twenty48.hs

import Data.List

groupN :: Int -> [a] -> [[a]]
groupN _ [] = []
groupN 0 _  = undefined
groupN n x  = take n x : groupN n (drop n x) 

transpose :: [[a]] -> [[a]]
transpose ([]:_) = []
transpose x = map head x : (transpose (map tail x))

removeZeroes = filter (/= 0)
pairPartitions = concatMap (groupN 2)
sumOf = foldl (+) 0
sumPairs = map sumOf
concatZeroes = (++ repeat 0)
compressLeft = concatZeroes . sumPairs . pairPartitions . group . removeZeroes

moveRowLeft = (take 4) . compressLeft
moveRowRight = reverse . moveRowLeft . reverse
moveGridLeft = map moveRowLeft
moveGridRight = map moveRowRight
moveGridUp = transpose . moveGridLeft . transpose
moveGridDown = transpose . moveGridRight . transpose