src/HOL/Relation.thy
author nipkow
Fri May 26 18:11:47 1995 +0200 (1995-05-26)
changeset 1128 64b30e3cc6d4
child 1454 d0266c81a85e
permissions -rw-r--r--
Trancl is now based on Relation which used to be in Integ.
     1 (*  Title: 	Relation.thy
     2     ID:         $Id$
     3     Author: 	Riccardo Mattolini, Dip. Sistemi e Informatica
     4         and	Lawrence C Paulson, Cambridge University Computer Laboratory
     5     Copyright   1994 Universita' di Firenze
     6     Copyright   1993  University of Cambridge
     7 *)
     8 
     9 Relation = Prod +
    10 consts
    11     id	        :: "('a * 'a)set"               (*the identity relation*)
    12     O	        :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
    13     trans       :: "('a * 'a)set => bool" 	(*transitivity predicate*)
    14     converse    :: "('a*'a) set => ('a*'a) set"
    15     "^^"        :: "[('a*'a) set,'a set] => 'a set" (infixl 90)
    16     Domain      :: "('a*'a) set => 'a set"
    17     Range       :: "('a*'a) set => 'a set"
    18 defs
    19     id_def	"id == {p. ? x. p = (x,x)}"
    20     comp_def	(*composition of relations*)
    21 		"r O s == {xz. ? x y z. xz = (x,z) & (x,y):s & (y,z):r}"
    22     trans_def	  "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
    23     converse_def  "converse(r) == {z. (? w:r. ? x y. w=(x,y) & z=(y,x))}"
    24     Domain_def    "Domain(r) == {z. ! x. (z=x --> (? y. (x,y):r))}"
    25     Range_def     "Range(r) == Domain(converse(r))"
    26     Image_def     "r ^^ s == {y. y:Range(r) &  (? x:s. (x,y):r)}"
    27 end