Haskellでシーザー暗号

--指定文字の個数を数える関数
count :: Char -> String -> Int
count c xs = length [c'| c' <- xs, c' == c]

--小文字を整数に変換する関数
let2int :: Char -> Int
let2int c = ord c - ord 'a'

--整数を小文字に変換する関数
int2let :: Int -> Char
int2let n = chr (ord 'a' + n)

--小文字をシフト数だけずらす関数
shift :: Int -> Char -> Char
shift n c | isLower c = int2let ((let2int c + n) `mod` 26)
          | otherwise = c

--シーザー暗号化する関数
encode :: Int -> String -> String
encode n xs = [shift n c | c <- xs]

--文字列中の小文字の出現頻度を返す関数
persent :: Int -> Int -> Float
persent n m = (fromIntegral n / fromIntegral m) * 100

freqs :: String -> [Float]
freqs xs = [persent (count c xs) n | c <- ['a'..'z']]
           where n = length xs

--カイ二乗検定
chisqr :: [Float] -> [Float] -> Float
chisqr os es = sum [((o - e)^2) / e | (o, e) <- zip os es]

--リストの要素を左に回転させる関数
rotate :: Int -> [a] -> [a]
rotate n xs = drop n xs ++ take n xs

--アルファベットの出現頻度
table :: [Float]
table = [8.2, 1.5, 2.8, 4.3, 12.7, 2.2, 2.0, 6.1, 7.0, 0.2, 0.8, 4.0, 2.4, 6.7, 7.5, 1.9, 0.1, 6.0, 6.3, 9.1, 2.8, 1.0, 2.4, 0.2, 2.0, 0.1]

--シーザー暗号を復号する関数
crack :: String -> String
crack xs = encode (-factor) xs
    where
        factor = head (positions (minimum chitab) chitab)
        chitab = [chisqr (rotate n table') table | n <- [0..25]]
        table' = freqs xs