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DOI: 10.4230/LIPIcs.FSCD.2024.30

homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories

Authors: Nathan Corbyn, Lukas Heidemann, Nick Hu, Chiara Sarti, Calin Tataru, and Jamie Vicary

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

We present the proof assistant homotopy.io for working with finitely-presented semistrict higher categories. The tool runs in the browser with a point-and-click interface, allowing direct manipulation of proof objects via a graphical representation. We describe the user interface and explain how the tool can be used in practice. We also describe the essential subsystems of the tool, including collapse, contraction, expansion, typechecking, and layout, as well as key implementation details including data structure encoding, memoisation, and rendering. These technical innovations have been essential for achieving good performance in a resource-constrained setting.

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Nathan Corbyn, Lukas Heidemann, Nick Hu, Chiara Sarti, Calin Tataru, and Jamie Vicary. homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 30:1-30:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{corbyn_et_al:LIPIcs.FSCD.2024.30,
  author =	{Corbyn, Nathan and Heidemann, Lukas and Hu, Nick and Sarti, Chiara and Tataru, Calin and Vicary, Jamie},
  title =	{{homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{30:1--30:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.30},
  URN =		{urn:nbn:de:0030-drops-203594},
  doi =		{10.4230/LIPIcs.FSCD.2024.30},
  annote =	{Keywords: Higher category theory, proof assistant, string diagrams}
}

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homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories

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