Functors

Functors.scala

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

// contravariant functor
trait Contravariant[F[_]] {
  def contramap[A, B](f: B => A): F[A] => F[B]
}

// exponential functors — defines the operation commonly known as xmap. Also known as invariant functors.
// exponential functor
trait Exponential[F[_]] {
  def xmap[A, B](f: (A => B, B => A)): F[A] => F[B]
}

// applicative functor1 — defines the operation commonly known as apply or <*>.
// applicative functor (abbreviated)
trait Applicative[F[_]] {
  def apply[A, B](f: F[A => B]): F[A] => F[B]
}

// monad2 — defines the operation commonly known as bind, flatMap or =<<.
// monad (abbreviated)
trait Monad[F[_]] {
  def flatMap[A, B](f: A => F[B]): F[A] => F[B]
}

// comonad3 — defines the operation commonly known as extend, coflatMap or <<=.
// comonad (abbreviated)
trait Comonad[F[_]] {
  def coflatMap[A, B](f: F[A] => B): F[A] => F[B]
}