ircs-93-03.ps

   1 %!PS-Adobe-2.0
   2 %%Creator: dvipsk 5.521a Copyright 1986, 1993 Radical Eye Software
   3 %%Title: ircs-93-03.dvi
   4 %%Pages: 10
   5 %%PageOrder: Ascend
   6 %%BoundingBox: 0 0 612 792
   7 %%EndComments
   8 %DVIPSCommandLine: dvips ircs-93-03
   9 %DVIPSSource:  TeX output 1994.03.10:2312
  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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1750 01F0018001F8030001F8030000F80300007C0600003E0C00001FF8000003F00019367EB4
1751 21>I E end
1752 %%EndProlog
1753 %%BeginSetup
1754 %%Feature: *Resolution 300dpi
1755 TeXDict begin
1756
1757 %%EndSetup
1758 %%Page: 1 1
1759 1 0 bop 21 165 a Fv(Screamer:)37 b(A)28 b(P)n(ortable)h(E\016cien)n(t)h
1760 (Implemen)n(tation)f(of)360 269 y(Nondeterministic)h(Common)d(Lisp)689
1761 416 y Fu(Je\013rey)19 b(Mark)h(Siskind)1232 395 y Ft(\003)611
1762 491 y Fu(Univ)n(ersit)n(y)f(of)h(P)n(ennsylv)m(ania)402
1763 566 y(Institute)f(for)i(Researc)n(h)e(in)h(Cognitiv)n(e)f(Science)543
1764 641 y(3401)g(W)-5 b(aln)n(ut)21 b(Street)f(Ro)r(om)e(407C)662
1765 715 y(Philadelphia)g(P)-5 b(A)20 b(19104)781 790 y(215/898{0367)530
1766 865 y(in)n(ternet:)27 b(Qobi@CIS.UP)n(enn.EDU)652 1014
1767 y(Da)n(vid)19 b(Allen)g(McAllester)1270 992 y Ft(y)416
1768 1089 y Fu(M.)g(I.)g(T.)h(Arti\014cial)f(In)n(telligence)e(Lab)r
1769 (oratory)429 1164 y(545)j(T)-5 b(ec)n(hnology)19 b(Square)h(Ro)r(om)e
1770 (NE43{412)673 1238 y(Cam)n(bridge)i(MA)f(02139)781 1313
1771 y(617/253{6599)581 1388 y(in)n(ternet:)27 b(dam@AI.MIT.EDU)759
1772 1505 y(Marc)n(h)20 b(10,)f(1994)860 1742 y Fs(Abstract)190
1773 1826 y Fr(Nondeterministic)k Fq(Lisp)d Fr(is)h(a)f(simple)i(extension)g
1774 (of)e Fq(Lisp)g Fr(whic)o(h)i(pro)o(vides)f(automatic)122
1775 1883 y(bac)o(ktrac)o(king.)e(Nondeterminism)14 b(allo)o(ws)f(concise)h
1776 (description)h(of)e(man)o(y)f(searc)o(h)h(tasks)f(whic)o(h)122
1777 1939 y(form)h(the)g(basis)h(of)f(m)o(uc)o(h)g(AI)h(researc)o(h.)19
1778 b(This)14 b(pap)q(er)g(discusses)h Fq(Screamer)q Fr(,)e(an)g(e\016cien)
1779 o(t)h(im-)122 1996 y(plemen)o(tation)e(of)e(nondeterministic)j
1780 Fq(Lisp)e Fr(as)g(a)f(fully)i(p)q(ortable)g(extension)g(of)e
1781 Fq(Common)16 b(Lisp)p Fr(.)122 2052 y(In)k(this)h(pap)q(er)f(w)o(e)f
1782 (presen)o(t)h(the)g(basic)g(nondeterministic)i Fq(Lisp)e
1783 Fr(constructs,)g(motiv)m(ate)g(the)122 2109 y(utilit)o(y)i(of)e(the)h
1784 (language)g(via)g(n)o(umerous)g(short)f(examples,)j(and)e(discuss)h
1785 (the)f(compilation)122 2165 y(tec)o(hniques.)p 0 2208
1786 768 2 v 56 2239 a Fp(\003)75 2254 y Fo(Supp)q(orted)16
1787 b(in)f(part)g(b)o(y)g(an)g(A)m(T&T)g(Bell)h(Lab)q(oratories)f(Ph.D.)f
1788 (sc)o(holarship)i(to)f(the)h(author,)f(b)o(y)g(a)g(Presiden)o(tial)0
1789 2304 y(Y)m(oung)10 b(In)o(v)o(estigator)g(Aw)o(ard)h(to)f(Professor)i
1790 (Rob)q(ert)f(C.)f(Berwic)o(k)h(under)g(National)f(Science)i(F)m
1791 (oundation)d(Gran)o(t)h(DCR{)0 2353 y(85552543,)f(b)o(y)j(a)f(gran)o(t)
1792 g(from)e(the)j(Siemens)f(Corp)q(oration,)g(and)g(b)o(y)h(the)g(Kap)q
1793 (or)f(F)m(amily)e(F)m(oundation.)15 b(Also)d(supp)q(orted)0
1794 2403 y(in)h(part)h(b)o(y)f(AR)o(O)g(gran)o(t)h(D)o(AAL)f(03{89{C{0031,)
1795 d(b)o(y)j(D)o(ARP)m(A)g(gran)o(t)g(N00014{90{J{1863,)d(b)o(y)k(NSF)f
1796 (gran)o(t)h(IRI)f(90{)0 2453 y(16592,)f(and)i(b)o(y)g(Ben)g(F)m
1797 (ranklin)f(gran)o(t)h(91S.3078C{1)57 2488 y Fp(y)75 2503
1798 y Fo(Supp)q(orted)k(in)e(part)i(b)o(y)e(the)i(Adv)n(anced)f(Researc)o
1799 (h)i(Pro)r(jects)f(Agency)g(of)e(the)i(Departmen)o(t)f(of)f(Defense)i
1800 (under)0 2553 y(O\016ce)d(of)e(Na)o(v)n(al)f(Researc)o(h)j(con)o(tract)
1801 g(N00014-91-J-4038.)948 2798 y Fn(1)p eop
1802 %%Page: 2 2
1803 2 1 bop 0 -37 a Fm(1)83 b(In)n(tro)r(duction)0 73 y Fn(Nondeterminism)
1804 14 b(is)k(a)g(useful)g(programming)e(paradigm)i(p)q(opularized)g(b)o(y)
1805 f Fl(Pr)o(olog)o Fn(.)26 b(It)18 b(has)h(long)0 133 y(b)q(een)13
1806 b(established)h(in)f(programming)f(language)i(folklore)f(that)h
1807 (nondeterminism)c(simpli\014es)h(the)j(task)0 193 y(of)19
1808 b(writing)g(com)o(binatorial)e(searc)o(h)h(programs.)29
1809 b(While)17 b(straigh)o(tforw)o(ard)j(blind)e(searc)o(h)h(tec)o(hniques)
1810 0 253 y(normally)c(asso)q(ciated)j(with)f(nondeterministic)e
1811 (programming)g(ma)o(y)h(not)h(yield)f(acceptable)g(p)q(erfor-)0
1812 314 y(mance,)f(nonetheless)i(the)f(simple)f(task)i(of)g(sp)q(ecifying)f
1813 (a)i(com)o(binatorial)d(searc)o(h)h(space,)h(for)g(smaller)0
1814 374 y(more)11 b(tractable)h(problems,)f(is)h(almost)f(alw)o(a)o(ys)h
1815 (easier)g(when)g(one)h(a)o(v)m(ails)f(oneself)f(of)i(nondeterministic)0
1816 434 y(constructs)k(than)f(when)h(one)f(uses)h(more)e(con)o(v)o(en)o
1817 (tional)f(programming)h(tec)o(hniques.)73 494 y(Nondeterminism)d(ho)o
1818 (w)o(ev)o(er,)h(need)i(not)h(remain)e(the)h(sole)g(pro)o(vince)f(of)i
1819 (logic)f(programming)f(lan-)0 554 y(guages.)30 b(An)o(y)17
1820 b(programming)h(language)h(can)g(b)q(e)g(extended)e(to)j(supp)q(ort)f
1821 (nondeterministic)d(searc)o(h)0 615 y(with)d(the)f(addition)h(of)h(t)o
1822 (w)o(o)e(new)h(constructs:)20 b(a)13 b(c)o(hoice)f(p)q(oin)o(t)h(op)q
1823 (erator)h(and)g(a)f(failure)f(op)q(erator.)21 b(W)l(e)0
1824 675 y(ha)o(v)o(e)14 b(done)h(precisely)e(this)i(for)g
1825 Fl(Lisp)o Fn(.)21 b(This)15 b(pap)q(er)g(describ)q(es)g
1826 Fl(Screamer)p Fn(,)g(our)g(implem)o(en)o(tati)o(on)e(of)0
1827 735 y(nondeterministic)j Fl(Common)i(Lisp)p Fn(.)28 b(Nondeterministic)
1828 16 b Fl(Lisp)i Fn(is)g(not)h(new)g(\(cf.)f(McCarth)o(y)g(1963,)0
1829 795 y(Clinger)f(1982,)i(Chapman)f(1985,)h(Zabih)f(1987,)h(Zabih)f(et)f
1830 (al.)h(1987,)h(Ha)o(ynes)e(1987\).)27 b(What)18 b(is)g(new)0
1831 855 y(with)23 b(our)h(w)o(ork)f(ho)o(w)o(ev)o(er,)h(is)f(a)h(p)q
1832 (ortable)g(and)f(e\016cien)o(t)f(implem)o(en)n(tation.)40
1833 b(Most)24 b(prior)f(imple-)0 916 y(men)o(tations)e(w)o(ere)h(complete)f
1834 (custom)g(impleme)o(n)o(tations)f(of)j(a)g(nondeterministic)d(ev)m
1835 (aluator.)41 b(In)0 976 y(con)o(trast,)25 b Fl(Screamer)e
1836 Fn(is)g(implem)o(en)o(ted)d(as)k(a)f(fully)f(p)q(ortable)i(macro)e(pac)
1837 o(k)m(age)i(whic)o(h)e(can)i(run)0 1036 y(under)18 b(an)o(y)g(implem)o
1838 (e)o(n)o(tation)d(of)k Fl(Common)f(Lisp)p Fn(.)26 b(This)18
1839 b(allo)o(ws)g Fl(Screamer)g Fn(programs)g(to)g(in)o(ter-)0
1840 1096 y(op)q(erate)f(in)g(the)g(same)e(en)o(vironmen)o(t)f(as)k(other)f
1841 Fl(Common)h(Lisp)f Fn(programs)g(and)g(to)g(lev)o(erage)f(o\013)i(of)0
1842 1156 y(the)f(ric)o(h)g(set)g(of)h(programming)e(language)i(features)f
1843 (and)h(the)f(comprehensiv)o(e)e(programming)h(en)o(vi-)0
1844 1217 y(ronmen)o(ts)d(a)o(v)m(ailable)g(with)h Fl(Common)19
1845 b(Lisp)o Fn(.)i(F)l(urthermore|for)12 b(reasons)k(to)e(b)q(e)g
1846 (discussed)h(later)e(in)0 1277 y(the)k(pap)q(er|prior)g(implem)o(en)n
1847 (tations)e(w)o(ere)h(ine\016cien)o(t.)21 b(This)c(ine\016ciency)d
1848 (precluded)i(using)h(these)0 1337 y(implem)o(en)o(tati)o(ons)h(for)h
1849 (practical)g(programming.)29 b Fl(Screamer)19 b Fn(on)h(the)f(other)h
1850 (hand,)g(has)g(b)q(een)f(in)0 1397 y(regular)d(use)h(b)o(y)e(n)o
1851 (umerous)h(p)q(eople)g(for)g(sev)o(eral)g(y)o(ears)g(no)o(w,)g(b)q(oth)
1852 h(as)g(a)g(basis)g(for)f(teac)o(hing)g(AI)f(and)0 1457
1853 y(as)h(a)f(substrate)g(supp)q(orting)i(curren)o(t)d(AI)g(researc)o(h.)
