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boolean.scala
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boolean.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 instances
import algebra.lattice.Bool
import algebra.ring.BoolRing
import algebra.ring.CommutativeRig
package object boolean extends BooleanInstances
trait BooleanInstances extends cats.kernel.instances.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 CommutativeRig[Boolean] {
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
}