Functions are Applicative, Functors and Monads

  def functionAsFunctorAndAsApplicativeAndAsMonad = {
    /* Functions are Functors also, so implement map */
    val f = (_:Int) + 3
    val g = (_:Int) * 2

    println((f ∘ g)(2)) // g(f(2))
    println(g(f(2)))

    /* Functions are also Applicatives, son implement |@| */
    val ff = (f |@| g) { _ + _ } // f(x) + g(x)
    val fff = (g |@| f) { _ + _} // g(x) + f(x)
    println(ff(2), fff(2))

    /* Functions are also Monads, keeps some value inside a context,
     * whose value is know  when we apply that function to some.
     * This is just a Reader Monad
     */
    val sumTwoFunctions:Int => Int = for {
      a <- f
      b <- g
    } yield a+b // f(x) + g(x)

    // f(x) + g(x)
    val sumTwoFunctions2 = f >>= (a => g >>= (b => (c:Int) => a + b))

    println(sumTwoFunctions(2))
    println(sumTwoFunctions2(2))
  }