Abstract
Recent work has shown that presheaf categories provide a general model of concurrency, with an inbuilt notion of bisimulation based on open maps. Here it is shown how this approach can also handle systems where the language of actions may change dynamically as a process evolves. The example is the π-calculus, a calculus for ‘mobile processes’ whose communication topology varies as channels are created and discarded. A denotational semantics is described for the π-calculus within an indexed category of profunctors; the model is fully abstract for bisimilarity, in the sense that bisimulation in the model, obtained from open maps, coincides with the usual bisimulation obtained from the operational semantics of the π-calculus. While attention is concentrated on the ‘late’ semantics of the π-calculus, it is indicated how the ‘early’ and other variants can also be captured.
Basic Research in Computer Science, a centre of the Danish National Research Foundation.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Bibliography
Francis Borceux. Handbook of Categorical Algebra, vol. 1, volume 50 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1994.
Gérard Boudol. Asynchrony and the π-calculus. Rapport de recherche 1702, INRIA, Sophia Antipolis, 1992.
Gian Luca Cattani and Glynn Winskel. Presheaf models for concurrency. In Computer Science Logic 1996, To appear in Lecture Notes in Computer Science. Springer-Verlag, 1997. A preliminary version appeared as BRIGS Report RS-96-35.
Brian J. Day. On closed categories of functors. In Reports of the Midwest Category Seminar IV, Lecture Notes in Mathematics 137, pages 1–38. Springer Verlag, 1970.
Marcelo Fiore, Eugenio Moggi, and Davide Sangiorgi. A fully-abstract model for the π-calculus. In (LICS 1996).
Matthew Hennessy. A fully abstract denotational semantics for the π-calculus. Technical Report 96:04, School of Cognitive and Computing Sciences, University of Sussex, 1996.
Matthew Hennessy and Gordon Plotkin. Full abstraction for a simple parallel programming language. In Mathematical Foundations of Computer Science: Proceedings of the 8th International Symposium, Lecture Notes in Computer Science 74, pages 108–120. Springer-Verlag, 1979.
André Joyal and Ieke Moerdijk. A completeness theorem for open maps. Annals of Pure and Applied Logic, 70:51–86, 1994.
André Joyal and Ieke Moerdijk. Algebraic Set Theory, volume 220 of London Mathematical Society Lecture Note Series. Cambridge University Press, 1995.
André Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation from open maps. Information and Computation, 127(2):164–185, 1996.
LICS 1996. Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, New Brunswick, New Jersey, July 27–30, 1996. IEEE Computer Society Press, 1996.
Robin Milner. The polyadic π-calculus — a tutorial. Technical Report ECSLFCS-91-180, Laboratory for Foundations of Computer Science, University of Edinburgh, 1991.
Robin Milner. Functions as processes. Mathematical Structures in Computer Science, 2(2):119–141, 1992.
Robin Milner, Joachim Parrow, and David Walker. A calculus of mobile processes, part I. Information and Computation, 100:1–40, 1992a.
Robin Milner, Joachim Parrow, and David Walker. A calculus of mobile processes, part II. Information and Computation, 100:41–77, 1992b.
Davide Sangiorgi. Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms. PhD Thesis CST-99-93, Department of Computer Science, University of Edinburgh, 1992.
Davide Sangiorgi. π-calculus, internal mobility, and agent-passing calculi. Rapport de recherche 2539, INRIA, Sophia Antipolis, 1995.
Ian Stark. A fully abstract domain model for the π-calculus. In (LICS 1996), pages 36–42.
Bent Thomsen. Plain CHOCS. Acta Informatica, 30:1–59, 1993.
Glynn Winskel. A presheaf semantics of value-passing processes. In CONCUR '96: Proceedings of the 7th International Conference on Concurrency Theory, Lecture Notes in Computer Science 1119, pages 98–114. Springer Verlag, 1996. An extended version appears as BRIGS Report RS-96-44.
Glynn Winskel and Mogens Nielsen. Models for concurrency. In Handbook of Logic in Computer Science, volume IV. Oxford University Press, 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cattani, G.L., Stark, I., Winskel, G. (1997). Presheaf models for the π-calculus. In: Moggi, E., Rosolini, G. (eds) Category Theory and Computer Science. CTCS 1997. Lecture Notes in Computer Science, vol 1290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026984
Download citation
DOI: https://doi.org/10.1007/BFb0026984
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63455-3
Online ISBN: 978-3-540-69552-3
eBook Packages: Springer Book Archive