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)
 

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