src/HOL/UNITY/Union.thy
author paulson
Wed Oct 27 13:03:32 1999 +0200 (1999-10-27)
changeset 7947 b999c1ab9327
parent 7915 c7fd7eb3b0ef
child 8055 bb15396278fb
permissions -rw-r--r--
working again; new treatment of LocalTo
     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 Do we need a Meet operator?  (Aka Intersection)
    11 
    12 CAN PROBABLY DELETE the "Disjoint" predicate
    13 *)
    14 
    15 Union = SubstAx + FP +
    16 
    17 constdefs
    18   JOIN  :: ['a set, 'a => 'b program] => 'b program
    19     "JOIN I F == mk_program (INT i:I. Init (F i), UN i:I. Acts (F i))"
    20 
    21   Join :: ['a program, 'a program] => 'a program      (infixl 65)
    22     "F Join G == mk_program (Init F Int Init G, Acts F Un Acts G)"
    23 
    24   SKIP :: 'a program
    25     "SKIP == mk_program (UNIV, {})"
    26 
    27   Diff :: "['a set, 'a program, ('a * 'a)set set] => 'a program"
    28     "Diff C G acts ==
    29        mk_program (Init G, (Restrict C `` Acts G) - (Restrict C `` acts))"
    30 
    31   (*The set of systems that regard "v" as local to F*)
    32   LOCALTO :: ['a => 'b, 'a set, 'a program] => 'a program set
    33                                            ("(_/ localTo[_]/ _)" [80,0,80] 80)
    34     "v localTo[C] F == {G. ALL z. Diff C G (Acts F) : stable {s. v s = z}}"
    35 
    36   (*The weak version of localTo, considering only G's reachable states*)
    37   LocalTo :: ['a => 'b, 'a program] => 'a program set  (infixl 80)
    38     "v LocalTo F == {G. G : v localTo[reachable (F Join G)] F}"
    39 
    40   (*Two programs with disjoint actions, except for identity actions.
    41     It's a weak property but still useful.*)
    42   Disjoint :: ['a set, 'a program, 'a program] => bool
    43     "Disjoint C F G ==
    44        (Restrict C `` (Acts F - {Id})) Int (Restrict C `` (Acts G - {Id}))
    45        <= {}"
    46 
    47 syntax
    48   "@JOIN1"     :: [pttrns, 'b set] => 'b set         ("(3JN _./ _)" 10)
    49   "@JOIN"      :: [pttrn, 'a set, 'b set] => 'b set  ("(3JN _:_./ _)" 10)
    50 
    51 translations
    52   "JN x:A. B"   == "JOIN A (%x. B)"
    53   "JN x y. B"   == "JN x. JN y. B"
    54   "JN x. B"     == "JOIN UNIV (%x. B)"
    55 
    56 end