https://github.com/thery/minirubik

Solving the mini Rubik (2x2) in Coq
https://github.com/thery/minirubik

2x2x2 coq formalization rubik-cube theorem-proving

Last synced: 3 months ago
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Solving the mini Rubik (2x2) in Coq

• Host: GitHub
• URL: https://github.com/thery/minirubik
• Owner: thery
• Created: 2019-03-15T11:37:57.000Z (almost 6 years ago)
• Default Branch: master
• Last Pushed: 2023-06-16T13:03:22.000Z (over 1 year ago)
• Last Synced: 2024-04-23T16:38:01.070Z (8 months ago)
• Topics: 2x2x2, coq, formalization, rubik-cube, theorem-proving
• Language: Coq
• Size: 164 KB
• Stars: 4
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        

# minirubik

[![Docker CI][docker-action-shield]][docker-action-link]

[docker-action-shield]: https://github.com/thery/minirubik/workflows/Docker%20CI/badge.svg?branch=master

[docker-action-link]: https://github.com/thery/minirubik/actions?query=workflow:"Docker%20CI"

This is a certified solver for the Rubik 2x2

The formalisation is explained in the file [paper.pdf](https://github.com/thery/minirubik/blob/master/paper.pdf),

A position of the cube is encoded by the constructor

``State`` that takes 7 cubes (`C1`, `C2`, `C3`, `C4`, `C5`, `C6`, `C7`)

and their respective orientation (`O1`, `O2`, `O3`).

For example, the initial configuration is

``State C1 C2 C3 C4 C5 C6 C7 O1 O1 O1 O1 O1 O1 O1``

Swapping two adjacent corners gives:

``State C2 C1 C3 C4 C5 C6 C7 O1 O1 O1 O1 O1 O1 O1``

Swapping two opposite corners gives

``State C7 C2 C3 C4 C5 C6 C1 O1 O1 O1 O1 O1 O1 O1``

There are 3 positive moves that corresponds to the right face, the back face and the down face.

Each move can be applied once (`Right`, `Back`, `Down`),

twice (`Right2`, `Back2`, `Down2`) or three times

(`Rightm1`, `Backm1`, `Downm1`) and is still considered

as a single move.

For example, applying the move `Right` to the initial

configuration gives

``State C2 C5 C3 C1 C4 C6 C7 O2 O3 O1 O3 O2 O1 O1``

The ``solve`` function takes a position and returns

a list of minimal length of the moves to return to

the initial position.

For example, solving

``State C2 C1 C3 C4 C5 C6 C7 O1 O1 O1 O1 O1 O1 O1``

returns a list of length 11

``Right :: Backm1 :: Down2 :: Rightm1 :: Back

:: Rightm1 :: Backm1 :: Right :: Down2 :: Right :: Back :: nil``

Other examples are given in the file [Example.v](https://github.com/thery/minirubik/blob/master/Example.v)

## Meta

- Author(s):

  - Laurent Théry

- License: [MIT License](LICENSE)

- Compatible Coq versions: 8.17 or later

- Additional dependencies:

  - [BigNums](https://github.com/coq/bignums)

- Coq namespace: `minirubik`

- Related publication(s): none

## Building and installation instructions

To build and install manually, do:

``` shell

git clone https://github.com/thery/minirubik.git

cd minirubik

make   # or make -j  

make install

```