Levenshtein distances in Haskell

levenshtein::[Char] -> [Char] -> Int
levenshtein "" "" = 0
levenshtein "" s2 = length s2
levenshtein s1 "" = length s1
levenshtein s1 s2
   | last s1 == last s2 = levenshtein (init s1) (init s2)
   | otherwise = minimum [1 + levenshtein (init s1) s2,
                          1 + levenshtein s1 (init s2),
                          1 + levenshtein (init s1) (init s2)]
levenshtein2::[Char] -> [Char] -> Int
levenshtein2 "" "" = 0
levenshtein2 "" s2 = length s2
levenshtein2 s1 "" = length s1
levenshtein2 s1 s2
   | head s1 == head s2 = levenshtein (tail s1) (tail s2)
   | otherwise = 1 + minimum [levenshtein (tail s1) s2,
                              levenshtein s1 (tail s2),
                              levenshtein (tail s1) (tail s2)]

levenshtein3 :: [Char] -> [Char] -> Int
levenshtein3 s t =
  d !! m !! n
  where m = length s
        n = length t
        d = [[d2 i j | j <- [0..n]] | i <- [0..m]]
        d2 0 0 = 0
        d2 i 0 = i
        d2 0 j = j
        d2 i j
          | s !! (i-1) == t !! (j-1)   = d !! (i-1) !! (j-1)
          | otherwise                  = 1 + minimum [
                                           d !! (i-1) !! j,
                                           d !! (i-1) !! (j-1),
                                           d !! i !! (j-1)
                                          ]