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A Presheaf Environment for the Explicit Fusion Calculus

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Abstract

Name passing calculi are nowadays one of the preferred formalisms for the specification of concurrent and distributed systems with a dynamically evolving topology. Despite their widespread adoption as a theoretical tool, though, they still face some unresolved semantic issues, since the standard operational, denotational and logical methods often proved inadequate to reason about these formalisms. A domain which has been successfully employed for languages with asymmetric communication, like the π-calculus, are presheaf categories based on (injective) relabellings, such as \(Set^{\mathbb{I}}\). Calculi with symmetric binding, in the spirit of the fusion calculus, give rise to novel research challenges. In this work we examine the explicit fusion calculus, and propose to model its syntax and semantics using the presheaf category \(Set^\mathbb{E}\), where \(\mathbb{E}\) is the category of equivalence relations and equivalence preserving morphisms.

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Article 14 September 2020

Guillaume Ambal, Sergueï Lenglet & Alan Schmitt

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Authors and Affiliations

  1. Laboratoire de l’Informatique du Parallélisme, CNRS and ENS Lyon, 46 Allée d’Italie, Lyon, 69364, France

    Filippo Bonchi

  2. IMT, IMT Lucca Institute for Advanced Studies, Piazza S. Ponziano 6, 55100, Lucca, Italy

    Maria Grazia Buscemi

  3. Institute for Logic, Language and Computation, University of Amsterdam, P.O. Box 94242, 1090, GE, Amsterdam, The Netherlands

    Vincenzo Ciancia

  4. Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3c, 56127, Pisa, Italy

    Fabio Gadducci

Authors
  1. Filippo Bonchi
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  2. Maria Grazia Buscemi
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  3. Vincenzo Ciancia
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  4. Fabio Gadducci
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Corresponding author

Correspondence to Fabio Gadducci.

Additional information

This work was carried out during the first author’s tenure of an ERCIM “Alain Bensoussan” Fellowship Programme. The third author has been supported by the Comunidad de Madrid program ProMeSaS (S-0505/TIC/0407) and by the Netherlands Organization for Scientific Research VICI grant 639.073.501. The fourth author has been partly supported by the Italian Ministry of University and Research project SisteR (PRIN 20088HXMYN).

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Bonchi, F., Buscemi, M.G., Ciancia, V. et al. A Presheaf Environment for the Explicit Fusion Calculus. J Autom Reasoning 49, 161–183 (2012). https://doi.org/10.1007/s10817-011-9224-3

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  • DOI: https://doi.org/10.1007/s10817-011-9224-3

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