algebra.lattice.BoundedDistributiveLattice.scala Maven / Gradle / Ivy

Go to download
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.
   */
  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
}