|
1474
|
1 |
(* Title: CCL/wfd.thy
|
|
0
|
2 |
ID: $Id$
|
|
1474
|
3 |
Author: Martin Coen, Cambridge University Computer Laboratory
|
|
0
|
4 |
Copyright 1993 University of Cambridge
|
|
|
5 |
|
|
|
6 |
Well-founded relations in CCL.
|
|
|
7 |
*)
|
|
|
8 |
|
|
|
9 |
Wfd = Trancl + Type +
|
|
|
10 |
|
|
|
11 |
consts
|
|
|
12 |
(*** Predicates ***)
|
|
|
13 |
Wfd :: "[i set] => o"
|
|
|
14 |
(*** Relations ***)
|
|
|
15 |
wf :: "[i set] => i set"
|
|
|
16 |
wmap :: "[i=>i,i set] => i set"
|
|
|
17 |
"**" :: "[i set,i set] => i set" (infixl 70)
|
|
|
18 |
NatPR :: "i set"
|
|
|
19 |
ListPR :: "i set => i set"
|
|
|
20 |
|
|
|
21 |
rules
|
|
|
22 |
|
|
|
23 |
Wfd_def
|
|
3837
|
24 |
"Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R --> y:P) --> x:P) --> (ALL a. a:P)"
|
|
0
|
25 |
|
|
3837
|
26 |
wf_def "wf(R) == {x. x:R & Wfd(R)}"
|
|
0
|
27 |
|
|
|
28 |
wmap_def "wmap(f,R) == {p. EX x y. p=<x,y> & <f(x),f(y)> : R}"
|
|
|
29 |
lex_def
|
|
3837
|
30 |
"ra**rb == {p. EX a a' b b'. p = <<a,b>,<a',b'>> & (<a,a'> : ra | (a=a' & <b,b'> : rb))}"
|
|
0
|
31 |
|
|
3837
|
32 |
NatPR_def "NatPR == {p. EX x:Nat. p=<x,succ(x)>}"
|
|
|
33 |
ListPR_def "ListPR(A) == {p. EX h:A. EX t:List(A). p=<t,h$t>}"
|
|
0
|
34 |
end
|