A Presheaf Environment for the Explicit Fusion Calculus

  • Authors:

  • Filippo Bonchi;Maria Grazia Buscemi;Vincenzo Ciancia;Fabio Gadducci

  • Affiliations:

  • Laboratoire de l'Informatique du Parallélisme, CNRS and ENS Lyon, Lyon, France 69364;IMT, IMT Lucca Institute for Advanced Studies, Lucca, Italy 55100;Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands 1090;Dipartimento di Informatica, University of Pisa, Pisa, Italy 56127

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2012

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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 驴-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.