Collatz Conjecture in Haskell

gistfile1.hs

collatzNaive :: Int -> [Int]
collatzNaive 1 = [1]
collatzNaive n = n:sequence
    where sequence
            | even n    = collatzNaive (n `div` 2)
            | otherwise = collatzNaive (n*3 + 1)

-- Store things as a linked list of tuples - [(1, 1), (2, 2), (3, 8), (4, 3)...]

addKV :: (Integral a) => [(a, a)] -> a -> a -> [(a, a)]
addKV [] k v = [(k, v)]
addKV (pair:t) k v
    | k0 == k = (k, v):t
    | k0 > k  = (k, v):pair:t
    | otherwise = pair:(addKV t k v)
    where (k0, v0) = pair

getValue :: (Integral a) => [(a, a)] -> a -> Maybe a
getValue dict k = 
    let match = find (\(k0, v0) -> k0 == k) dict
    in case match of
        Just (k, v) -> Just v
        Nothing     -> Nothing

collatz dict n = case getValue dict n of
    Just v  -> (dict, v)
    Nothing -> if n == 1 then (dict, 1) else (newDict val)
    where nextNum | even n    = (n `div` 2)
                  | otherwise = (n*3 + 1)
          (d, v) = collatz dict nextNum


        {- let (d, val) | even n    = collatz dict (n `div` 2) -}
                     {- | otherwise = collatz dict (n*3 + 1) -}
            {- newDict = addKV d n val -}
        {- in (newDict, val) -}

http://projecteuler.net/problem=14