(* 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 *) Union = SubstAx + FP + constdefs eqStates :: ['a set, 'a => 'b program] => bool "eqStates I F == EX St. ALL i:I. States (F i) = St" JOIN :: ['a set, 'a => 'b program] => 'b program "JOIN I F == mk_program (INT i:I. States (F i), 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 (States F Int States G, Init F Int Init G, Acts F Un Acts G)" SKIP :: 'a set => 'a program "SKIP states == mk_program (states, states, {})" Diff :: "['a program, ('a * 'a)set set] => 'a program" "Diff F acts == mk_program (States F, Init F, Acts F - acts)" (*The set of systems that regard "v" as local to F*) localTo :: ['a => 'b, 'a program] => 'a program set (infixl 80) "v localTo F == {G. ALL z. Diff G (Acts F) : stable {s. v s = z}}" (*Two programs with disjoint actions, except for identity actions *) Disjoint :: ['a program, 'a program] => bool "Disjoint F G == States F = States G & Acts F Int Acts G <= {diag (States G)}" syntax "@JOIN" :: [pttrn, 'a set, 'b set] => 'b set ("(3JN _:_./ _)" 10) translations "JN x:A. B" == "JOIN A (%x. B)" end