Projection.scala

trait Projection[P <: Poly]{
  def apply[A, B](a: A, b: B)(implicit law:Law[P, A, B]): law.Out = law(a, b)
}

//Witnessing that P can handle AxB -> O, AxO, BxO
//i.e. P is a projection onto a line
trait Law[P <: Poly, A, B]{
  type Out
  
  def apply(a: A, b: B): Out
}

object Law{
  def apply[P <: Poly, A, B](implicit law: Law[P, A, B]) = law
  
  implicit def mk[P <: Poly, A, B, O](implicit ev: Case2.Aux[P, A, B, O], rq: Case2[P, A, O], rq2: Case2[P, B, O]) =
    new Law[P, A, B]{
      type Out = ev.Result
      
      def apply(a: A, b: B) = ev(a, b)
    }
}