Explain Contramap

Question

Can someone explain contramap to me? What would this implementation look like? What would good examples of usage look like?

// contravariant functor
trait Contravariant[F[_]] {
  def contramap[A, B](f: B => A): F[A] => F[B]
}

Source: http://tmorris.net/posts/functors-and-things-using-scala/index.html

Answer 1

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. For instance:

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))
  }

}

Answer 2

If you look at the following Ordering.on method of the standard library:

def on[U](f: U => T): Ordering[U]

You'll see that on transforms an Ordering[T] into an Ordering[U] while taking a function from U to T. So the method on witnesses the fact that Ordering can be seen as a Contravariant functor with:

def contramap[A, B](f: B => A) = (fa: Ordering[A]) => fa.on(f)

I also saw the blog post from Tony and it helped me finally makes sense of this three year old answer from retronym to one of my question.