higher order functions and nested recursive lambdas in Scala

currying.scala

/*
 * Max DeLiso <[email protected]>
 * 1/8/13
 * higher order functions and nested recursive lambdas in Scala
 */

package lesson4

object currying {

   def mapReduce(
      f: Int => Int,
      combine: (Int, Int) => Int,
      zero: Int): (Int, Int) => Int = {
      (a: Int, b: Int) =>
         {
            if (a > b) zero
            else combine(f(a), mapReduce(f, combine, zero)(a + 1, b))
         }
   }

   def sum(f: Int => Int)(a: Int, b: Int): Int =
      mapReduce(f, (a, b) => a + b, 0)(a, b)

   def product(f: Int => Int)(a: Int, b: Int): Int =
      mapReduce(f, (a, b) => a * b, 1)(a, b)

   def factorial(n: Int): Int = {
      product(x => x)(1, n)
   }

   def main(args: Array[String]) = {
      Console.println("1 + ... + 10 = " + sum((x => x))(1, 10) + "\n" +
         "1 * ... * 10 = " + product((x => x))(1, 10) + "\n" +
         "10! = " + factorial(10) + "\n" +
         "1 + 2 + 3 = " + mapReduce((x => x), (a, b) => (a + b), 0)(1, 3))
   }
}

1 + ... + 10 = 55
1 * ... * 10 = 3628800
10! = 3628800
1 + 2 + 3 = 6