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4426 y(the)j(pro)r(ductivit)n(y)f(of)h(users.)648 4526
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(the)h(seman)n(tic)f(domain.)648 3928 y(These)18 b(c)n(haracteristics)e
(mak)n(e)h(higher-order)f(attribute)i(grammars)e(particularly)h(suit-)
523 4028 y(able)h(to)g(mo)r(del)h(in)n(teractiv)n(e)e(language-based)e
(en)n(vironmen)n(ts)i([TC90)o(,P)n(en94,KS98)n(,Sar99)o(].)523
4127 y(It)25 b(is)g(kno)n(wn)f(that)h(the)g(incremen)n(tal)f(attribute)
h(ev)-5 b(aluator)24 b(for)g(ordered)g(attribute)h(gram-)523
4227 y(mars)35 b([Kas80)m(,R)-7 b(T89])35 b(can)h(b)r(e)f(trivially)g
(adapted)g(for)g(the)h(incremen)n(tal)f(ev)-5 b(aluation)35
b(of)523 4327 y(higher-order)20 b(attribute)j(grammars.)d(The)j
(adapted)f(ev)-5 b(aluator,)21 b(ho)n(w)n(ev)n(er,)g(decorates)g(ev-)
523 4426 y(ery)h(instance)g(of)g(a)h(higher-order)d(attribute)i
(separately)f([TC90)o(].)i(Note)f(that)h(in)g(suc)n(h)f(tra-)523
4526 y(ditional)i(ev)-5 b(aluators)22 b(the)i(usual)f(represen)n
(tation)f(for)i(an)f(attributed)h(tree)g(is)f(an)h Fu(unshar)l(e)l(d)
523 4625 y(tr)l(e)l(e)p FB(.)30 b(Higher-order)e(attribute)j(grammars)d
(de\034ne)i(higher-order)e(attributes,)j(whic)n(h)f(in-)523
4725 y(stances)23 b(are)f(higher-order)f(trees.)h(Di\033eren)n(t)i
(instances)f(of)g(higher-order)e(attributes)i(ma)n(y)523
4825 y(b)r(e)h(equal)f(trees)g(or)g(share)f(common)h(subtrees.)g
(Consequen)n(tly)-7 b(,)23 b(the)h(most)g(e\036cien)n(t)f(repre-)523
4924 y(sen)n(tation)j(for)h(suc)n(h)g(high-order)e(trees)i(is)g(a)g
(shared)f(tree,)h Fu(i.e.)p FB(,)i(a)d Fu(dir)l(e)l(cte)l(d)k(acyclic)i
(gr)l(aph)p Black Black eop
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4 3 bop Black Black 523 448 a FB(\(D)n(A)n(G\).)27 b(Consequen)n(tly)-7
b(,)25 b(there)g(is)h(a)f(clash)g(b)r(et)n(w)n(een)h(the)g(t)n(w)n(o)f
(represen)n(tations,)e(namely)-7 b(,)523 548 y(tree)30
b(and)h(D)n(A)n(G.)g(There)f(are)f(t)n(w)n(o)h(w)n(a)n(ys)f(to)i(solv)n
(e)e(this)i(tension:)g(either)f(w)n(e)g(use)h(sp)r(eci\034c)523
648 y(tec)n(hniques)e(to)g(decorate)f(D)n(A)n(Gs)h(or)f(w)n(e)h(guaran)
n(tee)e(that)i(the)h(terms)f(are,)f(in)h(fact,)h(trees)523
747 y(that)e(are)e(decorated)h(b)n(y)g(an)g(adapted)h(ev)-5
b(aluator.)648 851 y(Let)34 b(us)h(discuss)e(\034rst)i(the)f(use)h(of)f
(adapted)g(ev)-5 b(aluators.)33 b(T)-7 b(eitelbaum)35
b([TC90)o(])f(pro-)523 950 y(p)r(oses)24 b(a)f(simple)i(approac)n(h)d
(to)i(handle)g(D)n(A)n(Gs:)g(whenev)n(er)f(a)h(higher-order)d
(attribute)k(has)523 1050 y(to)k(b)r(e)g(instan)n(tiated)f(with)h(a)g
(higher-order)d(tree)i(\()p Fu(i.e.)p FB(,)j(with)e(a)g(D)n(A)n(G\),)g
