%!PS-Adobe-2.0 %%Creator: dvips 5.76 Copyright 1997 Radical Eye Software (www.radicaleye.com) %%Title: jmc.dvi %%CreationDate: Fri Jan 18 15:02:06 2002 %%Pages: 13 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips jmc %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2002.01.18:1502 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N 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b(w)n(e)f(de\014ne)h(a)f(notation)g(for)g(describing) g(functions.)47 b(A)30 b(function)i(is)e(expressed)g(as)515 1274 y Fi(\(lambda)40 b(\()p Fe(p)949 1286 y Fl(1)1000 1274 y Fe(:)14 b(:)g(:)g(p)1153 1286 y Fc(n)1198 1274 y Fi(\))43 b Fe(e)p Fi(\))p Fm(,)29 b(where)f Fe(p)1703 1286 y Fl(1)1754 1274 y Fe(:)14 b(:)g(:)g(p)1907 1286 y Fc(n)1981 1274 y Fm(are)28 b(atoms)g(\(called)h Fk(p)l(ar)l(ameters)p Fm(\))h(and)f Fe(e)g Fm(is)515 1374 y(an)e(expression.)35 b(An)29 b(expression)d(whose)h(\014rst)g(elemen)n(t)h(is)f(suc)n(h)g (an)h(expression)515 1533 y Fi(\(\(lambda)40 b(\()p Fe(p)993 1545 y Fl(1)1043 1533 y Fe(:)14 b(:)g(:)g(p)1196 1545 y Fc(n)1241 1533 y Fi(\))43 b Fe(e)p Fi(\))g Fe(a)1498 1545 y Fl(1)1549 1533 y Fe(:)14 b(:)g(:)g(a)1704 1545 y Fc(n)1749 1533 y Fi(\))515 1693 y Fm(is)31 b(called)g(a)g Fk(function)i(c)l(al)t(l)f Fm(and)f(its)h(v)-5 b(alue)31 b(is)g(computed)h(as)e(follo)n(ws.)47 b(Eac)n(h)31 b(expression)515 1793 y Fe(a)559 1805 y Fc(i)618 1793 y Fm(is)h(ev)-5 b(aluated.)49 b(Then)32 b Fe(e)g Fm(is)f(ev)-5 b(aluated.)50 b(During)31 b(the)i(ev)-5 b(aluation)31 b(of)h Fe(e)p Fm(,)g(the)g(v)-5 b(alue)32 b(of)515 1892 y(an)n(y)26 b(o)r(ccurrence)f(of)i(one)f(of)h(the)g Fe(p)1606 1904 y Fc(i)1660 1892 y Fm(is)g(the)g(v)-5 b(alue)26 b(of)h(the)g(corresp)r (onding)e Fe(a)2911 1904 y Fc(i)2965 1892 y Fm(in)i(the)g(most)515 1992 y(recen)n(t)g(function)h(call.)515 2149 y Fi(>)43 b(\(\(lambda)d(\(x\))j(\(cons)e(x)i('\(b\)\)\))e('a\))515 2249 y(\(a)h(b\))515 2349 y(>)h(\(\(lambda)d(\(x)j(y\))g(\(cons)e(x)i (\(cdr)f(y\)\)\))645 2448 y('z)645 2548 y('\(a)h(b)g(c\)\))515 2648 y(\(z)f(b)i(c\))515 2805 y Fm(If)21 b(an)g(expression)f(has)g(as)g (its)i(\014rst)f(elemen)n(t)g(an)f(atom)h Fe(f)30 b Fm(that)21 b(is)g(not)g(one)g(of)g(the)g(primitiv)n(e)515 2905 y(op)r(erators)515 3064 y Fi(\()p Fe(f)51 b(a)695 3076 y Fl(1)746 3064 y Fe(:)14 b(:)g(:)g(a)901 3076 y Fc(n)946 3064 y Fi(\))515 3224 y Fm(and)32 b(the)g(v)-5 b(alue)32 b(of)g Fe(f)41 b Fm(is)32 b(a)g(function)h Fi(\(lambda)41 b(\()p Fe(p)2155 3236 y Fl(1)2205 3224 y Fe(:)14 b(:)g(:)g(p)2358 3236 y Fc(n)2403 3224 y Fi(\))43 b Fe(e)p Fi(\))31 b Fm(then)i(the)g(v)-5 b(alue)32 b(of)g(the)515 3324 y(expression)26 b(is)h(the)h(v)-5 b(alue)28 b(of)515 3483 y Fi(\(\(lambda)40 b(\()p Fe(p)993 3495 y Fl(1)1043 3483 y Fe(:)14 b(:)g(:)g(p)1196 3495 y Fc(n)1241 3483 y Fi(\))43 b Fe(e)p Fi(\))g Fe(a)1498 3495 y Fl(1)1549 3483 y Fe(:)14 b(:)g(:)g(a)1704 3495 y Fc(n)1749 3483 y Fi(\))515 3643 y Fm(In)32 b(other)f(w)n(ords,)g (parameters)f(can)h(b)r(e)h(used)g(as)f(op)r(erators)f(in)h (expressions)f(as)h(w)n(ell)h(as)515 3743 y(argumen)n(ts:)515 3889 y Fi(>)43 b(\(\(lambda)d(\(f\))j(\(f)f('\(b)h(c\)\)\))645 3988 y('\(lambda)e(\(x\))h(\(cons)g('a)g(x\)\)\))515 4088 y(\(a)g(b)i(c\))639 4234 y Fm(There)26 b(is)h(another)f(notation)g (for)g(functions)h(that)g(enables)f(the)h(function)g(to)f(refer)g(to) 515 4334 y(itself,)35 b(thereb)n(y)f(giving)e(us)i(a)f(con)n(v)n(enien) n(t)g(w)n(a)n(y)f(to)i(de\014ne)g(recursiv)n(e)d(functions.)3143 4303 y Fl(3)3236 4334 y Fm(The)p 515 4377 1146 4 v 607 4430 a Fh(2)642 4454 y Fg(Expressions)26 b(b)r(eginning)i(with)f(the)g (other)h(t)n(w)n(o)f(op)r(erators,)h Fb(quote)g Fg(and)f Fb(cond)p Fg(,)i(are)d(ev)l(aluated)j(dif-)515 4533 y(feren)n(tly)-6 b(.)36 b(When)26 b(a)g Fb(quote)g Fg(expression)g(is)f(ev)l(aluated,)i (its)e(argumen)n(t)g(is)g(not)h(ev)l(aluated,)h(but)f(is)f(simply)515 