Fy(.)25 b(PhD)17 b(thesis,)160 1592 y(Stanford)g(Univ)o(ersit)
5786 o(y)m(,)f(July)h(1979.)25 b(Also)17 b(a)o(v)n(ailable)d(as)j(Stanford)g
5787 (Computer)f(Science)i(Departmen)o(t)e(rep)q(ort)160 1642
5788 y(ST)m(AN-CS-79-746)c(and)i(as)g(XER)o(O)o(X)g(P)o(alo)f(Alto)g
5789 (Researc)o(h)i(Cen)o(ter)g(rep)q(ort)g(SSL-79-3.)96 1721
5790 y([2])k(Da)o(vid)c(Chapman.)22 b(Dep)q(endency-Directed)c
5791 Fv(Lisp)p Fy(.)23 b(Unpublished)16 b(man)o(uscript)f(receiv)o(ed)i
5792 (directly)f(from)e(au-)160 1771 y(thor.)96 1851 y([3])19
5793 b(Da)o(vid)13 b(Chapman.)j(Planning)d(for)h(conjunctiv)o(e)g(goals.)j
5794 (Master's)e(thesis,)f(Massac)o(h)o(usetts)i(Institute)f(of)e(T)m(ec)o
5795 (h-)160 1901 y(nology)m(,)f(Jan)o(uary)h(1985.)j(Also)d(a)o(v)n
5796 (ailable)e(as)i(M.)g(I.)g(T.)f(Arti\014cial)h(In)o(teligence)h(Lab)q
5797 (oratory)f(T)m(ec)o(hnical)g(Rep)q(ort)160 1951 y(802.)96
5798 2030 y([4])19 b(W.)13 b(Clinger.)j(Nondeterministic)d(call)g(b)o(y)g
5799 (need)h(is)f(neither)h(lazy)f(nor)g(b)o(y)g(name.)j(In)d
5800 Fu(Pr)n(o)n(c)n(e)n(e)n(dings)i(of)f(the)g(A)o(CM)160
5801 2080 y(Confer)n(enc)n(e)h(on)h Fv(Lisp)e Fu(and)i(F)m(unctional)f(Pr)n
5802 (o)n(gr)n(amming)p Fy(,)e(pages)h(226{234,)e(1982.)96
5803 2160 y([5])19 b(James)14 b(Gosling.)i Fu(A)o(lgebr)n(aic)e(Constr)n
5804 (aints)p Fy(.)k(PhD)13 b(thesis,)i(Carnegie-Mellon)e(Univ)o(ersit)o(y)m
5805 (,)g(1983.)96 2240 y([6])19 b(Christopher)c(T.)e(Ha)o(ynes.)19
5806 b(Logic)13 b(con)o(tin)o(uations.)k Fu(Journal)e(of)g(L)n(o)n(gic)g(Pr)
5807 n(o)n(gr)n(amming)p Fy(,)e(4:157{176,)e(1987.)96 2320
5808 y([7])19 b(Nevin)c(Hein)o(tze,)g(Spiro)g(Mic)o(ha)o(ylo)o(v,)d(and)j(P)
5809 o(eter)h(Stuc)o(k)o(ey)m(.)k Fv(clp)p Fy(\()p Fr(<)p
5810 Fy(\))15 b(and)f(some)g(electrical)h(engineering)g(prob-)160
5811 2369 y(lems.)28 b(In)18 b(Jean-Louis)f(Lassez,)j(editor,)e
