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Rewriting for Monoidal Closed Categories

Authors Mario Alvarez-Picallo , Dan Ghica , David Sprunger , Fabio Zanasi



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Author Details

Mario Alvarez-Picallo
  • Programming Languages Laboratory, Huawei Research Centre, UK
Dan Ghica
  • Department of Computer Science, University of Birmingham, UK
  • Programming Languages Laboratory, Huawei Research Centre, Reading, UK
David Sprunger
  • Department of Computer Science, University of Birmingham, UK
Fabio Zanasi
  • Department of Computer Science, University College London, UK

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Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi. Rewriting for Monoidal Closed Categories. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 29:1-29:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FSCD.2022.29

Abstract

This paper develops a formal string diagram language for monoidal closed categories. Previous work has shown that string diagrams for freely generated symmetric monoidal categories can be viewed as hypergraphs with interfaces, and the axioms of these categories can be realized by rewriting systems. This work proposes hierarchical hypergraphs as a suitable formalization of string diagrams for monoidal closed categories. We then show double pushout rewriting captures the axioms of these closed categories.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
Keywords
  • string diagrams
  • rewriting
  • hierarchical hypergraph
  • monoidal closed category

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