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Duoidally Enriched Freyd Categories

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Relational and Algebraic Methods in Computer Science (RAMiCS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13896))

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Abstract

Freyd categories provide a semantics for first-order effectful programming languages by capturing the two different orders of evaluation for products. We enrich Freyd categories in a duoidal category, which provides a new, third choice of parallel composition. Duoidal categories have two monoidal structures which account for the sequential and parallel compositions. The traditional setting is recovered as a full coreflective subcategory for a judicious choice of duoidal category. We give several worked examples of this uniform framework, including the parameterised state monad, basic separation semantics for resources, and interesting cases of change of enrichment.

J. Sigal—Partly funded by Huawei.

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Acknowledgments

We would like to thank Robin Kaarsgaard, Ohad Kammar, and Matthew Di Meglio for their input and encouragement, as well as the reviewers of all versions of this work.

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Authors and Affiliations

  1. School of Informatics, University of Edinburgh, Edinburgh, UK

    Chris Heunen & Jesse Sigal

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  1. Chris Heunen
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  2. Jesse Sigal
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Correspondence to Jesse Sigal .

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Editors and Affiliations

  1. Deutsches Zentrum für Luft- und Raumfahrt, Augsburg, Germany

    Roland Glück

  2. Aix-Marseille University, Marseille, France

    Luigi Santocanale

  3. Brock University, St Catharines, ON, Canada

    Michael Winter

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Heunen, C., Sigal, J. (2023). Duoidally Enriched Freyd Categories. In: Glück, R., Santocanale, L., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2023. Lecture Notes in Computer Science, vol 13896. Springer, Cham. https://doi.org/10.1007/978-3-031-28083-2_15

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  • DOI: https://doi.org/10.1007/978-3-031-28083-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-28082-5

  • Online ISBN: 978-3-031-28083-2

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