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• Semigroup.scala

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scalaz.Semigroup.scala Maven / Gradle / Ivy

package scalaz

/**
 * A Semigroup in type S must satisfy two laws:
 * 

 * 

 * Closure: ∀ a, b in S, append(a, b) is also in S. This is enforced by the type sys.
 * 
 * 

 * Associativity: ∀ a, b and c in S, the equation append(append(a, b), c) = append(a, append(b , c)) holds.
 * 
 * 
 * @see scalaz.Identity#⊹
 */
trait Semigroup[S] {
  def append(s1: S, s2: => S): S
}

trait Semigroups {
  def semigroup[S](f: (S, => S) => S): Semigroup[S] = new Semigroup[S] {
    def append(s1: S, s2: => S) = f(s1, s2)
  }
}

trait SemigroupLow {
  implicit def TraversableSemigroup[X, CC[Y] <: collection.TraversableLike[Y, CC[Y]] : CanBuildAnySelf]: Semigroup[CC[X]] = new Semigroup[CC[X]] {
    def append(s1: CC[X], s2: => CC[X]): CC[X] = {
      implicit val cbf = implicitly[CanBuildAnySelf[CC]].builder[X, X]
      s1 ++ s2
    }
  }  
}

object Semigroup extends SemigroupLow {
  import Scalaz._
  import xml.NodeSeq

  def FirstSemigroup[A]: Semigroup[A] = semigroup((a, b) => a)

  def LastSemigroup[A]: Semigroup[A] = semigroup((a, b) => b)

  implicit def DigitSemigroup: Semigroup[Digit] = semigroup((a, b) => a.toInt + b.toInt)

  /** lexicographical order for `scalaz.Ordering` */
  implicit def OrderingSemigroup: Semigroup[Ordering] = semigroup {
    case (EQ, a) => a
    case (LT, _) => LT
    case (GT, _) => GT
  }

  /** lexicographical order for `scalaz.Order` */
  implicit def OrderSemigroup[A]: Semigroup[Order[A]] = semigroup {
    (o1, o2) => order((a1, a2) => o1.order(a1, a2) |+| o2.order(a1, a2))
  }

  /** lexicographical order for `scala.Ordering` */
  implicit def ScalaOrderingSemigroup[A]: Semigroup[scala.Ordering[A]] = semigroup {
    (o1, o2) => new scala.Ordering[A] {
      def compare(x: A, y: A): Int = o1.compare(x, y) match {
        case 0 => o2.compare(x, y)
        case i => i
      }
    }
  }

  implicit def UnitSemigroup: Semigroup[Unit] = semigroup((_, _) => ())

  implicit def StringSemigroup: Semigroup[String] = semigroup(_ + _)

  implicit def IntSemigroup: Semigroup[Int] = semigroup(_ + _)

  implicit def IntMultiplicationSemigroup: Semigroup[IntMultiplication] = semigroup(_ * _ ∏)

  implicit def BooleanConjunctionSemigroup: Semigroup[BooleanConjunction] = semigroup(_ && _ |∧|)

  implicit def BooleanSemigroup: Semigroup[Boolean] = semigroup((a, b) => (a || b))

  implicit def CharSemigroup: Semigroup[Char] = semigroup((a, b) => (a + b).toChar)

  implicit def CharMultiplicationSemigroup: Semigroup[CharMultiplication] = semigroup((a, b) => (a * b).toChar ∏)

  implicit def ByteSemigroup: Semigroup[Byte] = semigroup((a, b) => (a + b).toByte)

  implicit def ByteMultiplicationSemigroup: Semigroup[ByteMultiplication] = semigroup((a, b) => (a * b).toByte ∏)

  implicit def LongSemigroup: Semigroup[Long] = semigroup((a, b) => (a + b).toLong)

  implicit def LongMultiplicationSemigroup: Semigroup[LongMultiplication] = semigroup((a, b) => (a * b).toLong ∏)

  implicit def ShortSemigroup: Semigroup[Short] = semigroup((a, b) => (a + b).toShort)

  implicit def ShortMultiplicationSemigroup: Semigroup[ShortMultiplication] = semigroup((a, b) => (a * b).toShort ∏)

  implicit def FloatSemigroup: Semigroup[Float] = semigroup((a, b) => (a + b).toFloat)

