RSI with composable folds

RSI.hs

import qualified Control.Foldl as Fold
import Control.Applicative
import Data.Profunctor

type Price = Double
type Prices = [ Price ]
type Period = Int

changes :: Prices -> Prices
changes ps = zipWith (-) (tail ps) ps

avg :: Period -> Fold.Fold Price (Maybe Price)
avg period = Fold.Fold step (Left []) (either (const Nothing) Just)
  where
    step :: Either Prices Price -> Price -> Either Prices Price
    step (Left ps) p =
      let ps' = p : ps
      in if (period == length ps')
         then Right (sum ps' / fromIntegral period)
         else Left ps'
    step (Right rs) p =
      let rs' = (rs * (fromIntegral period - 1) + p) / fromIntegral period
      in Right rs'

averageGain = lmap (\x -> if x>0 then x else 0) . avg
averageLoss = lmap (\x -> if x<0 then -x else 0) . avg
rs = (liftA2.liftA2.liftA2) (/) averageGain averageLoss
rsi =  (fmap.fmap.fmap) (\rs -> 100 - 100 / (1 + rs)) rs