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A congruence rule format for namepassing process calculi from mathematical structural operational semantics
 In Proc. LICS’06
, 2006
"... We introduce a GSOSlike rule format for namepassing process calculi. Specifications in this format correspond to theories in nominal logic. The intended models of such specifications arise by initiality from a general categorical model theory. For operational semantics given in this rule format, a ..."
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Cited by 20 (5 self)
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We introduce a GSOSlike rule format for namepassing process calculi. Specifications in this format correspond to theories in nominal logic. The intended models of such specifications arise by initiality from a general categorical model theory. For operational semantics given in this rule format, a natural behavioural equivalence — a form of open bisimilarity — is a congruence.
A unifying model of variables and names
 Foundations of Software Science and Computational Structures, vol. 3441, Lect. Notes in Comp. Sci
, 2005
"... Abstract. We investigate a category theoretic model where both “variables” and “names”, usually viewed as separate notions, are particular cases of the more general notion of distinction. The key aspect of this model is to consider functors over the category of irreflexive, symmetric finite relation ..."
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Cited by 13 (3 self)
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Abstract. We investigate a category theoretic model where both “variables” and “names”, usually viewed as separate notions, are particular cases of the more general notion of distinction. The key aspect of this model is to consider functors over the category of irreflexive, symmetric finite relations. The models previously proposed for the notions of “variables ” and “names ” embed faithfully in the new one, and initial algebra/final coalgebra constructions can be transferred from the formers to the latter. Moreover, the new model admits a definition of distinctionaware simultaneous substitutions. As a substantial application example, we give the first semantic interpretation of MillerTiu’s FOλ ∇ logic. 1
General structural operational semantics through categorical logic (Extended Abstract)
, 2008
"... Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rulebased definitions and proof techniques for congruence results. We formulate these principles in the general context of categorical logic. From this general formul ..."
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Cited by 7 (6 self)
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Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rulebased definitions and proof techniques for congruence results. We formulate these principles in the general context of categorical logic. From this general formulation we recover precise results for particular language idioms by interpreting the logic in particular categories. For instance, results for firstorder calculi, such as CCS, arise from considering the general results in the category of sets. Results for languages involving substitution and name generation, such as the πcalculus, arise from considering the general results in categories of sheaves and group actions. As an extended example, we develop a tyft/tyxtlike rule format for open bisimulation in the πcalculus.
A Category of Explicit Fusions
, 2008
"... Name passing calculi are nowadays an established field on its own. Besides their practical relevance, they offered an intriguing challenge, since the standard operational, denotational and logical methods often proved inadequate to reason about these formalisms. A domain which has been successfully ..."
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Cited by 1 (1 self)
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Name passing calculi are nowadays an established field on its own. Besides their practical relevance, they offered an intriguing challenge, 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 πcalculus, are presheaf categories based on (injective) relabelings, such as Set. Calculi with symmetric binding, in the spirit of the fusion calculus, give rise to new research problems. In this work we examine the calculus of explicit fusions, and propose to model its syntax and semantics using the presheaf category Set E,whereE is the category of equivalence relations and equivalence preserving morphisms.
Reactive Systems, (Semi)Saturated Semantics and Coalgebras on Presheaves
, 2009
"... The semantics of process calculi has traditionally been specified by labelled transition systems (ltss), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences ( ..."
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The semantics of process calculi has traditionally been specified by labelled transition systems (ltss), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences (bisimilarity, trace equivalence, etc.) defined for lts can be transferred to unlabelled transition systems. Recently, in order to answer this question, several proposals have been made with the aim of automatically deriving an lts from reaction rules in such a way that the resulting equivalences are congruences. Furthermore these equivalences should agree with the standard semantics, whenever one exists. In this paper we propose saturated semantics, based on a weaker notion of observation and orthogonal to all the previous proposals, and we demonstrate the appropriateness of our semantics by means of two examples: logic programming and open Petri nets. We also show that saturated semantics can be efficiently characterized through the so called semisaturated games. Finally, we provide coalgebraic models relying on presheaves.
HDautomata for open bisimulation
"... Abstract. HDautomata are a syntaxindependent operational model introduced for dealing with historydependent formalisms. This kind of enriched automata, where states, transitions, and labels are equipped with names and symmetries, have been successfully applied for modelling early and late bisimul ..."
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Abstract. HDautomata are a syntaxindependent operational model introduced for dealing with historydependent formalisms. This kind of enriched automata, where states, transitions, and labels are equipped with names and symmetries, have been successfully applied for modelling early and late bisimulation in πcalculus and hyperbisimulation in Fusion calculus. However, current HDautomata are not adequate for modelling open bisimulation, because in HDautomata two names cannot be unified, while open bisimulation is closed under all possible name substitution respecting name distinctions. In this paper we tackle the problem by integrating in the definition of named sets, the basic building blocks of HDautomata, a notion of distinction: names can coalesce if the distinction allows to. Then, we use HDautomata over named sets with distinctions for modelling the open bisimulation of πcalculus. Finally, we discuss the relationship between named sets with distinctions and their HDautomata, with the categorical counterparts based on presheaf categories. 1
MFPS 25 Preliminary Proceedings Two cotensors in one: Presentations of algebraic theories for local state and fresh names
"... Various situations in computer science call for categories that support both cartesian closed and monoidal closed structure. Such situations include (i) models of local state, where the monoidal product describes disjointness of memory, and (ii) treatment of fresh names, as required in models of the ..."
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Various situations in computer science call for categories that support both cartesian closed and monoidal closed structure. Such situations include (i) models of local state, where the monoidal product describes disjointness of memory, and (ii) treatment of fresh names, as required in models of the πcalculus. I propose a technique to embed the two closed structures into one single structure. To demonstrate the technique, I show how previously studied theories of local state and fresh names can be understood formally as presentations of (enriched) algebraic theories. 1
Ministry of University and Research project SisteR (PRIN 20088HXMYN).
, 2011
"... 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 sta ..."
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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 πcalculus, are presheaf categories based on (injective) relabellings, such as Set I.Calculiwithsymmetric binding, in the spirit of the fusion calculus, give rise to novel research challenges. In this work we examine the explicit fusion 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 (S0505/TIC/0407) and by the Netherlands Organization for Scientific
MFPS 2008 A categorical model of the Fusion calculus
"... We provide a categorical presentation of the Fusion calculus. 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 new, congruencefree presentat ..."
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We provide a categorical presentation of the Fusion calculus. 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 new, congruencefree 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 as 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. 1