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JoinSemilattice.scala
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JoinSemilattice.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 algebra
package lattice
import scala.{specialized => sp}
/**
* A join-semilattice (or upper semilattice) is a semilattice whose
* operation is called "join", and which can be thought of as a least
* upper bound.
*/
trait JoinSemilattice[@sp(Int, Long, Float, Double) A] extends Any with Serializable {
def join(lhs: A, rhs: A): A
def joinSemilattice: Semilattice[A] = join(_, _)
def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A] =
joinSemilattice.asJoinPartialOrder
}
trait JoinSemilatticeFunctions[J[A] <: JoinSemilattice[A]] {
def join[@sp(Int, Long, Float, Double) A](x: A, y: A)(implicit ev: J[A]): A =
ev.join(x, y)
}
object JoinSemilattice extends JoinSemilatticeFunctions[JoinSemilattice] {
/**
* Access an implicit `JoinSemilattice[A]`.
*/
@inline final def apply[@sp(Int, Long, Float, Double) A](implicit ev: JoinSemilattice[A]): JoinSemilattice[A] = ev
}