Advertisement

From π-calculus to higher-order π-calculus — and back

  • Davide Sangiorgi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 668)

Abstract

We compare the first-order and the higher-order paradigms for the representation of mobility in process algebras. The prototypical calculus in the first-order paradigm is the π -calculus. By generalising its sort mechanism we derive an ω-order extension, called Higher-Order π - calculus. We give examples of its use, including the encoding of λ-calculus. Surprisingly, we show that such an extension does not add expressiveness: Higher-order processes can be faithfully represented at first order. We conclude that the first-order paradigm, which enjoys a simpler and more intuitive theory, should be taken as basic. Nevertheless, the study of the λ-calculus encodings shows that a higher-order calculus can be very useful for reasoning at a more abstract level.

Keywords

Operational Semantic Operational Correspondence Label Transition System Reduction Rule Process Algebra 
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.

References

  1. [1]
    Abramsky, S., The Lazy Lambda Calculus, Research Topics in Functional Programming, pp65–116, Addison Wesley, 1989.Google Scholar
  2. [2]
    America, P. and de Bakker, J. and Kok, J. and Rutten, J., Denotational Semantics of a Parallel Object-Oriented Language, Information and Computation, 83(2), 1989.Google Scholar
  3. [3]
    America, P., Issues in the Design of a Parallel Object-Oriented Language, Formal Aspects of Computing, 1(4), pp366–411, 1989.CrossRefGoogle Scholar
  4. [4]
    Astesiano, E. and Giovini, A., Generalized Bisimulation in Relational Specifications, STACS 88, LNCS 294, pp207–226, 1988.Google Scholar
  5. [5]
    Amadio, R., A Uniform Presentation of CHOCS and π-calculus, Rapport de Recherche 1726, INRIA-Lorraine, Nancy, 1992.Google Scholar
  6. [6]
    Berry, G. and Boudol, G., The Chemical Abstract Machine, 17th POPL, 1990.Google Scholar
  7. [7]
    Bolognesi, T. and Brinksma, E., Introduction to the ISO Specification Language LOTOS, in The Formal Description Technique LOTOS, North Holland, 1989.Google Scholar
  8. [8]
    Boudol, G., Towards a Lambda Calculus for Concurrent and Communicating Systems, TAPSOFT 89, LNCS 351, pp149–161, 1989.Google Scholar
  9. [9]
    Degano, P. and Darondeau, P., Causal Trees, 15th ICALP, LNCS 372, pp234–248, 1989.Google Scholar
  10. [10]
    De Nicola, R. and Hennessy, R., Testing Equivalences for Processes, Theor. Comp. Sci. 34, pp83–133, 1984.CrossRefGoogle Scholar
  11. [11]
    Hoare, C.A.R., Communicating Sequential Processes, Prentice Hall, 1985.Google Scholar
  12. [12]
    Milner, R., Communication and Concurrency, Prentice Hall, 1989.Google Scholar
  13. [13]
    Milner, R., The polyadic π-calculus: a tutorial, Technical Report ECS-LFCS-91-180, LFCS, Dept. of Comp. Sci. Edinburgh Univ., 1991.Google Scholar
  14. [14]
    Milner, R., Functions as Processes, Technical Report 1154, INRIA Sofia-Antipolis, 1990. Final version in Journal of Mathem. Structures in Computer Science 2(2), pp119–141, 1992.Google Scholar
  15. [15]
    Milner, R. and Parrow, J. and Walker, D., A Calculus of Mobile Processes, (Parts I and II), Information and Computation, 100, pp1–77, 1992.CrossRefGoogle Scholar
  16. [16]
    Milner, R. and Sangiorgi, D., Barbed Bisimulation, 19th ICALP, LNCS 623, pp685–695, 1992.Google Scholar
  17. [17]
    Phillips, I.C.C., Refusal Testings, Theor. Comp. Sci., 50, pp241–284, 1987.CrossRefGoogle Scholar
  18. [18]
    Sangiorgi, D. Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms, PhD thesis, Edinburgh Univ., 1992, to appear.Google Scholar
  19. [19]
    Thomsen, B., Calculi for Higher Order Communicating Systems, PhD thesis, Dept. of Computing, Imperial College, 1990.Google Scholar
  20. [20]
    Walker, D., π-calculus Semantics of Object-Oriented Programming Languages, Technical Report ECS-LFCS-90-122 LFCS, Dept. of Comp. Sci. Edinburgh Univ., 1990. Also in Proc. Conference on Theoretical Aspects of Computer Software, Tohoku University, Japan, Sept. 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Davide Sangiorgi
    • 1
  1. 1.Dep. Comp. ScienceUniverstity Edinburgh, JCMBEdinburghUK

Personalised recommendations