author clasohm
Sat, 09 Dec 1995 13:36:11 +0100
changeset 1401 0c439768f45c
parent 1155 928a16e02f9f
child 1478 2b8c2a7547ab
permissions -rw-r--r--
removed quotes from consts and syntax sections

(*  Title: 	ZF/wf.thy
    ID:         $Id$
    Author: 	Tobias Nipkow and Lawrence C Paulson
    Copyright   1994  University of Cambridge

Well-founded Recursion

WF = Trancl + "mono" + "equalities" +
  wf           :: i=>o
  wf_on        :: [i,i]=>o			("wf[_]'(_')")

  wftrec,wfrec :: [i, i, [i,i]=>i] =>i
  wfrec_on     :: [i, i, i, [i,i]=>i] =>i	("wfrec[_]'(_,_,_')")
  is_recfun    :: [i, i, [i,i]=>i, i] =>o
  the_recfun   :: [i, i, [i,i]=>i] =>i

  (*r is a well-founded relation*)
  wf_def	 "wf(r) == ALL Z. Z=0 | (EX x:Z. ALL y. <y,x>:r --> ~ y:Z)"

  (*r is well-founded relation over A*)
  wf_on_def      "wf_on(A,r) == wf(r Int A*A)"

  is_recfun_def  "is_recfun(r,a,H,f) == 
   			(f = (lam x: r-``{a}. H(x, restrict(f, r-``{x}))))"

  the_recfun_def "the_recfun(r,a,H) == (THE f.is_recfun(r,a,H,f))"

  wftrec_def  	 "wftrec(r,a,H) == H(a, the_recfun(r,a,H))"

  (*public version.  Does not require r to be transitive*)
  wfrec_def "wfrec(r,a,H) == wftrec(r^+, a, %x f. H(x, restrict(f,r-``{x})))"

  wfrec_on_def   "wfrec[A](r,a,H) == wfrec(r Int A*A, a, H)"