| author | nipkow |
| Thu, 16 Nov 1995 19:50:40 +0100 | |
| changeset 1334 | 32a9fde85699 |
| parent 1128 | 64b30e3cc6d4 |
| child 1454 | d0266c81a85e |
| permissions | -rw-r--r-- |
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Trancl is now based on Relation which used to be in Integ.
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(* Title: Relation.thy |
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ID: $Id$ |
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Author: Riccardo Mattolini, Dip. Sistemi e Informatica |
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and Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1994 Universita' di Firenze |
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Copyright 1993 University of Cambridge |
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Trancl is now based on Relation which used to be in Integ.
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parents:
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*) |
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Trancl is now based on Relation which used to be in Integ.
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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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parents:
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trans :: "('a * 'a)set => bool" (*transitivity predicate*)
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Trancl is now based on Relation which used to be in Integ.
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converse :: "('a*'a) set => ('a*'a) set"
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"^^" :: "[('a*'a) set,'a set] => 'a set" (infixl 90)
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Domain :: "('a*'a) set => 'a set"
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Range :: "('a*'a) set => 'a set"
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defs |
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id_def "id == {p. ? x. p = (x,x)}"
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comp_def (*composition of relations*) |
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"r O s == {xz. ? x y z. xz = (x,z) & (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) == {z. (? w:r. ? x y. w=(x,y) & z=(y,x))}"
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Domain_def "Domain(r) == {z. ! x. (z=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. y:Range(r) & (? x:s. (x,y):r)}"
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end |