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Scala example source code file (Cofree.scala)

This example Scala source code file (Cofree.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

applicative, apply, cofree, cofreezip, foldable1, functor, some, traverse1

The Cofree.scala Scala example source code

package scalaz

/** A cofree comonad for some functor `S`, i.e. an `S`-branching stream. */
sealed abstract class Cofree[S[_], A] {

  def head: A

  def t: Free[Function0, S[Cofree[S,A]]]

  /** Applies `f` to the head and `g` through the tail. */
  def applyCofree[B](f: A => B, g: Cofree[S, A] => Cofree[S, B])(implicit S: Functor[S]): Cofree[S, B]

  /* Derived methods */

  def tail: S[Cofree[S, A]] = t.run

  /** Alias for `head`, for compatibility with Scalaz 6 */
  final def extract: A = head

  /** Alias for `head`, for compatibility with Scalaz 6 */
  final def copure: A = head

  /** Alias for `tail`, for compatibility with Scalaz 6 */
  final def out: S[Cofree[S, A]] = tail

  final def map[B](f: A => B)(implicit S: Functor[S]): Cofree[S, B] =
    applyCofree(f, _ map f)

  /** Alias for `extend` */
  final def =>>[B](f: Cofree[S, A] => B)(implicit S: Functor[S]): Cofree[S, B] = this extend f

  /** Redecorates this structure with a computation whose context is the entire structure under that value. */
  final def extend[B](f: Cofree[S, A] => B)(implicit S: Functor[S]): Cofree[S, B] =
    applyTail(f(this), _ extend f)

  /** Folds over this cofree structure, returning all the intermediate values in a new structure. */
  def scanr[B](g: (A, S[Cofree[S, B]]) => B)(implicit S: Functor[S]): Cofree[S, B] = {
    val qs = S.map(tail)(_ scanr g)
    Cofree(g(head, qs), qs)
  }

  /** Redecorates the structure with values representing entire substructures. */
  final def duplicate(implicit S: Functor[S]): Cofree[S, Cofree[S, A]] =
    applyTail(this, _.duplicate)

  /** Returns the components of this structure in a tuple. */
  final def toPair: (A, S[Cofree[S, A]]) = (head, tail)

  /** Changes the branching functor by the given natural transformation. */
  final def mapBranching[T[_]](f: S ~> T)(implicit S: Functor[S], T: Functor[T]): Cofree[T, A] =
    Cofree.delay(head, f(S.map(tail)(_ mapBranching f)))

  /** Modifies the first branching with the given natural transformation. */
  final def mapFirstBranching(f: S ~> S): Cofree[S, A] =
    Cofree.delay(head, f(tail))

  /** Injects a constant value into this structure. */
  final def inject[B](b: B)(implicit S: Functor[S]): Cofree[S, B] =
    applyTail(b, _ inject b)

   /** Replaces the head with `b` and applies `g` through the tail. */
  final def applyTail[B](b: B, g: Cofree[S, A] => Cofree[S, B])(implicit S: Functor[S]): Cofree[S, B] =
    applyCofree(x => b, g)

  /** Applies a function `f` to a value in this comonad and a corresponding value in the dual monad, annihilating both. */
  final def zapWith[G[_], B, C](bs: Free[G, B])(f: (A, B) => C)(implicit G: Functor[G], d: Zap[S, G]): C =
    Zap.comonadMonadZap.zapWith(this, bs)(f)

  /** Applies a function in a monad to the corresponding value in this comonad, annihilating both. */
  final def zap[G[_], B](fs: Free[G, A => B])(implicit G: Functor[G], d: Zap[S, G]): B =
    zapWith(fs)((a, f) => f(a))
}

object Cofree extends CofreeInstances {

  def apply[S[_], A](h: A, t: S[Cofree[S, A]]): Cofree[S,A] = applyT(h, Trampoline.done(t))

  def delay[S[_], A](h: A, t: => S[Cofree[S, A]]): Cofree[S,A] = applyT(h, Trampoline.delay(t))

  def unapply[S[_], A](c: Cofree[S, A]): Option[(A, S[Cofree[S,A]])] = Some( (c.head, c.tail) )

  //creates an instance of Cofree that trampolines all of the calls to the tail so we get stack safety
  def applyT[S[_],A](a: A, tf: Free[Function0,S[Cofree[S,A]]])(implicit T: Functor[λ[a => Free[Function0, a]]]): Cofree[S, A] =
    new Cofree[S,A] {

      def head = a

      def t = tf

      def applyCofree[B](f: A => B, g: Cofree[S, A] => Cofree[S, B])(implicit S: Functor[S]): Cofree[S,B] =
        applyT(f(head), T.map(t)(S.lift(g)))
    }

  private[scalaz] final type CofreeZip[F[_], A] = Cofree[F, A] @@ Tags.Zip

  private[scalaz] final def CofreeZip[F[_], A](head: A, tail: F[Cofree[F, A]]): CofreeZip[F, A] =
    Tags.Zip(Cofree(head, tail))

