[Haskell-beginners] A game of life implementation

[Michel Haber]

Hello everyone,
I'm a new haskeller, and (like many others, I assume) I thought I'd try my
hand
at Conway's "Game of Life".

So here is my code that seems to work (up to this point).
I am looking for feedback in order to improve my Haskell code on all levels.
Especially (In no particular order):
0- Find and fix bugs
1- Write more performance optimal code.
2- Good use of polymorphic types.
3- Good use of higher-order functions.
4- Good use of Haskell's common (and uncommon) abstractions.
5- Coding style (I'm finding it hard to let go of the function types :p)
6- Good code structuring allowing for reuse and updates.
7- Best options to give to the compiler.
8- Anything else that comes to your mind!

So I'd really appreciate your feedback :)

This is the wikipedia reference for the game of life:
https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life

And this is the code:

START OF CODE
-- Game of life Haskell Implementation

import Data.List
import Control.Monad.State
import qualified Data.Map as M

-- The cell state is isomorphic to Bool.
type CellState = Bool

-- The coordinates of a cell
type Coord = (Int, Int)

-- The board size is (length, width)
type Size = (Int, Int)

-- The state of the board is simply the coordinates of its live cells
type Board = [Coord]

-- The state carried in the State Monad, used to count tags for cells
type TallyState = State (M.Map Coord (CellState, Int)) ()

-- The type of the game rules
type Rules = (Coord, CellState, Int) -> CellState

-- The type for the neighbor functions
type Neighbors = Coord -> [Coord]

-- Tally the live neighbors of live cells and relevant dead cells
tallyBoard :: Neighbors -> Board -> TallyState
tallyBoard nb = mapM_ $ tallyCoord nb

-- Tally a live cell: Set its state to True (alive) and tag its neighbors
-- This function takes the neighbors function as its first argument. We can
use
-- different neighbor functions to change the zone of influence of a cell
tallyCoord :: Neighbors -> Coord -> TallyState
tallyCoord nb c = do
    let merge (a1,b1) (a2,b2) = (a1 || a2, b1 + b2)
    s <- get
    let s' = M.insertWith merge c (True, 0) s
    let neighbors = nb c
    put $ foldl' (\acc x -> M.insertWith merge x (False, 1) acc) s'
neighbors

-- Extract the results from a TallyState
toResults :: TallyState -> [(Coord, CellState, Int)]
toResults s = map flatten . M.toList . execState s $ M.empty
    where flatten (x,(y,z)) = (x,y,z)

-- Use A Rules and Neighbors function to advance the board one step in time
advance :: Rules -> Neighbors -> Board -> Board
advance rules nb = map first . filter rules . toResults . tallyBoard nb
    where first (x,_,_) = x

-- The standard neighbors function
stdNeighbors :: Neighbors
stdNeighbors (x,y) =
    [ (a,b)
    | a <- [x-1, x, x+1]
    , b <- [y-1, y, y+1]
    , (a /= x) || (b /= y)
    ]

-- Standard game rules
stdRules :: Size -> Rules
stdRules (a,b) ((x,y),_,_)
    | (x < 0) || (y < 0) || (x >= a) || (y >= b) = False
stdRules _ (_,True,c)
    | (c == 2) || (c == 3) = True
    | otherwise = False
stdRules _ (_,False,3) = True
stdRules _ _ = False


-- Main loop
loop :: (Board -> Board) -> Board -> IO ()
loop f b = do
    print b
    unless (null b) $ loop f (f b)

-- Main function
main :: IO ()
main = do
    putStrLn "Choose board size (x,y)"
    input <- getLine
    putStrLn "Choose starting points"
    start <- getLine
    putStrLn "Game:"
    let size = read input
    let rules = stdRules size
    let initial = map read . words $ start
    let game = advance rules stdNeighbors
    loop game initial

END OF CODE

Thanks :)
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