src/HOL/Induct/Term.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Induct/Term.thy	Wed May 07 12:50:26 1997 +0200
@@ -0,0 +1,55 @@
+(*  Title:      HOL/ex/Term
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+Terms over a given alphabet -- function applications; illustrates list functor
+  (essentially the same type as in Trees & Forests)
+
+There is no constructor APP because it is simply cons ($) 
+*)
+
+Term = SList +
+
+types   'a term
+
+arities term :: (term)term
+
+consts
+  term          :: 'a item set => 'a item set
+  Rep_term      :: 'a term => 'a item
+  Abs_term      :: 'a item => 'a term
+  Rep_Tlist     :: 'a term list => 'a item
+  Abs_Tlist     :: 'a item => 'a term list
+  App           :: ['a, ('a term)list] => 'a term
+  Term_rec      :: ['a item, ['a item , 'a item, 'b list]=>'b] => 'b
+  term_rec      :: ['a term, ['a ,'a term list, 'b list]=>'b] => 'b
+
+inductive "term(A)"
+  intrs
+    APP_I "[| M: A;  N : list(term(A)) |] ==> M$N : term(A)"
+  monos   "[list_mono]"
+
+defs
+  (*defining abstraction/representation functions for term list...*)
+  Rep_Tlist_def "Rep_Tlist == Rep_map(Rep_term)"
+  Abs_Tlist_def "Abs_Tlist == Abs_map(Abs_term)"
+
+  (*defining the abstract constants*)
+  App_def       "App a ts == Abs_term(Leaf(a) $ Rep_Tlist(ts))"
+
+  (*list recursion*)
+  Term_rec_def  
+   "Term_rec M d == wfrec (trancl pred_sexp)
+           (%g. Split(%x y. d x y (Abs_map g y))) M"
+
+  term_rec_def
+   "term_rec t d == 
+   Term_rec (Rep_term t) (%x y r. d (inv Leaf x) (Abs_Tlist(y)) r)"
+
+rules
+    (*faking a type definition for term...*)
+  Rep_term              "Rep_term(n): term(range(Leaf))"
+  Rep_term_inverse      "Abs_term(Rep_term(t)) = t"
+  Abs_term_inverse      "M: term(range(Leaf)) ==> Rep_term(Abs_term(M)) = M"
+end