Writer.scala

case class Writer[W, A](run: (W, A))

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

object Writer {

  def >==>[W: Monoid[W], A, B, C](a: A => Writer[W, B],
                                  b: B => Writer[W, C]): A => Writer[W, C] = {
    input: A =>
      val writerB: Writer[W, B] = a(input)
      flatMap(writerB)(b)
  }

  def run[W: Monoid[W], A]: Writer[W, A] => (W, A) = {
    case Writer((a, w)) => (a, w)
  }

  def map[A, W: Monoid[W], B](wa: Writer[W, A])(f: A => B): Writer[W, B] = {
    val (w, a) = wa.run
    Writer((w, f(a)))
  }

  def flatMap[A, W: Monoid[W], B](wa: Writer[W, A])(
      f: A => Writer[W, B]): Writer[W, B] = {
    val (a, w) = wa.run
    f(a)
  }
}