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Scala example source code file (Profunctor.scala)

This example Scala source code file (Profunctor.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

downstar, functor, profunctor, sndcovariant, upstar

The Profunctor.scala Scala example source code

package scalaz

////
/**
 * Profunctors are covariant on the right and contravariant on the left.
 */
////
trait Profunctor[=>:[_, _]]  { self =>
  ////
  /** Contramap on `A`. */
  def mapfst[A, B, C](fab: (A =>: B))(f: C => A): (C =>: B)

  /** Functor map on `B`. */
  def mapsnd[A, B, C](fab: (A =>: B))(f: B => C): (A =>: C)

  /** Functor map on `A` and `B`. */
  def dimap[A, B, C, D](fab: (A =>: B))(f: C => A)(g: B => D): (C =>: D) =
    mapsnd(mapfst(fab)(f))(g)

  protected[this] trait SndCovariant[C] extends Functor[C =>: ?] {
    override def map[A, B](fa: C =>: A)(f: A => B) = mapsnd(fa)(f)
  }

  def invariantFunctor: InvariantFunctor[λ[α => α =>: α]] =
    new InvariantFunctor[λ[α => α =>: α]] {
      def xmap[A, B](ma: A =>: A, f: A => B, g: B => A) =
        mapsnd(mapfst(ma)(g))(f)
    }

  def covariantInstance[C]: Functor[C =>: ?] =
    new SndCovariant[C]{}

  def contravariantInstance[C]: Contravariant[? =>: C] =
    new Contravariant[? =>: C] {
      def contramap[A, B](fa: A =>: C)(f: B => A): (B =>: C) =
        mapfst(fa)(f)
    }

  trait ProfunctorLaw {
    def identity[A, B](gab: (A =>: B))(implicit E: Equal[A =>: B]): Boolean = E.equal(dimap(gab)((a: A) => a)((b: B) => b), gab)

    def composite[A, B, C, D, E, F](gad: (A =>: D), fac: C => B, fba: B => A, fde: D => E, fef: E => F)(implicit E: Equal[C =>: F]): Boolean = {
      E.equal(dimap(dimap(gad)(fba)(fde))(fac)(fef), dimap(gad)(fba compose fac)(fef compose fde))
    }
  }

  def profunctorLaw = new ProfunctorLaw {}

  ////
  val profunctorSyntax = new scalaz.syntax.ProfunctorSyntax[=>:] { def F = Profunctor.this }
}

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

  ////
  sealed trait UpStarF
  type UpStar[F[_], D, C] = (D => F[C]) @@ UpStarF
  val UpStar = Tag.of[UpStarF]

  sealed trait DownStarF
  type DownStar[F[_], D, C] = (F[D] => C) @@ DownStarF
  val DownStar = Tag.of[DownStarF]

  implicit def upStarProfunctor[F[_]: Functor]: Profunctor[UpStar[F, ?, ?]] =
    new Profunctor[UpStar[F, ?, ?]] {
      def mapfst[A, B, C](h: UpStar[F, A, B])(f: C => A): UpStar[F, C, B] =
        UpStar(Tag unwrap h compose f)
      def mapsnd[A, B, C](h: UpStar[F, A, B])(f: B => C): UpStar[F, A, C] =
        UpStar(a => Functor[F].map(Tag.unwrap(h)(a))(f))
    }

  implicit def downStarProfunctor[F[_]: Functor]: Profunctor[DownStar[F, ?, ?]] =
    new Profunctor[DownStar[F, ?, ?]] {
      def mapfst[A, B, C](h: DownStar[F, A, B])(f: C => A): DownStar[F, C, B] =
        DownStar(fa => Tag.unwrap(h)(Functor[F].map(fa)(f)))
      def mapsnd[A, B, C](h: DownStar[F, A, B])(f: B => C): DownStar[F, A, C] =
        DownStar(f compose Tag.unwrap(h))
    }

  implicit def upStarFunctor[F[_]: Functor, D]: Functor[UpStar[F, D, ?]] =
    new Functor[UpStar[F, D, ?]] {
      def map[A, B](m: UpStar[F, D, A])(f: A => B) =
        upStarProfunctor[F].mapsnd(m)(f)
    }

  implicit def downStarFunctor[F[_], D]: Functor[DownStar[F, D, ?]] =
    new Functor[DownStar[F, D, ?]] {
      def map[A, B](f: DownStar[F, D, A])(k: A => B) =
        DownStar(k compose Tag.unwrap(f))
    }
  ////
}

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