rangeLoop scala function

gistfile1.scala

object Foo {
  
  def factorial(n:Int): Int = {
    
    def factorialIter( n: Int , acc: Int, initial: Int) : Int = {
      if (initial == n)
        acc * initial
      else
        factorialIter(n, acc * initial, initial + 1)
    }

    factorialIter(n, 1, 1);
  }

  def factorial2(n:Int): Int = product(x => x)(1, n);

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

  def rangeLoop(f:(Int, Int) => Int, acc:Int)(g: Int => Int)(a:Int, b:Int)  = {
    def loop(a:Int, acc:Int):Int = {
      if (a > b) acc
      else loop(a + 1, f(g(a), acc))
    }
    loop(a, acc)
  }

  /* write a product function that calculates
   * the values of a function for points on an interval?
   */
  def product(f: Int => Int)(a: Int, b:Int): Int = {
    def loop(a: Int, acc: Int): Int = {
      if (a > b) acc
      else loop(a+1, f(a) * acc)
    }
    loop(a, 1)
  }

  def product2(f: Int => Int)(a:Int, b:Int): Int = 
    rangeLoop((x, y) => x * y, 1)(f)(a, b)
   
  

  def main() = {
    sum(x=> x * x, 3, 5)
  }



}