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)


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.


Operational Semantic Operational Correspondence Label Transition System Reduction Rule Process Algebra 
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  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

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