{-# LANGUAGE NoImplicitPrelude, KindSignatures #-}
import Data.Kind (Type)

k :: a -> b -> a
k x _ = x

s :: (a -> b -> c) -> (a -> b) -> a -> c
s f g x = f x (g x)

b :: (b -> c) -> (a -> b) -> a -> c
b f g x = f (g x)

w :: (a -> a -> c) -> a -> c
w x y = x y y

c :: (a -> b -> c) -> b -> a -> c
c f x y = f y x

class Functor (f :: Type -> Type) where
  fmap :: (a -> b) -> f a -> f b

class (Functor f) => Applicative f where
  pure :: a -> f a
  (<*>) :: f (a -> b) -> f a -> f b

instance Functor ((->) a) where
  fmap = b

instance Applicative ((->) a) where
  pure = k
  (<*>) = s

class (Applicative f) => Monad f where
  join :: f (f a) -> f a

instance Monad ((->) a) where
  join = w

(.:) :: (b -> c) -> (a1 -> a2 -> b) -> a1 -> a2 -> c
(.:) = b b b

(>>=) :: (Monad f) => f a -> (a -> f b) -> f b
(>>=) = join .: c fmap
-- f >>= g = join (fmap g f)