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https://github.com/HoTT/Coq-HoTT
A Coq library for Homotopy Type Theory
https://github.com/HoTT/Coq-HoTT
homotopy-type-theory type-theory univalent-foundations
Last synced: 5 days ago
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A Coq library for Homotopy Type Theory
- Host: GitHub
- URL: https://github.com/HoTT/Coq-HoTT
- Owner: HoTT
- License: other
- Created: 2011-03-26T15:59:20.000Z (over 13 years ago)
- Default Branch: master
- Last Pushed: 2024-10-26T19:10:33.000Z (13 days ago)
- Last Synced: 2024-10-29T15:37:53.918Z (10 days ago)
- Topics: homotopy-type-theory, type-theory, univalent-foundations
- Language: Coq
- Homepage: http://homotopytypetheory.org/
- Size: 24.2 MB
- Stars: 1,250
- Watchers: 59
- Forks: 193
- Open Issues: 116
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
Awesome Lists containing this project
- awesome-starred - HoTT/Coq-HoTT - A Coq library for Homotopy Type Theory (others)
README
[![Github Actions CI][1]][2]
[![HoTT Zulip chat][3]][4][Homotopy Type Theory][5] is an interpretation of
Martin-Löf’s intensional type theory into abstract homotopy theory.
Propositional equality is interpreted as homotopy and type isomorphism as
homotopy equivalence. Logical constructions in type theory then correspond to
homotopy-invariant constructions on spaces, while theorems and even proofs in
the logical system inherit a homotopical meaning. As the natural logic of
homotopy, type theory is also related to higher category theory as it is used
e.g. in the notion of a higher topos.The HoTT library is a development of homotopy-theoretic ideas in the Coq proof
assistant. It draws many ideas from Vladimir Voevodsky's [Foundations][6]
library (which has since been incorporated into the [UniMath][7] library) and
also cross-pollinates with the [HoTT-Agda][8] library. See also: [HoTT in
Lean2][9], [Spectral Sequences in Lean2][10], and [Cubical Agda][11].More information about this library can be found in:
- _The HoTT Library: A formalization of homotopy type theory in Coq_, Andrej
Bauer, Jason Gross, Peter LeFanu Lumsdaine, Mike Shulman, Matthieu Sozeau, Bas
Spitters, 2016 [arXiv][12] [CPP17][13]Other publications related to the library can be found
[here][14].# Installation
The HoTT library is part of the [Coq
Platform][15] and can be installed using
the installation instructions there.More detailed installation instructions are provided in the file
[INSTALL.md](/INSTALL.md).# Usage
The HoTT library can be used like any other Coq library. If you wish to use the
HoTT library in your own project, make sure to put the following arguments in
your `_CoqProject` file:```
-arg -noinit
-arg -indices-matter
```For more advanced use such as contribution see [INSTALL.md](/INSTALL.md).
For **recommended text editors** see [our recommended editors
list](./INSTALL.md#4-editors). Other methods of developing in `coq` will work as
long as the correct arguments are passed.# Contributing
Contributions to the HoTT library are very welcome! For style guidelines and
further information, see the file [STYLE.md](/STYLE.md).# Licensing
The library is released under the permissive BSD 2-clause license, see the file
[LICENSE.txt](/LICENSE.txt) for further information. In brief, this means you
can do whatever you like with it, as long as you preserve the Copyright
messages. And of course, no warranty!# Wiki
More information can be found in the [Wiki][22].
[1]: https://github.com/HoTT/HoTT/workflows/CI/badge.svg?branch=master
[2]: https://github.com/HoTT/HoTT/actions?query=workflow%3ACI+branch%3Amaster
[3]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg
[4]: https://hott.zulipchat.com/[5]: http://homotopytypetheory.org/
[6]: https://github.com/vladimirias/Foundations
[7]: https://github.com/UniMath/UniMath
[8]: https://github.com/HoTT/HoTT-Agda
[9]: https://github.com/leanprover/lean2/tree/master/hott
[10]: https://github.com/cmu-phil/Spectral
[11]: https://agda.readthedocs.io/en/v2.6.0.1/language/cubical.html[12]: https://arxiv.org/abs/1610.04591
[13]: http://cpp2017.mpi-sws.org/
[14]: https://github.com/HoTT/HoTT/wiki/Publications-based-on-the-HoTT-library
[15]: https://github.com/coq/platform/releases[22]: https://github.com/HoTT/HoTT/wiki