(* Title: Relation.thy
ID: $Id$
Author: Riccardo Mattolini, Dip. Sistemi e Informatica
and Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 Universita' di Firenze
Copyright 1993 University of Cambridge
Functions represented as relations in Higher-Order Set Theory
*)
Relation = Trancl +
consts
converse :: "('a*'a) set => ('a*'a) set"
"^^" :: "[('a*'a) set,'a set] => 'a set" (infixl 90)
Domain :: "('a*'a) set => 'a set"
Range :: "('a*'a) set => 'a set"
defs
converse_def "converse(r) == {z. (? w:r. ? x y. w=<x,y> & z=<y,x>)}"
Domain_def "Domain(r) == {z. ! x. (z=x --> (? y. <x,y>:r))}"
Range_def "Range(r) == Domain(converse(r))"
Image_def "r ^^ s == {y. y:Range(r) & (? x:s. <x,y>:r)}"
end