wf.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/wf.thy	Thu Sep 16 12:21:07 1993 +0200
@@ -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"
+
+rules
+  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