added Induct/Binary_Trees.thy, Induct/Tree_Forest (converted from
former ex/TF.ML ex/TF.thy ex/Term.ML ex/Term.thy);
(* Title: ZF/ex/Primrec_defs.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 University of Cambridge
Primitive Recursive Functions: preliminary definitions of the constructors
[These must reside in a separate theory in order to be visible in the
con_defs part of prim_rec's inductive definition.]
*)
Primrec_defs = Main +
consts
SC :: i
CONST :: i=>i
PROJ :: i=>i
COMP :: [i,i]=>i
PREC :: [i,i]=>i
ACK :: i=>i
ack :: [i,i]=>i
translations
"ack(x,y)" == "ACK(x) ` [y]"
defs
SC_def "SC == \\<lambda>l \\<in> list(nat).list_case(0, %x xs. succ(x), l)"
CONST_def "CONST(k) == \\<lambda>l \\<in> list(nat).k"
PROJ_def "PROJ(i) == \\<lambda>l \\<in> list(nat). list_case(0, %x xs. x, drop(i,l))"
COMP_def "COMP(g,fs) == \\<lambda>l \\<in> list(nat). g ` List.map(%f. f`l, fs)"
(*Note that g is applied first to PREC(f,g)`y and then to y!*)
PREC_def "PREC(f,g) ==
\\<lambda>l \\<in> list(nat). list_case(0,
%x xs. rec(x, f`xs, %y r. g ` Cons(r, Cons(y, xs))), l)"
primrec
ACK_0 "ACK(0) = SC"
ACK_succ "ACK(succ(i)) = PREC (CONST (ACK(i) ` [1]),
COMP(ACK(i), [PROJ(0)]))"
end