1854 20 b(This)15 b(pap)q(er)g(fo)q(cuses)h(on)f(three)f(topics.)21
1855 b(First,)14 b(it)0 1518 y(prop)q(oses)k(nondeterminism)c(as)j(a)g
1856 (useful)f(and)i Fk(expr)n(essive)f Fn(construct)g(whic)o(h)f
1857 (encourages)h(a)g(simpler)0 1578 y(and)e(clearer)e(programming)g(st)o
1858 (yle)g(in)g Fl(Lisp)p Fn(.)21 b(W)l(e)14 b(will)f(attempt)g(to)h
1859 (illustrate)f(this)h(via)g(n)o(umerous)f(ex-)0 1638 y(amples.)23
1860 b(Second,)17 b(it)g(con)o(trasts)h(nondeterministic)d
1861 Fl(Lisp)i Fn(with)g Fl(Pr)o(olog)o Fn(,)g(illustrating)g(some)f(w)o(a)o
1862 (ys)0 1698 y(that)21 b(the)f(former)f(is)h(more)f(expressiv)o(e)g(than)
1863 i(the)f(latter.)33 b(Finally)l(,)19 b(it)h(discusses)h(the)f
1864 (compilation)0 1758 y(tec)o(hniques)15 b(whic)o(h)g(allo)o(w)h
1865 Fl(Screamer)h Fn(to)f(generate)g(e\016cien)o(t)f(co)q(de.)0
1866 1925 y Fm(2)83 b(Nondeterministic)25 b(Lisp)0 2034 y
1867 Fn(A)o(t)10 b(its)h(core,)h Fl(Screamer)f Fn(adds)h(only)f(t)o(w)o(o)g
1868 (new)g(constructs)g(to)h Fl(Common)18 b(Lisp)o Fn(.)i(The)11
1869 b(macro)f Fj(either)0 2094 y Fn(nondeterministically)16
1870 b(ev)m(aluates)j(one)h(of)g(an)g(arbitrary)f(n)o(um)o(b)q(er)f(of)i
1871 (sub)q(expressions)g(and)g(returns)0 2155 y(the)f(result.)30
1872 b(Op)q(erationally)l(,)19 b(this)g(can)h(b)q(e)f(view)o(ed)f(as)i(in)o
1873 (tro)q(ducing)f(a)h(c)o(hoice-p)q(oin)o(t.)29 b(The)19
1874 b(expres-)0 2215 y(sion)k Fj(\(either)g Fi(e)335 2222
1875 y Fh(1)380 2215 y Fi(e)403 2222 y Fh(2)430 2215 y Fi(:)8
1876 b(:)g(:)g(e)519 2222 y Fg(n)542 2215 y Fj(\))23 b Fn(\014rst)g(ev)m
1877 (aluates)g Fi(e)938 2222 y Fh(1)980 2215 y Fn(and)g(returns)g(its)g
1878 (result.)41 b(If)22 b(the)h(computation)0 2275 y(fails|either)14
1879 b(during)h(the)h(ev)m(aluation)f(of)h Fi(e)820 2282 y
1880 Fh(1)855 2275 y Fn(or)g(during)f(subsequen)o(t)g(computation)g(using)h
1881 (the)f(v)m(alue)0 2335 y(pro)q(duced)k(b)o(y)f Fi(e)308
1882 2342 y Fh(1)327 2335 y Fn(|the)g(computation)g(bac)o(ktrac)o(ks)f(to)i
1883 (ev)m(aluate)f Fi(e)1270 2342 y Fh(2)1308 2335 y Fn(and)h(return)f(its)
1884 g(v)m(alue)g(instead.)0 2395 y(F)l(ailures)g(are)h(in)o(tro)q(duced)f
1885 (b)o(y)h(calling)f(the)g(function)h Fj(fail)p Fn(,)f(the)g(second)h
1886 (primitiv)o(e)c(construct)k(pro-)0 2456 y(vided)j(b)o(y)g
1887 Fl(Screamer)p Fn(.)41 b(Rep)q(eated)22 b(failures)g(cause)h(the)f(ev)m
1888 (aluation)h(of)g(subsequen)o(t)g(sub)q(expres-)0 2516
1889 y(sions)16 b(in)f(the)h(dynamically)d(nested)i Fj(either)f
1890 Fn(expression)h(un)o(til)f(no)j(further)e(sub)q(expressions)h(remain.)0
1891 2576 y(Choice-p)q(oin)o(ts)23 b(are)g(dynamically)e(nested.)42
1892 b(F)l(ailing)22 b(to)i(a)f(c)o(hoice-p)q(oin)o(t)f(whose)i(alternativ)o
1893 (es)e(are)0 2636 y(exhausted)16 b(will)f(propagate)j(to)f(the)f(next)f
1894 (most)h(recen)o(t)f(c)o(hoice-p)q(oin)o(t.)948 2798 y(2)p
1895 eop
1896 %%Page: 3 3
1897 3 2 bop 73 -37 a Fn(The)13 b(utilit)o(y)d(of)j(these)f(t)o(w)o(o)h
1898 (constructs)g(is)f(illustrated)g(b)o(y)g(the)g(follo)o(wing)g(example.)
1899 18 b(The)12 b(follo)o(wing)0 24 y(function)j(nondeterministically)d
1900 (returns)j(an)g(in)o(teger)f(b)q(et)o(w)o(een)h(the)g(giv)o(en)f(b)q
1901 (ounds.)22 b(\(This)15 b(function)0 84 y(is)h(so)h(ubiquitous)f(that)h
1902 (it)e(is)i(built)e(in)o(to)h Fl(Screamer)p Fn(.\))25
1903 184 y Fj(\(defun)23 b(an-integer-)o(bet)o(we)o(en)f(\(low)j(high\))51
1904 244 y(\(if)f(\(>)h(low)g(high\))e(\(fail\)\))51 304 y(\(either)g(low)h
1905 (\(an-intege)o(r-b)o(etw)o(een)e(\(1+)i(low\))g(high\)\)\))0
1906 403 y Fn(Giv)o(en)e(the)h(nondeterministic)d(function)j
1907 Fj(an-integer-)o(bet)o(wee)o(n)p Fn(,)e(one)j(can)f(write)f(the)h
1908 (follo)o(wing)0 463 y(pro)q(cedure)16 b(to)h(\014nd)f(Pythagorean)i
1909 (triples.)25 560 y Fj(\(defun)23 b(pythagorean)o(-tr)o(ip)o(les)f
1910 (\(n\))51 621 y(\(all-valu)o(es)76 681 y(\(let)i(\(\(a)h(\(an-intege)o
1911 (r-)o(bet)o(wee)o(n)e(1)i(n\)\))230 741 y(\(b)g(\(an-intege)o(r-)o(bet)
1912 o(wee)o(n)e(1)i(n\)\))230 801 y(\(c)g(\(an-intege)o(r-)o(bet)o(wee)o(n)
1913 e(1)i(n\)\)\))102 861 y(\(unless)e(\(=)i(\(+)g(\(*)g(a)g(a\))g(\(*)g(b)
1914 g(b\)\))f(\(*)h(c)h(c\)\))e(\(fail\)\))102 922 y(\(list)g(a)h(b)g
1915 (c\)\)\)\))0 1020 y Fn(This)c(pro)q(cedure)h(deterministic)o(ally)c
1916 (returns)j(a)h(list)e(of)i(all)f(Pythagorean)h(triples)f(of)g(in)o
1917 (tegers)g(b)q(e-)0 1080 y(t)o(w)o(een)f(1)i(and)g Fi(n)p
1918 Fn(.)37 b(This)22 b(example)d(in)o(tro)q(duces)i Fj(all-values)p
1919 Fn(,)e(another)j(primitiv)o(e)c(construct)j(pro-)0 1140
1920 y(vided)f(b)o(y)h Fl(Screamer)p Fn(.)35 b Fj(All-values)17
1921 b Fn(rep)q(eatedly)j(ev)m(aluates)h(the)g(nondeterministic)d
1922 (expression)0 1200 y(in)j(its)g(b)q(o)q(dy)i(gathering)f(all)f(of)h
1923 (its)f(v)m(alues)h(in)o(to)f(a)h(list)e(whic)o(h)h(is)h(returned)f
1924 (deterministic)o(ally)-5 b(.)34 b(It)0 1261 y(is)20 b(th)o(us)g
1925 (analogous)i(to)e(the)g Fj(bag-of)e Fn(primitiv)o(e)e(in)k
1926 Fl(Pr)o(olog)o Fn(.)33 b Fl(Screamer)20 b Fn(also)g(pro)o(vides)g(a)g
1927 (sim-)0 1321 y(ilar)g(primitiv)o(e,)e Fj(one-value)p
1928 Fn(,)g(whic)o(h)i(deterministical)o(ly)d(returns)k(only)g(the)f
1929 (\014rst)h(v)m(alue)f(computed)0 1381 y(b)o(y)d(its)f(nondeterministic)
1930 f(b)q(o)q(dy)l(.)626 1363 y Fh(1)670 1381 y Fj(One-value)f
1931 Fn(is)j(similar)e(in)i(man)o(y)f(w)o(a)o(ys)h(to)g(the)g(cut)g
1932 (primitiv)o(e)c(in)0 1441 y Fl(Pr)o(olog)o Fn(.)73 1501
1933 y(The)f(previous)g(example)e(illustrates)h(a)h(t)o(ypical)f
1934 (nondeterministic)e(programming)i(clic)o(h)o(\023)-23
1935 b(e,)10 b(namely)0 1562 y Ff(generate-and-test)p Fn(.)29
1936 b(The)19 b(calls)f(to)h Fj(an-integer)o(-b)o(etw)o(een)c
1937 Fn(constitute)j(the)h(generator)1684 1543 y Fh(2)1723
1938 1562 y Fn(while)e(the)0 1622 y(expression)25 1723 y Fj(\(unless)23
1939 b Fi(:)8 b(:)g(:)25 b Fj(\(fail\)\))0 1825 y Fn(constitutes)c(the)g
1940 (test.)35 b(While)20 b(it)g(is)h(easy)g(to)g(form)o(ulate)f
1941 (generate-and-test)h(pro)q(cedures)h(in)e(non-)0 1885
1942 y(deterministic)14 b Fl(Lisp)o Fn(,)j(suc)o(h)g(pro)q(cedures)h(are)f
1943 (often)g(ine\016cien)o(t.)22 b(Nondeterministic)13 b(constructs)18
