Algebraic theories for name-passing calculi

  • Joachim Parrow
  • Davide Sangiorgi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 803)


In a theory of processes the names are atomic data items which can be exchanged and tested for identity, but which admit no other functions or predicates. A well-known example of a calculus for name-passing is the π-calculus, where names additionally are used as communication ports. We provide complete axiomatisations of late and early bisimulation equivalences in such calculi. Since neither of the equivalences is a congruence we also axiomatise the corresponding largest congruences. We consider a few variations of the signature of the language; among these, a calculus of deterministic processes which is reminiscent of sequential functional programs with a conditional construct. Most of our axioms have been shown to be independent. The structure of the systems reveals the symmetries of the calculi and equivalences since they differ only by a few simple axioms.


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  1. [BK85]
    J.A. Bergstra and J.W. Klop. Algebra of Communicating Processes with Abstraction. Theoretical Computer Science 33:77–121 (1985).Google Scholar
  2. [BB90]
    G. Berry and G. Boudol. The Chemical Abstract Machine. Theoretical Computer Science 96:217–248 (1992).Google Scholar
  3. [BT83]
    S. Bloom and R. Tindell. Varieties of “if-then-else”. SIAM J. Computing 12(4):677–707 (1983).Google Scholar
  4. [BD92]
    M. Boreale and R. DeNicola. Testing equivalence for mobile processes. In Cleaveland (Ed): Proceedings of CONCUR '92, Stony Brook, August 1992, pages 2–16, Springer Verlag LNCS 630 (1992).Google Scholar
  5. [GP90]
    J. Groote and A. Ponse. Process algebra with guards. CWI technical report CS-R9069, Amsterdam 1990. To appear in Formal Aspects of Computing.Google Scholar
  6. [GP91]
    J. Groote and A. Ponse. Proof Theory for μCRL. CWI technical report CS-R9138, Amsterdam 1991.Google Scholar
  7. [GM87]
    I. Guessarian and J. Meseguer. On the axiomatization of “if-then-else”. SIAM J. Computing 16(2):322–357 (1987).Google Scholar
  8. [He91]
    M. Hennessy. A Model for the π-calculus. Tech. Report 91/08, Department of Computer Science, University of Sussex, 1991.Google Scholar
  9. [He91b]
    M. Hennessy. A proof system for communicating processes with value-passing. Formal Aspects of Computing 3:346–366 (1991).Google Scholar
  10. [HI89]
    M. Hennessy and A. Ingólfsdóttir. A theory of communicating processes with value-passing. Technical Report 3/89, Univ. of Sussex 1989. To appear in Information and Computation.Google Scholar
  11. [HL93]
    M. Hennessy and H. Lin. Proof systems for message-passing process algebras. In Best (Ed): Proceedings of CONCUR '93, pages 202–216, Springer Verlag LNCS 715 (1993).Google Scholar
  12. [HL92]
    M. Hennessy and H. Lin. Symbolic bisimulations. Technical Report, University of Sussex 1992.Google Scholar
  13. [Hoa85]
    C.A.R. Hoare. Communicating Sequential Processes. Prentice Hall, 1985.Google Scholar
  14. [H+87]
    [H+87] C.A.R. Hoare, I. Hayes, He Jifeng, C. Morgan, A. Roscoe, J. Sanders, I. Sorensen, J. Spivey and B. Sufrin. Laws of programming. Comm. of the ACM 30(8):672–686 (1987).Google Scholar
  15. [JP89]
    B. Jonsson and J. Parrow. Deciding bisimulation equivalences for a class of non-finite-state programs. In Monien, Cori (Eds): Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science, February 1989, pages 421–433. Springer Verlag LNCS 349, 1989. Accepted for publication in Information and Computation.Google Scholar
  16. [Man85]
    E. Manes. Guard modules. Algebra Universalis 21:103–110 (1985).Google Scholar
  17. [Mauw91]
    S. Mauw. PSF — A Process Specification Formalism. Ph. D. Thesis, University of Amsterdam 1991.Google Scholar
  18. [McC63]
    J. McCarthy. A basis for a mathematical theory of computation. In Braffort, Hirschberg (Eds): Computer Programming and Formal Systems, pages 33–70, North-Holland (1963).Google Scholar
  19. [Mil80]
    R. Milner. A Calculus of Communicating Systems. Springer Verlag LNCS 92, 1980.Google Scholar
  20. [Mil89]
    R. Milner. Communication and Concurrency. Prentice Hall, 1989.Google Scholar
  21. [Mil92]
    R. Milner. Functions as Processes. J. of Mathem. Structures in Computer Science 2(2):119–141 (1992).Google Scholar
  22. [MPW91]
    R. Milner, J. Parrow and D. Walker. Modal logics for mobile processes. In Baeten, Groote (Eds): Proceedings of CONCUR '91, Amsterdam, August 1991, pages 45–60, Springer Verlag LNCS 527 (1991). Also in Theoretical Computer Science 114:149–171 (1993).Google Scholar
  23. [MPW92]
    R. Milner, J. Parrow and D. Walker. A Calculus of Mobile Processes, Part I and II. Information and Computation 100:1–77 (1992).Google Scholar
  24. [MS92]
    R. Milner and D. Sangiorgi. Barbed Bisimulation, In Kuich, W. Ed: Proceedings of ICALP '92, pages 685–695, Springer Verlag LNCS 623, (1992).Google Scholar
  25. [Par90]
    J. Parrow. ‘Mismatching’ and early equivalence (π-calculus note JP13). Manuscript, Swedish Institute of Computer Science 1990.Google Scholar
  26. [PS93]
    J. Parrow and D. Sangiorgi. Algebraic theories for name-passing calculi. Reserach Report ECS-LFCS-93-262, Department of Computer Science, University of Edinburgh, 1993.Google Scholar
  27. [San92]
    D. Sangiorgi. Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms. PhD thesis CST-99-93, Department of Computer Science, University of Edinburgh, 1992.Google Scholar
  28. [San93]
    D. Sangiorgi. A theory of bisimulation for π-calculus. In Best (Ed): Proceedings of CONCUR '93, pages 127–142, Springer Verlag LNCS 715 (1993).Google Scholar
  29. [Set78]
    R. Sethi. Conditional expressions with equality tests. J. ACM 25(4):667–674 (1978).Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Joachim Parrow
    • 1
    • 2
    • 3
  • Davide Sangiorgi
    • 4
  1. 1.Swedish Institute of Computer ScienceKistaSweden
  2. 2.Royal Institute of TechnologyStockholmSweden
  3. 3.Uppsala UniversitySweden
  4. 4.LFCS, Department of Computer ScienceUniversity of EdinburghEdinburghUK

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