union.scala

import shapeless.LowPriority

trait Dec[T] { type V }
object Dec {
  type ItIsYes
  type ItIsNo

  implicit def itIsNo[T](implicit l: LowPriority): No[T] = new Dec[T] { type V = ItIsNo }
  implicit def itIsYes[T](implicit t: T): Yes[T] = new Dec[T] { type V = ItIsYes }

  type Aux[T, V0] = Dec[T] { type V = V0 }
  type No[T] = Aux[T, ItIsNo]
  type Yes[T] = Aux[T, ItIsYes]
}

sealed trait Not[T]
object Not {
  implicit def not[T](implicit d: Dec.No[T]): Not[T] = new Not[T]{}
}

sealed trait Neither[T, A, B]
object Neither {
  implicit def neitherAOrB[T, A, B](implicit prfA: Not[T =:= A], prfB: Not[T =:= B]) = 
    new Neither[T, A, B]{}
}

sealed trait Or[T, A, B]
object Or {
  implicit def aOrB[T, A, B](implicit prf: Not[Neither[T, A, B]]) = 
    new Or[T, A, B]{}
}

object tests {
  def string[T](t: T)(implicit prf: T =:= String) = "IsAString"
  def notString[T](t: T)(implicit prf: Not[T =:= String]) = "IsNotAtring"
  def notnot[T](t: T)(implicit prf: Not[Not[T =:= String]]) = "IsNotNotString"
  def commutString[T](t: T)(implicit prf: String =:= T) = "IsAString(C)"
  def commutNotString[T](t: T)(implicit prf: Not[String =:= T]) = "IsNotAtring"
  def neitherIntOrString[T](t: T)(implicit prf: Neither[T, Int, String]) = "IsIntOrString"
  def intOrString[T](t: T)(implicit prf: Or[T, Int, String]) = "IsIntOrString"
}