Monads

Let's say we have a function, X => List[Y]. This function is transformed to another function, List[X] => List[Y]. A higher order function that does this transformation is Monad.

Figure 9.2: Monad translation

Again, choosing the List container for ease of understanding, we go with the following commands:

object Monad extends App {
  def monad[X, Y](f: X => List[Y]): List[X] => List[Y] = {
      def fun : (List[X]) => List[Y] = (arg: List[X]) => arg match { // 1
        case Nil => Nil
        case x :: xs => f(x) ::: fun(xs) // 2
      }
      fun
    }
  def f1(n: Int) = (1 to n).toList // 3
  val f = monad(f1) // 4
  println(f(List(7,8,9)))  // 5 
}

The salient points of the preceding code are as follows:

• We define a function, fun, that takes an argument, arg, of the type List[X].

• We iterate each element, x, of the input list. We invoke f(x) and get List[Y]. We flatten each list by concatenating the resulting lists together with the ::: operator.

• We have a function...