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DOI: 10.4230/LIPIcs.CONCUR.2019.37
URN: urn:nbn:de:0030-drops-109398
URL: http://drops.dagstuhl.de/opus/volltexte/2019/10939/
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Bonchi, Filippo ; Piedeleu, Robin ; Sobocinski, Pawel ; Zanasi, Fabio

Bialgebraic Semantics for String Diagrams

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Abstract

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, la Hoare and la Milner.

BibTeX - Entry

@InProceedings{bonchi_et_al:LIPIcs:2019:10939,
  author =	{Filippo Bonchi and Robin Piedeleu and Pawel Sobocinski and Fabio Zanasi},
  title =	{{Bialgebraic Semantics for String Diagrams}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{37:1--37:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Wan Fokkink and Rob van Glabbeek},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10939},
  URN =		{urn:nbn:de:0030-drops-109398},
  doi =		{10.4230/LIPIcs.CONCUR.2019.37},
  annote =	{Keywords: String Diagram, Structural Operational Semantics, Bialgebraic semantics}
}

Keywords: String Diagram, Structural Operational Semantics, Bialgebraic semantics
Seminar: 30th International Conference on Concurrency Theory (CONCUR 2019)
Issue Date: 2019
Date of publication: 26.08.2019


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