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https://github.com/coq-community/sudoku
A certified Sudoku solver in Coq [maintainers=@siraben,@thery]
https://github.com/coq-community/sudoku
coq nix-action sudoku
Last synced: 3 months ago
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A certified Sudoku solver in Coq [maintainers=@siraben,@thery]
- Host: GitHub
- URL: https://github.com/coq-community/sudoku
- Owner: coq-community
- License: lgpl-2.1
- Created: 2016-04-27T17:39:28.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2022-11-14T14:50:15.000Z (about 2 years ago)
- Last Synced: 2024-09-30T20:48:13.945Z (3 months ago)
- Topics: coq, nix-action, sudoku
- Language: Coq
- Homepage: https://coq-community.org/sudoku/
- Size: 318 KB
- Stars: 21
- Watchers: 5
- Forks: 3
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Sudoku
[![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]
[docker-action-shield]: https://github.com/coq-community/sudoku/workflows/Docker%20CI/badge.svg?branch=master
[docker-action-link]: https://github.com/coq-community/sudoku/actions?query=workflow:"Docker%20CI"
[nix-action-shield]: https://github.com/coq-community/sudoku/workflows/Nix%20CI/badge.svg?branch=master
[nix-action-link]: https://github.com/coq-community/sudoku/actions?query=workflow:"Nix%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
A formalisation of Sudoku in Coq. It implements a naive
Davis-Putnam procedure to solve Sudokus.
## Meta
- Author(s):
- Laurent Théry (initial)
- Coq-community maintainer(s):
- Ben Siraphob ([**@siraben**](https://github.com/siraben))
- Laurent Théry ([**@thery**](https://github.com/thery))
- License: [GNU Lesser General Public License v2.1 or later](LICENSE)
- Compatible Coq versions: 8.12 or later
- Additional dependencies: none
- Coq namespace: `Sudoku`
- Related publication(s):
- [Sudoku in Coq](https://hal.inria.fr/hal-03277886)
## Building and installation instructions
The easiest way to install the latest released version of Sudoku
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-sudoku
```
To instead build and install manually, do:
``` shell
git clone https://github.com/coq-community/sudoku.git
cd sudoku
make # or make -j
make install
```
## Documentation
A Sudoku is represented as a mono-dimensional list of natural
numbers. Zeros are used to represent empty cells. For example,
the 3x3 Sudoku:
```
-------------------------------------
| | | 8 | 1 | 6 | | 9 | | |
-------------------------------------
| | | 4 | | 5 | | 2 | | |
-------------------------------------
| 9 | 7 | | | | 8 | | 4 | 5 |
-------------------------------------
| | | 5 | | | | | | 6 |
-------------------------------------
| 8 | 9 | | | | | | 3 | 7 |
-------------------------------------
| 1 | | | | | | 4 | | |
-------------------------------------
| 3 | 6 | | 5 | | | | 8 | 4 |
-------------------------------------
| | | 2 | | 7 | | 5 | | |
-------------------------------------
| | | 7 | | 4 | 9 | 3 | | |
-------------------------------------
```
is represented as
```coq
0 :: 0 :: 8 :: 1 :: 6 :: 0 :: 9 :: 0 :: 0 ::
0 :: 0 :: 4 :: 0 :: 5 :: 0 :: 2 :: 0 :: 0 ::
9 :: 7 :: 0 :: 0 :: 0 :: 8 :: 0 :: 4 :: 5 ::
0 :: 0 :: 5 :: 0 :: 0 :: 0 :: 0 :: 0 :: 6 ::
8 :: 9 :: 0 :: 0 :: 0 :: 0 :: 0 :: 3 :: 7 ::
1 :: 0 :: 0 :: 0 :: 0 :: 0 :: 4 :: 0 :: 0 ::
3 :: 6 :: 0 :: 5 :: 0 :: 0 :: 0 :: 8 :: 4 ::
0 :: 0 :: 2 :: 0 :: 7 :: 0 :: 5 :: 0 :: 0 ::
0 :: 0 :: 7 :: 0 :: 4 :: 9 :: 3 :: 0 :: 0 :: nil
```
All functions are parametrized by the height and width of
a Sudoku's subrectangles. For example, for a 3x3 Sudoku:
```coq
sudoku 3 3: list nat -> Prop
check 3 3: forall l, {sudoku 3 3 l} + {~ sudoku 3 3 l}
find_one 3 3: list nat -> option (list nat)
find_all 3 3: list nat -> list (list nat)
```
See `Test.v`.
Corresponding correctness theorems are:
```coq
find_one_correct 3 3
: forall s,
length s = 81 ->
match find_one 3 3 s with
| Some s1 => refine 3 3 s s1 /\ sudoku 3 3 s1
| None =>
forall s, refine 3 3 s s1 -> ~ sudoku 3 3 s1
end
find_all_correct 3 3
: forall s s1, refine 3 3 s s1 -> (sudoku 3 3 s1 <-> In s1 (find_all 3 3 s))
```
See `Sudoku.v`.
More about the formalisation can be found in a [note](https://hal.inria.fr/hal-03277886).
The following files are included:
- `ListOp.v` some basic functions on list
- `Sudoku.v` main file
- `Test.v` test file
- `Tactic.v` contradict tactic
- `Div.v` division and modulo for nat
- `Permutation.v` permutation
- `UList.v` unique list
- `ListAux.v` auxillary facts on lists
- `OrderedList.v` ordered list
The Sudoku code can be extracted to JavaScript using
[js_of_ocaml](https://github.com/ocsigen/js_of_ocaml):
```shell
make Sudoku.js
```
Then, point your browser at `Sudoku.html`.