Theory Conclusion

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 * Project         : HOL-CSP_OpSem - Operational semantics for HOL-CSP
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 * Author          : Benoît Ballenghien, Burkhart Wolff
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chapter ‹ Conclusion›

theory  Conclusion
  imports OpSemFD OpSemDT OpSemFDBis OpSemDTBis OpSemFBis OpSemTBis NewLaws
          (* "HOL-Library.LaTeXsugar" *)
begin

text ‹We started by defining the operators const‹Sliding›, const‹Throw› and const‹Interrupt›
      and provided on them several new laws, especially monotony, "step-law"
      (behaviour with @{term [source] ‹□a ∈ A → P a›}) and continuity.›

text ‹We defined the const‹ready_set› notion, and described its behaviour with the reference
      processes and the operators of CSP (which is already a minor contribution).›

text ‹As main contribution, we defined the @{const [source] ‹After›} operator which represents
      a bridge between the denotational and the versions of operational semantics for CSP.
      Therefore we derive the correspondence between denotational and operational 
      semantics by construction. Based on failure divergence or trace divergence refinements, 
      the two operational semantics correspond to the versions described in
      cite‹"roscoe:csp:1998" and "DBLP:journals/entcs/Roscoe15"›.

      We only have a slight variation for the const‹Sync› operator: const‹STOP› is replaced
      by const‹SKIP›, probably because of the operator definition in session‹HOL-CSP›.

      Thus, we provided a formal theory of operational behaviour for CSP, which is, to our
      knowledge, done for the first time for the entire language and the complete FD-Semantics
      model. Some of the proofs turned out to be extremely complex and out of reach of
      paper-and-pencil reasoning.›

text ‹A notable point is that the experimental order term‹(⊑DT)› behaves surprisingly well:
      initially pushed in session‹HOL-CSP› for pure curiosity, it looks promising for future
      applications, since it gives a direct handle for an operational trace semantics for
      non-diverging processes which is executable.›

text ‹Another take-away is the development of alternatives allowing term‹(⊑F)› and
      term‹(⊑T)› orders to be used operational construction by modifying the definition of 
      @{const [source] ‹AfterExt.AfterExt›}. 

      But even if term‹(⊑FD)› and term‹(⊑DT)› constructions are (almost) not impacted by this
      change, this remains a bit disappointing because the monotony of term‹(⊑F)› and
      term‹(⊑T)› w.r.t. to some operators does not allow to recover all the laws of 
      cite‹"roscoe:csp:1998" and "DBLP:journals/entcs/Roscoe15"›.›

text ‹As a bonus we provided in theory‹HOL-CSP_OpSem.NewLaws› some powerful laws for CSP.
      Here, we recall only the most important ones:
  
      @{thm [eta_contract = false] bij_Renaming_Hiding bij_Renaming_Sync Hiding_Mprefix_non_disjoint}›

end