"Game of Life" in Haskell

This post includes a Haskell implementation of Conway’s game of life. There is nothing particularly fancy here and the implementation is not of the most efficient one either but, hi, this is my first interactive Haskell program (and it is not hard at all).

type Size = Int
type Cell = (Int, Int)

type Board = [Cell]
data Life = Life Size Board
      
instance Show Life where

  show (Life size board) =
      [if c == size then '\n'

       else if (r, c) `elem` board then '@'

       else '-' | r <- [0..size-1],

                  c <- [0..size]]

next_life :: Life -> Life

next_life (Life size board) = Life size new_board where
  new_board = survivors ++ births
  survivors = [cell | cell <- board,

                      let n = living_neighbors cell
                      in n == 2 || n == 3]

  births = [(r,c) | r <- [0..size-1],

                    c <- [0..size-1],
                    let cell = (r, c)

                    in (not (cell `elem` board)) && ((living_neighbors cell) == 3)]

  living_neighbors cell = length $ filter is_living $ neighbors cell
  is_living        cell = cell `elem` board
  neighbors      (r, c) = [((r - 1) `mod` size, ((c - 1) `mod` size)),

                           ((r - 1) `mod` size, c),

                           ((r - 1) `mod` size, ((c + 1) `mod` size)),

                           (r                 , ((c - 1) `mod` size)),

                           (r                 , ((c + 1) `mod` size)),

                           ((r + 1) `mod` size, ((c - 1) `mod` size)),

                           ((r + 1) `mod` size, c),

                           ((r + 1) `mod` size, ((c + 1) `mod` size))]

interactive :: Life -> IO ()
interactive life
  = do print life
       c <- getChar
       if c == 'q' then

           return ()
       else
           interactive $ next_life life

Loading the above program into Hugs and an interactive session goes like this:

Main> interactive $ Life 5 [(1,3), (2,1), (2,3), (3,2), (3,3)]
-----
---@-
-@-@-
--@@-
-----


-----
--@--
---@@
--@@-
-----


-----
---@-
----@
--@@@
-----


-----
-----
--@-@
---@@
---@-

q

Main>

Have fun!