src/CCL/Wfd.thy
 author clasohm Thu, 16 Sep 1993 12:20:38 +0200 changeset 0 a5a9c433f639 child 227 5415c6ad0028 permissions -rw-r--r--
Initial revision
```
(*  Title: 	CCL/wf.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
```