Unique merges

merge.scala

trait Merge[LSet, RSet]{
  type Out
}

object Merge extends LowPriorityMerge{
  implicit def left[L, R]: Aux[L, L|R, L|R] = new Merge[L, L|R]{ type Out = L|R }

  implicit def right[L, R]: Aux[R, L|R, L|R] = new Merge[R, L|R]{ type Out = L|R }
}

trait LowPriorityMerge extends LowPriorityMerge1{
  implicit def search[S, L, R](implicit m: Merge[S, R]): Aux[S, L|R, L|m.Out] =
    new Merge[S, L|R] { type Out = L|m.Out }
}

trait LowPriorityMerge1{
  type Aux[L, R, O] = Merge[L, R]{ type Out = O }
  
  implicit def one[S]: Aux[S, S, S] = new Merge[S, S]{ type Out = S }
  
  implicit def distinct[S, T]: Aux[S, T, S|T] = new Merge[S, T]{ type Out = S|T }
}