Is there infrastructure in shapeless that takes a type constructor to the power of a Nat?

Question

To me this appears as a very basic functionality, but I can't find it in current shapeless (2.3.3).

So I am looking for a type Induction[X,F[_],N <: Nat] with

Induction[X,F,Nat._0].Out =:= X
Induction[X,F,Nat._1].Out =:= F[X]
Induction[X,F,Nat._2].Out =:= F[F[X]]
...

Maybe it's also possible to chain a function along the type construction, e.g., to construct a Point instance?

Answer 1

No there isn't. As you observe this most likely needs a Point-like type class to be useful. I suggest adding something like this to Kittens which depends on both shapeless and Cats.