  implicit def DoubleSemigroup: Semigroup[Double] = semigroup((a, b) => (a + b).toDouble)

  implicit def BigIntegerSemigroup: Semigroup[java.math.BigInteger] = semigroup(_ add _)

  implicit def BigIntegerMultiplicationSemigroup: Semigroup[BigIntegerMultiplication] = semigroup(_.value multiply _.value ∏)

  implicit def BigIntSemigroup: Semigroup[BigInt] = semigroup(_ + _)

  implicit def BigIntMultiplicationSemigroup: Semigroup[BigIntMultiplication] = semigroup(_.value * _.value ∏)

  implicit def NodeSeqSemigroup: Semigroup[NodeSeq] = semigroup(_ ++ _)

  implicit def NonEmptyListSemigroup[A]: Semigroup[NonEmptyList[A]] = semigroup(_.list <::: _)
  
  implicit def ZipStreamSemigroup[A]: Semigroup[ZipStream[A]] = semigroup(_.value append _.value ʐ)

  implicit def StreamSemigroup[A]: Semigroup[Stream[A]] = semigroup(_ append _)

  implicit def OptionSemigroup[A : Semigroup]: Semigroup[Option[A]] = semigroup((a, b) => { (a,b) match {
    case (Some(va), Some(vb)) => Some(va ⊹ vb)
    case (Some(va), None) => Some(va)
    case (None, Some(vb)) => Some(vb)
    case (None, None) => None
  }})

  implicit def FirstOptionSemigroup[A]: Semigroup[FirstOption[A]] = semigroup((a, b) => a orElse b)

  implicit def LastOptionSemigroup[A]: Semigroup[LastOption[A]] = semigroup((a, b) => b orElse a)

  implicit def LazyOptionSemigroup[A : Semigroup]: Semigroup[LazyOption[A]] = semigroup((a, b) =>
     a.fold(aa => LazyOption.some(b.fold(bb => aa ⊹ bb, aa)), b.fold(bb => LazyOption.some(bb)))
  )

  implicit def FirstLazyOptionSemigroup[A]: Semigroup[FirstLazyOption[A]] = semigroup((a, b) => a orElse b)

  implicit def LastLazyOptionSemigroup[A]: Semigroup[LastLazyOption[A]] = semigroup((a, b) => b orElse a)

  implicit def ArraySemigroup[A: Manifest]: Semigroup[Array[A]] = semigroup(Array.concat(_, _))

  implicit def ArraySeqSemigroup[A]: Semigroup[ArraySeq[A]] = semigroup(_ ++ _)

  implicit def EitherLeftSemigroup[A, B]: Semigroup[Either.LeftProjection[A, B]] = semigroup((a, b) => if (a.e.isLeft) a else b)

  implicit def EitherRightSemigroup[A, B]: Semigroup[Either.RightProjection[B, A]] = semigroup((a, b) => if (a.e.isRight) a else b)

  implicit def IndSeqSemigroup[A]: Semigroup[IndSeq[A]] = semigroup(_ ++ _)

  implicit def Tuple2Semigroup[A, B](implicit as: Semigroup[A], bs: Semigroup[B]): Semigroup[(A, B)] =
    semigroup((a, b) => (a._1 |+| b._1, a._2 |+| b._2))

  implicit def Tuple3Semigroup[A, B, C](implicit as: Semigroup[A], bs: Semigroup[B], cs: Semigroup[C]): Semigroup[(A, B, C)] =
    semigroup((a, b) => (a._1 |+| b._1, a._2 |+| b._2, a._3 |+| b._3))

  implicit def Tuple4Semigroup[A, B, C, D](implicit as: Semigroup[A], bs: Semigroup[B], cs: Semigroup[C], ds: Semigroup[D]): Semigroup[(A, B, C, D)] =
    semigroup((a, b) => (a._1 |+| b._1, a._2 |+| b._2, a._3 |+| b._3, a._4 |+| b._4))

