https://github.com/rocq-community/coq-100-theorems
Statements of famous theorems proven in Coq [maintainer=@jmadiot]
https://github.com/rocq-community/coq-100-theorems
coq theorems
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Statements of famous theorems proven in Coq [maintainer=@jmadiot]
- Host: GitHub
- URL: https://github.com/rocq-community/coq-100-theorems
- Owner: rocq-community
- License: other
- Created: 2015-09-18T02:51:48.000Z (over 9 years ago)
- Default Branch: master
- Last Pushed: 2024-03-19T17:05:55.000Z (about 1 year ago)
- Last Synced: 2025-04-01T02:43:36.174Z (about 1 month ago)
- Topics: coq, theorems
- Language: HTML
- Homepage: https://madiot.fr/coq100/
- Size: 471 KB
- Stars: 59
- Watchers: 3
- Forks: 14
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# 100 famous theorems proved using Coq
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[![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/coq-100-theorems/workflows/Docker%20CI/badge.svg?branch=master
[docker-action-link]: https://github.com/coq-community/coq-100-theorems/actions?query=workflow:"Docker%20CI"
[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
[Freek Wiedijk's webpage](http://www.cs.ru.nl/~freek/100/) lists
[100 famous theorems](http://pirate.shu.edu/~kahlnath/Top100.html)
and how many of those have been formalised using proof assistants.
This repository keeps track of the statements that have been proved
using the [Coq proof assistant](https://coq.inria.fr/).
You can see the list on [this webpage](https://madiot.fr/coq100).
## Meta
- Author(s):
- Jean-Marie Madiot
- Frédéric Chardard
- Coq-community maintainer(s):
- Jean-Marie Madiot ([**@jmadiot**](https://github.com/jmadiot))
- License: [MIT License](LICENSE)
- Compatible Coq versions: 8.10 or later
- Additional dependencies:
- [Coquelicot 3.1.0 or later](http://coquelicot.saclay.inria.fr)
- Coq namespace: `Coq100Theorems`
- Related publication(s): none
## Building instructions
To build all theorems that are hosted in this repository,
run the following commands:
``` shell
git clone https://github.com/coq-community/coq-100-theorems
cd coq-100-theorems
make # or make -j
```
## Included proofs
This repository also contains Coq proofs of some of the 100 theorems:
- [ballot.v](ballot.v) for the [Ballot Theorem](https://en.wikipedia.org/wiki/Bertrand%27s_ballot_theorem)
- [birthday.v](birthday.v) for the [Birthday Problem](https://en.wikipedia.org/wiki/Birthday_problem)
- [cardan_ferrari.v](cardan_ferrari.v) for The Solution of a [Cubic](https://en.wikipedia.org/wiki/Cubic_equation) and the Solution of a [Quartic](https://en.wikipedia.org/wiki/Quartic_equation)
- [div3.v](div3.v) for [Divisibility by 3 Rule](https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_by_3_or_9)
- [inclusionexclusion.v](inclusionexclusion.v) for the [Inclusion/Exclusion Principle](https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle#Statement)
- [konigsberg_bridges.v](konigsberg_bridges.v) for the [Konigsberg Bridges Problem](https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg)
- [mean.v](mean.v) for the [Arithmetic Mean/Geometric Mean](https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means#The_inequality)
- [sumarith.v](sumarith.v) for [Sum of an arithmetic series](https://en.wikipedia.org/wiki/Arithmetic_progression#Sum)
- [sumkthpowers.v](sumkthpowers.v) for [Sum of kth powers](https://en.wikipedia.org/wiki/Bernoulli_polynomials#Sums_of_pth_powers)
## How to add a new statement
To add a new statement for one of the therorems, do not modify `index.html`
directly because it is automatically generated. Instead, edit `statements.yml`.
Then, if you have node installed, generate the index file with
`gen.js > index.html` and check it looks as intended in a browser.
Finally, make a pull request with both files.
If the proof does not belong to another repository, you can also add a single
self-contained `.v` proof file, in which case you should edit `LICENSE.md`
accordingly.