{-# LANGUAGE InstanceSigs, ScopedTypeVariables, MultiParamTypeClasses, FlexibleInstances #-}

-- reviewed HW5, HW6.  

data Cont r a = CT ((a -> r) -> r)

runCont :: Cont r a -> (a -> r) -> r
runCont (CT g) = g

instance Functor (Cont r) where
  fmap :: (a -> b) -> Cont r a -> Cont r b
  fmap f (CT c) = CT $ \ k -> c (\ x -> k (f x))


instance Applicative (Cont r) where

instance Monad (Cont r) where
  return :: a -> Cont r a
  return x = CT $ \ k -> k x

  (>>=) :: Cont r a -> (a -> Cont r b) -> Cont r b
  CT g >>= f = CT $ \ k -> g (\ x -> let CT h = f x in h k)

fac :: Int -> Int
fac 0 = 1
fac n | n > 0 = n * fac (n-1)

fac' :: Int -> Cont r Int
fac' 0 = return 1
fac' n | n > 0 = do
           r <- fac' (n-1)
           return (n * r)
           
fac'' :: Int -> (Int -> r) -> r
fac'' 0 k = k 1
fac'' n k | n > 0 = fac'' (n-1) (\ x -> k (n * x))