(* Title: CCL/wfd.thy
ID: $Id$
Author: Martin Coen, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Well-founded relations in CCL.
*)
Wfd = Trancl + Type +
consts
(*** Predicates ***)
Wfd :: "[i set] => o"
(*** Relations ***)
wf :: "[i set] => i set"
wmap :: "[i=>i,i set] => i set"
"**" :: "[i set,i set] => i set" (infixl 70)
NatPR :: "i set"
ListPR :: "i set => i set"
rules
Wfd_def
"Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R --> y:P) --> x:P) --> (ALL a.a:P)"
wf_def "wf(R) == {x.x:R & Wfd(R)}"
wmap_def "wmap(f,R) == {p. EX x y. p=<x,y> & <f(x),f(y)> : R}"
lex_def
"ra**rb == {p. EX a a' b b'.p = <<a,b>,<a',b'>> & (<a,a'> : ra | (a=a' & <b,b'> : rb))}"
NatPR_def "NatPR == {p.EX x:Nat. p=<x,succ(x)>}"
ListPR_def "ListPR(A) == {p.EX h:A.EX t:List(A). p=<t,h$t>}"
end