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Scala example source code file (Traverse1.scala)

This example Scala source code file (Traverse1.scala) is included in the "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

apply, traverse1

The Traverse1.scala Scala example source code

package scalaz

import scalaz.Id.Id

 * A [[scalaz.Traverse]] where `traverse` is total over
 * [[scalaz.Apply]]s.  That is, `toList` cannot return an empty list.
trait Traverse1[F[_]] extends Traverse[F] with Foldable1[F] { self =>

  /**The product of Traverse1 `F` and `G`, `[x](F[x], G[x]])`, is a Traverse1 */
  def product[G[_]](implicit G0: Traverse1[G]): Traverse1[λ[α => (F[α], G[α])]] =
    new ProductTraverse1[F, G] {
      implicit def F = self
      implicit def G = G0

  /**The product of Traverse1 `F` and Traverse `G`, `[x](F[x], G[x]])`, is a Traverse1 */
  def product0[G[_]](implicit G0: Traverse[G]): Traverse1[λ[α => (F[α], G[α])]] =
    new ProductTraverse1L[F, G] {
      def F = self
      def G = G0

  /**The composition of Traverse1 `F` and `G`, `[x]F[G[x]]`, is a Traverse1 */
  def compose[G[_]: Traverse1]: Traverse1[λ[α => F[G[α]]]] =
    new CompositionTraverse1[F, G] {
      def F = self
      def G = implicitly

  /** Transform `fa` using `f`, collecting all the `G`s with `ap`. */
  def traverse1Impl[G[_]:Apply,A,B](fa: F[A])(f: A => G[B]): G[F[B]]

  // derived functions
  override def traverseImpl[G[_]:Applicative,A,B](fa: F[A])(f: A => G[B]): G[F[B]] =

  override def foldMap1[A,B](fa: F[A])(f: A => B)(implicit F: Semigroup[B]): B =
    foldLeft1(traverse1Impl[Id, A, B](fa)(f))(F.append(_, _))

  def traverse1[G[_], A, B](fa: F[A])(f: A => G[B])(implicit a: Apply[G]): G[F[B]] =

  final def traverse1U[A, GB](fa: F[A])(f: A => GB)(implicit G: Unapply[Apply, GB]): G.M[F[G.A]] =

  def sequence1[G[_]:Apply,A](fga: F[G[A]]): G[F[A]] =
    traverse1Impl[G, G[A], A](fga)(identity)

  final def sequence1U[GA](fga: F[GA])(implicit G: Unapply[Apply, GA]): G.M[F[G.A]] =

  trait Traverse1Law extends TraverseLaw {
    /** Traversal through the [[scalaz.Id]] effect is equivalent to
      * `Functor#map`.
    def identityTraverse1[A, B](fa: F[A], f: A => B)(implicit FB: Equal[F[B]]) = {
      FB.equal(traverse1[Id, A, B](fa)(f), map(fa)(f))

    /** Two sequentially dependent effects can be fused into one,
      * their composition.
    def sequentialFusion1[N[_], M[_], A, B, C](fa: F[A], amb: A => M[B], bnc: B => N[C])
                                               (implicit N: Apply[N], M: Apply[M], MN: Equal[M[N[F[C]]]]): Boolean = {
      type MN[A] = M[N[A]]
      val t1: MN[F[C]] =[M, A, B](fa)(amb))(fb => traverse1[N, B, C](fb)(bnc))
      val t2: MN[F[C]] = traverse1[MN, A, C](fa)(a => compose N)
      MN.equal(t1, t2)

     * `naturality` specialized to `sequence1`.
    def naturality1[N[_], M[_], A](nat: (M ~> N))
                                 (fma: F[M[A]])
                                 (implicit N: Apply[N], M: Apply[M], NFA: Equal[N[F[A]]]): Boolean = {
      val n1: N[F[A]] = nat[F[A]](sequence1[M, A](fma))
      val n2: N[F[A]] = sequence1[N, A](map(fma)(ma => nat(ma)))
      NFA.equal(n1, n2)

    /** Two independent effects can be fused into a single effect, their product. */
    def parallelFusion1[N[_], M[_], A, B](fa: F[A], amb: A => M[B], anb: A => N[B])
                                        (implicit N: Apply[N], M: Apply[M], MN: Equal[(M[F[B]], N[F[B]])]): Boolean = {
      type MN[A] = (M[A], N[A])
      val t1: MN[F[B]] = (traverse1[M, A, B](fa)(amb), traverse1[N, A, B](fa)(anb))
      val t2: MN[F[B]] = traverse1[MN, A, B](fa)(a => (amb(a), anb(a)))(M product N)
      MN.equal(t1, t2)
  def traverse1Law = new Traverse1Law {}

  val traverse1Syntax = new scalaz.syntax.Traverse1Syntax[F] { def F = Traverse1.this }

object Traverse1 {
  @inline def apply[F[_]](implicit F: Traverse1[F]): Traverse1[F] = F



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