5812 Fu(L)n(o)n(gic)g(Pr)n(o)n(gr)n(amming:)25 b(Pr)n(o)n(c)n(e)n(e)n(dings)
5813 18 b(of)g(the)h(F)m(ourth)f(International)160 2419 y(Confer)n(enc)n(e)p
5814 Fy(,)c(pages)g(675{703,)e(Cam)o(bridge,)f(MA,)j(Ma)o(y)f(1987.)g(The)h
5815 (MIT)g(Press.)96 2499 y([8])19 b(Jo)o(xan)e(Ja\013ar)g(and)g(Spiro)g
5816 (Mic)o(ha)o(ylo)o(v.)26 b(Metho)q(dology)16 b(and)h(implemen)o(tati)o
5817 (on)d(of)j(a)f Fv(clp)h Fy(system.)28 b(In)17 b(Jean-)160
5818 2549 y(Louis)11 b(Lassez,)h(editor,)f Fu(L)n(o)n(gic)h(Pr)n(o)n(gr)n
5819 (amming:)17 b(Pr)n(o)n(c)n(e)n(e)n(dings)12 b(of)g(the)g(F)m(ourth)g
5820 (International)h(Confer)n(enc)n(e)p Fy(,)e(pages)160
5821 2599 y(196{218,)h(Cam)o(bridge,)g(MA,)h(Ma)o(y)h(1987.)e(The)i(MIT)g
5822 (Press.)992 2723 y(48)p eop
5823 %%Page: 49 49
5824 49 48 bop 96 195 a Fy([9])19 b(Kenneth)g(M.)e(Kahn.)29
5825 b(A)17 b(partial)g(ev)n(aluator)f(of)h Fv(Lisp)g Fy(written)h(in)f
5826 Fv(Pr)o(olog)q Fy(.)28 b(In)18 b Fu(Pr)n(o)n(c)n(e)n(e)n(dings)g(of)g
5827 (the)g(First)160 245 y(L)n(o)n(gic)d(Pr)n(o)n(gr)n(amming)f(Confer)n
5828 (enc)n(e)p Fy(,)g(Marseille,)f(F)m(rance,)h(1982.)75
5829 328 y([10])19 b(Kenneth)d(M.)f(Kahn.)20 b(Unique)15 b(features)h(of)e
5830 Fv(Lisp)h Fy(mac)o(hine)e Fv(Pr)o(olog)q Fy(.)20 b(UPMAIL)15
5831 b(Rep)q(ort)g(14,)f(Univ)o(ersit)o(y)h(of)160 378 y(Uppsala,)e(Sw)o
5832 (eden,)i(1983.)75 461 y([11])k(Kenneth)h(M.)e(Kahn)g(and)g(M.)g
5833 (Carlsson.)31 b(Ho)o(w)18 b(to)g(implemen)o(t)e Fv(Pr)o(olog)j
5834 Fy(on)f(a)g Fv(Lisp)g Fy(mac)o(hine.)30 b(In)18 b(J.)g(A.)160
5835 511 y(Campb)q(ell,)d(editor,)i Fu(Implementations)h(of)f
5836 Fv(Pr)o(olog)q Fy(,)g(c)o(hapter)h(2,)e(pages)h(117{134.)e(Ellis)h
5837 (Horw)o(o)q(o)q(d,)g(Chic)o(h-)160 560 y(ester,)f(1984.)75
5838 643 y([12])k(Da)o(vid)13 b(Allen)h(McAllester.)19 b(Lam)o(b)q(ex.)d
5839 (Unpublished)f(man)o(uscript)e(receiv)o(ed)i(directly)f(from)e(author.)
