diff -r 000000000000 -r a5a9c433f639 src/CCL/ex/List.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/CCL/ex/List.thy Thu Sep 16 12:20:38 1993 +0200 @@ -0,0 +1,44 @@ +(* Title: CCL/ex/list.thy + ID: $Id$ + Author: Martin Coen, Cambridge University Computer Laboratory + Copyright 1993 University of Cambridge + +Programs defined over lists. +*) + +List = Nat + + +consts + map :: "[i=>i,i]=>i" + "o" :: "[i=>i,i=>i]=>i=>i" (infixr 55) + "@" :: "[i,i]=>i" (infixr 55) + mem :: "[i,i]=>i" (infixr 55) + filter :: "[i,i]=>i" + flat :: "i=>i" + partition :: "[i,i]=>i" + insert :: "[i,i,i]=>i" + isort :: "i=>i" + qsort :: "i=>i" + +rules + + map_def "map(f,l) == lrec(l,[],%x xs g.f(x).g)" + comp_def "f o g == (%x.f(g(x)))" + append_def "l @ m == lrec(l,m,%x xs g.x.g)" + mem_def "a mem l == lrec(l,false,%h t g.if eq(a,h) then true else g)" + filter_def "filter(f,l) == lrec(l,[],%x xs g.if f`x then x.g else g)" + flat_def "flat(l) == lrec(l,[],%h t g.h @ g)" + + insert_def "insert(f,a,l) == lrec(l,a.[],%h t g.if f`a`h then a.h.t else h.g)" + isort_def "isort(f) == lam l.lrec(l,[],%h t g.insert(f,h,g))" + + partition_def + "partition(f,l) == letrec part l a b be lcase(l,,%x xs.\ +\ if f`x then part(xs,x.a,b) else part(xs,a,x.b)) \ +\ in part(l,[],[])" + qsort_def "qsort(f) == lam l. letrec qsortx l be lcase(l,[],%h t. \ +\ let p be partition(f`h,t) \ +\ in split(p,%x y.qsortx(x) @ h.qsortx(y))) \ +\ in qsortx(l)" + +end