MonadMemoの例 ref: http://qiita.com/items/019f6c4e5629c9e27e59

file0.txt

{-# LANGUAGE FlexibleContexts #-}
import Control.Applicative
import Control.Monad.Memo                                       

f :: (Functor m, Applicative m, MonadMemo Int Float m)
     => (Int -> m Float)
     -> (Int -> m Float)
     -> (Int -> m Float)
f a b 0 = (/) <$> memo a 0 <*> memo b 0
f a b n = do
  an1 <- memo a (n+1)
  b0  <- memo b 0
  cs  <- mapM (memo c) [0..(n-1)]
  bs  <- mapM (memo b) $ reverse [1..n]
  return $ (an1 - sum (zipWith (*) cs bs)) / b0
  where
    c = f a b

{-
f a b 0 = (a 0)/(b 0)
f a b n = ((a (n+1)) - sum (zipWith (*) cs bs)) / (b 0)
  where
    c = f a b
    cs = map c [0..(n-1)]
    bs = map b $ reverse[1..n]
-}

main :: IO ()
main = do
  let a n = return $ fromIntegral n
      b n = return $ fromIntegral n + 100
  print $ sum $ map (startEvalMemo . f a b) [1..100]