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A fully abstract model for a nonuniform concurrent language with parameterization and locality

  • Eiichi Horita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 666)

Abstract

Full abstraction of a denotational model w.r.t. operational ones for a concurrent language L is investigated. The language is nonuniform in that the meaning of atomic statements generally depends on the current state; it has parameterization with channel- and value-parameters and locality in the form of local variables and local channels, in addition to more conventional constructs: value assignments to variables, parallel composition with CSP/CCS-like communication, nondeterministic choice, and recursion. First two operational models OL and O L * for L are introduced in terms of a Plotkin-style transition system. Both models are linear in that they map each statement to the set of its possible execution paths of a certain kind; the second model O L * is more abstract than the first one in that O L * ignores states while OL involves them. Then a denotational model D is defined compositionally using interpreted operations of the language, with meanings of recursive programs as fixed points in an appropriate complete metric space. The the full abstraction of D w.r.t. OL and O L * established. That is, it is shown for O=OL, O L * that D is most abstract of those models C which are compositional and more distinctive than O.

Keywords

domain equations metric spaces concurrency imperative languages denotational semantics operational semantics correctness full abstraction linear time branching time parameterization local variables local channels 

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References

  1. [AR 89]
    P. America and J.J.M.M. Rutten (1989), Solving reflexive domain equations in a category of complete metric spaces, Journal of Computer and System Sciences, Vol. 39, No. 3, pp. 343–375.Google Scholar
  2. [BZ 82]
    J.W. de Barker and J.I. Zucker (1982), Processes and the denotational semantics of concurrency, Information and Control Vol. 54, pp. 70–120.Google Scholar
  3. [BKO 88]
    J.A. Bergstra, J.W. Klop, and E.-R. Olderog (1988), Readies and failures in the algebra of communicating processes, SIAM J. of Computing Vol. 17, No. 6, pp. 1134–1177.Google Scholar
  4. [BKPR92]
    F.S. de Boer, J.N. Kok, C. pAlamidesi, and J.J.M.M. Rutten (1992), On blocks: locality and asynchronous communication (extended abstract), to appear as a CWI Report, Amsterdam.Google Scholar
  5. [BHR84]
    S.D. Brookes, C.A.R. Hoare, and A.W. Roscoe (1984), A theory of communicating sequential processes, Journal of the Association for Computing Machinery, Vol. 31, pp. 560–599.Google Scholar
  6. [DH 83]
    R. De Nicola and M. Hennessy (1983), Testing equivalence and processes, Theoretical Computer Science, Vol. 34, pp. 83–133.Google Scholar
  7. [Dug 66]
    J. Dugundji (1966), Topology, Allyn and Bacon, Boston.Google Scholar
  8. [Eng 77]
    R. Engelking (1977), General topology, Polish Scientific Publishers.Google Scholar
  9. [HMT 71]
    L. Henkin, J.D. Monk, and A. Tarski (1971), Cylindric Algebras (Part 1), North-Holland.Google Scholar
  10. [Hen 85]
    M. Hennessy (1985), Acceptance trees, Journal of the Association for Computing Machinery, Vol. 32, pp. 896–928.Google Scholar
  11. [Hen 88]
    M. Hennessy (1988), Algebraic theory of processes, MIT Press.Google Scholar
  12. [HI 90]
    M. Hennessy and A. Ingólfsdóttir (1990), A theory of communicating processes with value-passing, in Proceedings 17th ICALP, Warwick University, Lecture Notes in Computer Science, Vol. 443, pp. 209–219, Springer.Google Scholar
  13. [Hor 92]
    E. Horita (1992), Fully abstract models for communicating processes with respect to weak linear semantics with divergence, IEICE Transactions on Information and Systems Vol. E75-D, No. 1, pp. 64–77.Google Scholar
  14. [Hor 92a]
    E. Horita (1992), Full abstraction of metric semantics for imperative concurrency with communication, to appear as a CWI Report, Amsterdam.Google Scholar
  15. [Hor 92b]
    E. Horita (1992), Full abstraction of metric semantics for communicating processes with value-passing, to appear as a CWI Report, Amsterdam.Google Scholar
  16. [HBR 90]
    E. Horita, J.W. de Barker, and J.J.M.M. Rutten (1990), Fully abstract denotational models for nonuniform concurrent languages, CWI Report CS-R9027, Amsterdam.Google Scholar
  17. [KR 90]
    J.N. Kok and J.J.M.M. Rutten (1990), Contractions in comparing concurrency semantics, in Theoretical Computer Science, Vol. 76, pp. 179–222.Google Scholar
  18. [Mil 73]
    R. Milner (1973), Processes: a mathematical model of computing agents, in Proceedings of Logic Colloquium 73 (H.E. Rose, J.C. Shepherdson, eds.), pp. 157–173, North-Holland.Google Scholar
  19. [Mil 89]
    R. Milner (1989), Communication and concurrency, Prentice Hall International.Google Scholar
  20. [Mit 90]
    J.C. Mitchell (1990), Type systems for programming languages, in Handbook of Theoretical Computer Science, Vol. B, Formal Models and Semantics (J.V. Leeuwen, ed.), pp. 365–458, The MIT Press/Elsevier.Google Scholar
  21. [OT 92]
    P.W. O'hearn and R.D. Tennent (1992), Semantics of local variables, LFCS Report ECS-LFCS-92-192, Department of Computer Science, University of Edinburgh.Google Scholar
  22. [Plo 81]
    G.D. Plotkin (1981), A structured approach to operational semantics, Report DAIMI FN-19, Computer Science Department, Aarhus University.Google Scholar
  23. [Rut 89]
    J.J.M.M. Rutten (1989), Correctness and full abstraction of metric semantics for concurrency, in Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency (J.W. de Barker, W.P. de Roever, G. Rozenberg, eds.), Lecture Notes in Computer Science Vol. 354, PP-628–658, Springer.Google Scholar
  24. [SRP 90]
    V.A. Saraswat, M. Rinard, and P. Panangaden, Semantic foundation of concurrent constraint programming (preliminary report), In Prod. of the eighteenth ACM Symposium on Principles of Programming Languages, pp. 333–352, ACM.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Eiichi Horita
    • 1
  1. 1.NTT Software LaboratoriesTokyoJapan

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