Uses Brent's Algorithm to compute the cycle length and offset of a function

Cycle.hs

import Data.List

alphaWrap :: Char -> Char
alphaWrap c
   | c == 'z' = 'a'
   | 'a' <= c && c < 'z' = succ c
   | otherwise = '?'

cycleLength :: Eq a => (a -> a) -> a -> Int
cycleLength f x = last $ 1 : unfoldr (cycleLength' f) (1, 1, x, f x)

cycleLength' f (power, l, tortoise, hare)
   | tortoise == hare = Nothing
   | power == l       = Just (1, (power * 2, 1, hare, f hare))
   | otherwise        = Just (l + 1, (power, l + 1, tortoise, f hare))

cycleOffset :: Eq a => (a -> a) -> a -> Int
cycleOffset f x = length . takeWhile (uncurry (/=)) $ values
   where values = iterate (pairMap f) (x, f' x)
         f' = foldr (.) id (replicate n f)  
         n = cycleLength f x 
         pairMap f (a, b) = (f a, f b)