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https://github.com/coq-community/qarith-stern-brocot
Binary rational numbers in Coq [maintainer=@herbelin]
https://github.com/coq-community/qarith-stern-brocot
coq coq-library docker-coq-action nix-action paper-artifacts rational-numbers
Last synced: about 1 month ago
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Binary rational numbers in Coq [maintainer=@herbelin]
- Host: GitHub
- URL: https://github.com/coq-community/qarith-stern-brocot
- Owner: coq-community
- License: lgpl-2.1
- Created: 2016-04-26T13:35:37.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2023-12-30T09:49:24.000Z (about 1 year ago)
- Last Synced: 2024-04-22T06:26:30.504Z (9 months ago)
- Topics: coq, coq-library, docker-coq-action, nix-action, paper-artifacts, rational-numbers
- Language: Coq
- Homepage:
- Size: 394 KB
- Stars: 12
- Watchers: 12
- Forks: 4
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Binary Rational Numbers
[![Docker CI][docker-action-shield]][docker-action-link]
[![Nix CI][nix-action-shield]][nix-action-link]
[![Contributing][contributing-shield]][contributing-link]
[![Code of Conduct][conduct-shield]][conduct-link]
[![Zulip][zulip-shield]][zulip-link]
[![DOI][doi-shield]][doi-link]
[docker-action-shield]: https://github.com/coq-community/qarith-stern-brocot/actions/workflows/docker-action.yml/badge.svg?branch=master
[docker-action-link]: https://github.com/coq-community/qarith-stern-brocot/actions/workflows/docker-action.yml
[nix-action-shield]: https://github.com/coq-community/qarith-stern-brocot/actions/workflows/nix-action.yml/badge.svg?branch=master
[nix-action-link]: https://github.com/coq-community/qarith-stern-brocot/actions/workflows/nix-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
[doi-shield]: https://zenodo.org/badge/DOI/10.1007/978-3-540-24849-1_20.svg
[doi-link]: https://doi.org/10.1007/978-3-540-24849-1_20
Development of rational numbers in Coq as finite binary lists and defining
field operations on them in two different ways: strict and lazy.
## Meta
- Author(s):
- Milad Niqui (initial)
- Yves Bertot (initial)
- Coq-community maintainer(s):
- Hugo Herbelin ([**@herbelin**](https://github.com/herbelin))
- License: [GNU Lesser General Public License v2.1 or later](LICENSE)
- Compatible Coq versions: 8.18 or later
- Additional dependencies: none
- Coq namespace: `QArithSternBrocot`
- Related publication(s):
- [QArith: Coq Formalisation of Lazy Rational Arithmetic](https://hal.inria.fr/inria-00077041) doi:[10.1007/978-3-540-24849-1_20](https://doi.org/10.1007/978-3-540-24849-1_20)
## Building and installation instructions
The easiest way to install the latest released version of Binary Rational Numbers
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-qarith-stern-brocot
```
To instead build and install manually, do:
``` shell
git clone https://github.com/coq-community/qarith-stern-brocot.git
cd qarith-stern-brocot
make # or make -j
make install
```
## Documentation
This project contains a rational arithmetic library for Coq. This includes:
- A binary representation for positive rational numbers `Qpositive` and its
extension to `Q` by adding a sign bit (also known as Stern-Brocot
tree encoding).
- Arithmetic operations on `Qpositive` and `Q` defined in an strict way.
- More efficient arithmetic operations on `Q` defined lazily using
homographic and quadratic algorithms for this binary representation
(exact rational arithmetic).
- Proof of the correctness of the homographic and quadratic algorithms
using the strict operations.
- The files enable the user to use Coq `field` tactic on `Q` with two
different field structures (using strict or lazy operations).
- The Haskell extraction of the lazy algorithms (`quadratic.hs`).
- A syntax for using the rational numbers as pair of integers, and writing
simple arithmetic operations on them.
- A proof of irrationality of the square root of 2.
- A proof that `Q` is Archimedean.
- A proof that `Q` is countable.