object Curry {

  // high order function
  def sum(f: Int => Int, a: Int, b: Int) = {
    def loop(a: Int, acc: Int): Int  =
      if (a > b) acc
      else loop(a + 1, f(a) + acc)
    loop(a, 0)
  }

  // curry version: this function return an (Int, Int) => Int function
  def sumCurry(f: Int => Int): (Int, Int) => Int = {
    def sumF(a: Int, b: Int): Int  =
      if (a > b) 0
      else f(a) + sumF(a + 1, b)
    sumF
  }

  def cube (x: Int): Int = x * x * x

  def sumInts   = sumCurry(x => x)
  def sumCubes  = sumCurry(x => x * x * x)

  // syntax shortcut
  def sumCurryShort(f: Int => Int)(a: Int, b: Int): Int =
    if (a > b) 0 else f(a) + sumCurryShort(f)(a + 1, b)

  // add _ if you want to treat it as a partially applied function
  def sumCubesShort  = sumCurryShort(cube)_

  // product
  def product(f: Int => Int)(a: Int, b: Int): Int =
    if (a > b) 1 else f(a) * product(f)(a + 1, b)

  def fact(n: Int) = product(x => x)(1, n)

  // add unit value and combining function => sum and product generalisation
  def mapReduce(f: Int => Int, c: (Int, Int) => Int, u: Int )(a: Int, b: Int): Int =
    if (a > b) u else c(f(a), mapReduce(f, c, u)(a + 1, b))

  def run = {
    println("Curry")
    println(sum(x => x * x, 3, 5))
    println(sumInts(3, 5))
    println(sumCurry(cube)(3, 5))
    println(sumCubes(3, 5))
    println(sumCurryShort(cube)(3, 5))
    println(sumCubesShort(3, 5))
    println(product(x => x * x)(3, 4))
    println(fact(4))
    println(mapReduce(x => x * x, (x, y)=> x + y, 0)(3, 5))
    println(mapReduce(x => x * x, (x, y)=> x * y, 1)(3, 4))
  }

}