Explain Contramap

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))
  }

}