1944 b(lik)o(e)0 1946 y Fj(either)d Fn(and)j Fj(fail)p Fn(,)d(ho)o(w)o(ev)o
1945 (er,)h(are)h(more)f(general,)h(and)h(supp)q(ort)g(man)o(y)e(other)h
1946 (more)f(e\016cien)o(t)f(pro-)0 2006 y(gramming)21 b(clic)o(h)o(\023)-23
1947 b(es.)40 b(Consider)23 b(for)g(example,)f(the)h Fi(N)5
1948 b Fn(-Queens)23 b(problem.)40 b(A)22 b(generate-and-test)0
1949 2066 y(solution)c(w)o(ould)g(\014rst)g(generate)f(arrangemen)o(ts)g
1950 (con)o(taining)h Fi(N)23 b Fn(queens)17 b(and)i(then)e(\014lter)g(out)i
1951 (those)0 2126 y(arrangemen)o(ts)e(where)g(some)f(queen)h(w)o(as)h
1952 (under)g(attac)o(k.)25 b(A)17 b(more)f(e\016cien)o(t)f(solution)j(w)o
1953 (ould)g(in)o(ter-)0 2186 y(lea)o(v)o(e)g(the)h(generate)g(and)h(test)f
1954 (phases,)h(testing)f(eac)o(h)g(queen)g(for)g(attac)o(ks)h(as)g(it)e(w)o
1955 (as)i(placed.)30 b(The)0 2247 y(co)q(de)16 b(in)g(\014gure)h(1)f
1956 (illustrates)g(ho)o(w)h(this)f(can)g(b)q(e)g(form)o(ulated)f(in)h
1957 (nondeterministic)d Fl(Lisp)p Fn(.)p 0 2290 768 2 v 56
1958 2321 a Fe(1)75 2336 y Fd(Screamer)k Fo(adopts)f(a)g(depth-\014rst)i
1959 (left-to-righ)o(t)d(tra)o(v)o(ersal)h(of)g(the)h(searc)o(h)g(tree)h
1960 (when)e(en)o(umerating)g(v)n(alues)g(of)0 2386 y(nondeterministic)g
1961 (expressions.)26 b(Th)o(us)17 b Fc(all-values)d Fo(and)i
1962 Fc(one-value)e Fo(ha)o(v)o(e)i(w)o(ell-de\014ned)g(denotations.)25
1963 b(F)m(urther-)0 2436 y(more,)10 b(users)j(can)e(\(and)h(often)f(m)o
1964 (ust\))f(rely)h(on)g(div)o(ergence)i(prop)q(erties)f(of)f(the)h(searc)o
1965 (h)g(order)g(when)g(writing)e Fd(Screamer)0 2485 y Fo(programs)j(whic)o
1966 (h)g(sp)q(ecify)i(in\014nite)f(searc)o(h)h(trees.)56
1967 2520 y Fe(2)75 2535 y Fo(W)m(e)e(adopt)g(the)i(\(unenforced\))g(con)o
1968 (v)o(en)o(tion)e(that)h(the)g(names)f(of)g(all)f(generator)i(functions)
1969 g(b)q(egin)g(with)f(the)h(pre\014x)0 2585 y Fc(a-)f Fo(or)h
1970 Fc(an-)p Fo(.)948 2798 y Fn(3)p eop
1971 %%Page: 4 4
1972 4 3 bop 190 -31 1540 2 v 190 837 2 868 v 229 24 a Fj(\(defun)24
1973 b(attacks?)f(\(qi)h(qj)h(distance\))255 84 y(\(or)g(\(=)g(qi)f(qj\))h
1974 (\(=)g(\(abs)f(\(-)h(qi)g(qj\)\))f(distance\)\))o(\))229
1975 204 y(\(defun)g(check-quee)o(ns)e(\(queen)i(queens)f(&optional)f
1976 (\(distance)h(1\)\))255 265 y(\(unless)g(\(null)h(queens\))281
1977 325 y(\(if)g(\(attacks?)f(queen)g(\(first)h(queens\))f(distance\))f
1978 (\(fail\)\))281 385 y(\(check-qu)o(een)o(s)h(queen)g(\(rest)h(queens\))
1979 f(\(1+)i(distance\))o(\)\)\))229 505 y(\(defun)f(n-queens)f(\(n)h
1980 (&optional)f(queens\))255 566 y(\(if)i(\(=)g(\(length)e(queens\))g(n\))
1981 358 626 y(queens)358 686 y(\(let)h(\(\(queen)f(\(an-intege)o(r-)o(bet)o
1982 (wee)o(n)g(1)i(n\)\)\))383 746 y(\(check-quee)o(ns)d(queen)i(queens\))
1983 383 806 y(\(n-queens)f(n)i(\(cons)f(queen)f(queens\)\)\)\)\))p
1984 1728 837 V 190 839 1540 2 v 297 970 a Fr(Figure)15 b(1:)20
1985 b(A)15 b Fq(Screamer)h Fr(program)e(for)h(solving)h(the)f
1986 Fb(N)5 b Fr(-Queens)16 b(problem.)0 1103 y Fm(3)83 b(Com)n(binatorial)
1987 26 b(Programming)0 1212 y Fn(Man)o(y)19 b(programming)f(tasks)j(in)o(v)
1988 o(olv)o(e)c(en)o(umerating)h(the)h(elemen)o(ts)e(of)j(a)g(com)o
1989 (binatorial)e(structure)0 1273 y(suc)o(h)24 b(as)h(the)e(subsets)i(or)g
1990 (partitions)f(of)g(a)h(giv)o(en)e(set.)44 b(While)24
1991 b(en)o(umerating)e(large)i(com)o(binato-)0 1333 y(rial)15
1992 b(structures)f(ma)o(y)g(b)q(e)h(in)o(tractable,)f(man)o(y)g(practical)g
1993 (programming)f(tasks)j(require)e(en)o(umerating)0 1393
1994 y(small)i(com)o(binatorial)f(structures.)24 b(F)l(or)17
1995 b(suc)o(h)g(tasks,)g(the)g(prime)e(problem)h(is)h(one)g(of)g
1996 (programming)0 1453 y(con)o(v)o(enience,)12 b(not)k(e\016ciency)l(.)i
1997 (W)l(riting)d(correct)f(com)o(binatorial)f(programs)i(can)g(b)q(e)g(an)
1998 g(arduous,)h(er-)0 1513 y(ror)f(prone)g(task.)21 b(W)l(e)15
1999 b(claim)d(that)j(nondeterministic)d Fl(Lisp)j Fn(allo)o(ws)g(more)e
2000 (transparen)o(t)i(sp)q(eci\014cation)0 1574 y(of)20 b(com)o(binatorial)
2001 f(programs)h(yielding)f(programs)h(whic)o(h)f(are)h(easier)g(to)g
2002 (write,)g(understand,)h(and)0 1634 y(debug)16 b(than)h(equiv)m(alen)o
2003 (t)d(deterministic)f(functional)j(programs.)21 b(W)l(e)16
2004 b(o\013er)g(the)g(follo)o(wing)g(examples)0 1694 y(in)g(supp)q(ort)h
2005 (of)g(this)f(claim.)73 1754 y(Consider)d(the)f(task)h(of)g(en)o
2006 (umerating)e(the)i(p)q(o)o(w)o(er)f(set)h(of)g(a)g(giv)o(en)f(set.)20
2007 b(This)12 b(can)h(b)q(e)g(accomplished)0 1814 y(b)o(y)j(the)g(follo)o
2008 (wing)g(function)g(whic)o(h)f(nondeterministically)e(returns)j(a)h
2009 (subset)f(of)h(a)g(giv)o(en)e(set.)25 1899 y Fj(\(defun)23
2010 b(a-subset-of)f(\(x\))51 1959 y(\(if)i(\(null)g(x\))153
2011 2020 y(nil)153 2080 y(\(let)g(\(\(y)h(\(a-subset)o(-of)d(\(rest)i
2012 (x\)\)\)\))g(\(either)f(\(cons)g(\(first)h(x\))h(y\))g(y\)\)\)\))0
2013 2166 y Fn(Giv)o(en)15 b(the)h(ab)q(o)o(v)o(e)g(function,)g(the)g(p)q(o)
2014 o(w)o(er)g(set)g(of)h Fi(x)f Fn(can)g(b)q(e)h(computed)e(b)o(y)g(ev)m
2015 (aluating)25 2255 y Fj(\(all-value)o(s)23 b(\(a-subset)o(-o)o(f)g
2016 Fi(x)p Fj(\)\).)0 2344 y Fn(Or)12 b(consider)g(the)h(task)f(of)h(en)o
2017 (umerating)e(the)h(set)g(of)h(all)e(partitions)i(of)g(a)g(giv)o(en)e
2018 (set.)20 b(T)l(o)13 b(solv)o(e)e(this)i(task)0 2404 y(w)o(e)h(\014rst)h
2019 (m)o(ust)f(de\014ne)g(the)g(follo)o(wing)h(function)f(whic)o(h)g
2020 (nondeterministically)d(returns)k(a)g(mem)o(b)q(er)d(of)0
2021 2464 y(a)17 b(giv)o(en)e(set.)21 b(\(Again,)16 b(this)g(function)g(is)g
2022 (so)h(ubiquitous)f(that)h(it)e(is)i(built)e(in)o(to)h
2023 Fl(Screamer)p Fn(.\))25 2552 y Fj(\(defun)23 b(a-member-of)f(\(x\))51
2024 2612 y(\(if)i(\(null)g(x\))h(\(fail\)\))51 2672 y(\(either)e(\(first)g
2025 (x\))i(\(a-member-)o(of)d(\(rest)i(x\)\)\)\))948 2798
2026 y Fn(4)p eop
2027 %%Page: 5 5
2028 5 4 bop 0 -37 a Fn(As)15 b(an)g(aside,)g Fj(a-member-)o(of)d
2029 Fn(and)j Fj(all-values)c Fn(are)k(duals)h(of)f(eac)o(h)f(other.)21
2030 b Fj(A-member-o)o(f)12 b Fn(con)o(v)o(erts)0 24 y(a)23
2031 b(spatial)f(represen)o(tation)g(of)h(a)g(set)f(of)h(c)o(hoices)e(in)o
2032 (to)i(a)f(temp)q(oral)g(one)h(based)g(on)f(bac)o(ktrac)o(king,)0
2033 84 y(while)e Fj(all-values)e Fn(con)o(v)o(erts)i(the)i(temp)q(oral)e
