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