(* Title: HOL/Lambda/Commutation.thy
ID: $Id$
Author: Tobias Nipkow
Copyright 1995 TU Muenchen
Abstract commutation and confluence notions.
*)
Commutation = Main +
consts
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 R^-1)^* --> (? z. (x,z) : R^* & (y,z) : R^*)"
translations
"confluent R" == "diamond(R^*)"
end