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CommutativeSemigroup.scala
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CommutativeSemigroup.scala
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/*
* Copyright (c) 2015 Typelevel
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
package cats.kernel
import scala.{specialized => sp}
/**
* CommutativeSemigroup represents a commutative semigroup.
*
* A semigroup is commutative if for all x and y, x |+| y === y |+| x.
*/
trait CommutativeSemigroup[@sp(Int, Long, Float, Double) A] extends Any with Semigroup[A] { self =>
override def reverse: CommutativeSemigroup[A] = self
override def intercalate(middle: A): CommutativeSemigroup[A] =
new CommutativeSemigroup[A] {
def combine(a: A, b: A): A =
self.combine(a, self.combine(middle, b))
override def combineN(a: A, n: Int): A =
if (n <= 1) self.combineN(a, n)
else {
// a + m + a ... = combineN(a, n) + combineN(m, n - 1)
self.combine(self.combineN(a, n), self.combineN(middle, n - 1))
}
}
}
object CommutativeSemigroup extends SemigroupFunctions[CommutativeSemigroup] {
/**
* Access an implicit `CommutativeSemigroup[A]`.
*/
@inline final def apply[A](implicit ev: CommutativeSemigroup[A]): CommutativeSemigroup[A] = ev
/**
* Create a `CommutativeSemigroup` instance from the given function.
*/
@inline def instance[A](cmb: (A, A) => A): CommutativeSemigroup[A] = cmb(_, _)
}