License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2021.12
URN: urn:nbn:de:0030-drops-139072
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13907/
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Chen, Joshua

Homotopy Type Theory in Isabelle

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LIPIcs-ITP-2021-12.pdf (0.7 MB)


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.

BibTeX - Entry

@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/opus/volltexte/2021/13907},
  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}
}

Keywords: Proof assistants, Logical frameworks, Dependent type theory, Homotopy type theory
Collection: 12th International Conference on Interactive Theorem Proving (ITP 2021)
Issue Date: 2021
Date of publication: 21.06.2021
Supplementary Material: Software (Source): https://github.com/jaycech3n/Isabelle-HoTT/tree/ITP2021 archived at: https://archive.softwareheritage.org/swh:1:dir:8c8943216a189d6b9144942ee0d37ab75b52e5fc


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