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https://github.com/coq-community/fourcolor
Formal proof of the Four Color Theorem [maintainer=@ybertot]
https://github.com/coq-community/fourcolor
coq coq-ci four-color-theorem mathcomp ssreflect
Last synced: about 1 month ago
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Formal proof of the Four Color Theorem [maintainer=@ybertot]
- Host: GitHub
- URL: https://github.com/coq-community/fourcolor
- Owner: coq-community
- License: other
- Created: 2018-11-06T17:43:35.000Z (about 6 years ago)
- Default Branch: master
- Last Pushed: 2024-08-06T08:14:36.000Z (3 months ago)
- Last Synced: 2024-09-30T20:45:41.347Z (about 1 month ago)
- Topics: coq, coq-ci, four-color-theorem, mathcomp, ssreflect
- Language: Coq
- Homepage:
- Size: 697 KB
- Stars: 160
- Watchers: 14
- Forks: 20
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# The Four Color Theorem
[![Docker CI][docker-action-shield]][docker-action-link]
[![Contributing][contributing-shield]][contributing-link]
[![Code of Conduct][conduct-shield]][conduct-link]
[![Zulip][zulip-shield]][zulip-link]
[docker-action-shield]: https://github.com/coq-community/fourcolor/actions/workflows/docker-action.yml/badge.svg?branch=master
[docker-action-link]: https://github.com/coq-community/fourcolor/actions/workflows/docker-action.yml
[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg
[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md
[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg
[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md
[zulip-shield]: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg
[zulip-link]: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users
This library contains a formal proof of the Four Color Theorem in Coq,
along with the theories needed to support stating and then proving the Theorem.
This includes an axiomatization of the setoid of classical real numbers,
basic plane topology definitions, and a theory of combinatorial hypermaps.
## Meta
- Author(s):
- Georges Gonthier (initial)
- Coq-community maintainer(s):
- Yves Bertot ([**@ybertot**](https://github.com/ybertot))
- License: [CeCILL-B](LICENSE)
- Compatible Coq versions: 8.16 or later
- Additional dependencies:
- [MathComp ssreflect 2.1.0 or later](https://math-comp.github.io)
- [MathComp algebra](https://math-comp.github.io)
- [Hierarchy Builder](https://github.com/math-comp/hierarchy-builder) 1.5.0 or later
- Coq namespace: `fourcolor`
- Related publication(s):
- [Formal Proof—The Four-Color Theorem](https://www.ams.org/notices/200811/tx081101382p.pdf)
- [A computer-checked proof of the Four Color Theorem](https://inria.hal.science/hal-04034866/document)
## Building and installation instructions
The easiest way to install the latest released version of The Four Color Theorem
is via [OPAM](https://opam.ocaml.org/doc/Install.html):
```shell
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-fourcolor
```
To instead build and install manually, do:
``` shell
git clone https://github.com/coq-community/fourcolor.git
cd fourcolor
make # or make -j
make install
```
## Documentation
The [Four Color Theorem](https://en.wikipedia.org/wiki/Four_color_theorem) (Appel & Haken, 1976) is a landmark result of graph theory.
The formal proof is based on the [Mathematical Components](https://github.com/math-comp/math-comp) library.