import Matrix

type Cell = Int
type Grid = Mat Cell


-- | Get the state of a cell
-- 0 when out of the grid
(!) :: Grid -> Pos -> Cell
(Mat g) ! (x, y) = case g ?? y >>= (?? x) of
  Nothing -> 0
  Just v  -> v

-- | List of neighbours cells
near :: Grid -> Pos -> [Cell]
near g (x, y) = [g ! (x+x', y+y') | x' <- [-1..1],
                                    y' <- [-1..1],
                                   (x',y') /= (0,0)]

-- | Find if a cell will be alive in the next generation
alive :: Grid -> Pos -> Cell
alive g p
  | v == 0 && n == 3             = 1
  | v == 1 && (n == 2 || n == 3) = 1
  | otherwise                    = 0
  where
    (n, v) = (sum (near g p), g ! p)

-- | Compute next generation
next :: Grid -> Grid
next g = fmap (alive g) (indeces g)

main :: IO ()
main = mapM_ print (iterate next grid)

grid = Mat [
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
  , [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
  , [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
  , [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
  , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
  , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
  , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
  ]