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SemigroupalTests.scala
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SemigroupalTests.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
package discipline
import cats.laws.discipline.SemigroupalTests.Isomorphisms
import org.scalacheck.Arbitrary
import org.scalacheck.Prop
import Prop._
import org.typelevel.discipline.Laws
trait SemigroupalTests[F[_]] extends Laws {
def laws: SemigroupalLaws[F]
def semigroupal[A: Arbitrary, B: Arbitrary, C: Arbitrary](implicit
iso: Isomorphisms[F],
ArbFA: Arbitrary[F[A]],
ArbFB: Arbitrary[F[B]],
ArbFC: Arbitrary[F[C]],
EqFA: Eq[F[A]],
EqFABC: Eq[F[(A, B, C)]]
): RuleSet =
new DefaultRuleSet(
name = "semigroupal",
parent = None,
"semigroupal associativity" -> forAll((fa: F[A], fb: F[B], fc: F[C]) =>
iso.associativity(laws.semigroupalAssociativity(fa, fb, fc))
)
)
}
object SemigroupalTests {
def apply[F[_]: Semigroupal](implicit ev: Isomorphisms[F]): SemigroupalTests[F] =
new SemigroupalTests[F] { val laws: SemigroupalLaws[F] = SemigroupalLaws[F] }
trait Isomorphisms[F[_]] {
def associativity[A, B, C](fs: (F[(A, (B, C))], F[((A, B), C)])): IsEq[F[(A, B, C)]]
def leftIdentity[A](fs: (F[(Unit, A)], F[A])): IsEq[F[A]]
def rightIdentity[A](fs: (F[(A, Unit)], F[A])): IsEq[F[A]]
}
object Isomorphisms {
import cats.kernel.laws._
implicit def invariant[F[_]](implicit F: Invariant[F]): Isomorphisms[F] =
new Isomorphisms[F] {
def associativity[A, B, C](fs: (F[(A, (B, C))], F[((A, B), C)])): IsEq[F[(A, B, C)]] =
F.imap(fs._1) { case (a, (b, c)) => (a, b, c) } { case (a, b, c) => (a, (b, c)) } <->
F.imap(fs._2) { case ((a, b), c) => (a, b, c) } { case (a, b, c) => ((a, b), c) }
def leftIdentity[A](fs: (F[(Unit, A)], F[A])): IsEq[F[A]] =
F.imap(fs._1) { case (_, a) => a } { a =>
((), a)
} <-> fs._2
def rightIdentity[A](fs: (F[(A, Unit)], F[A])): IsEq[F[A]] =
F.imap(fs._1) { case (a, _) => a } { a =>
(a, ())
} <-> fs._2
}
implicit def composedInvariant[F[_], G[_]](implicit
F: Invariant[F],
G: Invariant[G]
): Isomorphisms[λ[α => F[G[α]]]] =
invariant[λ[α => F[G[α]]]](F.compose[G])
}
}