2034 (bac)o(ktrac)o(king)g(represen)o(tation)h(of)h(a)f(set)g(of)h(c)o
2035 (hoices)0 144 y(in)o(to)d(a)g(list)f(represen)o(ted)g(spatially)l(.)29
2036 b(Giv)o(en)17 b(the)i(function)g Fj(a-member-o)o(f)p
2037 Fn(,)d(the)j(follo)o(wing)f(function)0 204 y(nondeterministically)13
2038 b(returns)j(a)h(partition)f(of)g(a)h(giv)o(en)e(set.)25
2039 279 y Fj(\(defun)23 b(a-partition)o(-of)f(\(x\))51 339
2040 y(\(if)i(\(null)g(x\))153 400 y(nil)153 460 y(\(let)g(\(\(y)h
2041 (\(a-partit)o(ion)o(-of)d(\(rest)i(x\)\)\)\))179 520
2042 y(\(either)f(\(cons)h(\(list)f(\(first)h(x\)\))g(y\))384
2043 580 y(\(let)g(\(\(z)g(\(a-member-o)o(f)f(y\)\)\))409
2044 640 y(\(cons)h(\(cons)g(\(first)f(x\))i(z\))563 701 y(\(remove)e(z)j(y)
2045 f(:test)f(#'eq)g(:count)f(1\)\)\)\)\)\)\))0 776 y Fn(This)14
2046 b(function)g(op)q(erates)g(b)o(y)g(taking)g(the)f(elemen)o(ts)e(of)j
2047 Fi(x)p Fn(,)g(one)g(at)g(a)g(time,)e(and)j(nondeterministicall)o(y)0
2048 837 y(either)g(placing)h(them)f(in)h(a)g(new)h(partition)f(or)g(in)g
2049 (one)h(of)f(the)g(existing)g(partitions.)0 999 y Fm(4)83
2050 b(Lo)r(cal)27 b(Side)g(E\013ects)0 1109 y Fn(All)13 b(of)h(the)g
2051 (examples)f(presen)o(ted)g(so)i(far)g(could)f(ha)o(v)o(e)f(b)q(een)h
2052 (written)g(in)g Fl(Pr)o(olog)n Fn(.)21 b(While)13 b(w)o(e)h(b)q(eliev)o
2053 (e)0 1169 y(that)g(nondeterministic)c(functional)j(programs)h
2054 (demonstrate)e(their)h(in)o(ten)o(t)f(more)g(clearly)g(than)i(their)0
2055 1229 y(logic)20 b(program)h(coun)o(terparts,)h(the)e(primitiv)o(es)e
2056 (added)j(b)o(y)f Fl(Screamer)p Fn(,)i(namely)d Fj(either)p
2057 Fn(,)g Fj(fail)p Fn(,)0 1289 y Fj(all-values)o Fn(,)e
2058 Fj(one-value)p Fn(,)g(and)j Fj(for-effect)o(s)d Fn(all)i(ha)o(v)o(e)g
2059 (analogs)i(in)e Fl(Pr)o(olog)n Fn(.)32 b(In)19 b(this)g(section)0
2060 1349 y(w)o(e)h(discuss)g(one)g(further)f(primitiv)o(e)e(construct)j
2061 (added)g(b)o(y)g Fl(Screamer)g Fn(whic)o(h)f(has)i(no)f(analog)h(in)0
2062 1410 y Fl(Pr)o(olog)o Fn(:)g(lo)q(cal)16 b(side)g(e\013ects.)73
2063 1470 y(Adding)e(nondeterminism)c(to)k Fl(Lisp)f Fn(raises)h(an)g(imp)q
2064 (ortan)o(t)f(design)h(decision:)19 b(should)14 b(side)f(e\013ects)0
2065 1530 y(b)q(e)22 b(undone)h(up)q(on)g(bac)o(ktrac)o(king?)37
2066 b(It)22 b(turns)g(out)h(that)f(it)g(is)g(useful)f(to)h(ha)o(v)o(e)g(t)o
2067 (w)o(o)f(t)o(yp)q(es)h(of)g(side)0 1590 y(e\013ects,)j(those)f(that)g
2068 (are)f(undone)h(up)q(on)h(bac)o(ktrac)o(king)d(and)j(those)f(that)g
2069 (are)f(not.)44 b Fl(Screamer)0 1650 y Fn(supp)q(orts)17
2070 b(b)q(oth)g(t)o(yp)q(es)e(under)h(user)g(con)o(trol.)k(The)c(former)e
2071 (are)i(termed)e Ff(lo)q(cal)i Fn(side)f(e\013ects)g(while)g(the)0
2072 1711 y(latter)d(are)g(termed)e Ff(global)p Fn(.)21 b(Global)12
2073 b(side)g(e\013ects)g(are)g(useful)g(for)g(gathering)h(statistics)f(ab)q
2074 (out)i(a)e(searc)o(h)0 1771 y(pro)q(cess,)21 b(or)f(for)g(passing)h
2075 (information)e(b)q(et)o(w)o(een)g(di\013eren)o(t)g(branc)o(hes)g(of)h
2076 (a)h(searc)o(h)e(tree)g(that)i(ma)o(y)0 1831 y(aid)15
2077 b(in)g(pruning)h(future)f(branc)o(hes.)21 b(This)15 b(section)g(will)f
2078 (demonstrate)h(the)g(expressiv)o(e)e(programming)0 1891
2079 y(p)q(o)o(w)o(er)j(a\013orded)i(b)o(y)d(lo)q(cal)h(side)g(e\013ects.)73
2080 1951 y(Consider)d(the)g(problem)e(of)i(en)o(umerating)e(all)i(simple)d
2081 (paths)k(b)q(et)o(w)o(een)e(t)o(w)o(o)h(v)o(ertices)e(in)h(a)h
2082 (directed)0 2011 y(graph.)23 b(A)16 b(simple)e(path)j(is)g(one)g(whic)o
2083 (h)e(do)q(es)j(not)f(visit)e(an)o(y)i(v)o(ertex)e(more)g(than)i(once.)
2084 22 b(Solving)16 b(this)0 2072 y(task)21 b(will)e(require)g(k)o(eeping)g
2085 (trac)o(k)h(of)g(whic)o(h)g(v)o(ertices)e(ha)o(v)o(e)i(b)q(een)g
2086 (visited)f(in)h(the)g(path)h(curren)o(tly)0 2132 y(b)q(eing)12
2087 b(constructed.)19 b(This)12 b(can)g(b)q(e)g(accomplished)e(most)g
2088 (e\016cien)o(tly)f(b)o(y)i(asso)q(ciating)i(a)f Fj(visited?)d
2089 Fn(\015ag)0 2192 y(with)16 b(eac)o(h)g(v)o(ertex.)21
2090 b(P)o(aths)c(are)g(en)o(umerated)d(b)o(y)i(starting)h(with)g(the)f
2091 (empt)o(y)e(path)j(emanating)f(from)0 2252 y(the)23 b(source)h(v)o
2092 (ertex)e(and)j(con)o(tin)o(ually)d(augmen)o(ting)h(this)g(path)h(with)g
2093 (a)g(neigh)o(b)q(or)g(of)g(the)g(v)o(ertex)0 2312 y(curren)o(tly)14
2094 b(at)i(the)f(head)h(of)g(the)g(path,)f(un)o(til)g(the)g(path)i(con)o
2095 (tains)e(the)h(sink)f(v)o(ertex.)k(Cho)q(osing)f(whic)o(h)0
2096 2373 y(v)o(ertex)h(to)h(add)h(to)f(the)g(path)h(ma)o(y)d(b)q(e)i
2097 (nondeterministic)e(since)h(a)i(giv)o(en)e(v)o(ertex)f(ma)o(y)h(ha)o(v)
2098 o(e)g(more)0 2433 y(than)j(one)g(neigh)o(b)q(or.)38 b(As)22
2099 b(a)g(v)o(ertex)e(is)h(added)i(to)f(the)f(curren)o(t)g(path,)i(its)f
2100 Fj(visited?)c Fn(\015ag)23 b(is)f(set.)0 2493 y(A)d(path)h(cannot)h(b)q
2101 (e)e(augmen)o(ted)g(with)g(a)h(v)o(ertex)e(whose)j Fj(visited?)16
2102 b Fn(\015ag)21 b(is)e(already)h(set.)31 b(Setting)0 2553
2103 y(the)18 b Fj(visited?)e Fn(\015ag)j(m)o(ust)e(b)q(e)i(p)q(erformed)e
2104 (b)o(y)h(lo)q(cal)h(side)f(e\013ect)g(to)h(allo)o(w)f(prop)q(er)h(en)o
2105 (umeration)e(of)0 2613 y(alternate)c(paths)g(b)o(y)g(bac)o(ktrac)o
2106 (king.)19 b(The)13 b(ab)q(o)o(v)o(e)f(algorithm)g(is)h(captured)g(b)o
2107 (y)f(the)h(follo)o(wing)f(function)0 2674 y(whic)o(h)k
2108 (nondeterministicall)o(y)d(returns)k(a)f(simple)e(path)j(from)e(v)o
2109 (ertex)g Fi(u)h Fn(to)g Fi(v)r Fn(.)948 2798 y(5)p eop
2110 %%Page: 6 6
2111 6 5 bop 25 -44 a Fj(\(defstruct)22 b(\(node)i(\(:conc-na)o(me)e
2112 (nil\)\))i(next-nodes)e(\(visited?)g(nil\)\))25 76 y(\(defun)h
2113 (simple-path)f(\(u)j(v\))51 136 y(\(if)f(\(visited?)e(u\))j(\(fail\)\))
2114 51 196 y(\(local)e(\(setf)h(\(visited?)e(u\))j(t\)\))51
2115 257 y(\(either)e(\(progn)g(\(unless)g(\(eq)i(u)g(v\))g(\(fail\)\))e
2116 (\(list)h(u\)\))256 317 y(\(cons)f(u)j(\(simple-p)o(ath)c(\(a-member-)o
2117 (of)g(\(next-node)o(s)h(u\)\))h(v\)\)\)\))0 415 y Fn(The)18
2118 b(e\016ciency)f(of)h(this)h(algorithm)e(dep)q(ends)i(crucially)e(on)i
2119 (the)f(abilit)o(y)f(to)h(c)o(hec)o(k)f(and)i(up)q(date)g(the)0
2120 475 y Fj(visited?)g Fn(status)k(of)g(a)f(v)o(ertex)f(in)h(constan)o(t)g
2121 (time.)37 b(Without)22 b(lo)q(cal)g(side)g(e\013ects)g(this)g(could)g
