Sequentiality and the π-Calculus

  • Martin Berger
  • Kohei Honda
  • Nobuko Yoshida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2044)


We present a type discipline for the π-calculus which precisely captures the notion of sequential functional computation as a specific class of name passing interactive behaviour. The typed calculus allows direct interpretation of both call-by-name and call-by-value sequential functions. The precision of the representation is demonstrated by way of a fully abstract encoding of PCF. The result shows how a typed π-calculus can be used as a descriptive tool for a significant class of programming languages without losing the latter’s semantic properties. Close correspondence with games semantics and process-theoretic reasoning techniques are together used to establish full abstraction.


Action Type Sequential Process Parallel Composition Reduction Rule Typing Rule 
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  1. 1.
    Abramsky, S., Computational interpretation of linear logic. TCS, Vol. 111, 1993.Google Scholar
  2. 2.
    Abramsky, S., Honda, K. and McCusker, G., A Fully Abstract Game Semantics for General References. LICS, 334–344, IEEE, 1998.Google Scholar
  3. 3.
    Abramsky, S., Jagadeesan, R. and Malacaria, P., Full Abstraction for PCF. Info. & Comp., Vol. 163, 2000.Google Scholar
  4. 4.
    Berger, M. Honda, K. and N. Yoshida. Sequentiality and the π-Calculus. To appear as a QMW DCS Technical Report, 2001.Google Scholar
  5. 5.
    Berger, M. Honda, K. and N. Yoshida. Genericity in the π-Calculus. To appear as a QMW DCS Technical Report, 2001.Google Scholar
  6. 6.
    Berry, G. and Curien, P. L., Sequential algorithms on concrete data structures TCS, 20(3), 265–321, North-Holland, 1982.zbMATHMathSciNetGoogle Scholar
  7. 7.
    Boreale, M. and Sangiorgi, D., Some congruence properties for π-calculus bisimilarities, TCS, 198, 159–176, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Boudol, G., Asynchrony and the pi-calculus, INRIA Research Report 1702, 1992.Google Scholar
  9. 9.
    Boudol, G., The pi-calculus in direct style, POPL’97, 228–241, ACM, 1997.Google Scholar
  10. 10.
    Curien, P. L., Sequentiality and full abstraction. Proc. of Application of Categories in Computer Science, LNM 177, 86–94, Cambridge Press, 1995.Google Scholar
  11. 11.
    Fiore, M. and Honda, K., Recursive Types in Games: axiomatics and process representation, LICS’98, 345–356, IEEE, 1998.Google Scholar
  12. 12.
    Gay, S. and Hole, M., Types and Subtypes for Client-Server Interactions, ESOP’99, LNCS 1576, 74–90, Springer, 1999.Google Scholar
  13. 13.
    Girard, J.-Y., Linear Logic, TCS, Vol. 50, 1–102, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Gunter, C., Semantics of Programming Languages: Structures and Techniques, MIT Press, 1992.Google Scholar
  15. 15.
    Honda, K., Types for Dyadic Interaction. CONCUR’93, LNCS 715, 509–523, 1993.Google Scholar
  16. 16.
    Honda, K., Composing Processes, POPL’96, 344–357, ACM, 1996.Google Scholar
  17. 17.
    Honda, K., Kubo, M. and Vasconcelos, V., Language Primitives and Type Discipline for Structured Communication-Based Programming. ESOP’98, LNCS 1381, 122–138. Springer-Verlag, 1998.Google Scholar
  18. 18.
    Honda, K. and Tokoro, M., An Object Calculus for Asynchronous Communication. ECOOP’91, LNCS 512, 133–147, Springer-Verlag 1991.Google Scholar
  19. 19.
    Honda, K. Vasconcelos, V., and Yoshida, N. Secure Information Flow as Typed Process Behaviour, ESOP’ 99, LNCS 1782, 180–199, Springer-Verlag, 2000.Google Scholar
  20. 20.
    Honda, K. and Yoshida, N. Game-theoretic analysis of call-by-value computation. TCS Vol. 221 (1999), 393–456, North-Holland, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Kobayashi, N., A partially deadlock-free typed process calculus, ACM TOPLAS, Vol. 20,No. 2, 436–482, 1998.CrossRefGoogle Scholar
  22. 22.
    Kobayashi, N., Pierce, B., and Turner, D., Linear Types and π-calculus, POPL’96, 358–371, ACM Press, 1996.Google Scholar
  23. 23.
    Hyland, M. and Ong, L., On Full Abstraction for PCF: I, II and III. 130 pages, 1994. To appear in Info. & Comp.Google Scholar
  24. 24.
    Hyland, M. and Ong, L., Pi-calculus, dialogue games and PCF, FPCA’95, ACM, 1995.Google Scholar
  25. 25.
    Laird, J., Full abstraction for functional languages with control, LICS’97, IEEE, 1997.Google Scholar
  26. 26.
    McCusker, G., Games and Full Abstraction for FPC. LICS’96, IEEE, 1996.Google Scholar
  27. 27.
    Milner, R., Fully abstract models of typed lambda calculi. TCS, 4:1–22, 1977.zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Milner, R., Functions as Processes. MSCS, 2(2), 119–146, CUP, 1992.zbMATHMathSciNetGoogle Scholar
  29. 29.
    Milner, R., Polyadic π-Calculus: a tutorial. Proceedings of the International Summer School on Logic Algebra of Specification, Marktoberdorf, 1992.Google Scholar
  30. 30.
    Pierce, B.C. and Sangiorgi. D, Typing and subtyping for mobile processes. LICS’93, 187–215, IEEE, 1993.Google Scholar
  31. 31.
    Quaglia, P. and Walker, D., On Synchronous and Asynchronous Mobile Processes, FoSSaCS 00, LNCS 1784, 283–296, Springer, 2000.Google Scholar
  32. 32.
    Sangiorgi, D., Expressing Mobility in Process Algebras: First Order and Higher Order Paradigms. Ph.D. Thesis, University of Edinburgh, 1992.Google Scholar
  33. 33.
    Sangiorgi, D. π-calculus, internal mobility, and agent-passing calculi. TCS, 167(2):235–271, North-Holland, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Sangiorgi, D., The name discipline of uniform receptiveness, ICALP’97, LNCS 1256, 303–313, Springer, 1997.Google Scholar
  35. 35.
    Vasconcelos, V., Typed concurrent objects. ECOOP’94, LNCS 821, 100–117. Springer, 1994.Google Scholar
  36. 36.
    Vasconcelos, V. and Honda, K., Principal Typing Scheme for Polyadic π-Calculus. CONCUR’93, LNCS 715, 524–538, Springer-Verlag, 1993.Google Scholar
  37. 37.
    Yoshida, N., Graph Types for Monadic Mobile Processes, FST/TCS’16, LNCS 1180, 371–387, Springer-Verlag, December, 1996.Google Scholar
  38. 38.
    Yoshida, N., Berger, M. and Honda, K., Strong Normalisation in the π-Calculus, To appear as a MCS Technical Report, University of Leicester, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Martin Berger
    • 1
  • Kohei Honda
    • 1
  • Nobuko Yoshida
    • 2
  1. 1.Queen Mary, University of LondonUK
  2. 2.University of LeicesterUK

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