(* Title: ZF/ex/Primrec.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 University of Cambridge
Primitive Recursive Functions: the inductive definition
Proof adopted from
Nora Szasz,
A Machine Checked Proof that Ackermann's Function is not Primitive Recursive,
In: Huet & Plotkin, eds., Logical Environments (CUP, 1993), 317-338.
See also E. Mendelson, Introduction to Mathematical Logic.
(Van Nostrand, 1964), page 250, exercise 11.
*)
Primrec = Primrec_defs +
consts
prim_rec :: i
inductive
domains "prim_rec" <= "list(nat)->nat"
intrs
SC "SC \\<in> prim_rec"
CONST "k \\<in> nat ==> CONST(k) \\<in> prim_rec"
PROJ "i \\<in> nat ==> PROJ(i) \\<in> prim_rec"
COMP "[| g \\<in> prim_rec; fs: list(prim_rec) |] ==> COMP(g,fs): prim_rec"
PREC "[| f \\<in> prim_rec; g \\<in> prim_rec |] ==> PREC(f,g): prim_rec"
monos list_mono
con_defs SC_def, CONST_def, PROJ_def, COMP_def, PREC_def
type_intrs "nat_typechecks @ list.intrs @
[lam_type, list_case_type, drop_type, map_type,
apply_type, rec_type]"
end