2122 (b)q(e)0 536 y(done)15 b(in)f(linear)f(time,)f(b)o(y)i(passing)h
2123 (around)h(a)f(list)e(of)i(visited)e(v)o(ertices)g(and)h(con)o(tin)o
2124 (ually)f(c)o(hec)o(king)g(for)0 596 y(mem)o(b)q(ership)e(in)i(that)h
2125 (list,)g(or)g(in)f(logarithmic)f(time,)g(b)o(y)i(using)g(balanced)g
2126 (binary)f(trees)h(to)g(represen)o(t)0 656 y(the)21 b(visited)g(v)o
2127 (ertex)f(list,)h(but)h(not)g(in)f(constan)o(t)h(time.)35
2128 b(The)22 b(imp)q(ortan)o(t)e(p)q(oin)o(t)i(here)f(is)g(that)h(the)0
2129 716 y(solution)16 b(based)g(on)g(lo)q(cal)f(side)h(e\013ects)f(is)g(b)q
2130 (oth)i(more)d(e\016cien)o(t)f(and)k(more)d(transparen)o(t)i(than)g
2131 (either)0 776 y(solution)d(not)g(using)h(side)e(e\013ects.)20
2132 b Fl(Pr)o(olog)o Fn(|lac)o(king)11 b(the)i(capabilit)o(y)e(for)j(lo)q
2133 (cal)e(side)h(e\013ects|could)0 837 y(express)j(only)g(the)g(inelegan)o
2134 (t)f(solutions)i(not)g(using)f(side)g(e\013ects.)73 897
2135 y(One)j(ma)o(y)e(raise)i(an)g(ob)s(jection)f(to)i(the)e(ab)q(o)o(v)o(e)
2136 h(claim)e(that)i Fl(Pr)o(olog)f Fn(lac)o(ks)g(the)g(capabilit)o(y)g
2137 (for)0 957 y(lo)q(cal)g(side)g(e\013ects.)26 b(Uni\014cation)17
2138 b(of)i(logic)e(v)m(ariables)h(pro)o(vides)g(a)g(form)f(of)h(lo)q(cal)g
2139 (side)g(e\013ect.)26 b(Using)0 1017 y(extra-logical)16
2140 b(extensions)g(to)h Fl(Pr)o(olog)o Fn(,)f(one)h(could)f(implem)o(en)n
2141 (t)e(a)j Fj(visited?)c Fn(\015ag)18 b(as)f(an)g(un)o(b)q(ound)0
2142 1077 y(logic)f(v)m(ariable.)23 b(Binding)16 b(that)h(v)m(ariable)g(w)o
2143 (ould)g(set)f(the)h Fj(visited?)d Fn(\015ag,)j(while)f(c)o(hec)o(king)f
2144 (whether)0 1137 y(it)k(w)o(as)g(b)q(ound)i(could)e(b)q(e)g
2145 (accomplished)e(via)i(the)g(extra-logical)g Fj(var)f
2146 Fn(primitiv)o(e.)27 b(This)19 b(solution|)0 1198 y(while)j(of)h
2147 (dubious)g(clarit)o(y|still)c(do)q(es)24 b(not)f(a\013ord)g(the)g(full)
2148 e(generalit)o(y)h(of)h(lo)q(cal)f(side)g(e\013ects)g(in)0
2149 1258 y Fl(Screamer)p Fn(.)38 b Fl(Pr)o(olog)20 b Fn(logic)h(v)m
2150 (ariables)h(are)g(single)f(assignmen)o(t)g(while)f Fl(Screamer)i
2151 Fn(allo)o(ws)g(re-)0 1318 y(p)q(eated)16 b(lo)q(cal)g(side)g(e\013ects)
2152 f(to)h(the)g(same)f(v)m(ariable.)21 b(The)16 b(follo)o(wing)f(example)f
2153 (illustrates)h(the)h(utilit)o(y)0 1378 y(of)h(m)o(ultiple)c(assignmen)o
2154 (t)i(lo)q(cal)h(side)g(e\013ects.)73 1438 y(Let)22 b(us)h(de\014ne)f(a)
2155 g Fi(k)r Fn(-simple)f(path)i(as)f(one)h(whic)o(h)e(do)q(es)i(not)g(con)
2156 o(tain)f(an)o(y)g(v)o(ertex)f(more)f(than)0 1499 y Fi(k)i
2157 Fn(times.)32 b(Consider)20 b(the)g(task)h(of)g(en)o(umerating)d(all)i
2158 Fi(k)r Fn(-simple)e(paths)k(b)q(et)o(w)o(een)d(t)o(w)o(o)h(v)o(ertices)
2159 f(in)h(a)0 1559 y(graph)c(for)g(some)f(\014xed)g Fi(k)r
2160 Fn(.)21 b(This)15 b(can)h(b)q(e)g(accomplished)d(b)o(y)i(main)o
2161 (taining)f(a)i Fj(visits)d Fn(coun)o(t)j(for)g(eac)o(h)0
2162 1619 y(v)o(ertex)g(instead)i(of)g(a)g Fj(visited?)d Fn(\015ag,)j
2163 (incremen)o(ting)d(that)j(coun)o(t)g(eac)o(h)f(time)f(the)h(v)o(ertex)f
2164 (is)i(added)0 1679 y(to)f(the)g(path,)g(and)g(c)o(hec)o(king)e(that)i
2165 (the)g(coun)o(t)g(is)f(less)h(than)g Fi(k)i Fn(b)q(efore)e(adding)g(it)
2166 g(to)g(the)f(path.)24 b(This)0 1739 y(algorithm)15 b(is)h(illustrated)g
2167 (b)o(y)f(the)h(follo)o(wing)g(co)q(de)h(fragmen)o(t.)25
2168 1837 y Fj(\(defstruct)22 b(\(node)i(\(:conc-na)o(me)e(nil\)\))i
2169 (next-nodes)e(\(visits)h(0\)\))25 1957 y(\(defun)g(k-simple-pa)o(th)f
2170 (\(u)j(v)g(k\))51 2017 y(\(if)f(\(=)h(\(visits)e(u\))i(k\))g
2171 (\(fail\)\))51 2078 y(\(local)e(\(incf)h(\(visits)f(u\)\)\))51
2172 2138 y(\(either)g(\(progn)g(\(unless)g(\(eq)i(u)g(v\))g(\(fail\)\))e
2173 (\(list)h(u\)\))256 2198 y(\(cons)f(u)j(\(k-simple)o(-pa)o(th)c
2174 (\(a-member-)o(of)g(\(next-nodes)g(u\)\))j(v)g(k\)\)\)\))0
2175 2296 y Fn(Note)18 b(that)g(this)g(algorithm)f(will)g(require)f(m)o
2176 (ultiple)f(assignmen)o(t)i(lo)q(cal)h(side)f(e\013ects)h(to)g(the)g
2177 Fj(visits)0 2357 y Fn(coun)o(t)e(and)h(th)o(us)f(could)g(not)h(b)q(e)f
2178 (accomplished)f(as)i(e\016cien)o(tly)c(or)k(transparen)o(tly)f(in)g
2179 Fl(Pr)o(olog)n Fn(.)73 2417 y(Also)k(note)f(that|as)i(the)e(ab)q(o)o(v)
2180 o(e)h(examples)d(demonstrate|)p Fl(Screamer)i Fn(supp)q(orts)i(lo)q
2181 (cal)e(side)0 2477 y(e\013ects)14 b(not)h(only)f(to)h(v)m(ariables)g
2182 (but)f(also)h(to)g(slots)g(of)g(data)g(structures)g(created)f(b)o(y)g
2183 Fj(defstruct)o Fn(.)k(The)0 2537 y Fl(Screamer)i Fn(lo)q(cal)f(side)g
2184 (e\013ect)g(mec)o(hanism)d(is)k(pro)q(ductiv)o(e)e(in)h(that)h(it)f
2185 (applies)g(to)h(all)f(side)g(e\013ects)0 2597 y(whic)o(h)13
2186 b(can)h(b)q(e)g(in)o(tro)q(duced)g(with)g Fj(setf)e Fn(and)j
2187 Fj(setq)d Fn(including,)h(for)h(example,)e(side)i(e\013ects)f(p)q
2188 (erformed)0 2657 y(on)24 b(arra)o(y)g(elemen)o(ts,)e(hash)i(tables,)h
2189 (and)f(CLOS)h(instance)e(slots.)44 b(F)l(urthermore,)23
2190 b(a)h Fl(Screamer)948 2798 y Fn(6)p eop
2191 %%Page: 7 7
2192 7 6 bop 0 -37 a Fj(local)21 b Fn(declaration)i(declares)g(all)g(side)g
2193 (e\013ect)f(expressions)h(nested)g(lexically)e(in)i(its)g(b)q(o)q(dy)h
2194 (to)g(b)q(e)0 24 y(lo)q(cal,)e(including)e(those)i(in)o(tro)q(duced)f
2195 (implicitl)o(y)d(via)j(macros.)36 b(This)21 b(allo)o(ws)g(one)h(to)f
2196 (use)h(existing)0 84 y Fl(Common)c(Lisp)k Fn(iteration)g(macros|suc)o
2197 (h)e(as)j Fj(dolist)p Fn(|within)c(nondeterministic)h(expressions,)0
2198 144 y(simply)14 b(b)o(y)i(wrapping)i(a)f(call)e(to)i(the)f(iteration)g
2199 (macro)g(with)g Fj(local)f Fn(to)i(con)o(v)o(ert)e(the)h(side)g
2200 (e\013ects)h(to)0 204 y(the)h(iteration)g(v)m(ariable)f(in)o(to)h(lo)q
2201 (cal)g(ones.)28 b(Th)o(us)18 b(the)g(follo)o(wing)g(expression)g(tak)o
2202 (es)g(a)g(list)g(of)g(lists)g Fi(l)q Fn(,)0 264 y(and)f
2203 (nondeterministically)c(returns)j(a)g(list)g(con)o(taining)g(one)h
2204 (elemen)o(t)c(from)i(eac)o(h)h(list.)25 362 y Fj(\(let)24
2205 b(\(\(a)h(nil\)\))51 422 y(\(local)e(\(dolist)g(\(x)i(l\))g(\(push)f
2206 (\(a-member)o(-of)e(x\))j(a\)\)\))51 482 y(\(reverse)d(a\)\))73
2207 581 y Fn(This)g(all)g(p)q(oin)o(ts)g(to)g(a)g(metho)q(dological)f(bias)
2208 h(of)h(our)f(w)o(ork.)38 b Fl(Pr)o(olog)21 b Fn(and)h
