src/CCL/Trancl.thy

+(*  Title: 	CCL/trancl.thy
+    ID:         $Id$
+    Author: 	Martin Coen, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Transitive closure of a relation
+*)
+
+Trancl = CCL +
+
+consts
+    trans   :: "i set => o" 	              (*transitivity predicate*)
+    id	    :: "i set"
+    rtrancl :: "i set => i set"	              ("(_^*)" [100] 100)
+    trancl  :: "i set => i set"	              ("(_^+)" [100] 100)  
+    O	    :: "[i set,i set] => i set"       (infixr 60)
+
+rules   
+
+trans_def	"trans(r) == (ALL x y z. <x,y>:r --> <y,z>:r --> <x,z>:r)"
+comp_def	(*composition of relations*)
+		"r O s == {xz. EX x y z. xz = <x,z> & <x,y>:s & <y,z>:r}"
+id_def		(*the identity relation*)
+		"id == {p. EX x. p = <x,x>}"
+rtrancl_def	"r^* == lfp(%s. id Un (r O s))"
+trancl_def	"r^+ == r O rtrancl(r)"
+
+end