(* 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 node set set"
Sexp_case :: "['a node set, 'a=>'b, nat=>'b, \
\ ['a node set,'a node set]=>'b] => 'b"
Sexp_rec :: "['a node set, 'a=>'b, nat=>'b, \
\ ['a node set,'a node set,'b,'b]=>'b] => 'b"
pred_Sexp :: "('a node set * 'a node set)set"
rules
Sexp_def "Sexp == lfp(%Z. range(Leaf) Un range(Numb) Un Z<*>Z)"
Sexp_case_def
"Sexp_case(M,c,d,e) == @ 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(M, c, d, %N1 N2. e(N1, N2, g(N1), g(N2))))"
end