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BoundedDistributiveLattice.scala
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BoundedDistributiveLattice.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}
import algebra.ring.CommutativeRig
/**
* A bounded distributive lattice is a lattice that both bounded and distributive
*/
trait BoundedDistributiveLattice[@sp(Int, Long, Float, Double) A]
extends Any
with BoundedLattice[A]
with DistributiveLattice[A] { self =>
/**
* Return a CommutativeRig using join and meet. Note this must obey the commutative rig laws since
* meet(a, one) = a, and meet and join are associative, commutative and distributive.
*/
private[algebra] def asCommutativeRig: CommutativeRig[A] =
new CommutativeRig[A] {
def zero: A = self.zero
def one: A = self.one
def plus(x: A, y: A): A = self.join(x, y)
def times(x: A, y: A): A = self.meet(x, y)
}
override def dual: BoundedDistributiveLattice[A] = new BoundedDistributiveLattice[A] {
def meet(a: A, b: A) = self.join(a, b)
def join(a: A, b: A) = self.meet(a, b)
def one = self.zero
def zero = self.one
override def dual = self
}
}
object BoundedDistributiveLattice
extends BoundedMeetSemilatticeFunctions[BoundedDistributiveLattice]
with BoundedJoinSemilatticeFunctions[BoundedDistributiveLattice] {
/**
* Access an implicit `BoundedDistributiveLattice[A]`.
*/
@inline final def apply[@sp(Int, Long, Float, Double) A](implicit
ev: BoundedDistributiveLattice[A]
): BoundedDistributiveLattice[A] = ev
def minMax[@sp(Int, Long, Float, Double) A](min: A, max: A)(implicit ord: Order[A]): BoundedDistributiveLattice[A] =
new MinMaxBoundedDistributiveLattice(min, max)
}
class MinMaxBoundedDistributiveLattice[A](min: A, max: A)(implicit o: Order[A])
extends MinMaxLattice[A]
with BoundedDistributiveLattice[A] {
def zero = min
def one = max
}