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DOI: 10.4230/LIPIcs.ITP.2021.12

Homotopy Type Theory in Isabelle

Authors: Joshua Chen

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract

This paper introduces Isabelle/HoTT, the first development of homotopy type theory in the Isabelle proof assistant. Building on earlier work by Paulson, I use Isabelle’s existing logical framework infrastructure to implement essential automation, such as type checking and term elaboration, that is usually handled on the source code level of dependently typed systems. I also integrate the propositions-as-types paradigm with the declarative Isar proof language, providing an alternative to the tactic-based proofs of Coq and the proof terms of Agda. The infrastructure developed is then used to formalize foundational results from the Homotopy Type Theory book.

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Joshua Chen. Homotopy Type Theory in Isabelle. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 12:1-12:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chen:LIPIcs.ITP.2021.12,
  author =	{Chen, Joshua},
  title =	{{Homotopy Type Theory in Isabelle}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{12:1--12:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.12},
  URN =		{urn:nbn:de:0030-drops-139072},
  doi =		{10.4230/LIPIcs.ITP.2021.12},
  annote =	{Keywords: Proof assistants, Logical frameworks, Dependent type theory, Homotopy type theory}
}

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Homotopy Type Theory in Isabelle

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