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Add two new laws for Bimonad. #596

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Nov 3, 2015
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Add two new laws for Bimonad. #596

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9 changes: 9 additions & 0 deletions laws/src/main/scala/cats/laws/BimonadLaws.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -3,6 +3,9 @@ package laws

/**
* Laws that must be obeyed by any `Bimonad`.
*
* For more information, see definition 4.1 from this paper:
* http://arxiv.org/pdf/0710.1163v3.pdf
*/
trait BimonadLaws[F[_]] extends MonadLaws[F] with ComonadLaws[F] {
implicit override def F: Bimonad[F]
Expand All @@ -12,6 +15,12 @@ trait BimonadLaws[F[_]] extends MonadLaws[F] with ComonadLaws[F] {

def extractPureIsId[A](fa: F[A]): IsEq[F[A]] =
F.pure(F.extract(fa)) <-> fa

def extractFlatMapEntwining[A](ffa: F[F[A]]): IsEq[A] =
F.extract(F.flatten(ffa)) <-> F.extract(F.map(ffa)(F.extract))

def pureCoflatMapEntwining[A](a: A): IsEq[F[F[A]]] =
F.coflatten(F.pure(a)) <-> F.map(F.pure(a))(F.pure)
}

object BimonadLaws {
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6 changes: 5 additions & 1 deletion laws/src/main/scala/cats/laws/discipline/BimonadTests.scala
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Expand Up @@ -11,14 +11,18 @@ trait BimonadTests[F[_]] extends MonadTests[F] with ComonadTests[F] {

def bimonad[A: Arbitrary: Eq, B: Arbitrary: Eq, C: Arbitrary: Eq]: RuleSet = {
implicit val arbfa: Arbitrary[F[A]] = ArbitraryK[F].synthesize[A]
implicit val arbffa: Arbitrary[F[F[A]]] = ArbitraryK[F].synthesize[F[A]]
implicit val eqfa: Eq[F[A]] = EqK[F].synthesize[A]
implicit val eqffa: Eq[F[F[A]]] = EqK[F].synthesize[F[A]]
new RuleSet {
def name: String = "bimonad"
def bases: Seq[(String, RuleSet)] = Nil
def parents: Seq[RuleSet] = Seq(monad[A, B, C], comonad[A, B, C])
def props: Seq[(String, Prop)] = Seq(
"pure andThen extract = id" -> forAll(laws.pureExtractIsId[A] _),
"extract andThen pure = id" -> forAll(laws.extractPureIsId[A] _)
"extract andThen pure = id" -> forAll(laws.extractPureIsId[A] _),
"extract/flatMap entwining" -> forAll(laws.extractFlatMapEntwining[A] _),
"pure/coflatMap entwining" -> forAll(laws.pureCoflatMapEntwining[A] _)
)
}
}
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