--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/WF.thy Fri Mar 03 12:02:25 1995 +0100
@@ -0,0 +1,30 @@
+(* Title: HOL/wf.ML
+ ID: $Id$
+ Author: Tobias Nipkow
+ Copyright 1992 University of Cambridge
+
+Well-founded Recursion
+*)
+
+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"
+
+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) (f y) (@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)"
+
+ wftrec_def "wftrec r a H == H a (the_recfun r a H)"
+
+ (*version not requiring transitivity*)
+ wfrec_def "wfrec r a H == wftrec (trancl r) a (%x f.(H x (cut f r x)))"
+end