--- a/src/HOL/WF.thy Mon Feb 05 14:44:09 1996 +0100
+++ b/src/HOL/WF.thy Mon Feb 05 21:27:16 1996 +0100
@@ -1,6 +1,6 @@
-(* Title: HOL/WF.thy
+(* Title: HOL/wf.ML
ID: $Id$
- Author: Tobias Nipkow
+ Author: Tobias Nipkow
Copyright 1992 University of Cambridge
Well-founded Recursion
@@ -8,23 +8,22 @@
WF = Trancl +
consts
- wf :: "('a * 'a)set => bool"
- cut :: "['a => 'b, ('a * 'a)set, 'a] => 'a => 'b"
- wftrec,wfrec :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'b"
- is_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b, 'a=>'b] => bool"
- the_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'a=>'b"
+ wf :: "('a * 'a)set => bool"
+ cut :: "('a => 'b) => ('a * 'a)set => 'a => 'a => 'b"
+ is_recfun :: "('a * 'a)set => (('a=>'b) => ('a=>'b)) =>'a=>('a=>'b) => bool"
+ the_recfun :: "('a * 'a)set => (('a=>'b) => ('a=>'b)) => 'a => 'a => 'b"
+ wfrec :: "('a * 'a)set => (('a=>'b) => ('a=>'b)) => 'a => 'b"
defs
wf_def "wf(r) == (!P. (!x. (!y. (y,x):r --> P(y)) --> P(x)) --> (!x.P(x)))"
- cut_def "cut f r x == (%y. if (y,x):r then f y else @z.True)"
+ cut_def "cut f r x == (%y. if (y,x):r then f y else @z.True)"
- is_recfun_def "is_recfun r a H f == (f = cut (%x.(H x (cut f r x))) r a)"
-
- the_recfun_def "the_recfun r a H == (@f.is_recfun r a H f)"
+ is_recfun_def "is_recfun r H a f == (f = cut (%x. H (cut f r x) x) r a)"
- wftrec_def "wftrec r a H == H a (the_recfun r a H)"
+ the_recfun_def "the_recfun r H a == (@f. is_recfun r H a f)"
- (*version not requiring transitivity*)
- wfrec_def "wfrec r a H == wftrec (trancl r) a (%x f.(H x (cut f r x)))"
+ wfrec_def
+ "wfrec r H == (%x. H (cut (the_recfun (trancl r) (%f v. H (cut f r v) v) x)
+ r x) x)"
end