src/HOL/WF.thy

+(*  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