A bottom up approach to category theory: Functors (2)

Functor.scala

trait Functor[F[_]] {
  def fmap[A, B](f: A => B): F[A] => F[B]
}

functor_identity.scala

def identity[F[_], A](fa: F[A], functor: Functor[F]): Boolean =
  fa == functor.fmap((a: A) => a)(fa)

functors.scala

implicit val listFunctor = new Functor[List] {
  def fmap[A, B](f: A => B): List[A] => List[B] = _ match {
    case Nil => Nil
    case a :: as => f(a) :: fmap(f)(as)
  }
}

val optionFunctor = new Functor[Option] {
  def fmap[A, B](f: A => B): Option[A] => Option[B] = _ match {
    case None => None
    case Some(a) => Some(f(a))
  }
}

functorSignature.scala

(A => B) => F[A] => F[B]

optionFunctor2.scala

val optionFunctor2 = new Functor[Option] {
  def fmap[A, B](f: A => B) = _ => None
}

signatures.scala

(A => B) => List[A] => List[B]
(A => B) => Option[A] => Option[B]

toJsonF.scala

implicit val listFunctor = new Functor[List] { … }
implicit val optionFunctor = new Functor[Option] { … }

def toJsonF[F[_]](fc: F[Contact])(implicit functor: Functor[F]): F[JsObject] =
  functor.fmap(toJson)(fc)

toJsonF0.scala

def toJsonF[F[_]](functor: Functor[F]): F[Contact] => F[JsObject] =
  functor.fmap(toJson)

toJsonF2.scala

def toJsonF[F[_]](fc: F[Contact])(implicit functor: Functor[F]): F[JsObject] =
  functor.fmap(toJson)(fc)