(* Title: HOL/Induct/Sexp.thy
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 by hand.
*)
Sexp = Univ + Inductive +
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(i): sexp"
SconsI "[| M: sexp; N: sexp |] ==> Scons 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 = Scons N1 N2 & z=e N1 N2)"
pred_sexp_def
"pred_sexp == UN M: sexp. UN N: sexp. {(M, Scons M N), (N, Scons M N)}"
sexp_rec_def
"sexp_rec M c d e == wfrec pred_sexp
(%g. sexp_case c d (%N1 N2. e N1 N2 (g N1) (g N2))) M"
end