Applicative_definition.scala

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

trait Applicative[F[_]] extends Functor[F]
{
  def map2[A,B,C](fa: F[A], fb: F[B])(f: (A,B) => C): F[C] = {
    apply(map(fa)(a => f(a,_:B)))(fb)
  }

  def apply[A,B](a: F[A => B])(fa:F[A]):F[B] = {
    map2(a,fa)((f,v) => f(v))
  }

  override def map[A,B](fa: F[A])(f: A => B):F[B] = {
    map2(unit(f),fa)((f,v) => f(v))
  }

  def unit[A](a: A):F[A]
}