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