A Categorical Model of the Fusion Calculus

  • Authors:
  • Marino Miculan

  • Affiliations:
  • Department of Mathematics and Computer Science, University of Udine Via delle Scienze 206, I-33100 Udine, Italy

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2008

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Abstract

We provide a categorical presentation of the Fusion calculus. First we give Working in a suitable category of presheaves, we describe the syntax as initial algebra of a signature endofunctor, and the semantics as coalgebras of a ''behaviour'' endofunctor. To this end, we first give a a new, congruence-free presentation of the Fusion calculus; then, the behaviour endofunctor is constructed by adding in a systematic way a notion of ''state'' to the intuitive endofunctor induced by the LTS. Coalgebras can be given a concrete presentation as ''stateful indexed labelled transition systems''; the bisimilarity over these systems is a congruence, and corresponds to hyperequivalence. Then, we model the labelled transition system of Fusion by abstract categorical rules. As a consequence, we get a semantics for the Fusion calculus which is both compositional and fully abstract: two processes have the same semantics iff they are bisimilar, that is, hyperequivalent.