| author | paulson |
| Tue, 17 Oct 1995 12:09:46 +0100 | |
| changeset 1283 | ea8b657a9c92 |
| parent 1276 | 42ccfd3e1fb4 |
| child 1475 | 7f5a4cd08209 |
| permissions | -rw-r--r-- |
| 1276 | 1 |
(* Title: HOL/WF.thy |
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ID: $Id$ |
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Author: Tobias Nipkow |
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Copyright 1992 University of Cambridge |
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Well-founded Recursion |
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*) |
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WF = Trancl + |
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consts |
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wf :: "('a * 'a)set => bool"
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cut :: "['a => 'b, ('a * 'a)set, 'a] => 'a => 'b"
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wftrec,wfrec :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'b"
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is_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b, 'a=>'b] => bool"
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the_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'a=>'b"
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defs |
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972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
965
diff
changeset
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wf_def "wf(r) == (!P. (!x. (!y. (y,x):r --> P(y)) --> P(x)) --> (!x.P(x)))" |
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972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
965
diff
changeset
|
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cut_def "cut f r x == (%y. if (y,x):r then f y else @z.True)" |
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is_recfun_def "is_recfun r a H f == (f = cut (%x.(H x (cut f r x))) r a)" |
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the_recfun_def "the_recfun r a H == (@f.is_recfun r a H f)" |
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wftrec_def "wftrec r a H == H a (the_recfun r a H)" |
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(*version not requiring transitivity*) |
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wfrec_def "wfrec r a H == wftrec (trancl r) a (%x f.(H x (cut f r x)))" |
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end |