  /** Cofree corecursion. */
  def unfoldC[F[_], A](a: A)(f: A => F[A])(implicit F: Functor[F]): Cofree[F, A] =
    Cofree.delay(a, F.map(f(a))(unfoldC(_)(f)))

  def unfold[F[_], A, B](b: B)(f: B => (A, F[B]))(implicit F: Functor[F], T: Functor[λ[a => Free[Function0, a]]]): Cofree[F, A] = {
    val (a, fb) = f(b)
    val nt = T.map(Trampoline.done(fb))(F.lift(unfold(_)(f)))
    Cofree.applyT(a, nt)
  }

  def mapUnfold[F[_],W[_],A](z: W[A])(f: W ~> F)(implicit W: Comonad[W]): Cofree[F,A] =
    Cofree.delay(W copoint z, f(W.extend(z)(mapUnfold(_:W[A])(f))))
}

import Cofree.CofreeZip

sealed abstract class CofreeInstances4 {
  /** low priority `Foldable1` instance */
  implicit def cofreeFoldable[F[_]: Foldable]: Foldable1[Cofree[F, ?]] =
    new CofreeFoldable[F]{
      def F = implicitly
    }
}

sealed abstract class CofreeInstances3 extends CofreeInstances4 {
  /** low priority `Traverse1` instance */
  implicit def cofreeTraverse[F[_]: Traverse]: Traverse1[Cofree[F, ?]] =
    new CofreeTraverse[F]{
      def F = implicitly
    }

  implicit def cofreeZipFunctor[F[_]: Functor]: Functor[CofreeZip[F, ?]] =
    new CofreeZipFunctor[F]{
      def F = implicitly
    }
}

sealed abstract class CofreeInstances2 extends CofreeInstances3 {
  /** high priority `Foldable1` instance. more efficient */
  implicit def cofreeFoldable1[F[_]: Foldable1]: Foldable1[Cofree[F, ?]] =
    new CofreeFoldable1[F]{
      def F = implicitly
    }

  implicit def cofreeBind[F[_]: Plus: Functor]: Bind[Cofree[F, ?]] =
    new CofreeBind[F]{
      def F = implicitly
      def G = implicitly
    }
}

sealed abstract class CofreeInstances1 extends CofreeInstances2 {
  /** high priority `Traverse1` instance. more efficient */
  implicit def cofreeTraverse1[F[_]: Traverse1]: Traverse1[Cofree[F, ?]] =
    new CofreeTraverse1[F] {
      def F = implicitly
    }

  implicit def cofreeZipApply[F[_]: Apply]: Apply[CofreeZip[F, ?]] =
    new CofreeZipApply[F]{
      def F = implicitly
    }
}

sealed abstract class CofreeInstances0 extends CofreeInstances1 {
  implicit def cofreeZipApplicative[F[_]: Applicative]: Applicative[CofreeZip[F, ?]] =
    new CofreeZipApplicative[F]{
      def F = implicitly
    }

  implicit def cofreeMonad[F[_]: PlusEmpty: Functor]: Monad[Cofree[F, ?]] =
    new CofreeMonad[F]{
      def F = implicitly
      def G = implicitly
    }
}

sealed abstract class CofreeInstances extends CofreeInstances0 {
  implicit def cofreeComonad[S[_]: Functor]: Comonad[Cofree[S, ?]] = new CofreeComonad[S] {
    def F = implicitly
  }
}

private trait CofreeComonad[S[_]] extends Comonad[Cofree[S, ?]] {
  implicit def F: Functor[S]

  def copoint[A](p: Cofree[S, A]) = p.head

  override def cojoin[A](a: Cofree[S, A]) = a.duplicate

  override final def map[A, B](fa: Cofree[S, A])(f: A => B) = fa map f

  def cobind[A, B](fa: Cofree[S, A])(f: (Cofree[S, A]) => B) = fa extend f
}

private trait CofreeZipFunctor[F[_]] extends Functor[CofreeZip[F, ?]]{
  implicit def F: Functor[F]

  override final def map[A, B](fa: CofreeZip[F, A])(f: A => B) = Tags.Zip(Tag unwrap fa map f)
}

private trait CofreeZipApply[F[_]] extends Apply[CofreeZip[F, ?]] with CofreeZipFunctor[F]{
  implicit def F: Apply[F]

  override final def ap[A, B](fa: => CofreeZip[F, A])(f: => CofreeZip[F, A => B]): CofreeZip[F, B] =
    Tags.Zip(
      Cofree.applyT(Tag.unwrap(f).head(Tag.unwrap(fa).head),
        Tag.unwrap(fa).t.flatMap(fat => Tag.unwrap(f).t.map(fab => F.apply2(Tags.Zip.subst(fat), Tags.Zip.subst(fab)) { (a, b) =>
          Tag.unwrap(ap(a)(b))
        }))
      )
    )
}

