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Scala example source code file (Foldable1.scala)

This example Scala source code file (Foldable1.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

foldable1, nonemptylist, option, order, semigroup, some

The Foldable1.scala Scala example source code

package scalaz

////
/**
 * A [[scalaz.Foldable]] where `foldMap` is total over semigroups.
 * That is, `toList` cannot return an empty list.
 */
////
trait Foldable1[F[_]] extends Foldable[F] { self =>
  ////

  /**The product of Foldable1 `F` and `G`, `[x](F[x], G[x]])`, is a Foldable1 */
  def product[G[_]](implicit G0: Foldable1[G]): Foldable1[λ[α => (F[α], G[α])]] =
    new ProductFoldable1[F, G] {
      implicit def F = self
      implicit def G = G0
    }

  /**The composition of Foldable1 `F` and `G`, `[x]F[G[x]]`, is a Foldable1 */
  def compose[G[_]: Foldable1]: Foldable1[λ[α => F[G[α]]]] =
    new CompositionFoldable1[F, G] {
      def F = self
      def G = implicitly
    }

  /** Map each element of the structure to a [[scalaz.Semigroup]], and combine the results. */
  def foldMap1[A,B](fa: F[A])(f: A => B)(implicit F: Semigroup[B]): B
  override def foldMap1Opt[A,B](fa: F[A])(f: A => B)(implicit F: Semigroup[B]): Option[B] = Some(foldMap1(fa)(f))

  /**Right-associative fold of a structure. */
  def foldMapRight1[A, B](fa: F[A])(z: A => B)(f: (A, => B) => B): B

  // derived functions
  override def foldMap[A,B](fa: F[A])(f: A => B)(implicit F: Monoid[B]): B =
    foldMap1(fa)(f)

  /**Right-associative fold of a structure. */
  def foldRight1[A](fa: F[A])(f: (A, => A) => A): A =
    foldMapRight1(fa)(identity)(f)

  override def foldRight[A, B](fa: F[A], z: => B)(f: (A, => B) => B): B =
    foldMapRight1(fa)(f(_, z))(f)

  /**Left-associative fold of a structure. */
  def foldMapLeft1[A, B](fa: F[A])(z: A => B)(f: (B, A) => B): B = {
    import std.option._
    foldLeft(fa, none[B]) {
      case (None, r) => some(z(r))
      case (Some(l), r) => some(f(l, r))
    }.getOrElse(sys.error("foldMapLeft1"))
  }

  /**Left-associative fold of a structure. */
  def foldLeft1[A](fa: F[A])(f: (A, A) => A): A =
    foldMapLeft1(fa)(identity)(f)

  // XXX Would make a ⊥ with default foldMapLeft1; you can use it if
  // you also overrode foldMapLeft1
  // override def foldLeft[A, B](fa: F[A], z: B)(f: (B, A) => B): B =
  //   foldMapLeft1(fa)(f(z, _))(f)

  /** Curried `foldRight1`. */
  final def foldr1[A](fa: F[A])(f: A => (=> A) => A): A = foldRight1(fa)((a, b) => f(a)(b))
  override def foldMapRight1Opt[A, B](fa: F[A])(z: A => B)(f: (A, => B) => B): Option[B] = Some(foldMapRight1(fa)(z)(f))
  override def foldr1Opt[A](fa: F[A])(f: A => (=> A) => A): Option[A] = Some(foldr1(fa)(f))
  /** Curried `foldLeft1`. */
  final def foldl1[A](fa: F[A])(f: A => A => A): A = foldLeft1(fa)((b, a) => f(b)(a))
  override def foldMapLeft1Opt[A, B](fa: F[A])(z: A => B)(f: (B, A) => B): Option[B] = Some(foldMapLeft1(fa)(z)(f))
  override def foldl1Opt[A](fa: F[A])(f: A => A => A): Option[A] = Some(foldl1(fa)(f))

  def fold1[M: Semigroup](t: F[M]): M = foldMap1[M, M](t)(identity)

  import Ordering.{GT, LT}

  /** The greatest element of `fa`. */
  def maximum1[A: Order](fa: F[A]): A =
    foldLeft1(fa)((x, y) => if (Order[A].order(x, y) == GT) x else y)

  /** The greatest value of `f(a)` for each element `a` of `fa`. */
  def maximumOf1[A, B: Order](fa: F[A])(f: A => B): B =
    Tag.unwrap(foldMap1(fa)(Tags.MaxVal.onF[A, B](f)))

  /** The element `a` of `fa` which yield the greatest value of `f(a)`. */
  def maximumBy1[A, B: Order](fa: F[A])(f: A => B): A =
    (maximumOf1(fa)(a => (a, f(a)))(Order.orderBy[(A, B), B](_._2)))._1

  /** The smallest element of `fa`. */
  def minimum1[A: Order](fa: F[A]): A =
    foldLeft1(fa)((x, y) => if (Order[A].order(x, y) == LT) x else y)

  /** The smallest value of `f(a)` for each element `a` of `fa`. */
  def minimumOf1[A, B: Order](fa: F[A])(f: A => B): B =
    Tag.unwrap(foldMap1(fa)(Tags.MinVal.onF[A, B](f)))