2209 Fl(Common)c(Lisp)0 641 y Fn(pro)o(vide)23 b(orthogonal)i(sets)f(of)g
2210 (features.)44 b(On)24 b(one)g(hand,)i Fl(Pr)o(olog)d
2211 Fn(pro)o(vides)g(nondeterminism)o(,)0 701 y(uni\014cation,)28
2212 b(logic)d(v)m(ariables,)j(and)e(pattern)g(directed)e(in)o(v)o(o)q
2213 (cation,)k(useful)d(features)h(lac)o(king)e(in)0 761
2214 y Fl(Common)18 b(Lisp)p Fn(.)39 b(On)23 b(the)f(other)g(hand,)i
2215 Fl(Common)18 b(Lisp)k Fn(pro)o(vides)g(n)o(umerous)f(useful)h(features)
2216 0 821 y(lac)o(king)17 b(in)g Fl(Pr)o(olog)o Fn(,)h(most)f(notably)h
2217 (data)g(structures)g(and)g(iteration.)26 b(Rather)18
2218 b(than)g(arguing)h(for)0 881 y(the)13 b(merits)e(of)j(one)f(language)h
2219 (o)o(v)o(er)e(the)h(other,)g(a)h(language)g(merging)e(the)h(features)g
2220 (of)g(b)q(oth)h Fl(Pr)o(olog)0 942 y Fn(and)e Fl(Common)19
2221 b(Lisp)11 b Fn(w)o(ould)h(b)q(e)g(b)q(etter)f(than)h(either)f(in)g
2222 (isolation.)20 b(Suc)o(h)11 b(a)i(language)f(can)g(b)q(e)g(arriv)o(ed)0
2223 1002 y(at)j(either)f(b)o(y)h(adding)h(the)e(missing)g(features)h(of)g
2224 Fl(Common)k(Lisp)14 b Fn(in)o(to)h Fl(Pr)o(olog)f Fn(or)h(vice)f(v)o
2225 (ersa.)20 b(W)l(e)0 1062 y(ha)o(v)o(e)15 b(adopted)h(the)f(latter)g
2226 (tactic)g(in)g(our)h(w)o(ork.)21 b(A)15 b(k)o(ey)g(claim)e(whose)j(v)m
2227 (alidit)o(y)e(is)i(demonstrated)f(b)o(y)0 1122 y(our)h(w)o(ork)g(is)g
2228 (that)g(it)g(is)g(p)q(ossible)g(to)g(add)h(nondeterminism)12
2229 b(to)17 b Fl(Common)h(Lisp)d Fn(in)h(a)g(w)o(a)o(y)g(whic)o(h)f(is)0
2230 1182 y(fully)c(p)q(ortable)i(across)h(all)e Fl(Common)18
2231 b(Lisp)12 b Fn(implem)o(en)o(tations,)e(do)q(es)j(not)g(require)e(an)o
2232 (y)i(mo)q(di\014cation)0 1243 y(to)g(the)f(underlying)g(implem)o(e)o(n)
2233 o(tation,)e(and)j(do)q(es)g(not)g(su\013er)g(p)q(erformance)e(p)q
2234 (enalties.)20 b(The)12 b(next)g(sec-)0 1303 y(tion)g(illustrates)f(ho)o
2235 (w)h(this)f(is)h(accomplished.)17 b(A)12 b(companion)f(pap)q(er)h
2236 (\(Siskind)f(and)h(McAllester)d(1993\))0 1363 y(demonstrates)16
2237 b(ho)o(w)h(to)f(add)i(uni\014cation)e(and)h(logic)f(v)m(ariables|as)h
2238 (w)o(ell)e(as)i(a)g(complete)d(constrain)o(t)0 1423 y(logic)i
2239 (programming)f(pac)o(k)m(age|on)h(top)h(of)g(this)f(basic)g(facilit)o
2240 (y)e(supp)q(orting)k(nondeterminism)o(.)0 1590 y Fm(5)83
2241 b(Implemen)n(tation)0 1699 y Fn(In)15 b(languages)h(with)e
2242 (nondeterminism)e(and)j(automatic)f(bac)o(ktrac)o(king,)g(the)g(o)q
2243 (ccurrence)g(of)i(a)f(failure)0 1759 y(ma)o(y)j(require)h(restarting)h
2244 (the)g(computation)f(at)i(a)f(p)q(oin)o(t)g(whic)o(h)f(is)h(no)h
2245 (longer)f(on)g(the)g(traditional)0 1819 y(con)o(trol)d(stac)o(k.)24
2246 b(Th)o(us,)18 b(bac)o(ktrac)o(king)e(requires)h(the)g(main)o(tenance)e
2247 (of)j(failure)e(con)o(tin)o(uations.)25 b(This)0 1880
2248 y(w)o(ould)17 b(b)q(e)h(straigh)o(tforw)o(ard)g(in)f(a)h(language)g
2249 (with)f(\014rst)h(class)f(con)o(tin)o(uations,)g(suc)o(h)g(as)h
2250 Fl(Scheme)g Fn(or)0 1940 y Fl(sml)p Fn(.)28 b(Since)18
2251 b Fl(Common)g(Lisp)g Fn(do)q(es)i(not)f(ha)o(v)o(e)e(\014rst)i(class)g
2252 (con)o(tin)o(uations,)g(w)o(e)f(construct)h(con)o(tin)o(u-)0
2253 2000 y(ations)f(b)o(y)f(p)q(erforming)f(CPS)i(con)o(v)o(ersion)f(on)h
2254 Fl(Screamer)f Fn(programs.)25 b(F)l(or)18 b(example,)d
2255 Fl(Screamer)0 2060 y Fn(con)o(v)o(erts)g(the)h(follo)o(wing)g
2256 (de\014nition)g(for)h Fj(a-member-)o(of)25 2158 y(\(defun)23
2257 b(a-member-of)f(\(x\))51 2218 y(\(if)i(\(null)g(x\))h(\(fail\)\))51
2258 2278 y(\(either)e(\(first)g(x\))i(\(a-member-)o(of)d(\(rest)i
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2260 o(erted)d(form.)948 2798 y(7)p eop
2261 %%Page: 8 8
2262 8 7 bop 25 -44 a Fj(\(defvar)23 b(*fail*)g(#'\(lambda)g(\(\))i(\(error)
2263 e("Top)h(level)g(fail"\)\)\))25 76 y(\(defun)f(fail)i(\(\))f(\(funcall)
2264 f(*fail*\)\))25 196 y(\(defun)g(a-member-of)486 178 y
2265 Fa(0)524 196 y Fj(\(c)h(x\))51 257 y(\(if)g(\(null)g(x\))h(\(fail\)\))
2266 51 317 y(\(let)f(\(\(*fail*)e(#'\(lambda)h(\(\))i(\(a-member)o(-of)1050
2267 299 y Fa(0)1088 317 y Fj(c)g(\(rest)f(x\)\)\)\)\))76
2268 377 y(\(funcall)f(c)i(\(first)f(x\)\)\)\))0 472 y Fn(Note)19
2269 b(that)i(the)e(con)o(tin)o(uation)g(is)h(the)g(\014rst)g(argumen)o(t)e
2270 (to)j(allo)o(w)e(nondeterministic)e(functions)j(full)0
2271 532 y(use)f(of)g Fl(Common)f(Lisp)g Fn(argumen)o(t)g(passing)h
2272 (capabilities.)27 b(Naiv)o(e)17 b(CPS)j(con)o(v)o(ersion)d(in)o(tro)q
2273 (duces)i(a)0 593 y(large)14 b(n)o(um)o(b)q(er)f(of)h(lexical)e
2274 (closures)j(not)f(presen)o(t)g(in)g(the)g(original)g(co)q(de.)20
2275 b(This)15 b(can)f(result)g(in)g(a)g(sev)o(ere)0 653 y(p)q(erformance)20
2276 b(p)q(enalt)o(y)l(.)35 b(Accordingly)l(,)20 b Fl(Screamer)h
2277 Fn(tak)o(es)g(great)g(pains)g(to)g(use)g(CPS)h(con)o(v)o(ersion)0
2278 713 y(sparingly)l(.)h(The)17 b Fl(Screamer)g Fn(implem)o(e)o(n)o
2279 (tation)d(do)q(es)k(a)f(global)g(static)g(analysis)g(to)g(\014nd)g(co)q
2280 (de)g(frag-)0 773 y(men)o(ts)i(whic)o(h)h(are)g(pro)o(v)m(ably)h
2281 (deterministic)c(and)k(a)o(v)o(oids)g(CPS)g(con)o(v)o(erting)e(those)i
2282 (fragmen)o(ts.)33 b(In)0 833 y(general)18 b(it)g(is)h(not)g(p)q
2283 (ossible)f(to)h(statically)f(determine)e(whether)i(or)h(not)g(a)g(giv)o
2284 (en)e(co)q(de)i(fragmen)o(t)e(is)0 893 y(deterministic.)g(Therefore,)12
2285 b Fl(Screamer)i Fn(conserv)m(ativ)o(ely)d(\014nds)i(only)g(a)g(subset)g
2286 (of)h(the)e(deterministic)0 954 y(co)q(de)18 b(fragmen)o(ts.)25
2287 b(One)18 b(can)g(apply)g(v)m(arying)g(degrees)g(of)g(sophistication)g
2288 (in)g(iden)o(tifying)e(determin-)0 1014 y(istic)k(co)q(de)h(fragmen)o
2289 (ts.)35 b(Considerable)21 b(e\013ort)h(has)g(b)q(een)f(in)o(v)o(ested)e
2290 (to)j(pro)o(vide)e Fl(Screamer)h Fn(with)0 1074 y(p)q(o)o(w)o(erful)16
2291 b(but)g(e\016cien)o(t)e(static)i(analysis.)73 1134 y(In)k(spite)g(of)g
2292 (the)g(fact)g(that)h Fl(Screamer)p Fn('s)f(compilation)e(tec)o(hniques)
2293 h(require)g(global)h(analysis,)0 1194 y Fl(Screamer)e
2294 Fn(do)q(es)h(supp)q(ort)h(incremen)o(tal)15 b(rede\014nition)i(of)h
2295 (pro)q(cedures.)28 b Fl(Screamer)18 b Fn(main)o(tains)f(a)0
2296 1255 y(who-calls)12 b(database)h(to)g(iden)o(tify)d(those)i(co)q(de)g
