// Contravariant Functors

//Formal definition says that a F[_] functor is contravariant if, instead of having the map method, it has a contramap method defined:
trait Contravariant[F[_]] {
  def contramap[A, B](fA: F[A])(f: B => A): F[B]
}

// Example:
type Comparison = Int
val Greater = 1
val Less    = -1
val Equal   = 0

trait Comparator[T]{
  def compare(t1: T, t2: T): Comparison
}

// Say we know how to compare Ints:
/** if I know how to compare integers and I know how to convert ‘cucumbers’ into integer numbers, I
  * do know how to compare ‘cucumbers’
  */

object ComparatorF extends Contravariant[Comparator] {
  def contramap[A, B](fa: Comparator[A])(f: B => A): Comparator[B] =
    new Comparator[B] {
      def compare(t1: B, t2: B): Comparison =
        fa.compare(f(t1), f(t2))
    }
}

trait Cucumber
val intC: Comparator[Int] = ???
val cucumberToInt: Cucumber => Int = ???
val cucumberC: Comparator[Cucumber] =
  ComparatorF.contramap(intC)(cucumberToInt)
 
cucumberC.compare(new Cucumber{}, new Cucumber{})


// Suppose that you have a class Conversion[X, Y] representing a conversion
// from a value of type X to a value of type Y. You can either combine it with
// a function ? => X to preprocess the input or with a function Y=>? to postprocess the output.
trait Conversion[X, Y] { self =>

  def apply(x: X): Y

  def map[Z](f: Y => Z) = new Conversion[X, Z] {
    def apply(x: X): Z = f(self.apply(x))
  }

  def contramap[W](f: W => X) = new Conversion[W, Y] {
    def apply(w: W): Y = self.apply(f(w))
  }

}