4612 y(returned)f(as)f(the)i(v)l(alue)f(of)f(the)i(whole)f Fb(quote)g Fg(expression.)32 b(And)23 b(in)h(a)f(v)l(alid)h Fb(cond)g Fg(expression,)g(only)g(an)515 4690 y(L-shap)r(ed)g(path)h (of)e(sub)r(expressions)h(will)e(b)r(e)i(ev)l(aluated.)607 4746 y Fh(3)642 4770 y Fg(Logically)33 b(w)n(e)g(don't)h(need)g(to)g (de\014ne)g(a)f(new)g(notation)i(for)d(this.)59 b(W)-6 b(e)34 b(could)g(de\014ne)g(recursiv)n(e)515 4848 y(functions)26 b(in)g(our)g(existing)g(notation)i(using)e(a)g(function)h(on)f (functions)h(called)f(the)h(Y)f(com)n(binator.)38 b(It)515 4927 y(ma)n(y)27 b(b)r(e)h(that)g(McCarth)n(y)g(did)g(not)g(kno)n(w)g (ab)r(out)h(the)g(Y)e(com)n(binator)g(when)i(he)f(wrote)g(his)f(pap)r (er;)i(in)515 5006 y(an)n(y)24 b(case,)g Fb(label)h Fg(notation)g(is)e (more)g(readable.)1926 5255 y Fm(4)p eop %%Page: 5 5 5 4 bop 515 523 a Fm(notation)515 683 y Fi(\(label)41 b Fe(f)52 b Fi(\(lambda)41 b(\()p Fe(p)1348 695 y Fl(1)1398 683 y Fe(:)14 b(:)g(:)g(p)1551 695 y Fc(n)1596 683 y Fi(\))43 b Fe(e)p Fi(\)\))515 842 y Fm(denotes)19 b(a)g(function)h (that)g(b)r(eha)n(v)n(es)e(lik)n(e)h Fi(\(lambda)41 b(\()p Fe(p)2237 854 y Fl(1)2287 842 y Fe(:)14 b(:)g(:)g(p)2440 854 y Fc(n)2485 842 y Fi(\))43 b Fe(e)p Fi(\))p Fm(,)21 b(with)f(the)g(additional)515 942 y(prop)r(ert)n(y)j(that)h(an)f(o)r (ccurrence)g(of)h Fe(f)32 b Fm(within)25 b Fe(e)f Fm(will)g(ev)-5 b(aluate)23 b(to)h(the)h Fi(label)c Fm(expression,)515 1042 y(as)27 b(if)h Fe(f)36 b Fm(w)n(ere)27 b(a)g(parameter)f(of)i(the) g(function.)639 1141 y(Supp)r(ose)33 b(w)n(e)g(w)n(an)n(t)f(to)h (de\014ne)g(a)f(function)i Fi(\(subst)41 b Fe(x)j(y)i(z)t Fi(\))p Fm(,)33 b(whic)n(h)g(tak)n(es)f(an)h(ex-)515 1241 y(pression)j Fe(x)p Fm(,)42 b(an)37 b(atom)h Fe(y)s Fm(,)i(and)e(a)f(list)i Fe(z)t Fm(,)g(and)f(returns)f(a)h(list)g(lik)n (e)g Fe(z)j Fm(but)d(with)h(eac)n(h)515 1340 y(instance)27 b(of)h Fe(y)i Fm(\(at)e(an)n(y)f(depth)h(of)f(nesting\))h(in)g Fe(z)j Fm(replaced)c(b)n(y)g Fe(x)p Fm(.)515 1506 y Fi(>)43 b(\(subst)e('m)i('b)g('\(a)f(b)h(\(a)g(b)g(c\))g(d\)\))515 1606 y(\(a)f(m)i(\(a)e(m)i(c\))e(d\))515 1772 y Fm(W)-7 b(e)28 b(can)f(denote)g(this)h(function)h(as)515 1955 y Fi(\(label)41 b(subst)g(\(lambda)g(\(x)i(y)g(z\))1169 2054 y(\(cond)e(\(\(atom)g(z\))1474 2154 y(\(cond)g(\(\(eq)h(z)h(y\))g (x\))1735 2254 y(\('t)f(z\)\)\))1430 2353 y(\('t)g(\(cons)g(\(subst)f (x)i(y)g(\(car)f(z\)\))1866 2453 y(\(subst)f(x)i(y)g(\(cdr)f (z\)\)\)\)\)\)\))515 2636 y Fm(W)-7 b(e)28 b(will)g(abbreviate)e Fe(f)36 b Fm(=)27 b 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b(to)f(what)h(w)n(e)f(migh)n(t)g(write)h(in)g(a)f (language)f(with)i(syn)n(tax)f(as)515 4397 y Fi(if)42 b Fe(x)j Fi(then)c Fe(y)47 b Fi(else)42 b Fe(z)515 4671 y Fj(3)134 b(Some)46 b(F)-11 b(unctions)515 4853 y Fm(No)n(w)32 b(that)h(w)n(e)f(ha)n(v)n(e)g(a)g(w)n(a)n(y)g(of)h(expressing)e (functions,)j(w)n(e)f(de\014ne)g(some)f(new)h(ones)f(in)515 4953 y(terms)27 b(of)h(our)f(sev)n(en)h(primitiv)n(e)f(op)r(erators.)36 b(First)28 b(it)g(will)g(b)r(e)h(con)n(v)n(enien)n(t)e(to)g(in)n(tro)r (duce)1926 5255 y(5)p eop %%Page: 6 6 6 5 bop 515 523 a Fm(some)19 b(abbreviations)g(for)g(common)h (patterns.)34 b(W)-7 b(e)20 b(will)h(use)e Fi(c)p Fe(x)p Fi(r)p Fm(,)j(where)d Fe(x)i Fm(is)f(a)g(sequence)515 623 y(of)34 b Fi(a)p Fm(s)f(or)g Fi(d)p Fm(s,)i(as)e(an)g(abbreviation) g(for)g(the)i(corresp)r(onding)c(comp)r(osition)j(of)g Fi(car)e Fm(and)515 722 y Fi(cdr)p Fm(.)61 b(So)36 b(for)f(example)h Fi(\(cadr)42 b Fe(e)p Fi(\))35 b Fm(is)h(an)g(abbreviation)f(for)g Fi(\(car)42 b(\(cdr)g Fe(e)p Fi(\)\))p Fm(,)37 b(whic)n(h)515 822 y(returns)27 b(the)h(second)f(elemen)n(t)g(of)h Fe(e)p Fm(.)515 996 y Fi(>)43 b(\(cadr)e('\(\(a)h(b\))h(\(c)g(d\))g(e\)\))515 1096 y(\(c)f(d\))515 1195 y(>)h(\(caddr)e('\(\(a)h(b\))h(\(c)f(d\))h (e\)\))515 1295 y(e)515 1395 y(>)g(\(cdar)e('\(\(a)h(b\))h(\(c)g(d\))g (e\)\))515 1494 y(\(b\))515 1668 y Fm(Also,)27 b(w)n(e)g(will)h(use)g Fi(\(list)41 b Fe(e)1448 1680 y Fl(1)1499 1668 y Fe(:)14 b(:)g(:)f(e)1648 1680 y Fc(n)1693 1668 y Fi(\))28 b Fm(for)f Fi(\(cons)41 b Fe(e)2192 1680 y Fl(1)2273 1668 y Fe(:)14 b(:)g(:)43 b Fi(\(cons)f Fe(e)2714 1680 y Fc(n)2802 1668 y Fi('\(\)\))g Fe(:)14 b(:)g(:)43 b Fi(\))p Fm(.)515 1843 y Fi(>)g(\(cons)e('a)i(\(cons)f('b)g(\(cons)g('c)h('\(\)\)\)\))515 1942 y(\(a)f(b)i(c\))515 2042 y(>)f(\(list)e('a)i('b)g('c\))515 2141 y(\(a)f(b)i(c\))639 2316 y Fm(No)n(w)19 b(w)n(e)g(de\014ne)g(some) g(new)g(functions.)35 b(I'v)n(e)19 b(c)n(hanged)f(the)h(names)g(of)g (these)h(functions)515 2415 y(b)n(y)k(adding)h(p)r(erio)r(ds)g(at)f (the)i(end.)36 b(This)25 b(distinguishes)g(primitiv)n(e)f(functions)i (from)e(those)515 2515 y(de\014ned)32 b(in)h(terms)f(of)g(them,)i(and)e (also)g(a)n(v)n(oids)e(clashes)i(with)g(existing)g(Common)g(Lisp)515 2615 y(functions.)616 2789 y(1.)41 b Fi(\(null.)g Fe(x)p Fi(\))28 b Fm(tests)g(whether)f(its)h(argumen)n(t)f(is)g(the)h(empt)n (y)g(list.)722 2994 y Fi(\(defun)41 b(null.)h(\(x\))809 3094 y(\(eq)h(x)g('\(\)\)\))722 3293 y(>)g(\(null.)f('a\))722 3393 y(\(\))722 3493 y(>)h(\(null.)f('\(\)\))722 3592 y(t)616 3798 y Fm(2.)f Fi(\(and.)h Fe(x)i(y)s Fi(\))27 b Fm(returns)g Fi(t)g Fm(if)h(b)r(oth)g(its)g(argumen)n(ts)e(do)h(and)h Fi(\(\))f Fm(otherwise.)722 4004 y Fi(\(defun)41 b(and.)h(\(x)h(y\))809 4103 y(\(cond)f(\(x)h(\(cond)e(\(y)i('t\))f(\('t)h('\(\)\)\)\))1071 4203 y(\('t)f('\(\)\)\)\))722 4402 y(>)h(\(and.)f(\(atom)f('a\))i(\(eq) f('a)h('a\)\))722 4502 y(t)722 4601 y(>)g(\(and.)f(\(atom)f('a\))i (\(eq)f('a)h('b\)\))722 4701 y(\(\))616 4907 y Fm(3.)e Fi(\(not.)h Fe(x)p Fi(\))37 b Fm(returns)g Fi(t)g Fm(if)g(its)h (argumen)n(t)e(returns)g Fi(\(\))p Fm(,)j(and)e Fi(\(\))g Fm(if)h(its)f(argumen)n(t)722 5006 y(returns)27 b Fi(t)p Fm(.)1926 5255 y(6)p eop %%Page: 7 7 7 6 bop 722 523 a Fi(\(defun)41 b(not.)h(\(x\))809 623 y(\(cond)g(\(x)h('\(\)\))1071 722 y(\('t)f('t\)\)\))722 922 y(>)h(\(not)f(\(eq)h('a)f('a\)\))722 1021 y(\(\))722 1121 y(>)h(\(not)f(\(eq)h('a)f('b\)\))722 1220 y(t)616 1436 y Fm(4.)f Fi(\(append.)g Fe(x)j(y)s Fi(\))27 b Fm(tak)n(es)f(t)n (w)n(o)h(lists)h(and)f(returns)g(their)g(concatenation.)722 1652 y Fi(\(defun)41 b(append.)g(\(x)i(y\))809 1752 y(\(cond)f (\(\(null.)f(x\))h(y\))1071 1851 y(\('t)g(\(cons)g(\(car)g(x\))h (\(append.)d(\(cdr)i(x\))g(y\)\)\)\)\))722 2051 y(>)h(\(append.)e('\(a) h(b\))h('\(c)f(d\)\))722 2150 y(\(a)h(b)g(c)g(d\))722 2250 y(>)g(\(append.)e('\(\))h('\(c)g(d\)\))722 2350 y(\(c)h(d\))616 2565 y Fm(5.)e Fi(\(pair.)g Fe(x)j(y)s Fi(\))27 b Fm(tak)n(es)g(t)n(w)n(o)f(lists)i(of)f(the)h(same)f(length)g (and)g(returns)g(a)g(list)h(of)f(t)n(w)n(o-)722 2665 y(elemen)n(t)h(lists)g(con)n(taining)e(successiv)n(e)g(pairs)h(of)h(an) f(elemen)n(t)h(from)f(eac)n(h.)722 2881 y Fi(\(defun)41 b(pair.)h(\(x)h(y\))809 2980 y(\(cond)f(\(\(and.)f(\(null.)g(x\))i (\(null.)e(y\)\))h('\(\)\))1071 3080 y(\(\(and.)f(\(not.)h(\(atom)f (x\)\))h(\(not.)g(\(atom)f(y\)\)\))1115 3180 y(\(cons)g(\(list)h(\(car) g(x\))g(\(car)g(y\)\))1376 3279 y(\(pair.)f(\(cdr)h(x\))h(\(cdr)f (y\)\)\)\)\)\))722 3479 y(>)h(\(pair.)f('\(x)g(y)h(z\))g('\(a)f(b)h (c\)\))722 3578 y(\(\(x)g(a\))f(\(y)h(b\))g(\(z)g(c\)\))616 3794 y Fm(6.)e Fi(\(assoc.)g Fe(x)j(y)s Fi(\))24 b Fm(tak)n(es)h(an)f (atom)h Fe(x)h Fm(and)f(a)f(list)i Fe(y)i Fm(of)d(the)g(form)g(created) f(b)n(y)h Fi(pair.)p Fm(,)722 3894 y(and)i(returns)g(the)h(second)e (elemen)n(t)i(of)f(the)h(\014rst)f(list)g(in)h Fe(y)i Fm(whose)d(\014rst)g(elemen)n(t)g(is)722 3993 y Fe(x)p Fm(.)722 4209 y Fi(\(defun)41 b(assoc.)g(\(x)i(y\))809 4309 y(\(cond)f(\(\(eq)g(\(caar)f(y\))i(x\))g(\(cadar)e(y\)\))1071 4408 y(\('t)h(\(assoc.)f(x)i(\(cdr)f(y\)\)\)\)\))722 4608 y(>)h(\(assoc.)e('x)i('\(\(x)f(a\))h(\(y)f(b\)\)\))722 