2297 (blo)q(c)o(ks)g(requiring)f(recompilation.)17 b(Th)o(us)c(if)e
2298 Fi(f)5 b Fn(,)12 b Fi(g)r Fn(,)f(and)i Fi(h)0 1315 y
2299 Fn(are)g(initially)e(deterministic|)o(and)g Fi(f)18 b
2300 Fn(calls)13 b Fi(g)i Fn(whic)o(h)d(in)g(turn)i(calls)e
2301 Fi(h)p Fn(|rede\014ning)g Fi(h)h Fn(to)h(b)q(e)f(nondeter-)0
2302 1375 y(ministic)e(will)h(cause)i Fl(Screamer)f Fn(to)h(automatically)e
2303 (recompile)f Fi(f)19 b Fn(and)14 b Fi(g)h Fn(as)f(w)o(ell,)f(after)g(p)
2304 q(erforming)0 1435 y(the)18 b(appropriate)g(CPS)h(con)o(v)o(ersion.)26
2305 b(The)18 b(full)f(pap)q(er)i(will)d(explain)i(b)q(oth)h(the)e(static)h
2306 (analysis)g(and)0 1495 y(incremen)o(tal)13 b(recompilation)h(in)i
2307 (greater)h(detail.)0 1661 y Fm(6)83 b(Related)27 b(W)-7
2308 b(ork)0 1771 y Fn(Nondeterministic)19 b Fl(Lisp)k Fn(is)f(not)h(new.)40
2309 b(The)23 b(addition)g(of)g(a)g(nondeterministic)c(c)o(hoice)j(op)q
2310 (erator)0 1831 y(\(sometimes)13 b(called)i Fj(amb)h Fn(or)g
2311 Fj(choose)p Fn(\))e(to)j Fl(Lisp)f Fn(dates)g(bac)o(k)g(to)h(McCarth)o
2312 (y)e(\(1963\).)23 b(Clinger)16 b(\(1982\))0 1891 y(discusses)f(the)h
2313 (di\016culties)d(in)o(v)o(olv)o(ed)g(in)i(giving)g(a)h(formal)f(seman)o
2314 (tics)e(to)j(a)g(nondeterministic)c(c)o(hoice)0 1951
2315 y(op)q(erator)17 b(in)f Fl(Lisp)p Fn(.)21 b(\(Chapman)16
2316 b(unpublished\))g(describ)q(es)g Fl(Dependency)h(Directed)j(Lisp)15
2317 b Fn(\(also)0 2011 y(kno)o(wn)k(as)g Fl(ddl)p Fn(\),)g(an)g(impleme)o
2318 (n)o(tation)d(of)j(nondeterministic)d Fl(Lisp)j Fn(used)g(to)g(implem)o
2319 (en)n(t)d Fl(Tweak)0 2072 y Fn(\(Chapman)e(1985\),)i(a)e(non-linear)g
2320 (constrain)o(t-p)q(osting)i(planner.)k Fl(ddl)14 b Fn(recorded)f(dep)q
2321 (endency)h(infor-)0 2132 y(mation)i(during)h(execution)f(to)i(supp)q
2322 (ort)g(selectiv)o(e)d(bac)o(ktrac)o(king.)22 b(Zabih)17
2323 b(\(1987\))i(and)f(Zabih)f(et)g(al.)0 2192 y(\(1987\))h(describ)q(e)d
2324 Fl(Schemer)p Fn(,)h(an)h(in)o(terpreter)d(for)i(nondeterministic)e
2325 Fl(Scheme)i Fn(that)h(recorded)e(and)0 2252 y(analyzed)g(dep)q(endency)
2326 f(information)g(to)h(p)q(erform)f(b)q(oth)h(selectiv)o(e)e(bac)o(ktrac)
2327 o(king)h(and)h(lateral)f(prun-)0 2312 y(ing.)21 b Fl(Schemer)16
2328 b Fn(and)g Fl(ddl)f Fn(w)o(ere)g(b)q(oth)h(in)o(terpreters)e(to)i(supp)
2329 q(ort)h(retaining)e(the)g(dep)q(endency)g(infor-)0 2373
2330 y(mation)c(needed)g(for)h(in)o(telligen)o(t)d(bac)o(ktrac)o(king.)18
2331 b(Ha)o(ynes)11 b(\(1987\))i(describ)q(es)f(ho)o(w)g(a)g
2332 (nondeterministic)0 2433 y(c)o(hoice)j(op)q(erator)i(can)g(b)q(e)f
2333 (added)h(to)f Fl(Scheme)h Fn(using)g(the)f Fj(call/cc)d
2334 Fn(function.)73 2493 y(The)23 b(tec)o(hniques)e(used)i(for)g(implem)o
2335 (e)o(n)o(ting)d(bac)o(ktrac)o(king)h(in)i Fl(Screamer)f
2336 Fn(are)h(analogous)i(to)0 2553 y(those)14 b(used)g(when)g(compiling)e
2337 Fl(Pr)o(olog)h Fn(in)o(to)h Fl(Lisp)f Fn(\(Kahn)i(1982,)g(1983,)g(Kahn)
2338 g(and)f(Carrlson)h(1984,)0 2613 y(Siskind)10 b(1989\).)21
2339 b(CPS)11 b(con)o(v)o(ersion)f(w)o(as)i(used)f(in)f(the)h
2340 Fl(Rabbit)f Fn(compiler)f(for)i Fl(Scheme)g Fn(\(Steele)e(and)j(Suss-)0
2341 2674 y(man)j(1976,)j(Steele)d(1976,)i(1978\).)948 2798
2342 y(8)p eop
2343 %%Page: 9 9
2344 9 8 bop 0 -37 a Fm(7)83 b(Summary)0 73 y Fn(Prior)17
2345 b(impleme)o(n)o(tations)e(of)j(nondeterministic)c Fl(Lisp)j
2346 Fn(w)o(ere)g(to)q(o)h(ine\016cien)o(t)d(to)j(b)q(e)f(used)h(for)f
2347 (practi-)0 133 y(cal)g(applications.)24 b Fl(Screamer)17
2348 b Fn(remedies)e(this)i(ine\016ciency)e(b)o(y)h(making)g(sev)o(eral)g
2349 (design)h(decisions)0 193 y(di\013eren)o(tly)j(than)i(prior)f(implem)o
2350 (en)n(tations.)34 b(First,)22 b Fl(Screamer)f Fn(op)q(erates)h(as)g(a)g
2351 Fl(Common)c(Lisp)0 253 y Fn(source)j(to)g(source)g(transform)f(allo)o
2352 (wing)h(the)f(resulting)h Fl(Common)d(Lisp)i Fn(co)q(de)h(generated)g
2353 (b)o(y)f(the)0 314 y(CPS)e(con)o(v)o(erter)d(to)i(b)q(e)g(compiled)e(b)
2354 o(y)i(the)f(underlying)h Fl(Common)h(Lisp)f Fn(implem)o(e)o(n)o
2355 (tation.)k(In)c(con-)0 374 y(trast,)i(most)f(prior)h(implem)o(en)o
2356 (tati)o(ons)e(w)o(ere)h(in)o(terpreters.)27 b(Second,)19
2357 b Fl(Screamer)f Fn(forego)q(es)i(in)o(telli-)0 434 y(gen)o(t)f(bac)o
2358 (ktrac)o(king)e(in)i(fa)o(v)o(or)f(of)h(c)o(hronological)g(bac)o(ktrac)
2359 o(king.)28 b(Exp)q(erience)17 b(has)j(sho)o(wn)f(that)g(the)0
2360 494 y(o)o(v)o(erhead)h(of)g(main)o(taining)f(dep)q(endencies)g(to)i
2361 (supp)q(ort)h(in)o(telligen)o(t)17 b(bac)o(ktrac)o(king)j(costs)h(far)f
2362 (more)0 554 y(than)e(the)e(computation)h(sa)o(v)o(ed)f(in)h(most)f
2363 (practical)g(applications.)24 b(W)l(e)17 b(b)q(eliev)o(e)e(that)i(c)o
2364 (hronological)0 615 y(bac)o(ktrac)o(king|represen)o(ted)f(via)h
2365 (nondeterminism|i)o(s)f(a)i(useful)g(programming)e(paradigm)i(when)0
2366 675 y(used)d(prop)q(erly)l(.)20 b(It)14 b(is)g(an)h(imp)q(ortan)o(t)f
2367 (con)o(trol)g(construct)g(whic)o(h)g(adds)h(signi\014can)o(t)f
2368 (expressiv)o(e)f(p)q(o)o(w)o(er)0 735 y(to)k Fl(Common)h(Lisp)p
2369 Fn(,)d(making)g(programs)i(easier)e(to)i(write,)e(debug,)h(and)h
2370 (understand.)73 795 y(W)l(e)i(ha)o(v)o(e)g(demonstrated)g(the)g(p)q(o)o
2371 (w)o(er)h(of)g Fl(Screamer)f Fn(b)o(y)g(using)h(it)f(as)i(a)f(v)o
2372 (ehicle)d(for)j(teac)o(hing)0 855 y(6.824)g(and)g(CIS520,)g(the)f
2373 (graduate)h(core)f(AI)f(courses)i(at)f(M.)g(I.)f(T.)h(and)g(the)g(Univ)
2374 o(ersit)o(y)e(of)i(P)o(enn-)0 916 y(sylv)m(ania.)25 b(As)17
2375 b(problem)f(sets)i(in)f(these)g(courses,)h(studen)o(ts)g(ha)o(v)o(e)e
2376 (used)i Fl(Screamer)g Fn(to)g(build)f(small)0 976 y(w)o(orking)f(v)o
2377 (ersions)f(of)h(a)g(n)o(um)o(b)q(er)e(of)i(programs)g(whic)o(h)f(ha)o
2378 (v)o(e)g(b)q(een)h(the)f(fo)q(cus)i(of)f(AI)f(researc)o(h)g(in)g(the)0
2379 1036 y(past)k(and)f(presen)o(t.)25 b(These)18 b(problem)e(sets)i(and)g
2380 (other)g(AI)f(course)h(material)e(based)i(on)h Fl(Screamer)0
2381 1096 y Fn(includes)i(crossw)o(ord)j(puzzle)d(solv)o(ers,)i(W)l(altz)f
2382 (line)f(lab)q(eling,)i(Allen's)e(temp)q(oral)g(logic,)j(hardw)o(are)0
2383 1156 y(fault)18 b(diagnosis,)g Fi(A)378 1138 y Fa(\003)416
2384 1156 y Fn(searc)o(h,)f(linear)g(and)h(non-linear)g(planners,)g(natural)