5840 75 726 y([13])19 b(John)10 b(McCarth)o(y)m(.)h(A)f(basis)g(for)g(a)f
5841 (mathematical)d(theory)11 b(of)e(computation.)g(In)h(P)m(.)f
5842 (Bra\013ort)i(and)e(D.)g(Hirsc)o(h)o(b)q(erg,)160 776
5843 y(editors,)14 b Fu(Computer)h(Pr)n(o)n(gr)n(aming)f(and)i(F)m(ormal)e
5844 (Systems)p Fy(.)g(Elsevier)g(North-Holland,)f(Amsterdam,)e(1963.)75
5845 859 y([14])19 b(Mann)o(y)h(Ra)o(yner,)469 852 y(\027)469
5846 859 y(Asa)g(Hugosson,)h(and)f(G\177)-21 b(oran)20 b(Hagert.)37
5847 b(Using)19 b(a)h(logic)f(grammar)e(to)j(learn)g(a)g(lexicon.)160
5848 909 y(T)m(ec)o(hnical)14 b(Rep)q(ort)g(R88001,)e(Sw)o(edish)i
5849 (Institute)h(of)e(Computer)g(Science,)i(1988.)75 992
5850 y([15])k(Je\013rey)k(Mark)d(Siskind.)38 b(The)21 b(culprit)f(p)q(oin)o
5851 (ter)h(metho)q(d)f(for)g(selectiv)o(e)i(bac)o(ktrac)o(king.)38
5852 b(Master's)22 b(thesis,)160 1042 y(Massac)o(h)o(usetts)16
5853 b(Institute)f(of)e(T)m(ec)o(hnology)m(,)f(Jan)o(uary)i(1989.)75
5854 1125 y([16])19 b(Je\013rey)14 b(Mark)e(Siskind.)i(Acquiring)e(core)h
5855 (meanings)d(of)i(w)o(ords,)g(represen)o(ted)i(as)f(Jac)o(k)o
5856 (endo\013-st)o(yle)f(conceptual)160 1175 y(structures,)23
5857 b(from)17 b(correlated)j(streams)f(of)f(linguistic)g(and)h
5858 (non-linguistic)e(input.)33 b(In)19 b Fu(Pr)n(o)n(c)n(e)n(e)n(dings)g
5859 (of)h(the)160 1225 y Fy(28)202 1210 y Fa(th)250 1225
5860 y Fu(A)o(nnual)d(Me)n(eting)g(of)f(the)h(Asso)n(ciation)f(for)g
5861 (Computational)h(Linguistics)p Fy(,)f(pages)g(143{156,)e(Univ)o(ersit)o
5862 (y)160 1274 y(of)g(Pittsburgh,)g(Pittsburgh,)g(P)m(A,)f(June)i(1990.)75
5863 1357 y([17])k(Je\013rey)d(Mark)e(Siskind.)k(Disp)q(elling)13
5864 b(m)o(yths)g(ab)q(out)h(language)g(b)q(o)q(otstrapping.)k(In)d
5865 Fu(The)g(AAAI)f(Spring)i(Sym-)160 1407 y(p)n(osium)g(Workshop)g(on)g
5866 (Machine)g(L)n(e)n(arning)f(of)h(Natur)n(al)e(L)n(anguage)j(and)f
5867 (Ontolo)n(gy)p Fy(,)e(pages)g(157{164,)f(Marc)o(h)160
5868 1457 y(1991.)75 1540 y([18])19 b(Iv)n(an)11 b(E.)g(Southerland.)j
5869 Fv(Sketchp)m(ad)r Fu(:)j(A)c(Man-Machine)h(Gr)n(aphic)n(al)e(Communic)n
5870 (ation)h(System)p Fy(.)h(PhD)e(thesis,)160 1590 y(Massac)o(h)o(usetts)k
5871 (Institute)f(of)e(T)m(ec)o(hnology)m(,)f(Jan)o(uary)i(1963.)75
5872 1673 y([19])19 b(Guy)f(Lewis)g(Steele)h(Jr.)31 b(Debunking)17
5873 b(the)i(\\exp)q(ensiv)o(e)g(pro)q(cedure)h(call")d(m)o(yth,)g(or)h(pro)
5874 q(cedure)i(call)d(imple-)160 1723 y(men)o(tations)d(considered)i
5875 (harmful,)d(or)i(lam)o(b)q(da,)e(the)i(ultimate)e(goto.)21
5876 b(A.)15 b(I.)f(Memo)g(443,)g(M.)h(I.)f(T.)h(Arti\014cial)160