(the)g(tree)f(sharing)523 1149 y(is)34 b(brok)n(en)e(and)h(the)h
(attribute)g(is)f(actually)g(instan)n(tiated)h(with)g(a)f(tree.)g(This)
h(tree)f(is)g(a)523 1249 y(\020)7 b Fu(tr)l(e)l(e-c)l(opy)p
FB(\021)30 b(of)23 b(the)g(D)n(A)n(G.)h(After)f(that,)h(the)f
(higher-order)e(tree)i(can)f(b)r(e)i(easily)e(decorated)523
1349 y(b)n(y)30 b(an)f(adapted)h Fu(change)j(pr)l(op)l(agator)e
FB(since)f(attribute)g(v)-5 b(alues)29 b(can)h(b)r(e)g(asso)r(ciated)f
(with)523 1448 y(the)37 b(tree)f(no)r(des)h(in)f(the)h(standard)f(w)n
(a)n(y)-7 b(.)35 b(This)i(approac)n(h,)d(ho)n(w)n(ev)n(er,)h(leads)h
(to)g(a)h(non-)523 1548 y(optimal)24 b(incremen)n(tal)g(b)r(eha)n
(viour)f(when)i(higher-order)d(attributes)i(are)g(a\033ected)g(b)n(y)g
(tree)523 1648 y(transformations,)g(as)g(sho)n(wn)h(in)h([CP96].)f
(Note)h(that)g(as)f(a)g(result)g(of)g(breaking)f(the)i(shar-)523
1747 y(ing,)c(di\033eren)n(t)h(instan)n(tiations)f(of)g(higher-order)e
(attributes)j(are,)e(indeed,)i(di\033eren)n(t)g(trees.)523
1847 y(Suc)n(h)h(trees)g(ha)n(v)n(e)e(to)i(b)r(e)h(decorated)d
(separately)-7 b(,)23 b(without)h(the)h(p)r(ossibilit)n(y)e(of)h
(reusing)f(at-)523 1946 y(tribute)38 b(v)-5 b(alues)37
b(across)e(the)j(di\033eren)n(t)g(decorations)e(of)h(those)g
(attributed)h(trees.)f(Note)523 2046 y(that)f(instances)e(of)i(the)f
(same)g(higher-order)e(attribute)i(are)f(lik)n(ely)h(to)g(b)r(e)h
(\(completely)523 2146 y(or)g(partially\))h(decorated)f(with)h(the)h
(same)f(attribute)g(v)-5 b(alues.)37 b(In)g(order)f(to)h(e\036cien)n
(tly)523 2245 y(\(and)26 b(incremen)n(tally\))g(ev)-5
b(aluate)26 b(suc)n(h)f(instances,)h(the)h(reuse)e(of)h(those)g(v)-5
b(alues)26 b(should)g(b)r(e)523 2345 y(ac)n(hiev)n(ed.)523
2613 y Fp(2.2)94 b(Visit-F)-8 b(unction)31 b(Memoization)523
2797 y FB(The)i(visit-function)g(memoization)f(prop)r(osed)g(b)n(y)g(P)
n(ennings)h([P)n(en94)o(])g(is)g(based)f(on)h(the)523
2897 y(follo)n(wing)26 b(com)n(bination)h(of)h(ideas:)523
3029 y Fp(Purely)e(functional)g(attribute)g(ev)-5 b(aluators:)22
b FB(Syn)n(tax)f(trees)h(are)f(decorated)h(b)n(y)g Fu(bind-)523
3129 y(ing-tr)l(e)l(e)41 b(b)l(ase)l(d)i(attribute)e(evaluators)h
FB([P)n(en94)o(].)f(Suc)n(h)g(ev)-5 b(aluators)39 b(are)h(strict,)g
(purely)523 3228 y(functional)c(attribute)g(ev)-5 b(aluators.)35
b(A)n(ttribute)h(instances)g(are)f(not)h(stored)f(in)h(the)g(tree)523
3328 y(no)r(des,)29 b(but,)i(instead,)e(they)h(are)e(the)i(argumen)n
(ts)e(and)i(the)g(results)f(of)g(\(side-e\033ect)h(free\))523
3428 y(functions:)f(the)f Fu(visit-functions)p FB(.)h(Binding-trees)e
(are)h(used)g(with)h(the)g(single)e(purp)r(ose)h(to)523
