dynamic-dispatch.scala

case class Rectangle(width: Double, height: Double)
case class Square(radius: Double)
case class Triangle(side: Double)

trait Area[A] {
  def area(shape: A): Double
}

object Area {
  def apply[A: Area]: Area[A] = implicitly[Area[A]]
  def instance[A](f: A => Double): Area[A] = new Area[A] {
    override def area(shape: A): Double = f(shape)
  }

  implicit val rectangleArea: Area[Rectangle] = instance(_ => 1)
  implicit val squareArea: Area[Square] = instance(_ => 2)
  implicit val triangleArea: Area[Triangle] = instance(_ => 3)
}

sealed trait ShapeEx {
  type Inner
  val value: Inner
  val evidence: Area[Inner]
  def area: Double = evidence.area(value)
}

object ShapeEx {
  implicit def mkShapeEx[A: Area](a: A): ShapeEx = ShapeBox(a)
}

case class ShapeBox[A](value: A)(implicit val evidence: Area[A])
    extends ShapeEx { type Inner = A }


val shapes: List[ShapeEx] = List(Rectangle(1, 2), Square(3), Triangle(4))

val totalArea = shapes.foldLeft(0.0)(_ + _.area)

assert(totalArea == 6)