5877 1773 y(In)o(telligence)f(Lab)q(oratory)m(,)f(Octob)q(er)i(1977.)75
5878 1856 y([20])k(Guy)d(Lewis)h(Steele)g(Jr.)25 b Fu(The)17
5879 b(De\014nition)h(and)g(Implementation)f(of)g(a)h(Computer)e(Pr)n(o)n
5880 (gr)n(amming)h(L)n(anguage)160 1905 y(Base)n(d)22 b(on)f(Constr)n
5881 (aints)p Fy(.)36 b(PhD)20 b(thesis,)i(Massac)o(h)o(usetts)g(Institute)f
5882 (of)e(T)m(ec)o(hnology)m(,)h(August)h(1980.)35 b(Also)160
5883 1955 y(a)o(vilable)13 b(as)i(M.)g(I.)f(T.)g(VLSI)h(Memo)f(80{32)f(and)i
5884 (as)f(M.)h(I.)f(T.)g(Arti\014cial)g(In)o(teligence)i(Lab)q(oratory)e(T)
5885 m(ec)o(hnical)160 2005 y(Rep)q(ort)h(595.)75 2088 y([21])k(Guy)13
5886 b(Lewis)g(Steele)i(Jr.)e(and)g(Gerald)f(Ja)o(y)h(Sussman.)j(Lam)o(b)q
5887 (da,)11 b(the)j(ultimate)d(imp)q(erativ)o(e.)16 b(A.)d(I.)f(Memo)g
5888 (353,)160 2138 y(M.)i(I.)f(T.)g(Arti\014cial)h(In)o(telligence)g(Lab)q
5889 (oratory)m(,)e(Marc)o(h)j(1976.)75 2221 y([22])k(Gerald)c(Ja)o(y)h
5890 (Sussman)f(and)g(Guy)g(Lewis)h(Steele)g(Jr.)24 b Fv(Constraints)p
5891 Fy(|a)15 b(language)f(for)h(expressing)i(almost-)160
5892 2271 y(hierarc)o(hical)10 b(descriptions.)j Fu(A)o(rti\014cial)e(Intel)
5893 r(ligenc)n(e)p Fy(,)f(14\(1\):1{39,)e(1980.)j(Also)f(a)o(v)n(ailable)e
5894 (as)j(M.)e(I.)h(T.)g(Arti\014cial)160 2320 y(In)o(telligence)k(Lab)q
5895 (oratory)g(Memo)f(502A.)75 2403 y([23])19 b(P)o(ascal)11
5896 b(V)m(an)f(Hen)o(tenryc)o(k.)k Fu(Constr)n(aint)e(Satisfaction)g(in)g
5897 (L)n(o)n(gic)g(Pr)n(o)n(gr)n(amming)p Fy(.)g(The)f(MIT)g(Press,)h(Cam)o
5898 (bridge,)160 2453 y(MA,)i(1989.)75 2536 y([24])19 b(Ramin)10
5899 b(D.)i(Zabih.)j(Dep)q(endency-directed)g(bac)o(ktrac)o(king)d(in)g
5900 (non-deterministic)f Fv(Scheme)q Fy(.)k(Master's)f(thesis,)160
5901 2586 y(Massac)o(h)o(usetts)i(Institute)f(of)e(T)m(ec)o(hnology)m(,)f
5902 (Jan)o(uary)i(1987.)992 2723 y(49)p eop
5903 %%Page: 50 50
5904 50 49 bop 75 195 a Fy([25])19 b(Ramin)g(D.)h(Zabih,)h(Da)o(vid)f(Allen)
5905 g(McAllester,)k(and)c(Da)o(vid)g(Chapman.)36 b(Non-deterministic)20
5906 b Fv(Lisp)h Fy(with)160 245 y(dep)q(endency-directe)q(d)c(bac)o(ktrac)o
5907 (king.)g(In)d Fu(Pr)n(o)n(c)n(e)n(e)n(dings)h(of)g(AAAI{87)p
5908 Fy(,)e(pages)i(59{64,)d(July)h(1987.)75 328 y([26])19
5909 b(Ramin)10 b(D.)i(Zabih,)g(Da)o(vid)f(Allen)h(McAllester,)h(and)f(Da)o
5910 (vid)f(Chapman.)j(Dep)q(endency-directed)h(bac)o(ktrac)o(king)160
5911 378 y(in)f(non-deterministic)f Fv(Lisp)p Fy(.)18 b Fu(A)o(rti\014cial)c
5912 (Intel)r(ligenc)n(e)p Fy(,)f(1988.)k(Submitted)c(for)g(publication.)992
5913 2723 y(50)p eop
5914 %%Trailer
5915 end
5916 userdict /end-hook known{end-hook}if
5917 %%EOF