author  paulson 
Fri, 22 Oct 1999 18:35:20 +0200  
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permissions  rwrr 
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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 (F Join 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 