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InvariantLaws.scala
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InvariantLaws.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 cats
package laws
import cats.Invariant
import cats.syntax.invariant._
/**
* Laws that must be obeyed by any `cats.Invariant`.
*/
trait InvariantLaws[F[_]] {
implicit def F: Invariant[F]
def invariantIdentity[A](fa: F[A]): IsEq[F[A]] =
fa.imap(identity[A])(identity[A]) <-> fa
def invariantComposition[A, B, C](fa: F[A], f1: A => B, f2: B => A, g1: B => C, g2: C => B): IsEq[F[C]] =
fa.imap(f1)(f2).imap(g1)(g2) <-> fa.imap(g1.compose(f1))(f2.compose(g2))
}
object InvariantLaws {
def apply[F[_]](implicit ev: Invariant[F]): InvariantLaws[F] =
new InvariantLaws[F] { def F: Invariant[F] = ev }
}