3527 y(\020glue\021)37 b(the)30 b(di\033eren)n(t)h(tra)n(v)n(ersal)d
(functions)j(of)f(the)h(ev)-5 b(aluator,)30 b Fu(i.e.)p
FB(,)i(they)f(con)n(v)n(ey)e(infor-)523 3627 y(mation)e(b)r(et)n(w)n
(een)h(tra)n(v)n(ersals.)523 3825 y Fp(Data)k(constructor)g
(memoization:)22 b FB(Since)27 b(attribute)g(v)-5 b(alues)26
b(are)g(not)h(stored)f(in)h(the)523 3924 y(syn)n(tax)20
b(tree,)g(m)n(ultiple)h(instances)f(of)g(the)h(syn)n(tax)f(tree)g(can)g
(b)r(e)h(shared.)e(That)i(is,)f(trees)g(are)523 4024
y(collapsed)j(in)n(to)g(minimal)h Fu(dir)l(e)l(ct)j(acyclic)h(gr)l
(aphs)p FB(.)d(D)n(A)n(Gs)f(are)f(obtained)g(b)n(y)h(constructing)523
4124 y(trees)k(b)r(ottom-up)g(and)g(b)n(y)f(using)h(constructor)f
(memoization)g(to)h(eliminate)g(replication)523 4223
y(of)23 b(common)g(sub-expressions.)e(This)i(tec)n(hnique,)g(also)f
(called)h Fu(hash-c)l(onsing)p FB(,)h(guaran)n(tees)523
4323 y(that)38 b(t)n(w)n(o)g(iden)n(tical)g(ob)5 b(jects)37
b(share)g(the)i(same)e(records)g(on)h(the)g(heap,)g(and)g(th)n(us)g
(are)523 4422 y(represen)n(ted)26 b(b)n(y)i(the)g(same)f(p)r(oin)n
(ter.)648 4526 y(The)i(basic)g(idea)h(of)f(hash-consing)f(is)h(v)n(ery)
g(simple:)h(whenev)n(er)e(a)h(new)h(no)r(de)g(is)f(allo-)523
4625 y(cated)e(\(or)g Fu(\020c)l(onse)l(d\021)6 b FB(\))28
b(w)n(e)f(c)n(hec)n(k)f(whether)h(there)g(exists)g(already)e(an)i(iden)
n(tical)g(record)f(in)523 4725 y(the)34 b(heap.)f(If)g(so,)g(w)n(e)g(a)
n(v)n(oid)e(the)j(allo)r(cation)e(and)h(simply)g(use)g(the)h(existing)e
(one.)h(Oth-)523 4825 y(erwise,)j(w)n(e)f(p)r(erform)h(the)h(allo)r
(cation)e(as)h(usual.)g(Generally)-7 b(,)35 b(a)h Fu(hash)j(table)e
FB(is)f(used)g(to)523 4924 y(searc)n(h)d(the)i(heap)g(for)f(a)g
(duplicated)h(record.)e(Hash-consing)g(can)h(b)r(e)h(applied)g(to)f
(pure)p Black Black eop
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5 4 bop Black Black 523 448 a FB(v)-5 b(alues)34 b(only)-7
b(,)34 b Fu(i.e.)p FB(,)i(v)-5 b(alues)33 b(that)i(nev)n(er)e(c)n
(hange)g(during)h(the)g(execution)g(of)g(a)g(program:)523
548 y(for)28 b(if)h(t)n(w)n(o)f(up)r(datable)g(records)f(ha)n(v)n(e)g
(iden)n(tical)i(v)-5 b(alues)28 b(no)n(w,)g(they)g(migh)n(t)h(not)f(b)r
(e)h(iden-)523 648 y(tical)36 b(later,)f(and)h(so)f(merging)g(them)i
(could)f(lead)f(to)h(incorrect)f(v)-5 b(alues.)35 b(Observ)n(e)g(that)
523 747 y(this)30 b(is)g(the)g(case)f(if)h(attributes)g(are)f(stored)g
(in)h(the)g(tree)g(no)r(des,)f(b)r(ecause)g(shared)g(no)r(des)523
847 y(ma)n(y)35 b(ha)n(v)n(e)g(to)h(store)g(di\033eren)n(t)g(attribute)
g(v)-5 b(alues)36 b(induced)g(b)n(y)g(di\033eren)n(t,)g(but)h(shared,)
523 946 y(attribute)28 b(instances)f(\(and)g(most)h(probably)e(will\).)
