import Control.Applicative
import Data.List  ((\\))
import Data.Maybe (fromMaybe)
import Matrix

type Cell = Int
type Grid = Mat Cell

-- | Print a grid
gprint :: Grid -> IO ()
gprint = putStrLn . map replace . show
  where
    replace '1' = '■'
    replace '0' = '.'
    replace a   = a

-- | Get the state of a cell
-- 0 when out of the grid
(!) :: Grid -> Pos -> Cell
(Mat g) ! (x, y) = fromMaybe 0 (g ?? y >>= (?? x))

-- | List of neighbours cells
near :: Grid -> Pos -> [Cell]
near g (x, y) = map state $ neighbours \\ [(0,0)]
  where
    neighbours = liftA2 (,) [-1..1] [-1..1]
    state (x', y') = g ! (x+x', y+y')

-- | 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 = alive g <$> indeces g

main :: IO ()
main = mapM_ gprint (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] ]