haskell merge sort

MergeSort.hs

mergesort :: (Ord a) => [a] -> [a]
mergesort xs =
  let sort :: (Ord a) => [[a]] -> [[a]]
      sort ys = case list of
        [a] -> [a]
        a -> sort a
        where
          list = concatAdjacentWith merge ys
   in concat $ sort (splitEvery 1 xs)


merge :: (Ord a) => [a] -> [a] -> [a]
merge x [] = x
merge [] x = x
merge (x : xs) (y : ys) = do
  case compare x y of
    GT -> y : merge (x : xs) ys
    LT -> x : merge xs (y : ys)
    EQ -> x : y : merge xs ys


concatAdjacentWith :: (Ord a) => ([a] -> [a] -> [a]) -> [[a]] -> [[a]]
concatAdjacentWith f (x : y : xs) = f x y : concatAdjacentWith f xs
concatAdjacentWith _ xs = xs

splitEvery :: Int -> [a] -> [[a]]
splitEvery _ [] = []
splitEvery n xs = first : splitEvery n rest
  where
    (first, rest) = splitAt n xs