  /** The element `a` of `fa` which yield the smallest value of `f(a)`. */
  def minimumBy1[A, B: Order](fa: F[A])(f: A => B): A =
    (minimumOf1(fa)(a => (a, f(a)))(Order.orderBy[(A, B), B](_._2)))._1

  override def maximum[A: Order](fa: F[A]): Option[A] = Some(maximum1(fa))
  override def maximumOf[A, B: Order](fa: F[A])(f: A => B): Option[B] = Some(maximumOf1(fa)(f))
  override def maximumBy[A, B: Order](fa: F[A])(f: A => B): Option[A] = Some(maximumBy1(fa)(f))
  override def minimum[A: Order](fa: F[A]): Option[A] = Some(minimum1(fa))
  override def minimumOf[A, B: Order](fa: F[A])(f: A => B): Option[B] = Some(minimumOf1(fa)(f))
  override def minimumBy[A, B: Order](fa: F[A])(f: A => B): Option[A] = Some(minimumBy1(fa)(f))

  /** ``O(n log n)`` complexity */
  def distinct1[A](fa: F[A])(implicit A: Order[A]): NonEmptyList[A] =
    foldMapLeft1[A,(ISet[A],NonEmptyList[A])](fa)(a => (ISet.singleton(a), NonEmptyList(a))) {
      case ((seen, acc), a) =>
        if (seen.notMember(a))
          (seen.insert(a), a <:: acc)
        else (seen, acc)
    }._2.reverse

  /** ``O(n^2^)`` complexity */
  def distinctE1[A](fa: F[A])(implicit A: Equal[A]): NonEmptyList[A] =
    foldMapLeft1[A,NonEmptyList[A]](fa)(a => NonEmptyList(a)) {
      case (seen, a) =>
        if (!NonEmptyList.nonEmptyList.element(seen,a))
          a <:: seen
        else seen
    }.reverse

  def sumr1[A](fa: F[A])(implicit A: Semigroup[A]): A =
    foldRight1(fa)(A.append)

  def suml1[A](fa: F[A])(implicit A: Semigroup[A]): A =
    foldLeft1(fa)(A.append(_, _))

  def msuml1[G[_], A](fa: F[G[A]])(implicit G: Plus[G]): G[A] =
    foldLeft1[G[A]](fa)(G.plus[A](_, _))

  /** Insert an `A` between every A, yielding the sum. */
  def intercalate1[A](fa: F[A], a: A)(implicit A: Semigroup[A]): A =
    foldLeft1(fa)((x, y) => A.append(x, A.append(a, y)))

  override def intercalate[A: Monoid](fa: F[A], a: A): A =
    intercalate1(fa, a)

  def traverse1_[M[_], A, B](fa: F[A])(f: A => M[B])(implicit a: Apply[M], x: Semigroup[M[B]]): M[Unit] =
    a.map(foldMap1(fa)(f))(_ => ())

  def sequence1_[M[_], A](fa: F[M[A]])(implicit a: Apply[M], x: Semigroup[M[A]]): M[Unit] =
    traverse1_(fa)(x => x)

  /** always return `false` */
  final override def empty[A](fa: F[A]): Boolean = false

  /**The product of Foldable1 `F` and Foldable `G`, `[x](F[x], G[x]])`, is a Foldable1 */
  def product0[G[_]](implicit G0: Foldable[G]): Foldable1[λ[α => (F[α], G[α])]] =
    new ProductFoldable1L[F, G] {
      def F = self
      def G = G0
    }

  def toNel[A](fa: F[A]): NonEmptyList[A] =
    foldMapRight1(fa)(NonEmptyList.nel(_, IList.empty))(_ <:: _)

  def scanLeft1[A](fa: F[A])(f: (A, A) => A): NonEmptyList[A] =
    foldMapLeft1(fa)(NonEmptyList(_))((xs, x) => f(xs.head, x) <:: xs).reverse

  def scanRight1[A](fa: F[A])(f: (A, A) => A): NonEmptyList[A] =
    foldMapRight1(fa)(NonEmptyList(_))((x, xs) => f(x, xs.head) <:: xs)

  trait Foldable1Law extends FoldableLaw {
    import std.vector._

    /** Left fold is consistent with foldMap1. */
    def leftFM1Consistent[A: Equal](fa: F[A]): Boolean =
      Equal[Vector[A]].equal(foldMap1(fa)(Vector(_)),
                             foldMapLeft1(fa)(Vector(_))(_ :+ _))

    /** Right fold is consistent with foldMap1. */
    def rightFM1Consistent[A: Equal](fa: F[A]): Boolean =
      Equal[Vector[A]].equal(foldMap1(fa)(Vector(_)),
                             foldMapRight1(fa)(Vector(_))(_ +: _))
  }
  def foldable1Law = new Foldable1Law {}

  ////
  val foldable1Syntax = new scalaz.syntax.Foldable1Syntax[F] { def F = Foldable1.this }
}

object Foldable1 {
  @inline def apply[F[_]](implicit F: Foldable1[F]): Foldable1[F] = F

  ////

  ////
}

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