src/ZF/ex/Term.thy

X-symbols for set theory

(*  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      :: i=>i

datatype
  "term(A)" = Apply ("a \\<in> A", "l \\<in> list(term(A))")
  monos        list_mono

  type_elims  "[make_elim (list_univ RS subsetD)]"
(*Or could have
    type_intrs  "[list_univ RS subsetD]"
*)

constdefs
  term_rec  :: [i, [i,i,i]=>i] => i
   "term_rec(t,d) == 
    Vrec(t, %t g. term_case(%x zs. d(x, zs, map(%z. g`z, zs)), t))"

  term_map  :: [i=>i, i] => i
    "term_map(f,t) == term_rec(t, %x zs rs. Apply(f(x), rs))"

  term_size :: i=>i
   "term_size(t) == term_rec(t, %x zs rs. succ(list_add(rs)))"

  reflect   :: i=>i
    "reflect(t) == term_rec(t, %x zs rs. Apply(x, rev(rs)))"

  preorder  :: i=>i
    "preorder(t) == term_rec(t, %x zs rs. Cons(x, flat(rs)))"

  postorder :: i=>i
    "postorder(t) == term_rec(t, %x zs rs. flat(rs) @ [x])"

end