gistfile1.scala

  def map[A,B](fa: F[A])(f: A => B): F[B] = bind(fa)(a => unit(f(a)))
  def join[A](f: F[F[A]]): F[A] = bind(f)(identity)
  def kleisli[A,B](f: A => B): A => F[B] = a => unit(f(a))
  def bind2[A,B](fa: F[A])(f: A => F[B]): F[B] = join(map(fa)(f))
  def ap[A,B](f: F[A => B])(fa: F[A]): F[B] = bind(f)(fab => map(fa)(fab))
  def map2[A,B,C](fa: F[A], fb: F[B])(f: (A,B) => C): F[C] = bind(fa)(a => map(fb)(b => f(a,b)))
  def map3[A,B,C,D](fa: F[A], fb: F[B], fc: F[C])(f: (A,B,C) => D): F[D] =
    bind(fa)(a => bind(fb)(b => map(fc)(c => f(a,b,c))))
  def lift2[A,B,C](f: (A,B) => C): (F[A],F[B]) => F[C] = (fa,fb) => map2(fa,fb)(f)

  def cons[A](a:A)(as:List[A]) = a :: as
  def sequence[A](fas: List[F[A]]): F[List[A]] = fas match {
    case Nil => unit(Nil)
    case x :: xs => ap(map(x)(cons))(sequence(xs))
  }

  def traverse[A,B](fas: List[A])(f: A => F[B]): F[List[B]] = sequence(fas.map(f))
  // TODO: re-read applicative chapter in LYAH
  // TODO: write sequence with fold