Fold

Fold.scala

import cats._
import cats.implicits._

object Main extends App {
  case class Fold[I, O, M: Monoid](
    tally: I => M,
    summarize: M => O
  )

  object Fold {
    def fold[I, O, M: Monoid](F: Fold[I, O, M])(is: List[I]): O =
      F.summarize(Foldable[List].combineAll(is.map(F.tally)))
  }

  case class Average[A: Numeric](
    numerator: A,
    denominator: Int
  )

  implicit def x[A: Numeric]: Monoid[Average[A]] = new Monoid[Average[A]] {
    def empty = Average(implicitly[Numeric[A]].zero, 0)
    def combine(x: Average[A], y: Average[A]): Average[A] =
      Average(
        implicitly[Numeric[A]].plus(x.numerator, y.numerator),
        x.denominator + y.denominator
      )
  }

  def average: Fold[Int, Double, Average[Int]] =
    Fold(i => Average(i, 1), a => a.numerator.toDouble / a.denominator)

  println(
    Fold.fold(average)((1 to 10).toList)
  )
}