[SOLVED] How would I allow polymorphic types in type families?

How would I allow polymorphic types in type families?

Given the natural numbers,

data Zero = Zero
  deriving (Show)
newtype Succ x = Succ x
  deriving (Show)

class MakeTuple num where 
    type TupleOf num
    makeTuplep :: TupleOf num 
-- This instance is invalid, as it is an "illegal polymorphic type".
instance MakeTuple (Succ (Succ Zero)) where
    type TupleOf (Succ (Succ Zero)) = forall v1 v2. v1 -> v2 -> (v1, v2)
    makeTuplep =  (,)

Can I lift this restriction? I actually decided to use type families as a functional dependency was impossible as the type of makeTuplep was polymorphic. Using polymorphic type in type family in haskell is the same error, however it is unanswered.

Solution

While it may not be possible with type families, here is a hacked up solution. It makes partial application tricky, but it is good enough.

class CurryN num a b | num a -> b, b -> a where 
    curryNp :: b -> a

makeTuple :: forall num a1 a2. CurryN num a1 (a2 -> a2) => a1 
makeTuple = curryNp @num id
instance CurryingN  (Succ (Succ Zero)) (v1 -> v2 -> v3) ((v1, v2) -> v3) where
    curryNp =curry
... for all tuples