import Prelude hiding ((.))
import Control.Category ((.), (<<<), (>>>), Category)

data InvertibleFunction a b = InvertibleFunction (a -> b) (b -> a)

instance Category InvertibleFunction where
  (InvertibleFunction b_c c_b) . (InvertibleFunction a_b b_a) = InvertibleFunction (b_c . a_b) (b_a . c_b)

inv (InvertibleFunction x y) = InvertibleFunction y x

add :: (Num n) => n -> InvertibleFunction n n
add x = InvertibleFunction (+x) (\y -> y - x)

class KindaApplicative f where
  (<$>) :: f a b -> a -> b

instance KindaApplicative InvertibleFunction where
  (InvertibleFunction f _) <$> x = f x
  
main = print $ ((inv (add 2)) <$> 5)