4707 y(a)722 4807 y(>)h(\(assoc.)e('x)i('\(\(x)f(new\))g(\(x)h(a\))f (\(y)h(b\)\)\))722 4907 y(new)1926 5255 y Fm(7)p eop %%Page: 8 8 8 7 bop 515 523 a Fj(4)134 b(The)45 b(Surprise)515 705 y Fm(So)28 b(w)n(e)f(can)h(de\014ne)g(functions)h(that)f(concatenate)f (lists,)h(substitute)h(one)f(expression)f(for)515 805 y(another,)42 b(etc.)76 b(An)41 b(elegan)n(t)e(notation,)k(p)r(erhaps,) g(but)e(so)f(what?)75 b(No)n(w)40 b(comes)g(the)515 904 y(surprise.)c(W)-7 b(e)29 b(can)e(also,)g(it)h(turns)g(out,)g(write)g (a)f(function)i(that)f(acts)f(as)h(an)f(in)n(terpreter)515 1004 y(for)22 b(our)g(language:)33 b(a)22 b(function)h(that)g(tak)n(es) f(as)g(an)h(argumen)n(t)e(an)n(y)h(Lisp)h(expression,)f(and)515 1103 y(returns)27 b(its)g(v)-5 b(alue.)37 b(Here)27 b(it)h(is:)515 1262 y Fi(\(defun)41 b(eval.)g(\(e)i(a\))602 1361 y(\(cond)689 1461 y(\(\(atom)e(e\))i(\(assoc.)e(e)i(a\)\))689 1560 y(\(\(atom)e(\(car)h(e\)\))733 1660 y(\(cond)820 1760 y(\(\(eq)g(\(car)g(e\))g('quote\))f(\(cadr)h(e\)\))820 1859 y(\(\(eq)g(\(car)g(e\))g('atom\))85 b(\(atom)129 b(\(eval.)41 b(\(cadr)g(e\))i(a\)\)\))820 1959 y(\(\(eq)f(\(car)g(e\))g ('eq\))173 b(\(eq)217 b(\(eval.)41 b(\(cadr)g(e\))i(a\))2084 2059 y(\(eval.)e(\(caddr)g(e\))i(a\)\)\))820 2158 y(\(\(eq)f(\(car)g (e\))g('car\))129 b(\(car)173 b(\(eval.)41 b(\(cadr)g(e\))i(a\)\)\))820 2258 y(\(\(eq)f(\(car)g(e\))g('cdr\))129 b(\(cdr)173 b(\(eval.)41 b(\(cadr)g(e\))i(a\)\)\))820 2357 y(\(\(eq)f(\(car)g(e\))g ('cons\))85 b(\(cons)129 b(\(eval.)41 b(\(cadr)g(e\))i(a\))2084 2457 y(\(eval.)e(\(caddr)g(e\))i(a\)\)\))820 2557 y(\(\(eq)f(\(car)g (e\))g('cond\))85 b(\(evcon.)41 b(\(cdr)h(e\))h(a\)\))820 2656 y(\('t)f(\(eval.)f(\(cons)h(\(assoc.)e(\(car)i(e\))h(a\))1561 2756 y(\(cdr)f(e\)\))1299 2856 y(a\)\)\)\))689 2955 y(\(\(eq)g(\(caar)g (e\))g('label\))733 3055 y(\(eval.)f(\(cons)g(\(caddar)g(e\))i(\(cdr)f (e\)\))1038 3154 y(\(cons)f(\(list)h(\(cadar)f(e\))i(\(car)f(e\)\))g (a\)\)\))689 3254 y(\(\(eq)g(\(caar)g(e\))g('lambda\))733 3354 y(\(eval.)f(\(caddar)f(e\))1038 3453 y(\(append.)g(\(pair.)h (\(cadar)g(e\))i(\(evlis.)e(\(cdr)h(e\))g(a\)\))1430 3553 y(a\)\)\)\)\))515 3752 y(\(defun)f(evcon.)g(\(c)i(a\))602 3852 y(\(cond)e(\(\(eval.)g(\(caar)h(c\))g(a\))907 3951 y(\(eval.)f(\(cadar)g(c\))i(a\)\))863 4051 y(\('t)g(\(evcon.)d(\(cdr)i (c\))h(a\)\)\)\))515 4250 y(\(defun)e(evlis.)g(\(m)i(a\))602 4350 y(\(cond)e(\(\(null.)g(m\))i('\(\)\))863 4450 y(\('t)g(\(cons)e (\(eval.)85 b(\(car)42 b(m\))h(a\))1299 4549 y(\(evlis.)e(\(cdr)h(m\))h (a\)\)\)\)\))515 4707 y Fm(The)24 b(de\014nition)g(of)g Fi(eval.)e Fm(is)i(longer)e(than)i(an)n(y)g(of)g(the)g(others)f(w)n (e'v)n(e)g(seen)h(b)r(efore.)35 b(Let's)515 4807 y(consider)26 b(ho)n(w)h(eac)n(h)g(part)g(w)n(orks.)639 4907 y(The)33 b(function)f(tak)n(es)g(t)n(w)n(o)f(argumen)n(ts:)45 b Fi(e)p Fm(,)33 b(the)g(expression)d(to)i(b)r(e)h(ev)-5 b(aluated,)33 b(and)515 5006 y Fi(a)p Fm(,)j(a)f(list)g(represen)n (ting)f(the)h(v)-5 b(alues)35 b(that)g(atoms)g(ha)n(v)n(e)e(b)r(een)j (giv)n(en)e(b)n(y)h(app)r(earing)f(as)1926 5255 y(8)p eop %%Page: 9 9 9 8 bop 515 523 a Fm(parameters)23 b(in)j(function)f(calls.)36 b(This)25 b(list)g(is)g(called)g(the)h Fk(envir)l(onment)p Fm(,)f(and)g(it)h(is)f(of)g(the)515 623 y(form)k(created)g(b)n(y)g Fi(pair.)p Fm(.)41 b(It)30 b(w)n(as)f(in)h(order)e(to)h(build)i(and)e (searc)n(h)f(these)i(lists)g(that)f(w)n(e)515 722 y(wrote)e Fi(pair.)e Fm(and)j Fi(assoc.)p Fm(.)639 822 y(The)e(spine)g(of)g Fi(eval.)e Fm(is)i(a)g Fi(cond)e Fm(expression)h(with)h(four)g (clauses.)35 b(Ho)n(w)26 b(w)n(e)f(ev)-5 b(aluate)515 922 y(an)29 b(expression)e(dep)r(ends)j(on)f(what)g(kind)g(it)h(is.)41 b(The)30 b(\014rst)f(clause)f(handles)h(atoms.)41 b(If)29 b Fi(e)515 1021 y Fm(is)e(an)h(atom,)f(w)n(e)g(lo)r(ok)g(up)h(its)g(v) -5 b(alue)27 b(in)h(the)g(en)n(vironmen)n(t:)515 1183 y