648 1046 y(A)n(ttribute)34 b(v)-5 b(alues)33 b(ma)n(y)g(b)r(e)h(large)f
(structures)f(\()p Fu(e.g.)p FB(,)k(sym)n(b)r(ol)d(tables,)h
(higher-order)523 1146 y(attributes,)18 b(etc\).)h(Therefore,)f(the)h
(constructors)d(for)i(user)g(de\034ned)h(t)n(yp)r(es)f(are)g(also)f
(shared.)523 1245 y(This)36 b(tec)n(hnique)g(solv)n(es)f(the)h(problem)
f(of)h(exp)r(ensiv)n(e)g(attribute)g(equalit)n(y)f(test)i(during)523
1345 y(ev)-5 b(aluation)29 b(and)g(it)g(also)g(settles)g(the)h(problem)
e(of)i(h)n(uge)e(memory)h(consumption)g(due)g(to)523
1445 y(m)n(ultiple)f(instances)f(of)h(the)g(same)f(attribute)g(v)-5
b(alue)28 b(in)f(a)h(syn)n(tax)e(tree.)523 1639 y Fp(F)-8
b(unction)35 b(memoization:)26 b FB(Due)k(to)g(the)h(pure)f(nature)f
(of)h(the)h(visit-functions,)f(incre-)523 1738 y(men)n(tal)19
b(ev)-5 b(aluation)18 b(can)h(no)n(w)f(b)r(e)i(obtained)e(b)n(y)h
(memoizing)g(calls)f(to)h(visit-functions.)g(The)523
1838 y(binding-tree)32 b(based)h(attribute)g(ev)-5 b(aluators)31
b(are)h(constructed)g(as)g(a)g(set)h(of)g(strict)g(func-)523
1938 y(tions.)26 b(Th)n(us,)g(standard)f(function)i(memoization)e(tec)n
(hniques)h(can)g(b)r(e)g(used)g(to)g(memoize)523 2037
y(their)34 b(calls.)g(Memoization)f(is)h(obtained)g(b)n(y)g(storing)f
(in)i(a)f Fu(memo)i(table)f FB(calls)e(to)h(visit-)523
2137 y(functions.)40 b(Ev)n(ery)f(call)g(corresp)r(onds)f(to)h(a)h
Fu(memo)h(entry)p FB(,)e(in)h(the)g Fu(memo)h(table)p
FB(,)g(that)523 2236 y(records)26 b(b)r(oth)i(the)g(argumen)n(ts)e(and)
h(the)h(results)f(of)h(one)f(call)g(to)h(a)f(visit-function.)648
2431 y(Let)37 b(us)g(describ)r(e)g(the)g(binding-tree)g(attribute)g(ev)
-5 b(aluators)35 b(in)j(more)e(detail.)h(Suc)n(h)523
2530 y(ev)-5 b(aluators)23 b(are)g(based)h(on)g(the)g(visit-sequence)f
(paradigm)g([Kas80)n(]:)i(the)f(visit-sequences)523 2630
y(induce)g(a)g(set)g(of)g Fu(visit-functions)p FB(,)h(eac)n(h)e(of)h
(them)h(p)r(erforming)e(the)h(computations)g(sc)n(hed-)523
2729 y(ule)31 b(for)g(a)f(particular)g(tra)n(v)n(ersal)e(of)j(the)h(ev)
-5 b(aluator.)29 b(The)i(di\033eren)n(t)g(tra)n(v)n(ersal)e(functions)
523 2829 y(are)19 b(\020glued\021)25 b(b)n(y)19 b(in)n(termediate)g
(data)g(structures:)g(the)h Fu(binding-tr)l(e)l(es)p
FB(.)g(The)f(visit-functions)523 2929 y(and)25 b(the)g(binding-tree)f
(data)g(t)n(yp)r(es)h(are)e(automatically)h(induced)h(b)n(y)f(a)g
Fu(binding)29 b(analysis)523 3028 y FB(of)f(the)g(visit-sequences)e([P)
n(en94)o(].)648 3128 y(As)j(a)h(result)f(of)h(the)g(binding)g
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Ft(visit)2758 3140 y Fo(v)2797 3128 y Fp(X)p Black 30
w FB(is)g(constructed)523 3228 y(for)22 b(ev)n(ery)g(terminal)p
