src/HOL/Induct/Sexp.thy

+(*  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