Fi(>)43 b(\(eval.)e('x)i('\(\(x)f(a\))g(\(y)h(b\)\)\))515 1283 y(a)639 1445 y Fm(The)29 b(second)f(clause)h(of)f Fi(eval.)f Fm(is)i(another)f Fi(cond)f Fm(for)h(handling)h(expressions) e(of)i(the)515 1544 y(form)i Fi(\()p Fe(a)43 b(:)14 b(:)g(:)p Fi(\))p Fm(,)32 b(where)f Fe(a)h Fm(is)f(an)h(atom.)48 b(These)31 b(include)h(all)g(the)g(uses)f(of)g(the)h(primitiv)n(e)515 1644 y(op)r(erators,)25 b(and)j(there)f(is)h(a)f(clause)g(for)g(eac)n (h)g(one.)515 1806 y Fi(>)43 b(\(eval.)e('\(eq)h('a)h('a\))f('\(\)\)) 515 1905 y(t)515 2005 y(>)h(\(eval.)e('\(cons)g(x)i('\(b)g(c\)\))907 2105 y('\(\(x)f(a\))h(\(y)f(b\)\)\))515 2204 y(\(a)g(b)i(c\))515 2366 y Fm(All)28 b(of)f(these)h(\(except)g Fi(quote)p Fm(\))e(call)h Fi(eval.)f Fm(to)h(\014nd)h(the)g(v)-5 b(alue)28 b(of)f(the)h(argumen)n(ts.)639 2466 y(The)j(last)g(t)n(w)n(o) g(clauses)f(are)g(more)g(complicated.)48 b(T)-7 b(o)30 b(ev)-5 b(aluate)31 b(a)g Fi(cond)f Fm(expression)515 2565 y(w)n(e)i(call)h(a)f(subsidiary)g(function)i(called)e Fi(evcon.)p Fm(,)g(whic)n(h)h(w)n(orks)f(its)h(w)n(a)n(y)e(through)i (the)515 2665 y(clauses)28 b(recursiv)n(ely)-7 b(,)28 b(lo)r(oking)h(for)g(one)g(in)h(whic)n(h)f(the)h(\014rst)f(elemen)n(t)h (returns)e Fi(t)p Fm(.)43 b(When)515 2765 y(it)28 b(\014nds)g(suc)n(h)f (a)g(clause)g(it)h(returns)f(the)h(v)-5 b(alue)27 b(of)h(the)g(second)f (elemen)n(t.)515 2927 y Fi(>)43 b(\(eval.)e('\(cond)g(\(\(atom)g(x\))i ('atom\))1212 3026 y(\('t)f('list\)\))907 3126 y('\(\(x)g('\(a)g (b\)\)\)\))515 3225 y(list)639 3387 y Fm(The)29 b(\014nal)g(part)f(of)h (the)h(second)e(clause)g(of)h Fi(eval.)e Fm(handles)i(calls)f(to)h (functions)g(that)515 3487 y(ha)n(v)n(e)e(b)r(een)h(passed)f(as)g (parameters.)37 b(It)28 b(w)n(orks)e(b)n(y)i(replacing)f(the)h(atom)g (with)g(its)g(v)-5 b(alue)515 3587 y(\(whic)n(h)27 b(ough)n(t)f(to)h(b) r(e)g(a)f Fi(lambda)f Fm(or)h Fi(label)f Fm(expression\))g(and)i(ev)-5 b(aluating)26 b(the)i(resulting)515 3686 y(expression.)35 b(So)515 3848 y Fi(\(eval.)41 b('\(f)h('\(b)h(c\)\))820 3948 y('\(\(f)f(\(lambda)e(\(x\))j(\(cons)e('a)i(x\)\)\)\)\))515 4110 y Fm(turns)27 b(in)n(to)515 4259 y Fi(\(eval.)41 b('\(\(lambda)f(\(x\))i(\(cons)g('a)g(x\)\))h('\(b)f(c\)\))820 4359 y('\(\(f)g(\(lambda)e(\(x\))j(\(cons)e('a)i(x\)\)\)\)\))515 4508 y Fm(whic)n(h)27 b(returns)g Fi(\(a)43 b(b)g(c\))p Fm(.)639 4608 y(The)34 b(last)g(t)n(w)n(o)f(clauses)h(in)g Fi(eval.)e Fm(handle)i(function)g(calls)g(in)g(whic)n(h)g(the)h (\014rst)e(ele-)515 4707 y(men)n(t)25 b(is)h(an)f(actual)g Fi(lambda)e Fm(or)h Fi(label)f Fm(expression.)35 b(A)26 b Fi(label)d Fm(expression)h(is)h(ev)-5 b(aluated)515 4807 y(b)n(y)26 b(pushing)h(a)g(list)g(of)g(the)g(function)h(name)f (and)g(the)g(function)h(itself)f(on)n(to)f(the)i(en)n(viron-)515 4907 y(men)n(t,)23 b(and)f(then)h(calling)e Fi(eval.)f Fm(on)i(an)g(expression)f(with)h(the)h(inner)f Fi(lambda)e Fm(expression)515 5006 y(substituted)28 b(for)f(the)h Fi(label)e Fm(expression.)35 b(That)28 b(is,)1926 5255 y(9)p eop %%Page: 10 10 10 9 bop 515 523 a Fi(\(eval.)41 b('\(\(label)f(firstatom)g(\(lambda)h (\(x\))1735 623 y(\(cond)h(\(\(atom)f(x\))i(x\))1997 722 y(\('t)f(\(firstatom)d(\(car)j(x\)\)\)\)\)\))907 822 y(y\))820 922 y('\(\(y)g(\(\(a)g(b\))h(\(c)g(d\)\)\)\)\))515 1104 y Fm(b)r(ecomes)515 1270 y Fi(\(eval.)e('\(\(lambda)f(\(x\))994 1370 y(\(cond)i(\(\(atom)f(x\))i(x\))1256 1469 y(\('t)f(\(firstatom)d (\(car)j(x\)\)\)\)\))907 1569 y(y\))820 1669 y('\(\(firstatom)951 1768 y(\(label)f(firstatom)f(\(lambda)g(\(x\))1779 1868 y(\(cond)h(\(\(atom)g(x\))i(x\))2040 1968 y(\('t)g(\(firstatom)c(\(car) j(x\)\)\)\)\)\)\))907 2067 y(\(y)h(\(\(a)f(b\))h(\(c)g(d\)\)\)\)\))515 2233 y Fm(whic)n(h)27 b(ev)n(en)n(tually)g(returns)g Fi(a)p Fm(.)639 2333 y(Finally)-7 b(,)21 b(an)e(expression)f(of)h(the)h (form)f Fi(\(\(lambda)40 b(\()p Fe(p)2317 2345 y Fl(1)2367 2333 y Fe(:)14 