ops.scala

trait BinaryOperation[T] {
  def apply(a: T, b: T): T
}

trait AssociativeBinaryOperation[T] extends BinaryOperation[T]

trait Reduce[F[_]] {
  def apply[T](xs: F[T])(op: BinaryOperation[T]): T
}

val sum = new AssociativeBinaryOperation[Int] {
  override def apply(a: Int, b: Int): Int = a + b
}

val div = new BinaryOperation[Int] {
  override def apply(a: Int, b: Int): Int = a / b
}

val reduce = new Reduce[Seq] {
  override def apply[T](xs: Seq[T])(op: BinaryOperation[T]): T = op match {
    case _: AssociativeBinaryOperation[_] ⇒ println("associative"); xs reduce op.apply
    case _ ⇒ println("non-associative");  xs reduceLeft op.apply
  }
}

val xs = Seq(100, 4, 5)
reduce(xs)(sum)
// associative
// res0: Int = 109

reduce(xs)(div)
// non-associative
// res1: Int = 5