src/HOL/UNITY/Union.thy
author paulson
Fri Nov 06 13:20:29 1998 +0100 (1998-11-06)
changeset 5804 8e0a4c4fd67b
parent 5648 fe887910e32e
child 6012 1894bfc4aee9
permissions -rw-r--r--
Revising the Client proof as suggested by Michel Charpentier. New lemmas
about composition (in Union.ML), etc. Also changed "length" to "size"
because it is displayed as "size" in any event.
     1 (*  Title:      HOL/UNITY/Union.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1998  University of Cambridge
     5 
     6 Unions of programs
     7 
     8 Partly from Misra's Chapter 5: Asynchronous Compositions of Programs
     9 *)
    10 
    11 Union = SubstAx + FP +
    12 
    13 constdefs
    14   JOIN  :: ['a set, 'a => 'b program] => 'b program
    15     "JOIN I F == mk_program (INT i:I. Init (F i), UN i:I. Acts (F i))"
    16 
    17   Join :: ['a program, 'a program] => 'a program      (infixl 65)
    18     "F Join G == mk_program (Init F Int Init G, Acts F Un Acts G)"
    19 
    20   SKIP :: 'a program
    21     "SKIP == mk_program (UNIV, {})"
    22 
    23   Diff :: "['a program, ('a * 'a)set set] => 'a program"
    24     "Diff F acts == mk_program (Init F, Acts F - acts)"
    25 
    26   (*The set of systems that regard "v" as local to F*)
    27   localTo :: ['a => 'b, 'a program] => 'a program set  (infixl 80)
    28     "v localTo F == {G. ALL z. Diff G (Acts F) : stable {s. v s = z}}"
    29 
    30   (*Two programs with disjoint actions, except for Id (idling)*)
    31   Disjoint :: ['a program, 'a program] => bool
    32     "Disjoint F G == Acts F Int Acts G <= {Id}"
    33 
    34 syntax
    35   "@JOIN"      :: [pttrn, 'a set, 'b set] => 'b set  ("(3JN _:_./ _)" 10)
    36 
    37 translations
    38   "JN x:A. B"   == "JOIN A (%x. B)"
    39 
    40 end