binary search function in Haskell for Int lists

binary-search.hs

binarySearch :: Ord a => a -> [a] -> Maybe Int
binarySearch s xs = let left = 0
                        right = length xs - 1
                     in fn left right
                    where fn l r = if l > r
                                      then Nothing
                                      else let m = (l + r) `div` 2
                                               e = xs !! m
                                            in if e < s
                                                  then fn (m+1) r
                                                  else if e > s
                                                  then fn l (m-1)
                                                  else Just m