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oai:drops-oai.dagstuhl.de:10939 2024-03-06T10:47:14Z ddc:004 open_access

Bialgebraic Semantics for String Diagrams Bonchi, Filippo Piedeleu, Robin Sobocinski, Pawel Zanasi, Fabio String Diagram Structural Operational Semantics Bialgebraic semantics Turi and Plotkin’s bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as a monad) and its dynamics (an endofunctor). This setup is instrumental in showing that a semantic specification (a coalgebra) satisfies desirable properties: in particular, that it is compositional. In this work, we use the bialgebraic approach to derive well-behaved structural operational semantics of string diagrams, a graphical syntax that is increasingly used in the study of interacting systems across different disciplines. Our analysis relies on representing the two-dimensional operations underlying string diagrams in various categories as a monad, and their bialgebraic semantics in terms of a distributive law for that monad. As a proof of concept, we provide bialgebraic compositional semantics for a versatile string diagrammatic language which has been used to model both signal flow graphs (control theory) and Petri nets (concurrency theory). Moreover, our approach reveals a correspondence between two different interpretations of the Frobenius equations on string diagrams and two synchronisation mechanisms for processes, à la Hoare and à la Milner. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Filippo Bonchi and Robin Piedeleu and Pawel Sobocinski and Fabio Zanasi 2019 Is Part Of LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2019.37 urn:nbn:de:0030-drops-109398 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.37 eng https://creativecommons.org/licenses/by/3.0/legalcode