gistfile1.txt

scala> trait Functor[F[_]] { def a[A, B](b: A => B): F[A] => F[B]}
defined trait Functor

scala> object Test extends Functor[Option] { def a[A, B](b: A=>B) = (a: Option[A]) => a map b}
defined module Test

scala> Test.a((a: String) => a.length)
res8: (Option[String]) => Option[Int] = <function1>

scala> res8(Some("teSt"))
res10: Option[Int] = Some(4)

scala> res8(None)
res12: Option[Int] = None

monad

new Monad[IntF] { 
  def map[A, B](f: A => B) = (a: IntF[A]) => IntF((i: Int) => f(a.k(i)))
  def flatMap[A, B](f: A => IntF[B]) = (a: IntF[A]) => IntF((i: Int) => f(a.k(i)).k(i))
  def point[A](a: A) = IntF((i: Int) => a)
}

scala> res3.flatMap((s: String) => res3.point(s.length()))
res16: (IntF[String]) => IntF[Int] = <function1>

scala> res16(IntF((a:Int) => a.toString))
res17: IntF[Int] = IntF(<function1>)

scala> res17.k(4)
res18: Int = 1

scala> res17.k(40)
res19: Int = 2

scala> res17.k(400)
res20: Int = 3

scala> res17.k(4000)
res21: Int = 4

new stuff

scala> new Functor[IntF] { def a[A,B](b: A=>B) = (a: IntF[A]) => IntF((c:Int) => b(a.k(c)))}
res16: java.lang.Object with Functor[IntF] = $anon$1@6ba26eb1

scala> res16.a((a: String) => a.length)
res17: (IntF[String]) => IntF[Int] = <function1>

scala> res18.k(3)
res22: Int = 1