Attempt to get single compose method between optics

optics.scala

package vanilla

sealed trait Optic[G[_,_] <: Optic[G, _, _], S, A] {
  def compose[F[_, _] <: Optic[F, _, _], B](o: F[A, B])(implicit lub : Lub[G,F]) : lub.T[S, B] =
    lub.compose(self, o)
  def self: G[S,A]
  def desc: List[String]
}

case class Traversal[A,B](desc : List[String]) extends Optic[Traversal,A,B] {
  def self = this
}

case class Lens[A,B](desc : List[String]) extends Optic[Lens,A,B] {
  def self = this
}

trait Lub[F[_, _] <: Optic[F, _, _], G[_, _] <: Optic[G, _, _]]{
  // add witness that F[_,_] <: T[_,_] and G[_,_] <: T[_,_]
  type T[_, _] <: Optic[T, _, _]

  def compose[A, B, C](o1: F[A, B], o2: G[B, C]): T[A, C]
}

object Lub {

 implicit val lensTraversal: Lub[Lens, Traversal] = new Lub[Lens, Traversal] {
   override type T[A, B] = Traversal[A, B]
   override def compose[A, B, C](o1: Lens[A, B], o2: Traversal[B, C]): Traversal[A, C] = Traversal(o1.desc ++ o2.desc)
 }

  implicit val traversalLens: Lub[Traversal, Lens] = new Lub[Traversal, Lens] {
    override type T[A, B] = Traversal[A, B]
    override def compose[A, B, C](o1: Traversal[A, B], o2: Lens[B, C]): Traversal[A, C] = Traversal(o1.desc ++ o2.desc)
  }

  implicit val lensLens: Lub[Lens, Lens] = new Lub[Lens, Lens] {
    override type T[A, B] = Lens[A, B]
    override def compose[A, B, C](o1: Lens[A, B], o2: Lens[B, C]): Lens[A, C] = ???
 }

  implicit val traversalTraversal: Lub[Traversal, Traversal] = new Lub[Traversal, Traversal] {
    override type T[A, B] = Traversal[A, B]
    override def compose[A, B, C](o1: Traversal[A, B], o2: Traversal[B, C]): Traversal[A, C] = ???
  }
}


object Test extends App {

  val foo: Lens[String, Int] = Lens(List("foo"))
  val bar: Traversal[Int, String] = Traversal(List("bar"))

  val foobar = foo compose bar

  println(foobar.isInstanceOf[Traversal[String ,String]]) // true

  // all below fail
  val _foobar: Traversal[String, String] = foobar
  val foobarfoo = foobar compose foo
  println((foo compose bar compose foo).desc)

}