b(:)g(:)g(p)2520 2345 y Fc(n)2565 2333 y Fi(\))43 b Fe(e)p Fi(\))g Fe(a)2822 2345 y Fl(1)2873 2333 y Fe(:)14 b(:)g(:)g(a)3028 2345 y Fc(n)3073 2333 y Fi(\))19 b Fm(is)g(ev)-5 b(al-)515 2433 y(uated)22 b(b)n(y)h(\014rst)f(calling)g Fi(evlis.)e Fm(to)i(get)h(a)f(list)h(of)f (v)-5 b(alues)22 b Fi(\()p Fe(v)2402 2445 y Fl(1)2483 2433 y Fe(:)14 b(:)g(:)43 b(v)2663 2445 y Fc(n)2709 2433 y Fi(\))22 b Fm(of)g(the)h(argumen)n(ts)515 2532 y Fe(a)559 2544 y Fl(1)610 2532 y Fe(:)14 b(:)g(:)f(a)764 2544 y Fc(n)809 2532 y Fm(,)25 b(and)e(then)g(ev)-5 b(aluating)23 b Fe(e)g Fm(with)g Fi(\()p Fe(p)1925 2544 y Fl(1)2006 2532 y Fe(v)2046 2544 y Fl(1)2083 2532 y Fi(\))g Fe(:)14 b(:)g(:)23 b Fi(\()p Fe(p)2356 2544 y Fc(n)2444 2532 y Fe(v)2484 2544 y Fc(n)2530 2532 y Fi(\))f Fm(app)r(ended)i(to)f(the)g (fron)n(t)515 2632 y(of)k(the)h(en)n(vironmen)n(t.)36 b(So)515 2814 y Fi(\(eval.)41 b('\(\(lambda)f(\(x)i(y\))h(\(cons)f(x)h (\(cdr)f(y\)\)\))907 2914 y('a)907 3014 y('\(b)g(c)i(d\)\))820 3113 y('\(\)\))515 3296 y Fm(b)r(ecomes)515 3462 y Fi(\(eval.)d ('\(cons)g(x)i(\(cdr)f(y\)\))820 3562 y('\(\(x)g(a\))h(\(y)f(\(b)h(c)g (d\)\)\)\))515 3728 y Fm(whic)n(h)27 b(ev)n(en)n(tually)g(returns)g Fi(\(a)43 b(c)g(d\))p Fm(.)515 4002 y Fj(5)134 b(Aftermath)515 4184 y Fm(No)n(w)35 b(that)g(w)n(e)g(understand)g(ho)n(w)g Fi(eval)f Fm(w)n(orks,)h(let's)h(step)f(bac)n(k)g(and)g(consider)f (what)515 4284 y(it)f(means.)53 b(What)34 b(w)n(e)e(ha)n(v)n(e)g(here)h (is)g(a)f(remark)-5 b(ably)32 b(elegan)n(t)g(mo)r(del)h(of)g (computation.)515 4383 y(Using)24 b(just)g Fi(quote)p Fm(,)f Fi(atom)p Fm(,)h Fi(eq)p Fm(,)g Fi(car)p Fm(,)f Fi(cdr)p Fm(,)h Fi(cons)p Fm(,)g(and)f Fi(cond)p Fm(,)h(w)n(e)g(can)f (de\014ne)i(a)e(function,)515 4483 y Fi(eval.)p Fm(,)c(that)h(actually) f(implemen)n(ts)h(our)f(language,)g(and)h(then)g(using)f(that)h(w)n(e)g (can)f(de\014ne)515 4583 y(an)n(y)27 b(additional)g(function)h(w)n(e)f (w)n(an)n(t.)639 4682 y(There)39 b(w)n(ere)f(already)g(mo)r(dels)h(of)h (computation,)i(of)d(course|most)f(notably)h(the)515 4782 y(T)-7 b(uring)29 b(Mac)n(hine.)45 b(But)30 b(T)-7 b(uring)30 b(Mac)n(hine)f(programs)f(are)h(not)i(v)n(ery)e(edifying)h (to)g(read.)515 4881 y(If)35 b(y)n(ou)g(w)n(an)n(t)f(a)h(language)f (for)g(describing)h(algorithms,)g(y)n(ou)g(migh)n(t)g(w)n(an)n(t)g (something)515 4981 y(more)27 b(abstract,)f(and)i(that)f(w)n(as)g(one)g (of)h(McCarth)n(y's)e(aims)h(in)h(de\014ning)g(Lisp.)1905 5255 y(10)p eop %%Page: 11 11 11 10 bop 639 523 a Fm(The)26 b(language)e(he)h(de\014ned)h(in)g(1960)d (w)n(as)i(missing)g(a)g(lot.)36 b(It)26 b(has)f(no)g(side-e\013ects,)g (no)515 623 y(sequen)n(tial)c(execution)h(\(whic)n(h)h(is)f(useful)g (only)g(with)h(side)f(e\013ects)h(an)n(yw)n(a)n(y\),)e(no)h(practical) 515 722 y(n)n(um)n(b)r(ers,)846 692 y Fl(4)925 722 y Fm(and)39 b(dynamic)f(scop)r(e.)72 b(But)39 b(these)g(limitations)g (can)g(b)r(e)h(remedied)f(with)515 822 y(surprisingly)28 b(little)j(additional)f(co)r(de.)44 b(Steele)31 b(and)f(Sussman)g(sho)n (w)f(ho)n(w)g(to)i(do)e(it)i(in)f(a)515 922 y(famous)d(pap)r(er)g (called)g("The)g(Art)h(of)g(the)g(In)n(terpreter.")2331 891 y Fl(5)639 1021 y Fm(If)e(y)n(ou)f(understand)h(McCarth)n(y's)e Fi(eval)p Fm(,)h(y)n(ou)g(understand)g(more)g(than)h(just)g(a)f(stage) 515 1121 y(in)d(the)h(history)f(of)g(languages.)33 b(These)22 b(ideas)g(are)f(still)i(the)g(seman)n(tic)f(core)f(of)h(Lisp)h(to)r(da) n(y)-7 b(.)515 1220 y(So)24 b(studying)g(McCarth)n(y's)f(original)g (pap)r(er)h(sho)n(ws)f(us,)i(in)g(a)f(sense,)g(what)h(Lisp)f(really)f (is.)515 1320 y(It's)e(not)h(something)f(that)h(McCarth)n(y)f(designed) g(so)g(m)n(uc)n(h)g(as)g(something)g(he)h(disco)n(v)n(ered.)515 1420 y(It's)34 b(not)g(in)n(trinsically)g(a)f(language)g(for)g(AI)i(or) e(for)h(rapid)f(protot)n(yping,)i(or)e(an)n(y)h(other)515 1519 y(task)f(at)i(that)f(lev)n(el.)57 b(It's)34 