(* 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
(*FIXME: conjoin Init F Int Init G ~= {} *)
ok :: ['a program, 'a program] => bool (infixl 65)
"F ok G == Acts F <= AllowedActs G &
Acts G <= AllowedActs F"
(*FIXME: conjoin (INT i:I. Init (F i)) ~= {} *)
OK :: ['a set, 'a => 'b program] => bool
"OK I F == (ALL i:I. ALL j: I-{i}. Acts (F i) <= AllowedActs (F j))"
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),
INT i:I. AllowedActs (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,
AllowedActs F Int AllowedActs G)"
SKIP :: 'a program
"SKIP == mk_program (UNIV, {}, UNIV)"
(*Characterizes safety properties. Used with specifying AllowedActs*)
safety_prop :: "'a program set => bool"
"safety_prop X == SKIP: X & (ALL G. Acts G <= UNION X Acts --> G : X)"
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)"
syntax (xsymbols)
SKIP :: 'a program ("\\<bottom>")
"op Join" :: ['a program, 'a program] => 'a program (infixl "\\<squnion>" 65)
"@JOIN1" :: [pttrns, 'b set] => 'b set ("(3\\<Squnion> _./ _)" 10)
"@JOIN" :: [pttrn, 'a set, 'b set] => 'b set ("(3\\<Squnion> _:_./ _)" 10)
end