Looping over a function in Haskell
split :: [a] -> ([a],[a])
split xs = splitAt (length xs `div` 2) xs

riffle :: [a] -> [a] -> [a]
riffle xs [] = xs
riffle [] ys = ys
riffle (x:xs) (y:ys) = x:y:riffle xs ys

shuffle :: Int -> [a] -> [a]
shuffle 0 xs = xs
shuffle n xs = shuffle (n-1) (riffle a b)
    where (a, b) = split xs

riffle [1,2,3] [4,5,6] = [1,4,2,5,3,6]

repeats :: [Int] -> Int

> iterate (uncurry riffle . split) "ABCDEF"
["ABCDEF","ADBECF","AEDCBF","ACEBDF","ABCDEF","ADBECF","AEDCBF","ACEBDF", ...]

> takeWhile (/= "ABCDEF") . tail $ iterate (uncurry riffle . split) "ABCDEF"
["ADBECF","AEDCBF","ACEBDF"]

iterate f x = [x, f x, f (f x), f (f (f x)) ....]

repeats xs = iter 1 (...) where
    iter n ys = if ys == xs
        then n
        else iter (...) (...)

repeats xs = (...) $ takeWhile (...) $ iterate (shuffle 1) (...)