Here is a simple model for a Rubik's Cube.
The basic idea is that you only need to keep track of the corners and edges. Each corner has three faces. Each edge has two faces. Keeping track of a face means telling where it was before any moves were made and where it is in the current state.
Choose, as a convention, the ordering, right, up, front. (Math/Physics folk: this is in anology to the "right hand rule" convention which assigns an ordering to the "x y and z" axes and determines that z will be "out of" rather than "into" the plane)
For example, the lower left front corner would be represented as (Left Left) (Down Down) (Front Front) before any moves are made Then, after a rotation about the Front face, the same corner, now in the right down front position would be represented as (Left Down) (Down Right) (Front Front).
Edit by somebody else: I'm not the author of this, however I think there are some erros in the definition of all the datas below. I think they all are missing the constructor, when you're reading the code keep that in mind. also:
You can read the paper by Richard E. Korf named "Finding Optimal Solutions to Rubik's Cube Using Pattern Databases."1 to have a better understanding of the Edged/Corners approach
#!/usr/bin/runhugs module Main (main) where main :: IO () main = do putStr "Not your ordinary language" data Cube = Edges Corners type Edges = [Edge] -- or Edges = Edge Edge Edge Edge Edge Edge Edge Edge Edge Edge Edge Edge type Corners = [Corner] data Edge = Face Face data Corner = Face Face Face data Face = Was Is data Was = R|L|U|D|F|B data Is = R|L|U|D|F|B