2385 g(language)h(query)e(pro)q(ces-)0 1217 y(sors)j(based)h(on)f(Mon)o
2386 (tague)g(grammar,)e Fl(Pr)o(olog)g Fn(in)o(terpreters)h(and)h
2387 (compilers,)e(theorem)g(pro)o(v)o(ers)0 1277 y(based)c(on)f(seman)o
2388 (tic)e(tableaux,)j(congruence)f(closure,)f(resolution,)i(and)g
2389 Fl(Pr)o(olog)d Fn(tec)o(hnology)l(,)i(Rete,)0 1337 y(qualitativ)o(e)f
2390 (sim)o(ulation,)h(rob)q(ot)i(path)f(planning,)h(and)f(mo)q(del-based)g
2391 (vision.)20 b(All)13 b(of)h(these)g(examples)0 1397 y(can)21
2392 b(b)q(e)h(written)f(m)o(uc)o(h)e(more)h(clearly)g(and)i(concisely)e
2393 (using)h(nondeterministic)e(constructs)i(than)0 1457
2394 y(without.)g(F)l(urthermore,)14 b(researc)o(hers)h(at)h(M.)f(I.)f(T.,)i
2395 (the)f(Univ)o(ersit)o(y)e(of)j(P)o(ennsylv)m(ania,)f(and)h(sev)o(eral)0
2396 1518 y(other)c(institutions)g(w)o(orld-wide)g(ha)o(v)o(e)f(b)q(egun)i
2397 (using)g Fl(Screamer)f Fn(as)h(part)f(of)h(their)e(ongoing)j(researc)o
2398 (h)0 1578 y(programming)h(activit)o(y)l(.)73 1638 y(The)29
2399 b(curren)o(t)e(v)o(ersion)h(of)h Fl(Screamer)f Fn(is)h(a)o(v)m(ailable)
2400 e(b)o(y)h(anon)o(ymous)g(FTP)h(from)e(the)i(\014le)0
2401 1698 y Fj(ftp.ai.mit)o(.ed)o(u:)o(/co)o(m/f)o(tp/)o(pu)o(b/s)o(cre)o
2402 (ame)o(r.)o(tar)o(.Z)p Fn(.)36 b(W)l(e)22 b(encourage)h(y)o(ou)f(to)h
2403 (obtain)g(a)f(cop)o(y)0 1758 y(of)17 b Fl(Screamer)f
2404 Fn(and)h(giv)o(e)e(us)i(feedbac)o(k)e(on)i(y)o(our)f(exp)q(eriences)e
2405 (using)j(it.)0 1925 y Fm(References)24 2034 y Fn([1])24
2406 b(Da)o(vid)c(Chapman.)34 b(Dep)q(endency-Directed)20
2407 b Fl(Lisp)o Fn(.)34 b(Unpublished)20 b(man)o(uscript)f(receiv)o(ed)f
2408 (di-)100 2094 y(rectly)d(from)g(author.)24 2196 y([2])24
2409 b(Da)o(vid)18 b(Chapman.)28 b(Planning)18 b(for)h(conjunctiv)o(e)e
2410 (goals.)28 b(Master's)18 b(thesis,)g(Massac)o(h)o(usetts)h(In-)100
2411 2256 y(stitute)f(of)h(T)l(ec)o(hnology)l(,)g(Jan)o(uary)g(1985.)30
2412 b(Also)18 b(a)o(v)m(ailable)g(as)h(M.)f(I.)g(T.)g(Arti\014cial)f(In)o
2413 (teligence)100 2316 y(Lab)q(oratory)i(T)l(ec)o(hnical)14
2414 b(Rep)q(ort)j(802.)24 2418 y([3])24 b(W.)14 b(Clinger.)k
2415 (Nondeterministic)11 b(call)j(b)o(y)g(need)g(is)g(neither)g(lazy)g(nor)
2416 h(b)o(y)f(name.)j(In)d Fk(Pr)n(o)n(c)n(e)n(e)n(dings)100
2417 2478 y(of)k(the)f(A)o(CM)g(Confer)n(enc)n(e)i(on)e Fl(Lisp)g
2418 Fk(and)h(F)l(unctional)h(Pr)n(o)n(gr)n(amming)p Fn(,)c(pages)i
2419 (226{234,)h(1982.)24 2580 y([4])24 b(Christopher)19 b(T.)g(Ha)o(ynes.)
2420 28 b(Logic)20 b(con)o(tin)o(uations.)29 b Fk(Journal)19
2421 b(of)h(L)n(o)n(gic)f(Pr)n(o)n(gr)n(amming)p Fn(,)f(4:157{)100
2422 2640 y(176,)f(1987.)948 2798 y(9)p eop
2423 %%Page: 10 10
2424 10 9 bop 24 -37 a Fn([5])24 b(Kenneth)15 b(M.)g(Kahn.)21
2425 b(A)15 b(partial)h(ev)m(aluator)g(of)g Fl(Lisp)f Fn(written)g(in)g
2426 Fl(Pr)o(olog)o Fn(.)20 b(In)15 b Fk(Pr)n(o)n(c)n(e)n(e)n(dings)h(of)100
2427 24 y(the)i(First)f(L)n(o)n(gic)g(Pr)n(o)n(gr)n(amming)f(Confer)n(enc)n
2428 (e)p Fn(,)g(Marseille,)e(F)l(rance,)i(1982.)24 125 y([6])24
2429 b(Kenneth)17 b(M.)g(Kahn.)25 b(Unique)16 b(features)i(of)g
2430 Fl(Lisp)f Fn(mac)o(hine)e Fl(Pr)o(olog)o Fn(.)24 b(UPMAIL)17
2431 b(Rep)q(ort)h(14,)100 185 y(Univ)o(ersit)o(y)c(of)i(Uppsala,)h(Sw)o
2432 (eden,)e(1983.)24 287 y([7])24 b(Kenneth)16 b(M.)g(Kahn)h(and)g(M.)e
2433 (Carlsson.)23 b(Ho)o(w)16 b(to)h(implem)o(en)o(t)c Fl(Pr)o(olog)i
2434 Fn(on)i(a)g Fl(Lisp)f Fn(mac)o(hine.)100 347 y(In)21
2435 b(J.)g(A.)f(Campb)q(ell,)h(editor,)h Fk(Implementations)h(of)f
2436 Fl(Pr)o(olog)o Fn(,)g(c)o(hapter)e(2,)j(pages)f(117{134.)100
2437 408 y(Ellis)16 b(Horw)o(o)q(o)q(d,)h(Chic)o(hester,)d(1984.)24
2438 509 y([8])24 b(John)15 b(McCarth)o(y)l(.)h(A)d(basis)i(for)f(a)g
2439 (mathematical)c(theory)k(of)g(computation.)i(In)e(P)l(.)f(Bra\013ort)h
2440 (and)100 569 y(D.)21 b(Hirsc)o(h)o(b)q(erg,)g(editors,)h
2441 Fk(Computer)g(Pr)n(o)n(gr)n(aming)e(and)i(F)l(ormal)g(Systems)p
2442 Fn(.)f(Elsevier)f(North-)100 630 y(Holland,)c(Amsterdam,)d(1963.)24
2443 731 y([9])24 b(Je\013rey)15 b(Mark)g(Siskind.)j(The)d(culprit)f(p)q
2444 (oin)o(ter)h(metho)q(d)f(for)i(selectiv)o(e)c(bac)o(ktrac)o(king.)18
2445 b(Master's)100 792 y(thesis,)e(Massac)o(h)o(usetts)g(Institute)g(of)g
2446 (T)l(ec)o(hnology)l(,)g(Jan)o(uary)g(1989.)0 893 y([10])24
2447 b(Je\013rey)19 b(Mark)h(Siskind)f(and)h(Da)o(vid)f(Allen)f(McAllester.)
2448 29 b(Nondeterministic)16 b Fl(Lisp)j Fn(as)h(a)g(sub-)100
2449 953 y(strate)15 b(for)g(constrain)o(t)g(logic)f(programming.)j(In)d
2450 Fk(Pr)n(o)n(c)n(e)n(e)n(dings)h(of)h(the)g(Eleventh)j(National)d(Con-)
2451 100 1014 y(fer)n(enc)n(e)i(on)g(A)o(rti\014c)n(al)g(Intel)r(ligenc)o(e)
2452 p Fn(,)g(July)e(1993.)0 1115 y([11])24 b(Guy)d(Lewis)f(Steele)f(Jr.)33
2453 b(Lam)o(b)q(da,)20 b(the)g(ultimate)e(declarativ)o(e.)31
2454 b(A.)20 b(I.)f(Memo)g(379,)i(M.)f(I.)f(T.)100 1176 y(Arti\014cial)c(In)
2455 o(telligence)e(Lab)q(oratory)l(,)18 b(No)o(v)o(em)o(b)q(er)13
2456 b(1976.)0 1277 y([12])24 b(Guy)15 b(Lewis)g(Steele)e(Jr.)18
2457 b(Rabbit:)j(A)14 b(compiler)e(for)j Fl(Scheme)p Fn(.)j(T)l(ec)o(hnical)
2458 13 b(Rep)q(ort)i(474,)h(M.)e(I.)f(T.)100 1337 y(Arti\014cial)i(In)o
2459 (telligence)e(Lab)q(oratory)l(,)18 b(1978.)0 1439 y([13])24
2460 b(Guy)e(Lewis)g(Steele)f(Jr.)g(and)h(Gerald)g(Ja)o(y)g(Sussman.)37
2461 b(Lam)o(b)q(da,)23 b(the)f(ultimate)d(imp)q(erativ)o(e.)100
2462 1499 y(A.)d(I.)f(Memo)g(353,)i(M.)e(I.)h(T.)g(Arti\014cial)e(In)o
2463 (telligence)g(Lab)q(oratory)l(,)j(Marc)o(h)f(1976.)0
2464 1601 y([14])24 b(Ramin)c(D.)h(Zabih.)37 b(Dep)q(endency-directed)20
2465 b(bac)o(ktrac)o(king)g(in)h(non-deterministic)e Fl(Scheme)p
2466 Fn(.)100 1661 y(Master's)d(thesis,)g(Massac)o(h)o(usetts)g(Institute)g
2467 (of)g(T)l(ec)o(hnology)l(,)g(Jan)o(uary)g(1987.)0 1763
2468 y([15])24 b(Ramin)c(D.)g(Zabih,)h(Da)o(vid)g(Allen)e(McAllester,)g(and)
2469 i(Da)o(vid)g(Chapman.)34 b(Non-deterministic)100 1823
2470 y Fl(Lisp)18 b Fn(with)f(dep)q(endency-directed)g(bac)o(ktrac)o(king.)
2471 24 b(In)18 b Fk(Pr)n(o)n(c)n(e)n(e)n(dings)g(of)g(AAAI{87)p
2472 Fn(,)g(pages)h(59{)100 1883 y(64,)e(July)f(1987.)936
2473 2798 y(10)p eop
2474 %%Trailer
2475 end
2476 userdict /end-hook known{end-hook}if
2477 %%EOF