Deriving typeclass instances for higher-kinded type in Scala 3

TraverseK.scala

// This could be very useful for https://github.com/kubukoz/datas/blob/2d7ba9d1b4974bc03500c556279152ce441226ea/core/src/main/scala/datas/tagless.scala


trait TraverseK[Alg[_[_]]]:

  def traverseK[F[_], G[_]: Applicative, H[_]](alg: Alg[F])(fk: F ~> ([a] =>> G[H[a]])): G[Alg[H]]

  def sequenceK[F[_]: Applicative, G[_]](alg: Alg[[a] =>> F[G[a]]]): F[Alg[G]] =
    traverseK(alg)(FunctionK.id)

  def mapK[F[_], G[_]](af: Alg[F])(fk: F ~> G): Alg[G] = traverseK[F, cats.Id, G](af)(fk)

  def sequenceKId[F[_]: Applicative](alg: Alg[F]): F[Alg[cats.Id]] = sequenceK[F, cats.Id](alg)

object TraverseK:

  extension [Alg[_[_]]: TraverseK, F[_]](alg: Alg[F])
    def sequenceKId(using Applicative[F]) = summon[TraverseK[Alg]].sequenceKId(alg)
    def mapK[G[_]](fk: F ~> G) = summon[TraverseK[Alg]].mapK(alg)(fk)

  private[example] def toTuple(list: List[Any]): Tuple = list match
    case h :: t => h *: toTuple(t)
    case Nil    => EmptyTuple

  def derived[Alg[_[_]]](using s: Mirror.Product { type MirroredType[F[_]] = Alg[F] }): TraverseK[Alg] = new TraverseK[Alg]:

    import cats.implicits.*

    def traverseK[F[_], G[_]: Applicative, H[_]](alg: Alg[F])(fk: F ~> ([a] =>> G[H[a]])): G[Alg[H]] =
      alg.asInstanceOf[Product].productIterator.toList.map(field => fk(field.asInstanceOf[F[Any]])).sequence.map { listHAny =>
        s.fromProduct(toTuple(listHAny)).asInstanceOf[Alg[H]]
      }