In Scala we can define the type-level identity function for lower-kinded types like so,
type Id[A] = A
Can we also define something similar for higher-kinded types? Ie. can we fill in the blanks in,
type HKId[A[...]] = ...
so that something similar to HKId[List] gets us back to the List type constructor?
Binding of free names in things like,
type Foo[X] = List[X]
val l : Foo[Int] = List(1, 2, 3)
Might lead us to expect that a higher-kinded type-level identity would look like,
type HKId[A[X]] = A[X]
but scalac complains that type X is not found on the RHS.
Is there some clever encoding that will do the trick? Or is it just not possible right now?