src/HOL/WF.thy
author clasohm
Mon Oct 09 14:57:55 1995 +0100 (1995-10-09)
changeset 1276 42ccfd3e1fb4
parent 972 e61b058d58d2
child 1475 7f5a4cd08209
permissions -rw-r--r--
corrected title
     1 (*  Title: 	HOL/WF.thy
     2     ID:         $Id$
     3     Author: 	Tobias Nipkow
     4     Copyright   1992  University of Cambridge
     5 
     6 Well-founded Recursion
     7 *)
     8 
     9 WF = Trancl +
    10 consts
    11    wf		:: "('a * 'a)set => bool"
    12    cut		:: "['a => 'b, ('a * 'a)set, 'a] => 'a => 'b"
    13    wftrec,wfrec	:: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'b"
    14    is_recfun	:: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b, 'a=>'b] => bool"
    15    the_recfun	:: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'a=>'b"
    16 
    17 defs
    18   wf_def  "wf(r) == (!P. (!x. (!y. (y,x):r --> P(y)) --> P(x)) --> (!x.P(x)))"
    19   
    20   cut_def 	 "cut f r x == (%y. if (y,x):r then f y else @z.True)"
    21 
    22   is_recfun_def  "is_recfun r a H f == (f = cut (%x.(H x (cut f r x))) r a)"
    23 
    24   the_recfun_def "the_recfun r a H == (@f.is_recfun r a H f)"
    25 
    26   wftrec_def     "wftrec r a H == H a (the_recfun r a H)"
    27 
    28   (*version not requiring transitivity*)
    29   wfrec_def	"wfrec r a H == wftrec (trancl r) a (%x f.(H x (cut f r x)))"
    30 end