  // Uglified to help diagnose https://github.com/scalaz/scalaz/issues/25
  // was: semigroup((a1, a2) => a => a1(a) ⊹ a2.apply(a))
  implicit def Function1ABSemigroup[A, B: Semigroup]: Semigroup[A => B] = semigroup {
    val S = implicitly[Semigroup[B]]
    (a1, a2) => {a =>
      val b1 = a1(a)
      lazy val b2 = a2.apply(a)
      S.append(b1, b2)
    }
  }

  implicit def EndoSemigroup[A]: Semigroup[Endo[A]] = semigroup((x, y) => (EndoTo(x compose y)))

  implicit def DualSemigroup[A: Semigroup]: Semigroup[Dual[A]] =
    semigroup((x, y) => y.value ⊹ x.value)

  implicit def FingerTreeSemigroup[V, A](implicit m: Reducer[A, V]): Semigroup[FingerTree[V, A]]=
    semigroup((x, y) => x <++> y)

  implicit def SemigroupKleisliSemigroup[M[_],A,B](implicit ss: Semigroup[M[B]]): Semigroup[Kleisli[M,A,B]] = semigroup((k1, k2) => ☆((a : A) => k1(a) ⊹ k2.apply(a)))

  implicit def MapSemigroup[K, V](implicit ss: Semigroup[V]): Semigroup[Map[K, V]] = semigroup {
    (m1, m2) => {
      // semigroups are not commutative, so order may matter. 
      val (from, to, semigroup) = {
        if (m1.size > m2.size) (m2, m1, ss.append(_: V, _: V))
        else (m1, m2, (ss.append(_: V, _: V)).flip)
      }

      from.foldLeft(to) {
        case (to, (k, v)) => to + (k -> to.get(k).map(semigroup(_, v)).getOrElse(v))
      }
    }
  }


  import concurrent.Strategy
  
  implicit def StrategySemigroup: Semigroup[Strategy] =
    semigroup((x, y) => new Strategy {
      def apply[A](a: => A) = x(y.apply(a).apply)
    })

  import java.util._
  import java.util.concurrent._

  implicit def JavaArrayListSemigroup[A]: Semigroup[ArrayList[A]] = semigroup((a, b) => {
    val k = a.clone.asInstanceOf[ArrayList[A]]
    k addAll b
    k
  })

  implicit def JavaLinkedListSemigroup[A]: Semigroup[LinkedList[A]] = semigroup((a, b) => {
    val k = a.clone.asInstanceOf[LinkedList[A]]
    k addAll b
    k
  })

  implicit def JavaPriorityQueueSemigroup[A]: Semigroup[PriorityQueue[A]] = semigroup((a, b) => {
    val k = new PriorityQueue[A](a)
    k addAll b
    k
  })

  implicit def JavaStackSemigroup[A]: Semigroup[Stack[A]] = semigroup((a, b) => {
    val k = a.clone.asInstanceOf[Stack[A]]
    k addAll b
    k
  })

  implicit def JavaVectorSemigroup[A]: Semigroup[Vector[A]] = semigroup((a, b) => {
    val k = a.clone.asInstanceOf[Vector[A]]
    k addAll b
    k
  })

  implicit def JavaArrayBlockingQueueSemigroup[A]: Semigroup[ArrayBlockingQueue[A]] = semigroup((a, b) => {
    val k = new ArrayBlockingQueue[A](a.remainingCapacity + b.remainingCapacity)
    k addAll a
    k addAll b
    k
  })

  implicit def JavaConcurrentLinkedQueueSemigroup[A]: Semigroup[ConcurrentLinkedQueue[A]] = semigroup((a, b) => {
    val k = new ConcurrentLinkedQueue[A](a)
    k addAll b
    k
  })

  implicit def JavaCopyOnWriteArrayListSemigroup[A]: Semigroup[CopyOnWriteArrayList[A]] = semigroup((a, b) => {
    val k = a.clone.asInstanceOf[CopyOnWriteArrayList[A]]
    k addAll b
    k
  })

  implicit def JavaLinkedBlockingQueueSemigroup[A]: Semigroup[LinkedBlockingQueue[A]] = semigroup((a, b) => {
    val k = new LinkedBlockingQueue[A](a)
    k addAll b
    k
  })

  implicit def JavaSynchronousQueueSemigroup[A]: Semigroup[SynchronousQueue[A]] = semigroup((a, b) => {
    val k = new SynchronousQueue[A]
    k addAll a
    k addAll b
    k
  })
}