{-# LANGUAGE FlexibleInstances
            ,OverlappingInstances #-}
module Main where

import Control.Monad
import Data.Function.YaMemo
import Data.Map (Map)

instance (Monad m, Num a) => Num (m a) where
  (+) = liftM2 (+)
  (-) = liftM2 (-)
  (*) = liftM2 (*)
  negate = liftM negate
  abs    = liftM abs
  signum = liftM signum
  fromInteger = return . fromInteger

fibF :: (Num a, Eq a, Num b) => (a -> b) -> a -> b
fibF _ 0 = 0
fibF _ 1 = 1
fibF f n = f (n-2) + f (n-1)

fib :: Integer -> Integer
fib = memo (undefined :: (Memo Map) Integer Integer) fibF

fib' :: Int -> Integer
fib' = memo (undefined :: (Memo Map) Int Integer) fibF

main :: IO ()
main = undefined