--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/CCL/Trancl.thy Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,28 @@
+(* 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