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package scalaz

////
/**
 *
 */
////
trait Comonad[F[_]] extends Cobind[F] { self =>
  ////
  /** Also known as `extract` / `copure` */
  def copoint[A](p: F[A]): A

  // derived functions

  /** alias for `copoint` */
  final def copure[A](p: F[A]): A = copoint(p)

  trait ComonadLaws extends CobindLaws {
    def cobindLeftIdentity[A](fa: F[A])(implicit F: Equal[F[A]]): Boolean =
      F.equal(cobind(fa)(copoint), fa)
    def cobindRightIdentity[A, B](fa: F[A], f: F[A] => B)(implicit F: Equal[B]): Boolean =
      F.equal(copoint(cobind(fa)(f)), f(fa))
  }

  def comonadLaw: ComonadLaws = new ComonadLaws {}

  ////
  val comonadSyntax: scalaz.syntax.ComonadSyntax[F] =
    new scalaz.syntax.ComonadSyntax[F] { def F = Comonad.this }
}

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

  import Isomorphism._

  def fromIso[F[_], G[_]](D: F <~> G)(implicit E: Comonad[G]): Comonad[F] =
    new IsomorphismComonad[F, G] {
      override def G: Comonad[G] = E
      override def iso: F <~> G = D
    }

  ////
  implicit def idInstance: Comonad[Id.Id] = Id.id

  ////
}

trait IsomorphismComonad[F[_], G[_]] extends Comonad[F] with IsomorphismCobind[F, G]{
  implicit def G: Comonad[G]
  ////

  override def copoint[A](p: F[A]): A =
    G.copoint(iso.to(p))
  ////
}