b(what)h(y)n(ou)e(get) h(\(or)g(one)g(thing)g(y)n(ou)g(get\))g(when)h(y)n(ou)e(try)h(to)515 1619 y(axiomatize)26 b(computation.)639 1719 y(Ov)n(er)g(time,)h(the)g (median)g(language,)e(meaning)h(the)h(language)e(used)i(b)n(y)f(the)h (median)515 1818 y(programmer,)h(has)h(gro)n(wn)f(consisten)n(tly)h (closer)f(to)i(Lisp.)43 b(So)29 b(b)n(y)h(understanding)f Fi(eval)515 1918 y Fm(y)n(ou're)36 b(understanding)g(what)h(will)h (probably)e(b)r(e)h(the)h(main)f(mo)r(del)g(of)g(computation)515 2017 y(w)n(ell)27 b(in)n(to)g(the)h(future.)p 515 2071 1146 4 v 607 2124 a Fh(4)642 2148 y Fg(It)c(is)f(p)r(ossible)h(to)g(do) g(arithmetic)f(in)h(McCarth)n(y's)f(1960)i(Lisp)e(b)n(y)h(using)g(e.g.) 31 b(a)24 b(list)f(of)h Fa(n)f Fg(atoms)g(to)515 2227 y(represen)n(t)h(the)h(n)n(um)n(b)r(er)d Fa(n)p Fg(.)607 2282 y Fh(5)642 2306 y Fg(Guy)34 b(Lewis)f(Steele,)j(Jr.)60 b(and)34 b(Gerald)g(Ja)n(y)g(Sussman,)g("The)g(Art)f(of)g(the)h(In)n (terpreter,)j(or)c(the)515 2385 y(Mo)r(dularit)n(y)23 b(Complex)g(\(P)n(arts)h(Zero,)g(One,)f(and)i(Tw)n(o\),")f(MIT)f(AI)h (Lab)g(Memo)f(453,)h(Ma)n(y)f(1978.)1905 5255 y Fm(11)p eop %%Page: 12 12 12 11 bop 515 523 a Fj(Notes)515 705 y Fm(In)26 b(translating)f (McCarth)n(y's)g(notation)h(in)n(to)g(running)g(co)r(de)g(I)g(tried)h (to)f(c)n(hange)f(as)g(little)515 805 y(as)33 b(p)r(ossible.)56 b(I)34 b(w)n(as)f(tempted)i(to)f(mak)n(e)f(the)h(co)r(de)g(easier)f(to) g(read,)i(but)g(I)f(w)n(an)n(ted)f(to)515 904 y(k)n(eep)27 b(the)h(\015a)n(v)n(or)d(of)j(the)g(original.)639 1004 y(In)h(McCarth)n(y's)e(pap)r(er,)h(falsit)n(y)g(is)h(represen)n(ted)e (b)n(y)h Fi(f)p Fm(,)g(not)h(the)g(empt)n(y)f(list.)40 b(I)28 b(used)515 1103 y Fi(\(\))f Fm(to)h(represen)n(t)f(falsit)n(y)g (so)g(that)i(the)f(examples)f(w)n(ould)h(w)n(ork)e(in)j(Common)e(Lisp.) 38 b(The)515 1203 y(co)r(de)31 b(no)n(where)f(dep)r(ends)h(on)g(falsit) n(y)g(happ)r(ening)g(also)f(to)h(b)r(e)g(the)h(empt)n(y)f(list;)i (nothing)515 1303 y(is)27 b(ev)n(er)g(consed)g(on)n(to)f(the)i(result)g (returned)f(b)n(y)g(a)g(predicate.)639 1402 y(I)g(skipp)r(ed)g (building)g(lists)g(out)g(of)g(dotted)g(pairs,)f(b)r(ecause)h(y)n(ou)f (don't)h(need)g(them)g(to)515 1502 y(understand)22 b Fi(eval)p Fm(.)33 b(I)23 b(also)e(skipp)r(ed)h(men)n(tioning)g Fi(apply)p Fm(,)g(though)g(it)g(w)n(as)g Fi(apply)e Fm(\(a)i(v)n(ery) 515 1602 y(early)28 b(form)h(of)h(it,)h(whose)e(main)g(purp)r(ose)g(w)n (as)g(to)g(quote)h(argumen)n(ts\))e(that)i(McCarth)n(y)515 1701 y(called)19 b(the)i(univ)n(ersal)d(function)j(in)f(1960;)h Fi(eval)d Fm(w)n(as)h(then)h(just)h(a)e(subroutine)h(that)g Fi(apply)515 1801 y Fm(called)27 b(to)g(do)h(all)f(the)h(w)n(ork.)639 1900 y(I)g(de\014ned)g Fi(list)e Fm(and)h(the)h Fi(c)p Fd(x)p Fi(r)p Fm(s)e(as)h(abbreviations)f(b)r(ecause)h(that's)g(ho)n(w) g(McCarth)n(y)515 2000 y(did)32 b(it.)51 b(In)32 b(fact)g(the)g Fi(c)p Fd(x)p Fi(r)p Fm(s)f(could)h(all)g(ha)n(v)n(e)e(b)r(een)j (de\014ned)f(as)g(ordinary)e(functions.)50 b(So)515 2100 y(could)34 b Fi(list)e Fm(if)i(w)n(e)g(mo)r(di\014ed)g Fi(eval)p Fm(,)h(as)e(w)n(e)g(easily)h(could,)h(to)f(let)g(functions)h (tak)n(e)e(an)n(y)515 2199 y(n)n(um)n(b)r(er)27 b(of)h(argumen)n(ts.) 639 2299 y(McCarth)n(y's)39 b(pap)r(er)h(only)g(had)g(\014v)n(e)g (primitiv)n(e)g(op)r(erators.)74 b(He)40 b(used)g Fi(cond)f Fm(and)515 2399 y Fi(quote)26 b Fm(but)j(ma)n(y)e(ha)n(v)n(e)g(though)n (t)h(of)g(them)h(as)f(part)f(of)h(his)h(metalanguage.)36 b(He)29 b(lik)n(ewise)515 2498 y(didn't)35 b(de\014ne)g(the)g(logical)e (op)r(erators)g Fi(and)g Fm(and)i Fi(not)p Fm(,)g(but)g(this)g(is)g (less)f(of)g(a)h(problem)515 2598 y(b)r(ecause)27 b(adequate)g(v)n (ersions)f(can)h(b)r(e)h(de\014ned)g(as)f(functions.)639 2697 y(In)g(the)g(de\014nition)g(of)g Fi(eval.)34 b Fm(w)n(e)26 b(called)g(other)g(functions)h(lik)n(e)g Fi(pair.)34 b Fm(and)26 b Fi(assoc.)p Fm(,)515 