Right, so the definition of higher-kinded types is that the _parameter_ to the trait (here, `Self`) is higher-kinded (here, `* → *`) not that the trait is parameterized. So `impl Functor for List[A]` is not (semantically) correct: it's not `List[A]` that implements `Functor` but `List` itself.†‡ The important thing you get out of that is precisely the ability to talk about these kinds of universals: you can associate items to the type constructor itself before its eventual parameter is even in scope, and so the value of all such things must be the same independent of the parameter ‘for free’. As soon as you introduce the type parameter you incur a proof burden if you want to claim that the associated item is the same regardless of the value of the parameter, because you have introduced the syntactic possibility that they could vary.

† There's an encoding of higher-kinded types in some languages that don't really have them as first-class citizens (e.g. Rust with associated type constructors) that does this by adding a ‘rewrap’ item to the trait: you implement `Functor` for `List<A>`, but also (as part of the trait) includes a type constructor `Rewrap<B> = List<B>`. This lets you encode the fact that the `Functor` instance is defined for `List<A>` for all values of `A`, but you still struggle to prove that some of their items are independent of the choice of `A`.

‡ To see both of these side-by-side, consider the instance for pairs, which are functorial in their right parameter (as well as the left parameter: they are bifunctorial, but that's not relevant here). So if you have a curried pair type constructor `Pair : * → * → *` it really is true that `Pair[A]`, not `Pair`, is a `Functor`:

    impl Functor for Pair[A]:
        fun fmap[B, C](f: B -> C, self: Pair[A][B]) -> Pair[B][C]):
            Pair(self.0, f(self.1))