A Game Semantics of the Asynchronous π-Calculus

  • Jim Laird
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)


This paper studies the denotational semantics of the typed asynchronous π-calculus. We describe a simple game semantics of this language, placing it within a rich hierarchy of games models for programming languages,

A key element of our account is the identification of suitable categorical structures for describing the interpretation of types and terms at an abstract level. It is based on the notion of closed Freyd category, establishing a connection between our semantics, and that of the λ-calculus. This structure is also used to define a trace operator, with which name binding is interpreted. We then show that our categorical characterization is sufficient to prove a weak soundness result.

Another theme of the paper is the correspondence between justified sequences, on which our model is based, and traces in a labelled transition system in which only bound names are passed. We show that the denotations of processes are equivalent, via this correspondence, to their sets of traces. These results are used to show that the games model is fully abstract with respect to may-equivalence.


Game Model Monoidal Category Trace Operator Label Transition System Initial Move 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramsky, S., Jagadeesan, R.: Games and full completeness for multiplicative linear logic. Journal of Symbolic Logic 59, 543–574 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. Information and Computation 163, 409–470 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Berger, M., Honda, K., Yoshida, N.: Sequentiality and the π-calculus. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, p. 29. Springer, Heidelberg (2001)Google Scholar
  4. 4.
    Berger, M., Honda, K., Yoshida, N.: Strong normalization in the π-calculus. In: Proceedings of LICS 2001. IEEE Press, Los Alamitos (2001)Google Scholar
  5. 5.
    Boudol, G.: Asynchrony in the pi-calculus. Technical Report 1702, INRIA (1992) Google Scholar
  6. 6.
    Ghica, D., McCusker, G.: The regular language semantics of second-order Idealised Algol. Theoretical Computer Science (2003) (to appear) Google Scholar
  7. 7.
    Ghica, D., Murawski, A.: Angelic semantics of fine-grained concurrency. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 211–225. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Harmer, R., McCusker, G.: A fully abstract games semantics for finite nondeterminism. In: Proceedings of the Fourteenth Annual Symposium on Logic in Computer Science, LICS 1999. IEEE Computer Society Press, Los Alamitos (1998)Google Scholar
  9. 9.
    Hennessy, M.: A fully abstract denotational semantics for the π-calculus. Technical Report 041996, University of Sussex (COGS) (2996) Google Scholar
  10. 10.
    Honda, K., Tokoro, M.: An object calculus for asynchronous communication. In: America, P. (ed.) ECOOP 1991. LNCS, vol. 512, pp. 133–147. Springer, Heidelberg (1991)Google Scholar
  11. 11.
    Hyland, J.M.E., Ong, C.-H.L.: On full abstraction for PCF: I, II and III. Information and Computation 163, 285–408 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Jagadeesan, L.J., Jagadeesan, R.: Causality and true concurrency: A data-flow analysis of the pi-calculus. In: Alagar, V.S., Nivat, M. (eds.) AMAST 1995. LNCS, vol. 936, Springer, Heidelberg (1995)Google Scholar
  13. 13.
    Jeffrey, A.S.A., Rathke, J.: Contextual equivalence for higher-order pi-calculus revisited. Technical Report 0402, University of Sussex (COGS) (2002) Google Scholar
  14. 14.
    Jeffrey, A.S.A., Rathke, J.: A fully abstract may-testing semantics for concurrent objects. In: Proceedings of LICS 2002, pp. 101–112 (2002)Google Scholar
  15. 15.
    Joyal, A., Street, R., Verity, D.: Traced monoidal categories. Math. Proc. Camb. Phil. Soc. 119, 447–468 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Laird, J.: A game semantics of ICSP. In: Proceedings of MFPS XVII. Electronic notes in Theoretical Computer Science, vol. 45. Elsevier, Amsterdam (2001)Google Scholar
  17. 17.
    Laird, J.: A categorical semantics of higher-order store. In: Proceedings of CTCS 2002. ENTCS, vol. 69. Elsevier, Amsterdam (2002)Google Scholar
  18. 18.
    Laird, J.: A game semantics of local names and good variables. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 289–303. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    de Nicola, R., Boreale, M., Pugliese, R.: Trace and testing equivalence on asynchronous processes. Information and Computation 172(2), 139–164 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Moggi, E., Fiore, M., Sangiorgi, D.: A fully abstract model for the π-calculus. In: Proceedings of LICS 1996 (1996)Google Scholar
  21. 21.
    Malacaria, P., Hankin, C.: Generalised flowcharts and games. In: Proceedings of the 25th International Colloquium on Automata, Langugages and Programming (1998)Google Scholar
  22. 22.
    McCusker, G.: Games and full abstraction for a functional metalanguage with recursive types. PhD thesis, Imperial College London, Published by Cambridge University Press (1996) Google Scholar
  23. 23.
    Milner, R.: Polyadic π-calculus: a tutorial. In: Proceedings of the Marktoberdorf Summer School on Logic and Algebra of Specification (1992)Google Scholar
  24. 24.
    Power, J., Thielecke, H.: Environments in Freyd categories and k-categories. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, p. 625. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  25. 25.
    Sangiorgi, D.: Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms. PhD thesis, University of Edinburgh (1993) Google Scholar
  26. 26.
    Stark, I.: A fully abstract domain model for the π-calculus. In: Proceedings of LICS 1996 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jim Laird
    • 1
  1. 1.Dept. of InformaticsUniversity of SussexUK

Personalised recommendations