2797 y(but)20 b(an)n(y)f(call)h(to)g (one)f(of)h(the)g(functions)h(w)n(e)e(de\014ned)h(in)h(terms)e(of)h (the)g(primitiv)n(e)g(op)r(erators)515 2897 y(could)27 b(b)r(e)h(replaced)f(b)n(y)g(a)g(call)h(to)f Fi(eval.)p Fm(.)35 b(That)27 b(is,)515 3079 y Fi(\(assoc.)40 b(\(car)i(e\))h(a\)) 515 3262 y Fm(could)27 b(ha)n(v)n(e)g(b)r(een)h(written)f(as)515 3428 y Fi(\(eval.)41 b('\(\(label)f(assoc.)1212 3528 y(\(lambda)h(\(x)i(y\))1299 3627 y(\(cond)f(\(\(eq)g(\(caar)f(y\))i (x\))g(\(cadar)e(y\)\))1561 3727 y(\('t)h(\(assoc.)f(x)i(\(cdr)f (y\)\)\)\)\)\))907 3827 y(\(car)g(e\))907 3926 y(a\))863 4026 y(\(cons)g(\(list)f('e)i(e\))g(\(cons)e(\(list)h('a)h(a\))g (a\)\)\))639 4192 y Fm(There)36 b(w)n(as)f(a)h(small)g(bug)g(in)h (McCarth)n(y's)e Fi(eval)p Fm(.)61 b(Line)37 b(16)e(w)n(as)h(\(equiv)-5 b(alen)n(t)36 b(to\))515 4291 y Fi(\(evlis.)k(\(cdr)i(e\))h(a\))30 b Fm(instead)h(of)f(just)i Fi(\(cdr)42 b(e\))p Fm(,)30 b(whic)n(h)h(caused)f(the)h(argumen)n(ts)f(in)515 4391 y(a)i(call)g(to)h(a)f(named)h(function)g(to)f(b)r(e)h(ev)-5 b(aluated)33 b(t)n(wice.)52 b(This)32 b(suggests)f(that)i(this)g(de-) 515 4491 y(scription)27 b(of)h Fi(eval)f Fm(had)h(not)g(y)n(et)g(b)r (een)g(implemen)n(ted)h(in)f(IBM)g(704)f(mac)n(hine)h(language)515 4590 y(when)j(the)g(pap)r(er)f(w)n(as)g(submitted.)48 b(It)31 b(also)f(sho)n(ws)f(ho)n(w)i(hard)f(it)h(is)g(to)f(b)r(e)i (sure)e(of)h(the)515 4690 y(correctness)25 b(of)j(an)n(y)f(length)h(of) f(program)f(without)i(trying)f(to)g(run)h(it.)639 4790 y(I)h(encoun)n(tered)f(one)g(other)g(problem)g(in)h(McCarth)n(y's)e(co) r(de.)39 b(After)29 b(giving)f(the)h(def-)515 4889 y(inition)34 b(of)g Fi(eval)f Fm(he)h(go)r(es)g(on)f(to)h(giv)n(e)g(some)f(examples) h(of)g(higher-order)e(functions|)515 4989 y(functions)c(that)g(tak)n(e) e(other)h(functions)h(as)f(argumen)n(ts.)36 b(He)28 b(de\014nes)f Fi(maplist)p Fm(:)1905 5255 y(12)p eop %%Page: 13 13 13 12 bop 515 523 a Fi(\(label)41 b(maplist)820 623 y(\(lambda)g(\(x)h (f\))907 722 y(\(cond)g(\(\(null)f(x\))h('\(\)\))1169 822 y(\('t)g(\(cons)f(\(f)i(x\))g(\(maplist)d(\(cdr)i(x\))h (f\)\)\)\)\)\))515 1005 y Fm(then)33 b(uses)f(it)h(to)g(write)f(a)h (simple)f(function)i Fi(diff)d Fm(for)h(sym)n(b)r(olic)g(di\013eren)n (tiation.)52 b(But)515 1104 y Fi(diff)29 b Fm(passes)g Fi(maplist)f Fm(a)i(function)i(that)f(uses)f Fi(x)g Fm(as)g(a)g (parameter,)g(and)h(the)g(reference)515 1204 y(to)c(it)h(is)g(captured) f(b)n(y)g(the)h(parameter)e Fi(x)i Fm(within)g Fi(maplist)p Fm(.)2445 1174 y Fl(6)639 1303 y Fm(It's)34 b(an)g(elo)r(quen)n(t)f (testimon)n(y)h(to)f(the)h(dangers)f(of)g(dynamic)h(scop)r(e)f(that)h (ev)n(en)g(the)515 1403 y(v)n(ery)d(\014rst)h(example)g(of)h (higher-order)d(Lisp)i(functions)h(w)n(as)f(brok)n(en)f(b)r(ecause)h (of)h(it.)52 b(It)515 1503 y(ma)n(y)22 b(b)r(e)h(that)g(McCarth)n(y)e (w)n(as)h(not)h(fully)g(a)n(w)n(are)d(of)j(the)g(implications)f(of)h (dynamic)g(scop)r(e)515 1602 y(in)34 b(1960.)56 b(Dynamic)34 b(scop)r(e)g(remained)g(in)h(Lisp)f(implemen)n(tations)h(for)f(a)g (surprisingly)515 1702 y(long)28 b(time|un)n(til)h(Sussman)g(and)f (Steele)h(dev)n(elop)r(ed)g(Sc)n(heme)f(in)h(1975.)39 b(Lexical)28 b(scop)r(e)515 1802 y(do)r(es)20 b(not)g(complicate)f(the) i(de\014nition)g(of)f Fi(eval)e Fm(v)n(ery)h(m)n(uc)n(h,)j(but)f(it)f (ma)n(y)g(mak)n(e)f(compilers)515 1901 y(harder)26 b(to)i(write.)p 515 4771 1146 4 v 607 4825 a Fh(6)642 4848 y Fg(Presen)n(t)d(da)n(y)h (Lisp)e(programmers)e(w)n(ould)j(use)g Fb(mapcar)h Fg(instead)g(of)e Fb(maplist)j Fg(here.)35 b(This)24 b(example)515 4927 y(do)r(es)18 b(clear)h(up)f(one)h(m)n(ystery:)28 b(wh)n(y)18 b Fb(maplist)i Fg(is)e(in)f(Common)g(Lisp)h(at)g(all.)29 b(It)19 b(w)n(as)f(the)h(original)e(mapping)515 5006 y(function,)24 b(and)g Fb(mapcar)h Fg(a)f(later)g(addition.)1905 5255 y Fm(13)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF