cats.MonoidK.scala Maven / Gradle / Ivy

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package cats

import simulacrum.typeclass

/**
 * MonoidK is a universal monoid which operates on kinds.
 *
 * This type class is useful when its type parameter F[_] has a
 * structure that can be combined for any particular type, and which
 * also has an "empty" representation. Thus, MonoidK is like a Monoid
 * for kinds (i.e. parameterized types).
 *
 * A MonoidK[F] can produce a Monoid[F[A]] for any type A.
 *
 * Here's how to distinguish Monoid and MonoidK:
 *
 *  - Monoid[A] allows A values to be combined, and also means there
 *    is an "empty" A value that functions as an identity.
 *
 *  - MonoidK[F] allows two F[A] values to be combined, for any A.  It
 *    also means that for any A, there is an "empty" F[A] value. The
 *    combination operation and empty value just depend on the
 *    structure of F, but not on the structure of A.
 */
@typeclass trait MonoidK[F[_]] extends SemigroupK[F] { self =>

  /**
   * Given a type A, create an "empty" F[A] value.
   */
  def empty[A]: F[A]

  /**
   * Given a type A, create a concrete Monoid[F[A]].
   */
  override def algebra[A]: Monoid[F[A]] =
    new Monoid[F[A]] {
      def empty: F[A] = self.empty
      def combine(x: F[A], y: F[A]): F[A] = self.combine(x, y)
    }
}