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Fq(v)k FB(suc)n(h)d(that)g Fr(1)f Fs(\024)h Fq(v)j Fs(\024)d
Fq(n)p FB(,)g(with)g Fq(n)g FB(the)g(n)n(um)n(b)r(er)f(of)523
3327 y(visits)29 b(to)p 0 TeXcolorgray 30 w Fu(X)p Black
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Black FB(,)g(the)523 3427 y(inherited)e(attributes)f(of)g(visit)h
Fq(v)j FB(and)c(the)h(binding-trees)f(computed)g(in)h(previous)e
(visits)523 3526 y(that)36 b(are)f(destructed)h(b)n(y)g(visit)g
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(wing)523 3626 y(visits)e(and)f(the)i(syn)n(thesized)e(attributes)h(of)
g(visit)g Fq(v)s FB(.)g(The)g(\034rst)g(visit)f(do)r(es)h(not)g
(inherit)523 3726 y(an)n(y)22 b(binding-tree,)h(and)g(the)g(last)g(one)
g(do)r(es)g(not)g(syn)n(thesize)f(them.)i(The)f(in)n(tro)r(duction)g
(of)523 3825 y(binding-trees)28 b(is)h(re\035ected)g(in)h(the)f(t)n(yp)
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%%Page: 12 12
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%%BeginDocument: microc.ps
% remember original state
/origstate save def
% build a temporary dictionary
20 dict begin
% define string to hold a scanline's worth of data
/pix 1683 string def
% define space for color conversions
/grays 561 string def % space for gray scale line
/npixls 0 def
/rgbindx 0 def
% lower left corner
25 434 translate
% size of image (on paper, in 1/72inch coords)
224.42400 153.57600 scale
% define 'colorimage' if it isn't defined
% ('colortogray' and 'mergeprocs' come from xwd2ps
% via xgrab)
/colorimage where % do we know about 'colorimage'?
{ pop } % yes: pop off the 'dict' returned
{ % no: define one
/colortogray { % define an RGB->I function
/rgbdata exch store % call input 'rgbdata'
rgbdata length 3 idiv
/npixls exch store
/rgbindx 0 store
0 1 npixls 1 sub {
grays exch
rgbdata rgbindx get 20 mul % Red
rgbdata rgbindx 1 add get 32 mul % Green
rgbdata rgbindx 2 add get 12 mul % Blue
add add 64 idiv % I = .5G + .31R + .18B
put
/rgbindx rgbindx 3 add store
} for
grays 0 npixls getinterval
} bind def
% Utility procedure for colorimage operator.
% This procedure takes two procedures off the
% stack and merges them into a single procedure.
/mergeprocs { % def
dup length
3 -1 roll
dup
length
dup
5 1 roll
3 -1 roll
add
array cvx
dup
3 -1 roll
0 exch
putinterval
dup
4 2 roll
putinterval
} bind def
/colorimage { % def
pop pop % remove 'false 3' operands
{colortogray} mergeprocs
image
} bind def
} ifelse % end of 'false' case
561 384 8 % dimensions of data
[561 0 0 -384 0 384] % mapping matrix
{currentfile pix readhexstring pop}
false 3 colorimage
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