continuations Kleisli & monad example

main = print . evalCont $ (lazySum <== lazySq <== liftCont product) [[1,2,3],[4,5]]

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

runCont :: Cont r a -> (a -> r) -> r
runCont (Cont f) = f

lazySum :: [[Int]] -> Cont Int [Int]
lazySum xs = Cont $ \f -> sum $ map f xs

square x = x * x

lazySq :: [Int] -> Cont Int [Int]
lazySq xs = Cont $ \f -> square $ f xs

contpose :: (a -> Cont r b)
         -> (b -> Cont r c)
         -> (a -> Cont r c)
contpose c1 c2 ys = Cont $ \f -> (runCont $ c1 ys) (\xs -> runCont (c2 xs) f)

contFish :: Cont r a -> (a -> Cont r b) -> Cont r b
contFish c f = (contpose (\_ -> c) f) ()

contRet :: a -> Cont r a
contRet x = Cont $ \f -> f x

liftCont :: (a -> b) -> a -> Cont r b
liftCont f = \x -> contRet $ f x

contposeAll (c:[]) = c
contposeAll (c1:cs) = contpose c1 (contposeAll cs)

evalCont :: Cont a a -> a
evalCont c = runCont c id

(<==) = contpose