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Scala example source code file (Category.scala)

This example Scala source code file (Category.scala) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Scala by Example" TM.

Learn more about this Scala project at its project page.

Java - Scala tags/keywords

boolean, category, categorylaw, compose, composelaw, composesemigroup, equal, monoid, plusempty

The Category.scala Scala example source code

package scalaz

////
/**
 * [[scalaz.Compose]] with identity.
 *
 * @see [[scalaz.Category.CategoryLaw]]
 */
////
trait Category[=>:[_, _]] extends Compose[=>:] { self =>
  ////
  // TODO GeneralizedCategory, GeneralizedFunctor, et al, from Scalaz6 ?

  /** The left and right identity over `compose`. */
  def id[A]: A =>: A

  /** `monoid`, but universally quantified. */
  def empty: PlusEmpty[λ[α => α =>: α]] =
    new PlusEmpty[λ[α => α =>: α]] with ComposePlus {
      def empty[A] = id
    }

  /** The endomorphism monoid, where `zero`=`id` and
    * `append`=`compose`.
    */
  def monoid[A]: Monoid[A =>: A] =
    new Monoid[A =>: A] with ComposeSemigroup[A] {
      def zero = id
    }

  trait CategoryLaw extends ComposeLaw {
    /** `_ <<< id` is vacuous. */
    def leftIdentity[A, B](ab: (A =>: B))(implicit E: Equal[A =>: B]): Boolean = {
      val ab1 = compose(ab, id[A])
      E.equal(ab, ab1)
    }
    /** `id <<< _` is vacuous. */
    def rightIdentity[A, B](ab: (A =>: B))(implicit E: Equal[A =>: B]): Boolean = {
      val ab1 = compose(id[B], ab)
      E.equal(ab, ab1)
    }
  }

  def categoryLaw = new CategoryLaw {}

  ////
  val categorySyntax = new scalaz.syntax.CategorySyntax[=>:] { def F = Category.this }
}

object Category {
  @inline def apply[F[_, _]](implicit F: Category[F]): Category[F] = F

  ////
  ////
}

Other Scala examples (source code examples)

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