Functor, Applicative Functor and Monad

gistfile1.scala

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

// F[A => B]
trait Applicative[F[_]] extends Functor[F] {
  def pure[A](a: A): F[A] 
  def apply[A, B](f: F[A => B]): F[A] => F[B]
}

// A => F[B]
trait Monad[F[_]] extends Applicative[F] { 
  def flatMap[A, B](f: A => F[B]): F[A] => F[B]
}
 
object Applicative {
  // to implement 
  // ... 
}

/*
Your test codes
 
val add = (a: Int) => (b: Int) => (c: Int) => a + b + c
val none: Option[Int] = None
 
println(Some(7) <*> (Some(8) <*> (Some(9) > add)))
println(Some(7) <*> (none <*> (Some(9) > add)))
println(List(1, 2, 3) <*> (List(77) <*> (List(9, 13) > add)))
*/

Functors: http://tmorris.net/posts/functors-and-things-using-scala/index.html
Applicative Functors: http://tmorris.net/posts/applicative-functors-in-scala/index.html
Applicatives are generalized functors: http://hseeberger.wordpress.com/2011/01/31/applicatives-are-generalized-functors/

Functors, Applicatives, And Monads In Pictures (한글)
https://github.com/netpyoung/netpyoung.Notes/tree/master/external/haskell/functors_applicatives_and_monads_in_pictures