author  paulson 
Thu, 03 Dec 1998 10:45:06 +0100  
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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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*) 
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Union = SubstAx + FP + 

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constdefs 

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eqStates :: ['a set, 'a => 'b program] => bool 
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"eqStates I F == EX St. ALL i:I. States (F i) = St" 
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JOIN :: ['a set, 'a => 'b program] => 'b program 
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"JOIN I F == mk_program (INT i:I. States (F i), 
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INT i:I. Init (F i), 
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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 (States F Int States G, 
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Init F Int Init G, 
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Acts F Un Acts G)" 
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SKIP :: 'a set => 'a program 
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"SKIP states == mk_program (states, states, {})" 
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Diff :: "['a program, ('a * 'a)set set] => 'a program" 
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"Diff F acts == mk_program (States F, Init F, Acts F  acts)" 
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(*The set of systems that regard "v" as local to F*) 
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localTo :: ['a => 'b, 'a program] => 'a program set (infixl 80) 
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"v localTo F == {G. ALL z. Diff G (Acts F) : stable {s. v s = z}}" 
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(*Two programs with disjoint actions, except for identity actions *) 
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Disjoint :: ['a program, 'a program] => bool 
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"Disjoint F G == States F = States G & 
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Acts F Int Acts G <= {diag (States G)}" 
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syntax 
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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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end 