(* Title: HOL/UNITY/Union.thy ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1998 University of Cambridge Unions of programs Partly from Misra's Chapter 5: Asynchronous Compositions of Programs Do we need a Meet operator? (Aka Intersection) *) Union = SubstAx + FP + constdefs JOIN :: ['a set, 'a => 'b program] => 'b program "JOIN I F == mk_program (INT i:I. Init (F i), UN i:I. Acts (F i))" Join :: ['a program, 'a program] => 'a program (infixl 65) "F Join G == mk_program (Init F Int Init G, Acts F Un Acts G)" SKIP :: 'a program "SKIP == mk_program (UNIV, {})" Diff :: "['a set, 'a program, ('a * 'a)set set] => 'a program" "Diff C G acts == mk_program (Init G, (Restrict C `` Acts G) - (Restrict C `` acts))" (*The set of systems that regard "v" as local to F*) LOCALTO :: ['a => 'b, 'a set, 'a program] => 'a program set ("(_/ localTo[_]/ _)" [80,0,80] 80) "v localTo[C] F == {G. ALL z. Diff C G (Acts F) : stable {s. v s = z}}" (*The weak version of localTo, considering only G's reachable states*) LocalTo :: ['a => 'b, 'a program] => 'a program set (infixl 80) "v LocalTo F == {G. G : v localTo[reachable G] F}" (*Two programs with disjoint actions, except for identity actions. It's a weak property but still useful.*) Disjoint :: ['a set, 'a program, 'a program] => bool "Disjoint C F G == (Restrict C `` (Acts F - {Id})) Int (Restrict C `` (Acts G - {Id})) <= {}" syntax "@JOIN1" :: [pttrns, 'b set] => 'b set ("(3JN _./ _)" 10) "@JOIN" :: [pttrn, 'a set, 'b set] => 'b set ("(3JN _:_./ _)" 10) translations "JN x:A. B" == "JOIN A (%x. B)" "JN x y. B" == "JN x. JN y. B" "JN x. B" == "JOIN UNIV (%x. B)" end