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package cats.kernel
import scala.{specialized => sp}
import compat.scalaVersionSpecific._
/**
* A monoid is a semigroup with an identity. A monoid is a specialization of a
* semigroup, so its operation must be associative. Additionally,
* `combine(x, empty) == combine(empty, x) == x`. For example, if we have `Monoid[String]`,
* with `combine` as string concatenation, then `empty = ""`.
*/
trait Monoid[@sp(Int, Long, Float, Double) A] extends Any with Semigroup[A] {
/**
* Return the identity element for this monoid.
*
* Example:
* {{{
* scala> import cats.kernel.instances.int._
* scala> import cats.kernel.instances.string._
*
* scala> Monoid[String].empty
* res0: String = ""
*
* scala> Monoid[Int].empty
* res1: Int = 0
* }}}
*/
def empty: A
/**
* Tests if `a` is the identity.
*
* Example:
* {{{
* scala> import cats.kernel.instances.string._
*
* scala> Monoid[String].isEmpty("")
* res0: Boolean = true
*
* scala> Monoid[String].isEmpty("something")
* res1: Boolean = false
* }}}
*/
def isEmpty(a: A)(implicit ev: Eq[A]): Boolean =
ev.eqv(a, empty)
/**
* Return `a` appended to itself `n` times.
*
* Example:
* {{{
* scala> import cats.kernel.instances.string._
*
* scala> Monoid[String].combineN("ha", 3)
* res0: String = hahaha
*
* scala> Monoid[String].combineN("ha", 0)
* res1: String = ""
* }}}
*/
override def combineN(a: A, n: Int): A =
if (n < 0) throw new IllegalArgumentException("Repeated combining for monoids must have n >= 0")
else if (n == 0) empty
else repeatedCombineN(a, n)
/**
* Given a sequence of `as`, sum them using the monoid and return the total.
*
* Example:
* {{{
* scala> import cats.kernel.instances.string._
*
* scala> Monoid[String].combineAll(List("One ", "Two ", "Three"))
* res0: String = One Two Three
*
* scala> Monoid[String].combineAll(List.empty)
* res1: String = ""
* }}}
*/
def combineAll(as: IterableOnce[A]): A =
as.iterator.foldLeft(empty)(combine)
override def combineAllOption(as: IterableOnce[A]): Option[A] =
if (as.iterator.isEmpty) None else Some(combineAll(as))
}
@suppressUnusedImportWarningForScalaVersionSpecific
abstract class MonoidFunctions[M[T] <: Monoid[T]] extends SemigroupFunctions[M] {
def empty[@sp(Int, Long, Float, Double) A](implicit ev: M[A]): A =
ev.empty
def isEmpty[@sp(Int, Long, Float, Double) A](a: A)(implicit m: M[A], ev: Eq[A]): Boolean =
m.isEmpty(a)
def combineAll[@sp(Int, Long, Float, Double) A](as: IterableOnce[A])(implicit ev: M[A]): A =
ev.combineAll(as)
}
object Monoid extends MonoidFunctions[Monoid] {
/**
* Access an implicit `Monoid[A]`.
*/
@inline final def apply[A](implicit ev: Monoid[A]): Monoid[A] = ev
/**
* Create a `Monoid` instance from the given function and empty value.
*/
@inline def instance[A](emptyValue: A, cmb: (A, A) => A): Monoid[A] = new Monoid[A] {
override val empty: A = emptyValue
override def combine(x: A, y: A): A = cmb(x, y)
}
}
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