Missing Ykind-projector usecase that prevent cross-compilation with Scala 2 : higher-kind-parameterised type-lambdas

[Baccata]

The documentation of kind-projector provides valuable information as to what is and what isn't possible to cross-compile. This is greatly appreciated, however, here's a usecase that doesn't seem to have a non-projection-based way of cross-compilng with Scala 2.

Compiler version

3.2.1

Minimized example

The problem can be described as a formulation a type lambda that depends on a method bound and that expresses partial application where of a parametric type, where the free type variable is higher-kinded.

We're trying to express when its F paramerter is fixed, PolyFunction forms a FunctorK

Scala 3 :

//> using option "-Ykind-projector"

object Test {
  trait PolyFunction[F[_], G[_]]
  trait FunctorK[Alg[_[_]]]

  def polyFunctionFunctorK[F[_]] : FunctorK[[G[_]] =>> PolyFunction[F, G]] = ???
}

Scala 2 (using the kind-projector compiler plugin)

//> using plugin "org.typelevel:::kind-projector:0.13.2"
//> using scala "2.13.10"

object Test {

  trait PolyFunction[F[_], G[_]]
  trait FunctorK[Alg[_[_]]]

  def polyFunctionFunctorK[F[_]] : FunctorK[PolyFunction[F, *[_]]] = ???

}

The only way I'm aware of cross-compiling this is to resort to the de-sugared Scala 2 encoding :

Desugared encoding, which compiles on both Scala 2 and Scala 3

object Test {

  trait PolyFunction[F[_], G[_]]
  object PolyFunction {
    type Curried[F[_]] = {
      type λ[G[_]] = PolyFunction[F, G]
    }
  }


  trait FunctorK[Alg[_[_]]]

  def polyFunctionFunctorK[F[_]] : FunctorK[PolyFunction.Curried[F]#λ] = ???
}

Expectation

I'd personally appreciate if the support for λ in Scala 3 was not limited to *-kinded type parameters, and if we could write the following, which compiles in Scala 2 using kind-projector.

object Test {

  trait PolyFunction[F[_], G[_]]
  trait FunctorK[Alg[_[_]]]

  def polyFunctionFunctorK[F[_]] : FunctorK[λ[G[_] => PolyFunction[F, G]]] = ???

}

[smarter]

Moving this to feature request since we make no guarantees about -Ykind-projector, but contributions to reach parity with the scala 2 plugin are welcome!

[smarter]

The relevant PRs are #7775 and #12378, see also #5379