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On the axiomatic treatment of concurrency

  • Stephen D. Brookes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 197)

Abstract

This paper describes a semantically-based axiomatic treatment of a simple parallel programming language. We consider an imperative language with shared variable concurrency and a critical region construct. After giving a structural operational semantics for the language we use the semantic structure to suggest a class of assertions for expressing semantic properties of commands. The structure of the assertions reflects the structure of the semantic representation of a command. We then define syntactic operations on assertions which correspond precisely to the corresponding syntactic constructs of the programming language; in particular, we define sequential and parallel composition of assertions. This enables us to design a truly compositional proof system for program properties. Our proof system is sound and relatively complete. We examine the relationship between our proof system and the Owicki-Gries proof system for the same language, and we see how Owicki's parallel proof rule can be reformulated in our setting. Our assertions are more expressive than Owicki's, and her proof outlines correspond roughly to a special subset of our assertion language. Owicki's parallel rule can be thought of as being based on a slightly different form of parallel composition of assertions; our form does not require interference-freedom, and our proof system is relatively complete without the need for auxiliary variables. Connections with the “Generalized Hoare Logic” of Lamport and Schneider, and with the Transition Logic of Gerth, are discussed briefly, and we indicate how to extend our ideas to include some more programming constructs, including conditional commands, conditional critical regions, and loops.

Keywords

Proof System Parallel Composition Atomic Action Communicate Sequential Process Partial Correctness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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6. References

  1. [1]
    Apt, K. R., Ten Years of Hoare's Logic: A Survey, ACM TOPLAS, vol. 3 no. 4 (October 1981) 431–483.Google Scholar
  2. [2]
    Apt, K. R., Francez, N., and de Roever, W. P., A proof system for communicating sequential processes, ACM TOPLAS, vol. 2 no. 3 (July 1980), 359–385.Google Scholar
  3. [3]
    Ashcroft, E. A., Proving assertions about parallel programs, J. Comput. Syst. Sci. 10 (Jan. 1975), 110–135.Google Scholar
  4. [4]
    Barringer, H., Kuiper, R., and Pnueli, A., Now You May Compose Temporal Logic Assertions, Proc. 16th ACM Symposium on Theory of Computing, Washington, May 1984.Google Scholar
  5. [5]
    Best, E., A relational framework for concurrent programs using atomic actions, Proc. IFIP TC2 Conference (1982).Google Scholar
  6. [6]
    Brookes, S. D., On the Relationship of CCS and CSP, Proc. ICALP 83, Springer LNCS (1983).Google Scholar
  7. [7]
    Brookes, S. D., A Fully Abstract Semantics and Proof System for An ALGOL-like Language with Sharing, CMU Technical Report (1984).Google Scholar
  8. [8]
    Cook, S., Soundness and Completeness of an Axiom System for Program Verfification, SIAM J. Comput. vol. 7. no. 1 (February 1978) 70–90.Google Scholar
  9. [9]
    Dijkstra, E. W., Cooperating Sequential Processes, in: Programming Languages, F. Genuys (Ed.), Academic Press, NY (1968) 43–112.Google Scholar
  10. [10]
    Dijkstra, E. W., A Discipline of Programming, Prentice-Hall, New Jersey (1976).Google Scholar
  11. [11]
    Gerth, R., Transition Logic, Proceedings of the 16th ACM STOC Conference, 1983.Google Scholar
  12. [12]
    Hoare, C. A. R., An axiomatic basis for computer programming, CACM 12, 10 (Oct. 1969), 576–580.Google Scholar
  13. [13]
    Hoare, C. A. R., Communicating Sequential Processes, CACM 21, 8 (Aug. 1978), 666–677.Google Scholar
  14. [14]
    Jones, C. B., Tentative Steps Towards a Development Method for Interfering Programs, ACM TOPLAS vol. 5 no. 4, (October 1983) 596–619.Google Scholar
  15. [15]
    Keller, R. M., Formal verification of parallel programs, CACM 19,7 (July 1976), 371–384.Google Scholar
  16. [16]
    Lamport, L., The ‘Hoare Logic’ of concurrent programs, Acta Informatica 14 (1980), 21–37.Google Scholar
  17. [17]
    Lamport, L., and Schneider, F., The “Hoare Logic” of CSP, and All That, ACM TOPLAS 6, 2 (April 1984), 281–296.Google Scholar
  18. [18]
    Levin, G. M., and Gries, D., A proof technique for communicating sequential processes, Acta Informatica 15 (1981), 281–302.Google Scholar
  19. [19]
    Manna, Z., and Pnueli, A., Verification of Concurrent Programs: The Temporal Framework, in: “The Correctness Problem in Computer Science”, ed. R. S. Boyer and J. S. Moore, Academic Press, London (1982).Google Scholar
  20. [20]
    Owicki, S. S., and Gries, D., An Axiomatic proof technique for parallel programs, Acta Informatica 6 (1976), 319–340.Google Scholar
  21. [21]
    Owicki, S. S., Axiomatic proof techniques for parallel programs, Ph. D. dissertation, Cornell University (Aug. 1975).Google Scholar
  22. [22]
    Hennessy, M., and Plotkin, G. D., Full Abstraction for a Simple Parallel Programming Language, Proc. MFCS 1979, Springer LNCS vol. 74, pp. 108–120.Google Scholar
  23. [23]
    Milner, R., Fully Abstract Models of Typed Lambda-Calculi, Theoretical Computer Science (1977).Google Scholar
  24. [24]
    Milner, R., A Calculus of Communicating Systems, Springer LNCS vol. 92 (1980).Google Scholar
  25. [25]
    O'Donnell, M., A Critique of the Foundations of Hoare-Style Programming Logic, CACM vol. 25 no. 12 (December 1982) 927–934.Google Scholar
  26. [26]
    Plotkin, G. D., A Structural Approach to Operational Semantics, DAIMI Report FN-19, Aarhus University (1981).Google Scholar
  27. [27]
    Plotkin, G. D., An Operational Semantics for CSP, Proceedings of the W. G. 2.2 Conference, 1982.Google Scholar
  28. [28]
    Winskel, G., Synchronisation Trees, Proc. ICALP 1983, Springer LNCS vol. 154. (1983).Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Stephen D. Brookes
    • 1
  1. 1.Department of Computer ScienceCarnegie-Mellon UniversityPittsburgh

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