How to write a function whose both parameters and results are polymorphic in Haskell

How can I write a function like int gog(float i) and float gog(int i) (which is usually called "overloading")? Some simple overloads can be achieved by

class PP a where
  gog :: a -> Int

instance PP Bool where
  gog _ = 1

instance PP Char where
  gog _ = 1

But the above example only makes the parameter polymorphic. If we want to make both the parameter and result polymorphic, we have to write something like this:

class PP a where
  gog :: Uu b => a -> b

class UU a where
  -- This function can convert between different types of UU.
  fromUuToUu :: UU b => a -> b 

Without fromUuToUu, the polymorphism in the result of gog is impossible. But I can't write fromUuToUu, and that is relevant to the theme of this question, which is how to make a function whose parameter and result are both polymorphic.


{-# LANGUAGE MultiParamTypeClasses, TypeSynonymInstances, FlexibleInstances #-}

class Poly a b where
  gog :: a -> b

instance Poly Int String where
  gog = show

instance Poly String Int where
  gog = read

instance Poly Int Float where
  gog = fromIntegral

instance Poly Float Float where
  gog = (*) 2

gog is now "full" polymorphic.

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