[Haskell-cafe] Parametric kinds

[Gautier DI FOLCO]

Hello all,

I'm trying to port typeclasses to kind-level, here are my data types:
-- newtype Fix f a = Fix (f (Fix f a))
-- data Mu f = In (f (Mu f))
data Fix (f :: k1 -> k0) (n :: k1) = Fx

data Maybe a = Nothing | Just a

If I try to create type families to represent Functors, I end up with this:

-- type family MapFix (f :: (* -> k) -> * -> k) a :: * where
-- type family MapFix f a where
type family MapFix (f :: (k0 -> k1) -> k0 -> k1) (a :: k2) :: * where
  MapFix f (Fix a n) = Fix (f a) (MapFix f n)

-- type family MapMaybe (f :: k -> k) (a :: Maybe k) :: Maybe k where
-- type family MapMaybe f a where
type family MapMaybe (f :: k0 -> k1) (a :: Maybe k0) :: Maybe k1 where
  MapMaybe f ('Just a) = 'Just (f a)
  MapMaybe f 'Nothing = 'Nothing

But I can't defined a single open type family for these two data types.
I think I lack of parametric kinds, for example: `*k p*` could let me
fit `*Maybe
k*`. Currently, in the way I see kinds, on `*k0 -> k1*` allow me to
parameterize kinds, but `*Maybe k*` doesn't fit.

I know that this is certainly unclear, don't hesitate to ask me for
clarifications.
I also know that my  `*Fix*` sucks, any good idea on how to do it is
welcome :)
Also, if you have any links to have a deeper insight of Kinds it will save
me from mental illness.

Thanks in advance for your help,
Regards.
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