Type Classes in Scala

monoid.scala

trait Semigroup[A] {
  def combine(a: A, b: A): A
}

trait Monoid[A] extends Semigroup[A] {
  def empty: A
}

object Monoid {
  def apply[A : Monoid]: Monoid[A] = implicitly[Monoid[A]]
}

implicit val intMonoidInstance = new Monoid[Int] {
  def empty: Int = 0
  def combine(a: Int, b: Int): Int = a + b
}

implicit val stringMonoidInstance = new Monoid[String] {
  def empty: String = ""
  def combine(a: String, b: String): String = a + b
}

case class Pair[A, B](x: A, y: B)

implicit def pairMonoidInstance[A : Monoid, B : Monoid] =
  new Monoid[Pair[A, B]] {
    def empty: Pair[A, B] =
      Pair(Monoid[A].empty, Monoid[B].empty)
    def combine(a: Pair[A, B], b: Pair[A, B]): Pair[A, B] =
      Pair(
        Monoid[A].combine(a.x, b.x),
        Monoid[B].combine(a.y, b.y)
      )
  }

def combineAll[A : Monoid](xs: List[A]): A =
  xs.foldRight(Monoid[A].empty)(Monoid[A].combine)

combineAll(List(1, 2, 3, 4))
combineAll(List("foo", "bar", "baz"))
combineAll(List(Pair(1, 2), Pair(3, 4)))
combineAll(List(Pair(1, "foo"), Pair(2, "bar")))