Scala Type Classes example

typeclassExample.scala

// type classes example

// based on material from SICP 1.3.1 high-order procedures
// inspired by
// The Neophyte's Guide to Scala Part 12: Type Classes
// http://danielwestheide.com/blog/2013/02/06/the-neophytes-guide-to-scala-part-12-type-classes.html

// scala.math.Numeric is a type class
// that define an interface

// abstract numeric increment (can be int, can be double)
def inc[T : Numeric](x: T) = implicitly[Numeric[T]].plus(x, implicitly[Numeric[T]].one)
// one way to access an implicit value

// abstract numeric cube
def cube[T](x: T)(implicit ev: Numeric[T]) = ev.times(x, ev.times(x, x))
// another way to access

// abstract sum for abstract sequence
def sum[T](op: T => T,
           a: T,
           next: T => T,
           b: T)
          (implicit ev: Numeric[T]): T = {
    if (ev.gt(a, b)) ev.zero
    else ev.plus(op(a), sum(op, next(a), next, b))
}

// int
def sumCubes(a: Int, b: Int): Int = sum[Int](cube[Int], a, inc[Int], b)
sumCubes(1, 10) // 3025

def sumIntegers(a: Int, b: Int): Int = sum[Int](identity, a, inc[Int], b)
sumIntegers(1, 10) // 55

// double
def piterm(x: Double): Double = 1.0 / (x * (x + 2))
def pinext(x: Double): Double = x + 4
def piSum(a: Int, b: Int): Double = sum[Double](piterm, a, pinext, b)
piSum(1, 1000) * 8 // 3.139

// or, you can cast int to double and forget about Numeric type class
def alldouble() = {
    def cube(x: Double): Double = x * x * x
    def inc(n: Double): Double = n + 1

    def sum(op: Double => Double,
            a: Double,
            next: Double => Double,
            b: Double): Double = {
        if (a > b) 0
        else op(a) + sum(op, next(a), next, b)
    }

    def sumCubes(a: Int, b: Int) = sum(cube, a, inc, b)
    println(sumCubes(1, 10)) // 3025.0

    def sumIntegers(a: Int, b: Int) = sum(identity, a, inc, b)
    println(sumIntegers(1, 10)) // 55.0

    def piterm(x: Double): Double = 1.0 / (x * (x + 2))
    def pinext(x: Double): Double = x + 4
    def piSum(a: Int, b: Int) = sum(piterm, a, pinext, b)
    piSum(1, 1000) * 8 // 3.139
}
alldouble()