src/HOL/Relation.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Relation.thy	Fri May 26 18:11:47 1995 +0200
@@ -0,0 +1,27 @@
+(*  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
+*)
+
+Relation = Prod +
+consts
+    id	        :: "('a * 'a)set"               (*the identity relation*)
+    O	        :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
+    trans       :: "('a * 'a)set => bool" 	(*transitivity predicate*)
+    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
+    id_def	"id == {p. ? x. p = (x,x)}"
+    comp_def	(*composition of relations*)
+		"r O s == {xz. ? x y z. xz = (x,z) & (x,y):s & (y,z):r}"
+    trans_def	  "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
+    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