src/ZF/ex/Term.thy

installation of new inductive/datatype sections

(*  Title: 	ZF/ex/Term.thy
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1994  University of Cambridge

Terms over an alphabet.
Illustrates the list functor (essentially the same type as in Trees & Forests)
*)

Term = List +
consts
  term_rec  :: "[i, [i,i,i]=>i] => i"
  term_map  :: "[i=>i, i] => i"
  term_size :: "i=>i"
  reflect   :: "i=>i"
  preorder  :: "i=>i"

  term      :: "i=>i"

datatype
  "term(A)" = Apply ("a: A", "l: list(term(A))")
  monos	      "[list_mono]"
  type_intrs  "[list_univ RS subsetD]"

rules
  term_rec_def
   "term_rec(t,d) == \
\   Vrec(t, %t g. term_case(%x zs. d(x, zs, map(%z.g`z, zs)), t))"

  term_map_def	"term_map(f,t) == term_rec(t, %x zs rs. Apply(f(x), rs))"

  term_size_def	"term_size(t) == term_rec(t, %x zs rs. succ(list_add(rs)))"

  reflect_def	"reflect(t) == term_rec(t, %x zs rs. Apply(x, rev(rs)))"

  preorder_def	"preorder(t) == term_rec(t, %x zs rs. Cons(x, flat(rs)))"

end