The Higher-Order Function (HOF)

A higher-order function (HOF) is a function that can take another function as an input (parameter) or return a function as its output, or both.

Function as a parameter

Fig. 1: A function as a parameter

SMLScala

    fun fold_list (list_a) = fn (accumulator) => fn (operator) => let
      fun supporter (list_b) = if null(list_b)
        then
        accumulator
        else
        operator(hd(list_b) ) (supporter(tl(list_b) ) )
    in
      supporter(list_a)
    end
    fun sum (a) = fn (b) => (a + b)
    val application_of_fold = fold_list([17, 2, 2004]) (0) (sum)

/* Scala doesn't support type variable on lambda */

Return a function

Fig. 2: Return a function

SMLScala

  fun f_continuation (param_1) = fn (param_2) => fn (param_3) => (param_1 ^ (param_2 ^ param_3) )
  val first_app = f_continuation("Hello ")
  val second_app = first_app("World")
  val the_result = second_app("!")

  def f_continuation (param_1: String) : (String) => (String) => String = (param_2 : String) => (param_3 : String) => (param_1 + (param_2 + param_3) )
  val first_app = f_continuation("Hello ")
  val second_app = first_app("World")
  val the_result = second_app("!")