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(* Title: HOLCF/IOA/meta_theory/CompoExecs.thy
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ID: $Id$
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Author: Olaf M"uller
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Copyright 1996 TU Muenchen
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Compositionality on Execution level.
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*)
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CompoExecs = Traces +
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consts
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ProjA ::"('a,'s * 't)execution => ('a,'s)execution"
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ProjA2 ::"('a,'s * 't)pairs -> ('a,'s)pairs"
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ProjB ::"('a,'s * 't)execution => ('a,'t)execution"
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ProjB2 ::"('a,'s * 't)pairs -> ('a,'t)pairs"
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Filter_ex ::"'a signature => ('a,'s)execution => ('a,'s)execution"
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Filter_ex2 ::"'a signature => ('a,'s)pairs -> ('a,'s)pairs"
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stutter ::"'a signature => ('a,'s)execution => bool"
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stutter2 ::"'a signature => ('a,'s)pairs -> ('s => tr)"
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par_execs ::"[('a,'s)execution_module,('a,'t)execution_module] => ('a,'s*'t)execution_module"
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defs
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ProjA_def
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"ProjA ex == (fst (fst ex), ProjA2`(snd ex))"
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ProjB_def
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"ProjB ex == (snd (fst ex), ProjB2`(snd ex))"
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ProjA2_def
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"ProjA2 == Map (%x.(fst x,fst(snd x)))"
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ProjB2_def
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"ProjB2 == Map (%x.(fst x,snd(snd x)))"
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Filter_ex_def
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"Filter_ex sig ex == (fst ex,Filter_ex2 sig`(snd ex))"
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Filter_ex2_def
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"Filter_ex2 sig == Filter (%x.fst x:actions sig)"
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stutter_def
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"stutter sig ex == ((stutter2 sig`(snd ex)) (fst ex) ~= FF)"
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stutter2_def
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"stutter2 sig ==(fix`(LAM h ex. (%s. case ex of
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nil => TT
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| x##xs => (flift1
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(%p.(If Def ((fst p)~:actions sig)
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then Def (s=(snd p))
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else TT fi)
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andalso (h`xs) (snd p))
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`x)
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)))"
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par_execs_def
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"par_execs ExecsA ExecsB ==
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let exA = fst ExecsA; sigA = snd ExecsA;
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exB = fst ExecsB; sigB = snd ExecsB
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in
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( {ex. Filter_ex sigA (ProjA ex) : exA}
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Int {ex. Filter_ex sigB (ProjB ex) : exB}
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Int {ex. stutter sigA (ProjA ex)}
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Int {ex. stutter sigB (ProjB ex)}
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Int {ex. Forall (%x.fst x:(actions sigA Un actions sigB)) (snd ex)},
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asig_comp sigA sigB)"
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end |