(* Title: HOL/Sexp
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1992 University of Cambridge
S-expressions, general binary trees for defining recursive data structures
*)
Sexp = Univ +
consts
sexp :: "'a item set"
sexp_case :: "['a=>'b, nat=>'b, ['a item, 'a item]=>'b,
'a item] => 'b"
sexp_rec :: "['a item, 'a=>'b, nat=>'b,
['a item, 'a item, 'b, 'b]=>'b] => 'b"
pred_sexp :: "('a item * 'a item)set"
inductive "sexp"
intrs
LeafI "Leaf(a): sexp"
NumbI "Numb(a): sexp"
SconsI "[| M: sexp; N: sexp |] ==> M$N : sexp"
defs
sexp_case_def
"sexp_case(c,d,e,M) == @ z. (? x. M=Leaf(x) & z=c(x))
| (? k. M=Numb(k) & z=d(k))
| (? N1 N2. M = N1 $ N2 & z=e(N1,N2))"
pred_sexp_def
"pred_sexp == UN M: sexp. UN N: sexp. {<M, M$N>, <N, M$N>}"
sexp_rec_def
"sexp_rec(M,c,d,e) == wfrec(pred_sexp, M,
%M g. sexp_case(c, d, %N1 N2. e(N1, N2, g(N1), g(N2)), M))"
end