algebra.std.boolean.scala Maven / Gradle / Ivy

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package algebra
package std

import algebra.lattice.Bool
import algebra.ring.BoolRing
import algebra.ring.CommutativeRig

package object boolean extends BooleanInstances

trait BooleanInstances {
  implicit val booleanAlgebra: BooleanAlgebra =
    new BooleanAlgebra

  val booleanRing = new BoolRing[Boolean] {
    def zero: Boolean = false
    def one: Boolean = true
    def plus(x: Boolean, y: Boolean): Boolean = x ^ y
    def times(x: Boolean, y: Boolean): Boolean = x && y
  }
}

/**
 * This commutative rig is different than the one obtained from GF(2).
 *
 * It uses || for plus, and && for times.
 */
class BooleanAlgebra extends Bool[Boolean] with Order[Boolean] with CommutativeRig[Boolean] {
  def compare(x: Boolean, y: Boolean): Int =
    if (x == y) 0 else if (x) 1 else -1

  override def eqv(x:Boolean, y:Boolean): Boolean = x == y
  override def neqv(x:Boolean, y:Boolean): Boolean = x != y
  override def gt(x: Boolean, y: Boolean): Boolean = x && !y
  override def lt(x: Boolean, y: Boolean): Boolean = !x && y
  override def gteqv(x: Boolean, y: Boolean): Boolean = x == y || x
  override def lteqv(x: Boolean, y: Boolean): Boolean = x == y || y

  override def min(x: Boolean, y: Boolean): Boolean = x && y
  override def max(x: Boolean, y: Boolean): Boolean = x || y

  def zero: Boolean = false
  def one: Boolean = true

  override def isZero(x: Boolean)(implicit ev: Eq[Boolean]): Boolean = !x
  override def isOne(x: Boolean)(implicit ev: Eq[Boolean]): Boolean = x

  def and(x: Boolean, y: Boolean): Boolean = x && y
  def or(x: Boolean, y: Boolean): Boolean = x || y
  def complement(x: Boolean): Boolean = !x

  def plus(a:Boolean, b:Boolean): Boolean = a || b
  override def pow(a:Boolean, b:Int): Boolean = a
  override def times(a:Boolean, b:Boolean): Boolean = a && b
}