Rewriting for Monoidal Closed Categories

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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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.

Original languageEnglish
Title of host publication7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)
EditorsAmy P. Felty
PublisherSchloss Dagstuhl
Number of pages20
ISBN (Electronic)9783959772334
DOIs
Publication statusPublished - 28 Jun 2022
Event7th International Conference on Formal Structures for Computation and Deduction, FSCD 2022 - Haifa, Israel
Duration: 2 Aug 20225 Aug 2022

Publication series

NameLeibniz international proceedings in informatics
Volume228
ISSN (Electronic)1868-8969

Conference

Conference7th International Conference on Formal Structures for Computation and Deduction, FSCD 2022
Country/TerritoryIsrael
CityHaifa
Period2/08/225/08/22

Bibliographical note

Funding Information:
Funding This work was supported by the Engineering and Physical Sciences Research Council [grant numbers EP/V001612/1 and EP/V002376/1].

Publisher Copyright:
© Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi

Keywords

  • hierarchical hypergraph
  • monoidal closed category
  • rewriting
  • string diagrams

ASJC Scopus subject areas

  • Software

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