package Chap2

import scala.language.higherKinds

trait AbstractTypes {

  type Rational[A]

  def makeRat[A](x: A, y: A): Rational[A]

  def numer[A](r: Rational[A]): A

  def denom[A](r: Rational[A]): A
}

trait AbstractOps extends AbstractTypes {

  def equalRat[A](x: Rational[A], y: Rational[A])(implicit numeric: Numeric[A]): Boolean = {
    import numeric._
    numer(x) * denom(y) == numer(y) * denom(x)
  }


  def addRat[A](x: Rational[A], y: Rational[A])(implicit numeric: Numeric[A]): Rational[A] = {
    import numeric._
    makeRat(numer(x) * denom(y) + numer(y) * denom(x), denom(x) * denom(y))
  }
}

object RationalsAsTuples extends AbstractOps {

  type Rational[A] = (A,A)

  def makeRat[A](x: A, y: A) = (x,y)

  def numer[A](r: (A, A)): A = r._1

  def denom[A](r: (A, A)): A = r._2
}

object TuplesAsFunctions extends AbstractOps {

  sealed trait Ind
  object Fst extends Ind
  object Snd extends Ind

  type Rational[A] = Ind => A


  def cons[A](x: A, y: A) = (i: Ind) => i match {
    case Fst => x
    case Snd => y
  }

  def fst[A](z: Rational[A]) = z(Fst)
  def snd[A](z: Rational[A]) = z(Snd)


  def makeRat[A](x: A, y: A) = cons(x,y)

  def numer[A](r: Rational[A]) = fst(r)

  def denom[A](r: Rational[A]) = snd(r)

  type Rat = Rational[Int]

  def printRat(x: Rat) = s"${numer(x)} / ${denom(x)}"
}