src/HOL/Relation.thy
author wenzelm
Thu Jan 23 14:19:16 1997 +0100 (1997-01-23)
changeset 2545 d10abc8c11fb
parent 1983 f3f7bf0079fa
child 3439 54785105178c
permissions -rw-r--r--
added AxClasses test;
     1 (*  Title:      Relation.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1996  University of Cambridge
     5 *)
     6 
     7 Relation = Prod +
     8 consts
     9     id          :: "('a * 'a)set"               (*the identity relation*)
    10     O           :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
    11     trans       :: "('a * 'a)set => bool"       (*transitivity predicate*)
    12     converse    :: "('a*'b) set => ('b*'a) set"
    13     "^^"        :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
    14     Domain      :: "('a*'b) set => 'a set"
    15     Range       :: "('a*'b) set => 'b set"
    16 defs
    17     id_def        "id == {p. ? x. p = (x,x)}"
    18     comp_def      "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
    19     trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
    20     converse_def  "converse(r) == {(y,x). (x,y):r}"
    21     Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
    22     Range_def     "Range(r) == Domain(converse(r))"
    23     Image_def     "r ^^ s == {y. ? x:s. (x,y):r}"
    24 end