134 lines
3.9 KiB
Plaintext
134 lines
3.9 KiB
Plaintext
// Koka language test module
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// This module implements the GarsiaWachs algorithm.
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// It is an adaptation of the algorithm in ML as described by JeanChristophe Filli<6C>tre:
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// in ''A functional implementation of the GarsiaWachs algorithm. (functional pearl). ML workshop 2008, pages 91--96''.
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// See: http://www.lri.fr/~filliatr/publis/gwWml08.pdf
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//
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// The algorithm is interesting since it uses mutable references shared between a list and tree but the
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// side effects are not observable from outside. Koka automatically infers that the final algorithm is pure.
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// Note: due to a current limitation in the divergence analysis, koka cannot yet infer that mutually recursive
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// definitions in "insert" and "extract" are terminating and the final algorithm still has a divergence effect.
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// However, koka does infer that no other effect (i.e. an exception due to a partial match) can occur.
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module garcsiaWachs
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import test = qualified std/flags
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# pre processor test
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public function main() {
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wlist = Cons1(('a',3), [('b',2),('c',1),('d',4),('e',5)])
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tree = wlist.garsiaWachs()
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tree.show.println()
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}
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//----------------------------------------------------
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// Trees
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//----------------------------------------------------
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public type tree<a> {
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con Leaf(value :a)
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con Node(left :tree<a>, right :tree<a>)
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}
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function show( t : tree<char> ) : string {
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match(t) {
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Leaf(c) -> core/show(c)
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Node(l,r) -> "Node(" + show(l) + "," + show(r) + ")"
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}
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}
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//----------------------------------------------------
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// Non empty lists
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//----------------------------------------------------
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public type list1<a> {
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Cons1( head : a, tail : list<a> )
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}
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function map( xs, f ) {
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val Cons1(y,ys) = xs
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return Cons1(f(y), core/map(ys,f))
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}
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function zip( xs :list1<a>, ys :list1<b> ) : list1<(a,b)> {
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Cons1( (xs.head, ys.head), zip(xs.tail, ys.tail))
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}
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//----------------------------------------------------
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// Phase 1
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//----------------------------------------------------
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function insert( after : list<(tree<a>,int)>, t : (tree<a>,int), before : list<(tree<a>,int)> ) : div tree<a>
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{
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match(before) {
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Nil -> extract( [], Cons1(t,after) )
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Cons(x,xs) -> {
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if (x.snd < t.snd) then return insert( Cons(x,after), t, xs )
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match(xs) {
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Nil -> extract( [], Cons1(x,Cons(t,after)) )
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Cons(y,ys) -> extract( ys, Cons1(y,Cons(x,Cons(t,after))) )
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}
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}
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}
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}
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function extract( before : list<(tree<a>,int)>, after : list1<(tree<a>,int)> ) : div tree<a>
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{
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val Cons1((t1,w1) as x, xs ) = after
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match(xs) {
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Nil -> t1
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Cons((t2,w2) as y, ys) -> match(ys) {
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Nil -> insert( [], (Node(t1,t2), w1+w2), before )
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Cons((_,w3),_zs) ->
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if (w1 <= w3)
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then insert(ys, (Node(t1,t2), w1+w2), before)
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else extract(Cons(x,before), Cons1(y,ys))
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}
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}
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}
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function balance( xs : list1<(tree<a>,int)> ) : div tree<a> {
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extract( [], xs )
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}
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//----------------------------------------------------
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// Phase 2
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//----------------------------------------------------
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function mark( depth :int, t :tree<(a,ref<h,int>)> ) : <write<h>> () {
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match(t) {
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Leaf((_,d)) -> d := depth
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Node(l,r) -> { mark(depth+1,l); mark(depth+1,r) }
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}
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}
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function build( depth :int, xs :list1<(a,ref<h,int>)> ) : <read<h>,div> (tree<a>,list<(a,ref<h,int>)>)
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{
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if (!(xs.head.snd) == depth) return (Leaf(xs.head.fst), xs.tail)
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l = build(depth+1, xs)
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match(l.snd) {
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Nil -> (l.fst, Nil)
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Cons(y,ys) -> {
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r = build(depth+1, Cons1(y,ys))
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(Node(l.fst,r.fst), r.snd)
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}
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}
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}
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//----------------------------------------------------
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// Main
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//----------------------------------------------------
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public function garsiaWachs( xs : list1<(a,int)> ) : div tree<a>
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{
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refs = xs.map(fst).map( fun(x) { (x, ref(0)) } )
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wleafs = zip( refs.map(Leaf), xs.map(snd) )
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tree = balance(wleafs)
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mark(0,tree)
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build(0,refs).fst
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}
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