Functor laws

package cats
package laws

import cats.syntax.functor._

/**
 * Laws that must be obeyed by any `Functor`.
 */
trait FunctorLaws[F[_]] extends InvariantLaws[F] {
  implicit override def F: Functor[F]

  def covariantIdentity[A](fa: F[A]): IsEq[F[A]] =
    fa.map(identity) <-> fa

  def covariantComposition[A, B, C](fa: F[A], f: A => B, g: B => C): IsEq[F[C]] =
    fa.map(f).map(g) <-> fa.map(f andThen g)
}

object FunctorLaws {
  def apply[F[_]](implicit ev: Functor[F]): FunctorLaws[F] =
    new FunctorLaws[F] { def F: Functor[F] = ev }
}

Mutable structures cannot be functors because they fail the identity law.

Set does not obey the second law:

  case class Bad(a: Int) { override def hashCode = 1; override def equals(a:Any) = true }
  val f = (n:Int) => Bad(n)
  val g = (b:Bad) => b.a
  Set(1,2,3).map(f andThen g) == Set(1,2,3).map(f).map(g) // false