Add FAQ section on Functor[Set]

[satorg]

Based on this discussion.

I feel it would be beneficial for everyone to have this section to avoid coming back to this matter over and over again.

[satorg]

I'm also considering adding a special check to FunctorLaws that could enforce this rule. Currently FunctorLaws (along with ApplicativeLaws, MonadLaws) do not fail for Set unless a special edge-case type is used for data. But it is not exactly obvious for users that they should check the laws with such types.

For example, it should be fairly easy to add a specialized rule:

// defined it cats-laws
private[cats] case class Weirdo[A](value: A) {
  override def hashCode(): Int = 12345 // it can be just a constant
  override def equals(that: Any): Boolean = that match {
    case _: Weirdo[?] => true
    case _ => super.equals(that)
  }
}

Then add a dedicated rule to FunctorLaws:

def covariantCompositionUniversalEq[A](fa: F[A], f: A => Weirdo[A], g: Weirdo[A]=> A): IsEq[F[A]] =
  fa.map(f).map(g) <-> fa.map(f.andThen(g))

This way it will become apparent that neither Functor[Set] nor similar type that relies on universal equality are lawful functors.

So, wdyt?

[rossabaker]

I like this and the concept of a law.