A large variety of process calculi extend the π-calculus with more general notions of messages. Bengtson et al. have shown that many of these π-like calculi can be expressed as so-called ψ-calculi. In this paper, we describe a simple type system for ψ-calculi. The type system satisfies a subject reduction property and a general notion of channel safety. A number of existing systems are shown to be instances of our system, and other, new type systems can also be obtained. We first present a new type system for the calculus of explicit fusions by Wischik and Gardner, then one for the distributed π-calculus of Hennessy and Riely and finally show how existing type systems for secrecy and authenticity in the spi calculus can be represented and shown to be safe.


Type System Side Condition Type Rule Type Environment Mobile Process 
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.
    Abadi, M.: Secrecy by typing in security protocols. J. ACM 46(5), 749–786 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Abadi, M., Blanchet, B.: Secrecy types for asymmetric communication. Theor. Comput. Sci. 298(3), 387–415 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Abadi, M., Gordon, A.D.: A calculus for cryptographic protocols: the spi calculus. In: Proc. CCS 1997, pp. 36–47. ACM, New York (1997)Google Scholar
  4. 4.
    Bengtson, J., Johansson, M., Parrow, J., Victor, B.: Psi-calculi: Mobile Processes, Nominal Data, and Logic. In: Proc. of LICS 2009, pp. 39–48. IEEE, Los Alamitos (2009)Google Scholar
  5. 5.
    Carbone, M., Maffeis, S.: On the expressive power of polyadic synchronisation in π-calculus. Nordic Journal of Computing 10(2), 70–98 (2003)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Cardelli, L., Gordon, A.D.: Mobile ambients. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, p. 140. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Deng, Y., Sangiorgi, D.: Ensuring termination by typability. Inf. Comput. 204(7), 1045–1082 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Elsborg, E., Hildebrandt, T., Sangiorgi, D.: Type systems for bigraphs. In: Kaklamanis, C., Nielson, F. (eds.) TGC 2008. LNCS, vol. 5474, pp. 126–140. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Fournet, C., Gordon, A.D., Maffeis, S.: A type discipline for authorization policies. ACM Trans. Program. Lang. Syst. 29(5) (2007)Google Scholar
  10. 10.
    Gabbay, M.J., Mathijssen, A.: Nominal (universal) algebra: Equational logic with names and binding. J. Log. Comput. 19(6), 1455–1508 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gordon, A.D., Jeffrey, A.: Authenticity by typing for security protocols. J. Comput. Secur. 11(4), 451–519 (2003)CrossRefGoogle Scholar
  12. 12.
    Honda, K.: Composing processes. In: Proc. of POPL 1996, pp. 344–357. ACM, New York (1996)Google Scholar
  13. 13.
    Igarashi, A., Kobayashi, N.: A generic type system for the Pi-calculus. Theor. Comput. Sci. (11), 121–163 (2004)Google Scholar
  14. 14.
    Kobayashi, N., Pierce, B.C., Turner, D.N.: Linearity and the pi-calculus. ACM Trans. Program. Lang. Syst. 21(5), 914–947 (1999)CrossRefGoogle Scholar
  15. 15.
    Kobayashi, N., Sangiorgi, D.: A hybrid type system for lock-freedom of mobile processes. ACM Trans. Program. Lang. Syst. 32(5) (2010)Google Scholar
  16. 16.
    Makholm, H., Wells, J.B.: Instant polymorphic type systems for mobile process calculi: Just add reduction rules and close. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, pp. 389–407. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Milner, R.: The polyadic pi-calculus: a tutorial, pp. 203–246. Springer, Heidelberg (1993)Google Scholar
  18. 18.
    Milner, R.: The Space and Motion of Communicating Agents. Cambridge University Press, Cambridge (2009)CrossRefzbMATHGoogle Scholar
  19. 19.
    Pierce, B.C., Sangiorgi, D.: Typing and subtyping for mobile processes. Mathematical Structures in Computer Science 6(5), 409–453 (1996)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Riely, J., Hennessy, M.: A typed language for distributed mobile processes. In: Proceedings of POPL 1998, pp. 378–390. ACM, New York (1998)Google Scholar
  21. 21.
    Riely, J., Hennessy, M.: Trust and partial typing in open systems of mobile agents. J. Autom. Reasoning 31(3-4), 335–370 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Sangiorgi, D.: The name discipline of uniform receptiveness. Theor. Comput. Sci. 221(1-2), 457–493 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Sangiorgi, D., Walker, D.: The π-Calculus - A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar
  24. 24.
    Wischik, L., Gardner, P.: Explicit fusions. Theor. Comput. Sci. 340(3), 606–630 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hans Hüttel
    • 1
  1. 1.Department of Computer ScienceAalborg UniversityDenmark

Personalised recommendations