private trait CofreeZipApplicative[F[_]] extends Applicative[CofreeZip[F, ?]] with CofreeZipApply[F]{
  implicit def F: Applicative[F]

  def point[A](a: => A) = Tags.Zip(Cofree.delay(a, F.point(Tag.unwrap[Cofree[F, A], Tags.Zip](point(a)))))
}

private trait CofreeBind[F[_]] extends Bind[Cofree[F, ?]] with CofreeComonad[F]{
  implicit def F: Functor[F]
  implicit def G: Plus[F]

  def bind[A, B](fa: Cofree[F, A])(f: A => Cofree[F, B]): Cofree[F, B] = {
    val c = f(fa.head)
    Cofree.applyT(c.head, c.t.map(ct => G.plus(c.tail, F.map(fa.tail)(bind(_)(f))) ) )
  }
}

private trait CofreeMonad[F[_]] extends Monad[Cofree[F, ?]] with CofreeBind[F]{
  implicit def G: PlusEmpty[F]

  def point[A](a: => A): Cofree[F, A] = Cofree(a, G.empty)
}

private trait CofreeFoldable[F[_]] extends Foldable1[Cofree[F, ?]]{
  implicit def F: Foldable[F]

  override final def foldMap[A, B](fa: Cofree[F, A])(f: A => B)(implicit M: Monoid[B]): B =
    M.append(f(fa.head), F.foldMap(fa.tail)(foldMap(_)(f)))

  override final def foldRight[A, B](fa: Cofree[F, A], z: => B)(f: (A, => B) => B): B =
    f(fa.head, F.foldRight(fa.tail, z)(foldRight(_, _)(f)))

  override final def foldLeft[A, B](fa: Cofree[F, A], z: B)(f: (B, A) => B): B =
    F.foldLeft(fa.tail, f(z, fa.head))((b, c) => foldLeft(c, b)(f))

  override final def foldMapLeft1[A, B](fa: Cofree[F, A])(z: A => B)(f: (B, A) => B): B =
    F.foldLeft(fa.tail, z(fa.head))((b, c) => foldLeft(c, b)(f))

  override def foldMapRight1[A, B](fa: Cofree[F, A])(z: A => B)(f: (A, => B) => B): B = {
    import std.option.none
    foldRight(fa, none[B]){
      case (l, None) => Some(z(l))
      case (l, Some(r)) => Some(f(l, r))
    }.getOrElse(sys.error("foldMapRight1"))
  }

  override def foldMap1[A, B](fa: Cofree[F, A])(f: A => B)(implicit S: Semigroup[B]): B = {
    val h = f(fa.head)
    F.foldMap1Opt(fa.tail)(foldMap1(_)(f)).map(S.append(h, _)).getOrElse(h)
  }
}

private trait CofreeFoldable1[F[_]] extends Foldable1[Cofree[F, ?]] with CofreeFoldable[F]{
  implicit def F: Foldable1[F]

  override final def foldMap1[A, B](fa: Cofree[F, A])(f: A => B)(implicit S: Semigroup[B]): B =
    S.append(f(fa.head), F.foldMap1(fa.tail)(foldMap1(_)(f)))
}

private trait CofreeTraverse[F[_]] extends Traverse1[Cofree[F, ?]] with CofreeFoldable[F] with CofreeComonad[F]{
  implicit def F: Traverse[F]

  override final def traverseImpl[G[_], A, B](fa: Cofree[F,A])(f: A => G[B])(implicit G: Applicative[G]): G[Cofree[F,B]] =
    G.apply2(f(fa.head), F.traverse(fa.tail)(traverse(_)(f)))(Cofree(_, _))

  override def traverse1Impl[G[_], A, B](fa: Cofree[F,A])(f: A => G[B])(implicit G: Apply[G]): G[Cofree[F,B]] =
    G.applyApplicative.traverse(fa.tail)(a => -\/(traverse1(a)(f)))
      .fold(ftl => G.apply2(f(fa.head), ftl)(Cofree(_, _)),
         tl => G.map(f(fa.head))(Cofree.apply(_, tl)))
}

private trait CofreeTraverse1[F[_]] extends Traverse1[Cofree[F, ?]] with CofreeTraverse[F] with CofreeFoldable1[F]{
  implicit def F: Traverse1[F]

  override def traverse1Impl[G[_], A, B](fa: Cofree[F,A])(f: A => G[B])(implicit G: Apply[G]): G[Cofree[F,B]] =
    G.apply2(f(fa.head), F.traverse1(fa.tail)(traverse1(_)(f)))(Cofree(_, _))
}

Other Scala examples (source code examples)

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my book on functional programming

 

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