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BoolRng.scala
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BoolRng.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 ring
/**
* A Boolean rng is a rng whose multiplication is idempotent, that is
* `a⋅a = a` for all elements ''a''. This property also implies `a+a = 0`
* for all ''a'', and `a⋅b = b⋅a` (commutativity of multiplication).
*
* Every `BoolRng` is equivalent to `algebra.lattice.GenBool`.
* See `algebra.lattice.GenBoolFromBoolRng` for details.
*/
trait BoolRng[A] extends Any with CommutativeRng[A] { self =>
final override def negate(x: A): A = x
}
object BoolRng extends AdditiveGroupFunctions[BoolRng] with MultiplicativeSemigroupFunctions[BoolRng] {
@inline final def apply[A](implicit r: BoolRng[A]): BoolRng[A] = r
}