Clean construction of coproducts

ProgramTypeHelpers.scala

    trait Co[F[_], G[_]] {
      case class Product[A](value: Either[F[A], G[A]])
    }

    trait ProgramType[F[_]]
    object ProgramType {
      def apply[T](implicit to: ToParameterized[T]): ProgramType[to.Out] = ???
    }

    trait ToParameterized[T] {
      type Out[_]
    }

    object ToParameterized {
      implicit def withEmpty[F[_]]:ToParameterized[F +: Nil] {
        type Out[A] = F[A]
      } = null
      
      implicit def typeSet[F[_], G[_], X](
          implicit to: ToParameterized[G +: X]):ToParameterized[F +: G +: X] {
        type Out[A] = Co[F, to.Out]#Product[A]
      } = null
    }

    trait +:[F[_], Types]

    trait Nil

    implicit val programType = ProgramType[Store +: Json +: Utilities +: Nil]