| author | paulson |
| Wed, 13 Nov 1996 10:47:08 +0100 | |
| changeset 2183 | 8d42a7bccf0b |
| parent 1983 | f3f7bf0079fa |
| child 3439 | 54785105178c |
| permissions | -rw-r--r-- |
| 1475 | 1 |
(* Title: Relation.thy |
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ID: $Id$ |
| 1983 | 3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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*) |
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Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
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64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
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Relation = Prod + |
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consts |
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id :: "('a * 'a)set" (*the identity relation*)
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O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
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trans :: "('a * 'a)set => bool" (*transitivity predicate*)
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converse :: "('a*'b) set => ('b*'a) set"
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"^^" :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
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Domain :: "('a*'b) set => 'a set"
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Range :: "('a*'b) set => 'b set"
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defs |
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id_def "id == {p. ? x. p = (x,x)}"
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comp_def "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
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trans_def "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)" |
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converse_def "converse(r) == {(y,x). (x,y):r}"
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Domain_def "Domain(r) == {x. ? y. (x,y):r}"
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Range_def "Range(r) == Domain(converse(r))" |
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Image_def "r ^^ s == {y. ? x:s. (x,y):r}"
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end |