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Equivalence of Denotational and Operational Semantics for Interaction Languages

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Theoretical Aspects of Software Engineering (TASE 2022)

Abstract

Message Sequence Charts (MSC) and Sequence Diagrams (SD) are graphical models representing the behaviours of distributed and concurrent systems via the scheduling of discrete emission and reception events. So as to exploit them in formal methods, a mathematical semantics is required. In the literature, different kinds of semantics are proposed: denotational semantics, well suited to reason about algebraic properties and operational semantics, well suited to establish verification algorithms. We define an algebraic language to specify so-called interactions, similar to the MSC and SD models. It is equipped with a denotational semantics associating sets of traces (sequences of observed events) to interactions. We then define a structural operational semantics in the style of process algebras and prove the equivalence of the two semantics.

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Notes

  1. 1.

    For a set E, \(\mathcal{P}(E)\) is the set of all subsets of E.

  2. 2.

    The free term \(\mathcal {F}\)-algebra is defined by interpreting symbols of \(\mathcal {F}\) as constructors of new terms: for \(f \in \mathcal {F}\) of arity j, for \(t_1, \ldots t_j \in \mathbb {I}_\varOmega \), \(f(t_1, \ldots t_j)\) is interpreted as itself.

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Mahe, E., Gaston, C., Gall, P.L. (2022). Equivalence of Denotational and Operational Semantics for Interaction Languages. In: Aït-Ameur, Y., Crăciun, F. (eds) Theoretical Aspects of Software Engineering. TASE 2022. Lecture Notes in Computer Science, vol 13299. Springer, Cham. https://doi.org/10.1007/978-3-031-10363-6_8

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  • DOI: https://doi.org/10.1007/978-3-031-10363-6_8

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