Sexp.thy

added IOA to isabelle/HOL

(*  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"

rules

  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