Basic typeclasses [Scala]

typeclasses.scala

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

  trait Apply[F[_]] extends Functor[F] {
    def map2[A, B, C](fa: F[A], fb: F[B])(f: (A, B) => C): F[C]
    
    def ap[A, B](ff: F[A => B])(fa: F[A]): F[B] =
      map2(ff, fa)(_(_))
  }

  trait Applicative[F[_]] extends Apply[F] {
    def pure[A](a: A): F[A]
  }
  
  trait Bind[F[_]] extends Apply[F] {
    def flatMap[A, B](fa: F[A])(f: A => F[B]): F[B]

    override def map2[A, B, C](fa: F[A], fb: F[B])(f: (A, B) => C): F[C] =
      flatMap(fa)(a => map(fb)(b => f(a, b)))
  }

  trait Monad[F[_]] extends Bind[F] with Applicative[F] {
    override def map[A, B](fa: F[A])(f: A => B): F[B] =
      flatMap(fa)(a => pure(f(a)))
  }
    
  trait MonadOps[F[_], A] {
    def map[B](f: A => B): F[B]
    def flatMap[B](f: A => F[B]): F[B]
  }

  implicit def monadSyntax[F[_], A](fa: F[A])(implicit ev: Monad[F]): MonadOps[F, A] = new MonadOps[F, A] {
    override def map[B](f: A => B): F[B] = ev.map(fa)(f)
    override def flatMap[B](f: A => F[B]): F[B] = ev.flatMap(fa)(f)
  }
}