Compositional Event Structure Semantics for the Internal π-Calculus

  • Silvia Crafa
  • Daniele Varacca
  • Nobuko Yoshida
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4703)


We propose the first compositional event structure semantics for a very expressive π-calculus, generalising Winskel’s event structures for CCS. The π-calculus we model is the πI-calculus with recursive definitions and summations. First we model the synchronous calculus, introducing a notion of dynamic renaming to the standard operators on event structures. Then we model the asynchronous calculus, for which a new additional operator, called rooting, is necessary for representing causality due to new name binding. The semantics are shown to be operationally adequate and sound with respect to bisimulation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berger, M., Honda, K., Yoshida, N.: Sequentiality and the π-calculus. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, pp. 29–45. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Boreale, M.: On the expressiveness of internal mobility in name-passing calculi. Theor. Comp. Sci. 195(2), 205–226 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Boreale, M., Sangiorgi, D.: A fully abstract semantics for causality in the π-calculus. Acta Inf. 35(5), 353–400 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Boudol, G.: Asynchrony and the π-calculus. Research Report 1702, INRIA (1992)Google Scholar
  5. 5.
    Bruni, R., Melgratti, H., Montanari, U.: Event structure semantics for nominal calculi. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 295–309. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Busi, N., Gorrieri, R.: A petri net semantics for pi-calculus. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 145–159. Springer, Heidelberg (1995)Google Scholar
  7. 7.
    Cattani, G.L., Sewell, P.: Models for name-passing processes: Interleaving and causal. In: Proc. of LICS, pp. 322–332. IEEE Computer Society Press, Los Alamitos (2000)Google Scholar
  8. 8.
    Crafa, S., Varacca, D., Yoshida, N.: Compositional event structure semantics for the internal pi-calculus. Full version, available at
  9. 9.
    Curien, P.-L., Faggian, C.: L-nets, strategies and proof-nets. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 167–183. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Degano, P., De Nicola, R., Montanari, U.: On the consistency of “truly concurrent” operational and denotational semantics. In: Proc. of LICS, pp. 133–141. IEEE Computer Society Press, Los Alamitos (1988)Google Scholar
  11. 11.
    Degano, P., Priami, C.: Non-interleaving semantics for mobile processes. Theor. Comp. Sci. 216(1-2), 237–270 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Engelfriet, J.: A multiset semantics for the pi-calculus with replication. Theor. Comp. Sci. 153(1&2), 65–94 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Faggian, C., Piccolo, M.: A graph abstract machine describing event structure composition. In: GT-VC workshop, ENTCS (2007)Google Scholar
  14. 14.
    Faggian, C., Piccolo, M.: Ludics is a model for the (finitary) linear pi-calculus. In: Proc. of TLCA. LNCS, Springer, Heidelberg (2007)Google Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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, pp. 277–291. Springer, Heidelberg (1995)Google Scholar
  17. 17.
    Merro, M., Sangiorgi, D.: On asynchrony in name-passing calculi. Math. Struct. Comp. Sci. 14, 715–767 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Nielsen, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains, part I. Theor. Comp. Sci. 13(1), 85–108 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Palamidessi, C.: Comparing the expressive power of the synchronous and asynchronous pi-calculi. Math. Struct. Comp. Sci. 13(5), 685–719 (2003)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Sangiorgi, D.: π-calculus, internal mobility and agent passing calculi. Theor. Comp. Sci. 167(2), 235–271 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Varacca, D., Yoshida, N.: Typed event structures and the π-calculus. In: Proc. of MFPS XXII. ENTCS, vol. 158, pp. 373–397. Elsevier, Amsterdam (2006), Full version available at Google Scholar
  22. 22.
    Winskel, G.: Event structure semantics for CCS and related languages. In: Nielsen, M., Schmidt, E.M. (eds.) Automata, Languages, and Programming. LNCS, vol. 140, pp. 561–576. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  23. 23.
    Winskel, G.: Event structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) Advances in Petri Nets 1986. Proceedings of an Advanced Course. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)Google Scholar
  24. 24.
    Winskel, G.: Name generation and linearity. In: Proc. of LICS, pp. 301–310. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  25. 25.
    Winskel, G.: Relations in concurrency. In: Proc. of LICS, pp. 2–11. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  26. 26.
    Winskel, G., Nielsen, M.: Models for concurrency. In: Handbook of logic in Computer Science, vol. 4, Clarendon Press, Oxford (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Silvia Crafa
    • 1
  • Daniele Varacca
    • 2
  • Nobuko Yoshida
    • 3
  1. 1.Università di Padova 
  2. 2.PPS - Université Paris 7 & CNRS 
  3. 3.Imperial College London 

Personalised recommendations