ExtendRightT.scala

import shapeless._
import shapeless.ops.coproduct._
import cats.~>

trait ExtendRightT[F[_] <: Coproduct, G[_]] {
  type Out[_] <: Coproduct

  def apply[H[_]](f: F ~> H, g: G ~> H): Out ~> H
}

object ExtendRightT {
  type Aux[F[_] <: Coproduct, G[_], Out0[_] <: Coproduct] = ExtendRightT[F, G] { type Out[x] = Out0[x] }

  implicit def extendRightTSingleton[F[_], G[_]]: Aux[
    ({ type L[A] = F[A] :+: CNil })#L,
    G,
    ({ type L[A] = F[A] :+: G[A] :+: CNil })#L
  ] = new ExtendRightT[({ type L[A] = F[A] :+: CNil })#L, G] {
    type Out[x] = F[x] :+: G[x] :+: CNil

    def apply[H[_]](f: ({ type L[A] = F[A] :+: CNil })#L ~> H, g: G ~> H): Out ~> H =
      new (Out ~> H) {
        def apply[A](c: F[A] :+: G[A] :+: CNil): H[A] =
          c match {
            case Inl(fa) => f(Inl(fa))
            case Inr(Inl(ga)) => g(ga)
          }
      }
  }

  implicit def extendRightTCoproduct[
    F[_],
    T[_] <: Coproduct,
    G[_]
  ](implicit extendRightT: ExtendRightT[T, G]): Aux[
    ({ type L[A] = F[A] :+: T[A] })#L,
    G,
    ({ type L[A] = F[A] :+: extendRightT.Out[A] })#L
  ] = new ExtendRightT[({ type L[A] = F[A] :+: T[A] })#L, G] {
    type Out[x] = F[x] :+: extendRightT.Out[x]

    def apply[H[_]](f: ({ type L[A] = F[A] :+: T[A] })#L ~> H, g: G ~> H): Out ~> H =
      new (Out ~> H) {
        def apply[A](c: F[A] :+: extendRightT.Out[A]): H[A] =
          c match {
            case Inl(fa) => f(Inl(fa))
            case Inr(ta) => extendRightT(
              new (T ~> H) {
                def apply[B](b: T[B]): H[B] = f(Inr(b))
              },
              g
            )(ta)
          }
      }
  }
}

def or2[F[_] <: Coproduct, G[_], H[_]](f: F ~> H, g: G ~> H)(implicit
  e: ExtendRightT[F, G]
): e.Out ~> H = e(f, g)