src/HOL/Lambda/Commutation.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Lambda/Commutation.thy	Wed Oct 11 10:09:56 1995 +0100
@@ -0,0 +1,31 @@
+(*  Title: 	HOL/Lambda/Commutation.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1995  TU Muenchen
+
+Abstract commutation and confluence notions.
+*)
+
+Commutation = Trancl +
+
+consts
+  reflcl  :: "('a*'a)set => ('a*'a)set"               ("(_^=)" [100] 100)
+  square  :: "[('a*'a)set,('a*'a)set,('a*'a)set,('a*'a)set] => bool"
+  commute :: "[('a*'a)set,('a*'a)set] => bool"
+  confluent, diamond, Church_Rosser :: "('a*'a)set => bool"
+
+defs
+  square_def
+ "square R S T U == !x y.(x,y):R --> (!z.(x,z):S --> (? u. (y,u):T & (z,u):U))"
+
+  commute_def "commute R S == square R S S R"
+  diamond_def "diamond R   == commute R R"
+
+  Church_Rosser_def "Church_Rosser(R) ==   
+  !x y. (x,y) : (R Un converse(R))^* --> (? z. (x,z) : R^* & (y,z) : R^*)"
+
+translations
+  "r^="   == "r Un id"
+  "confluent R" == "diamond(R^*)"
+
+end