Abstract
The π-calculus is the paradigmatic calculus of mobile processes. With respect to previous formalisms for concurrency, most notably CCS, the most novel aspect of π-calculus is probably its rich theory of types. We explain the importance of types in the π-calculus on a concrete example: the termination property.
A process M terminates if it cannot produce an infinite sequence of reductions M τ→ M1 τ→ M2.... Termination is a useful property in concurrency. For instance, a terminating applet, when loaded on a machine, will not run for ever, possibly absorbing all computing resources (a ‘denial of service’ attack). Similarly, termination guarantees that queries to a given service originate only finite computations.
We consider the problem of proving termination of non-trivial subsets of CCS and π-calculus. In CCS the proof is purely combinatorial, and is very simple. In the π-calculus, by contrast, combinatorial proofs appear to be very hard.We show how to solve the problem by taking into account type information.
Work supported by the EC project “PROFUNDIS” (IST-2001-33100)
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References
G. Boudol and C. Laneve. λ-calculus, multiplicities and the π-calculus. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.
M. Dezani-Ciancaglini, U. de Liguoro, and U. Piperno. Fully abstract semantics for concurrent λ-calculus. In M. Hagiya and J. C. Mitchell, editors, Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 16–35. Springer Verlag, 1994.
C. Fournet and G. Gonthier. The Reflexive Chemical Abstract Machine and the Join calculus. In Proc. 23th POPL. ACM Press, 1996.
J.-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types. Cambridge Tracts in Theoretical Computer Science 7. Cambridge University Press, 1988.
M. Hicks, P. Kakkar, J. T. Moore, C. A. Gunter, and S. Nettles. PLAN: A packet language for active networks. In Conf. on Functional Programming (ICFP’98), volume 34(1) of ACM SIGPLAN Notices, pages 86–93. ACM, June 1999.
F. Honsell, I. A. Mason, S. F. Smith, and C. L. Talcott. A Variable Typed Logic of Effiects. Information and Computation, 119(1):55–90, 1995.
N. Kobayashi. Type systems for concurrent processes: From deadlockfreedom to livelock-freedom, time-boundedness. In J. van Leeuwen, O. Watanabe, M. Hagiya, P. D. Mosses, and T. Ito, editors, IFIP Conf. TCS 2000, volume 1872 of Lecture Notes in Computer Science, pages 365–389. IFIP, Springer Verlag, August 2000.
M. Merro. Locality in the π-calculus and applications to object-oriented languages. PhD thesis, Ecoles des Mines de Paris, 2001.
R. Milner. Communicating and Mobile Systems: the π-Calculus. Cambridge University Press, 1999.
J. C. Mitchell. Foundations for Programming Languages. MIT Press, Cambridge, MA, 1996.
D. Sangiorgi. The name discipline of uniform receptiveness. Theoretical Computer Science, 221:457–493, 1999.
D. Sangiorgi. Termination of processes. ftp://ftp-sop.inria.fr/mimosa/ personnel/davides/ter.ps, December 2001.
D. Sangiorgi and D. Walker. The π-calculus: a Theory of Mobile Processes. Cambridge University Press, 2001.
N. D. Turner. The polymorphic pi-calculus: Theory and Implementation. PhD thesis, Department of Computer Science, University of Edinburgh, 1996.
N. Yoshida, M. Berger, and Honda. K. Strong normalisation in the π-Calculus. In 16th Annual IEEE Symposium on Logic in Computer Science (LICS-01), pages 311–322. IEEE Computer Society, 2001.
N. Yoshida. Graph types for monadic mobile processes. In Proc. FST & TCS, volume 1180 of Lecture Notes in Computer Science, pages 371–386. Springer Verlag, 1996. Full paper appeared as Technical Report, ECSLFCS-96-350, 1996, Edinburgh.
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Sangiorgi, D. (2002). Types, or: Where’s the Difference Between CCS and π?. In: Brim, L., Křetínský, M., Kučera, A., Jančar, P. (eds) CONCUR 2002 — Concurrency Theory. CONCUR 2002. Lecture Notes in Computer Science, vol 2421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45694-5_5
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DOI: https://doi.org/10.1007/3-540-45694-5_5
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