How to add a class constraint to a Functor instance declaration in Haskell?

Question

I have defined the following data type:

data Probability a = PD { mass :: [(a, Ratio Int)] } 

Now I want to write that it is an instance of

Answer 1

Sadly, you can't do that—Functor instances must accept any kind of mapping function without restriction.

You can kind of fake it, though.

newtype PF a = PF { unPF :: forall r . Eq r => (a -> r) -> Probability r }

instance Functor PF where
  fmap f (PF p) = PF (\mp -> p (mp . f))

Here, all of the functions that would be mapped over Probability have been "deferred" by PF. We run them all at once by "lowering" back into Probability when possible

lowerPF :: Eq a => PF a -> Probability a
lowerPF pf = unPF pf id

And in order to convert a Probability into a fmappable PF we must "lift" it

liftPF :: Probability a -> PF a
liftPF p = PF $ \mp -> PD (collect $ map (first mp) (mass p))