(* 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