Diagrams.RubiksCube.Model

Constructing cubes

data Side a

One side of the Rubik's Cube with 3*3 facets.

Constructors

Side

Fields

_topLeft :: a

_topCenter :: a

_topRight :: a

_middleLeft :: a

_middleCenter :: a

_middleRight :: a

_bottomLeft :: a

_bottomCenter :: a

_bottomRight :: a

Instances

Functor Side

Applicative Side

Foldable Side

Traversable Side

Eq a => Eq (Side a)

Show a => Show (Side a)

Reversing (Side a)

topLeft :: forall a. Lens' (Side a) a

topCenter :: forall a. Lens' (Side a) a

topRight :: forall a. Lens' (Side a) a

middleLeft :: forall a. Lens' (Side a) a

middleCenter :: forall a. Lens' (Side a) a

middleRight :: forall a. Lens' (Side a) a

bottomLeft :: forall a. Lens' (Side a) a

bottomCenter :: forall a. Lens' (Side a) a

bottomRight :: forall a. Lens' (Side a) a

rotateSideCW :: Aut (Side a)

Rotate the side clockwise.

rotateSideCCW :: Aut (Side a)

Rotate the side counter-clockwise.

data Cube a

A cube with six sides.

     +---+
     | u |
 +---+---+---+---+
 | l | f | r | b |
 +---+---+---+---+
     | d |
     +---+

Constructors

Cube

Fields

_frontSide :: a

_backSide :: a

_leftSide :: a

_rightSide :: a

_upSide :: a

_downSide :: a

Instances

Functor Cube

Applicative Cube

Foldable Cube

Traversable Cube

Eq a => Eq (Cube a)

Show a => Show (Cube a)

frontSide :: forall a. Lens' (Cube a) a

backSide :: forall a. Lens' (Cube a) a

leftSide :: forall a. Lens' (Cube a) a

rightSide :: forall a. Lens' (Cube a) a

upSide :: forall a. Lens' (Cube a) a

downSide :: forall a. Lens' (Cube a) a

newtype RubiksCube a

A normal Rubik's cube with 6 sides with 9 facets each.

Constructors

RubiksCube

Fields

_cube :: Cube (Side a)

Instances

Functor RubiksCube

Applicative RubiksCube

Eq a => Eq (RubiksCube a)

Show a => Show (RubiksCube a)

cube :: forall a a. Iso (RubiksCube a) (RubiksCube a) (Cube (Side a)) (Cube (Side a))

Selecting rows and columns

data Vec3 a

A list of fixed length 3.

Constructors

Vec3 a a a

Instances

Functor Vec3

Applicative Vec3

Foldable Vec3

Traversable Vec3

Eq a => Eq (Vec3 a)

Show a => Show (Vec3 a)

Reversing (Vec3 a)

topRow :: Lens' (Side a) (Vec3 a)

The top three facets (from left to right).

middleRow :: Lens' (Side a) (Vec3 a)

The middle three facets (from left to right).

bottomRow :: Lens' (Side a) (Vec3 a)

The bottom three facets (from left to right).

leftCol :: Lens' (Side a) (Vec3 a)

The left column (from top to down).

centerCol :: Lens' (Side a) (Vec3 a)

The center column (from top to down).

rightCol :: Lens' (Side a) (Vec3 a)

The right column (from top to down).

Traversing facets

By layer

topLayerFacets :: Traversal' (RubiksCube a) a

The 21=4*3+9 facets in the top layer.

middleLayerFacets :: Traversal' (RubiksCube a) a

The 12=4*3 facets in the middle layer.

bottomLayerFacets :: Traversal' (RubiksCube a) a

The 21=4*3+9 facets in the bottom layer.

By position

centerFacets :: Traversal' (RubiksCube a) a

The six facets that are the center of their side.

cornerFacets :: Traversal' (RubiksCube a) a

The 24=6*4=8*3 corner facets.

edgeFacets :: Traversal' (RubiksCube a) a

The 24=6*4=12*2 edge facets.

Rotating the whole cube

type Aut a = Iso' a a

The type of automorphisms

rotateLeft :: Aut (RubiksCube a)

Rotate the whole Rubik's Cube such that the front side becomes the new left side and the top and bottom sides stay fixed.

rotateRight :: Aut (RubiksCube a)

Rotate the whole Rubik's Cube such that the front side becomes the new right side and the top and bottom sides stay fixed.

rotateDown :: Aut (RubiksCube a)

Rotate the whole Rubik's Cube such that the front side becomes the new bottom side and the left and right sides stay fixed.

rotateUp :: Aut (RubiksCube a)

Rotate the whole Rubik's Cube such that the front side becomes the new top side and the left and right sides stay fixed.

rotateCW :: Aut (RubiksCube a)

Rotate the whole Rubik's Cube such that the top side becomes the new right side and the front and back sides stay fixed.

rotateCCW :: Aut (RubiksCube a)

Rotate the whole Rubik's Cube such that the top side becomes the new left side and the front and back sides stay fixed.

Moving layers of the cube

move :: Move -> Aut (RubiksCube a)

Perform a move.

doMoves :: [Move] -> Aut (RubiksCube a)

Perform a list of moves.

undoMoves :: [Move] -> Aut (RubiksCube a)

Undo the actions of a list of moves.