src/HOL/Relation.thy
author clasohm
Mon, 05 Feb 1996 21:27:16 +0100
changeset 1475 7f5a4cd08209
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child 1695 0f9b9eda2a2c
permissions -rw-r--r--
expanded tabs; renamed subtype to typedef; incorporated Konrad's changes
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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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*)
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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. y:Range(r) &  (? x:s. (x,y):r)}"
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end