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DOI: 10.4230/LIPIcs.ITP.2021.12
URN: urn:nbn:de:0030-drops-139072
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13907/
Chen, Joshua
Homotopy Type Theory in Isabelle
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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 | |
| Seminar: | 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 |
