Scalaで型クラスを使おう！ ref: http://qiita.com/kmizu/items/b656d8cf45abc442598a

file0.scala

List(1, 2, 3).sum // => 6

file1.scala

class Rational(n: Int, d: Int) {
  private[this] val g = gcd(n.abs, d.abs)
  val numer = n / g
  val denom = d / g

  def this(n: Int) = this(n, 1)

  def unary_- : Rational = new Rational(-numer, denom)

  def negative: Boolean = numer < 0

  def positive: Boolean = numer > 0

  def + (that: Rational): Rational = {
    new Rational(
      numer * that.denom + that.numer * denom,
      denom * that.denom
    )
  }

  def + (i: Int): Rational = {
    new Rational(numer + i * denom, denom)
  }

  def - (that: Rational): Rational = {
    new Rational(
      numer * that.denom - that.numer * denom,
      denom * that.denom
    )
  }

  def - (i: Int): Rational = {
    new Rational(numer - i * denom, denom)
  }

  def * (that: Rational): Rational = {
    new Rational(numer * that.numer, denom * that.denom)
  }

  def * (i: Int): Rational = {
    new Rational(numer * i, denom)
  }

  def / (that: Rational): Rational = {
    new Rational(numer * that.denom, denom * that.numer)
  }

  def / (i: Int): Rational = {
    new Rational(numer, denom * i)
  }

  override def equals(that: Any): Boolean = that match {
    case that:Rational => this.numer == that.numer && this.denom == that.denom
    case _ => false
  }

  override def toString = numer +"/"+ denom

  private[this] def gcd(a: Int, b: Int): Int = {
    if (b == 0) a else gcd(b, a % b)
  }
}

file2.scala

def sum[B >: A](implicit num: Numeric[B]): B

file3.scala

object Rational {
  implicit object NumericRational extends Numeric[Rational] {
    override def plus(x: Rational, y: Rational): Rational = x + y

    override def minus(x: Rational, y: Rational): Rational = x - y

    override def times(x: Rational, y: Rational): Rational =  x * y

    override def negate(x: Rational): Rational = -x

    override def fromInt(x: Int): Rational = new Rational(x, 1)

    override def toInt(x: Rational): Int = x.numer / x.denom

    override def toLong(x: Rational): Long = toInt(x).toLong

    override def toFloat(x: Rational): Float = (x.numer.toFloat / x.denom)

    override def toDouble(x: Rational): Double = (x.numer.toDouble / x.denom)

    override def compare(x: Rational, y: Rational): Int = {
      val r = (x - y)
      if(r.negative) -1 else if (r.positive) 1 else 0
    }
  }
}

file4.txt

assert(List(new Rational(1, 3), new Rational(1, 4), new Rational(1, 5)).sum == new Rational(47, 60))

file5.txt

assert(List(new Rational(1, 3), new Rational(1, 4), new Rational(1, 5)).product== new Rational(1, 60))