Simple Example from "Fun with type functions" in Scala

Fun-with-type-functions.scala

/*

  Simple Example from "Fun with type functions"

  class Add a b where
    type SumTy a b
    add :: a -> b -> SumTy a b
  
  instance Add Integer Double where
    type SumTy Integer Double = Double
    add x y = fromIntegral x + y
  
  instance Add Double Integer where
    type SumTy Double Integer = Double
    add x y = x + fromIntegral y
  
  instance (Num a) => Add a a where
    type SumTy a a = a
    add x y = x + y
*/

trait Add[A,B] {
  type SumTy[A,B]
  def add(a: A, b: B): SumTy[A,B]
}

implicit object AddIntDouble extends Add[Int, Double] {
  type SumTy[Int, Double] = Double
  def add(a: Int, b: Double) = a.toDouble + b
}

implicit object AddDOubleInteger extends Add[Double, Int] {
  type SumTy[Double, Int] = Double
  def add(a: Double, b: Int) = a + b.toDouble
}

// implicit object AddNumeric extends Add[Numeric[_], Numeric[_]] {
//   type SumTy[???, ???] = Numeric[_] // I want to ensure that A and B are Numeric[_]
//   def add(a: Numeric[_], b: Numeric[_]) = a plus b
// }

// Doesn't compile currently: illegal dependent method type
def addSomething[A,B](a: A, b: B)(implicit addTC: Add[A,B]): addTC.SumTy[A,B] = 
  addTC.add(a,b)