| author | clasohm |
| Tue, 30 Jan 1996 15:24:36 +0100 | |
| changeset 1465 | 5d7a7e439cec |
| parent 1276 | 42ccfd3e1fb4 |
| child 1475 | 7f5a4cd08209 |
| permissions | -rw-r--r-- |
| 1276 | 1 |
(* Title: HOL/WF.thy |
| 923 | 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 |
|
|
972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
965
diff
changeset
|
18 |
wf_def "wf(r) == (!P. (!x. (!y. (y,x):r --> P(y)) --> P(x)) --> (!x.P(x)))" |
| 923 | 19 |
|
|
972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
965
diff
changeset
|
20 |
cut_def "cut f r x == (%y. if (y,x):r then f y else @z.True)" |
| 923 | 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 |