monoids.scala

import scalaz._

trait Monoid[A] {
  def mappend(a1: A, a2: A): A
  def mzero: A
}

object Monoid {
  implicit val IntMonoid: Monoid[Int] = new Monoid[Int] {
    def mappend(a: Int, b: Int): Int = a + b
    def mzero: Int = 0
  }

  implicit val StringMonoid: Monoid[String] = new Monoid[String] {
    def mappend(a: String, b: String): String = a + b
    def mzero = ""
  }
}

trait FoldLeft[F[_]] {
  def foldLeft[A, B](xs: F[A], b: B, f: (B, A) => B): B
}

object FoldLeft {
  implicit val FoldLeftList: FoldLeft[List] = new FoldLeft[List] {
    def foldLeft[A, B](xs: List[A], b: B, f: (B, A) => B) = xs.foldLeft(b)(f)
  }
}

trait MonoidOp[A] {
  val F: Monoid[A]
  val value: A
  def |+|(a2: A) = F.mappend(value, a2)
}

object Main extends App {
  implicit def toMonoidOp[A: Monoid](a: A): MonoidOp[A] = new MonoidOp[A] {
    val F: Monoid[A] = implicitly[Monoid[A]]
    val value: A = a
  }

  def sum[M[_]: FoldLeft, A: Monoid](xs: M[A]): A = {
    val m = implicitly[Monoid[A]]
    val fl = implicitly[FoldLeft[M]]

    fl.foldLeft(xs, m.mzero, m.mappend)
  }

  def plus[A: Monoid](a: A, b: A): A = implicitly[Monoid[A]].mappend(a, b)

  println(sum(List("a", "b", "c")))
  println(sum(List(1, 2, 3)))
  println(plus(666, 666))
  println("a" |+| "b")
}