Add CommutativeApply and Applicative and an instance for Validated[Co…

…mmutativeSemigroup, ?]

core/src/main/scala/cats/CommutativeApplicative.scala

@@ -0,0 +1,14 @@
+package cats
+
+import simulacrum.typeclass
+
+/**
+  * Commutative Applicative.
+  *
+  * Further than an Applicative, which just allows composition of independent effectful functions,
+  * in a Commutative Applicative those functions can be composed in any order, which guarantees
+  * that their effects do not interfere.
+  *
+  * Must obey the laws defined in cats.laws.CommutativeApplicativeLaws.
+  */
+@typeclass trait CommutativeApplicative[F[_]] extends Applicative[F] with CommutativeApply[F]

core/src/main/scala/cats/CommutativeApply.scala

@@ -0,0 +1,14 @@
+package cats
+
+import simulacrum.typeclass
+
+/**
+  * Commutative Apply.
+  *
+  * Further than an Apply, which just allows composition of independent effectful functions,
+  * in a Commutative Apply those functions can be composed in any order, which guarantees
+  * that their effects do not interfere.
+  *
+  * Must obey the laws defined in cats.laws.CommutativeApplyLaws.
+  */
+@typeclass trait CommutativeApply[F[_]] extends Apply[F]

core/src/main/scala/cats/CommutativeFlatMap.scala

@@ -11,4 +11,4 @@ import simulacrum.typeclass
  *
  * Must obey the laws defined in cats.laws.CommutativeFlatMapLaws.
  */
-@typeclass trait CommutativeFlatMap[F[_]] extends FlatMap[F]
+@typeclass trait CommutativeFlatMap[F[_]] extends FlatMap[F] with CommutativeApply[F]

core/src/main/scala/cats/CommutativeMonad.scala

@@ -11,4 +11,4 @@ import simulacrum.typeclass
  *
  * Must obey the laws defined in cats.laws.CommutativeMonadLaws.
  */
-@typeclass trait CommutativeMonad[F[_]] extends Monad[F] with CommutativeFlatMap[F]
+@typeclass trait CommutativeMonad[F[_]] extends Monad[F] with CommutativeFlatMap[F] with CommutativeApplicative[F]

core/src/main/scala/cats/data/Validated.scala

@@ -2,6 +2,7 @@ package cats
 package data
 
 import cats.data.Validated.{Invalid, Valid}
+import cats.kernel.CommutativeSemigroup
 
 import scala.reflect.ClassTag
 import scala.util.{Failure, Success, Try}
@@ -374,6 +375,20 @@ private[data] sealed abstract class ValidatedInstances1 extends ValidatedInstanc
       def combine(x: Validated[A, B], y: Validated[A, B]): Validated[A, B] = x combine y
     }
 
+  implicit def catsDataCommutativeApplicativeForValidated[E: CommutativeSemigroup]: CommutativeApplicative[Validated[E, ?]] =
+    new CommutativeApplicative[Validated[E, ?]] {
+      override def map[A, B](fa: Validated[E, A])(f: A => B): Validated[E, B] =
+        fa.map(f)
+
+      def pure[A](a: A): Validated[E, A] = Validated.valid(a)
+
+      def ap[A, B](ff: Validated[E, (A) => B])(fa: Validated[E, A]): Validated[E, B] =
+        fa.ap(ff)(Semigroup[E])
+
+      override def product[A, B](fa: Validated[E, A], fb: Validated[E, B]): Validated[E, (A, B)] =
+        fa.product(fb)(Semigroup[E])
+    }
+
   implicit def catsDataPartialOrderForValidated[A: PartialOrder, B: PartialOrder]: PartialOrder[Validated[A, B]] =
     new PartialOrder[Validated[A, B]] {
       def partialCompare(x: Validated[A, B], y: Validated[A, B]): Double = x partialCompare y

laws/src/main/scala/cats/laws/CommutativeApplicativeLaws.scala

@@ -0,0 +1,12 @@
+package cats.laws
+
+import cats.CommutativeApplicative
+
+trait CommutativeApplicativeLaws[F[_]] extends CommutativeApplyLaws[F] with ApplicativeLaws[F] {
+  implicit override def F: CommutativeApplicative[F]
+}
+
+object CommutativeApplicativeLaws {
+  def apply[F[_]](implicit ev: CommutativeApplicative[F]): CommutativeApplicativeLaws[F] =
+    new CommutativeApplicativeLaws[F] { def F: CommutativeApplicative[F] = ev }
+}

laws/src/main/scala/cats/laws/CommutativeApplyLaws.scala

@@ -0,0 +1,19 @@
+package cats.laws
+
+import cats.CommutativeApply
+
+/**
+  * Laws that must be obeyed by any `CommutativeApply`.
+  */
+trait CommutativeApplyLaws[F[_]] extends ApplyLaws[F] {
+  implicit override def F: CommutativeApply[F]
+
+  def applyCommutative[A, B, C](fa: F[A], fb: F[B], f: (A, B) => C): IsEq[F[C]] =
+    F.map2(fa, fb)(f) <-> F.map2(fb, fa)((b, a) => f(a, b))
+
+}
+
+object CommutativeApplyLaws {
+  def apply[F[_]](implicit ev: CommutativeApply[F]): CommutativeApplyLaws[F] =
+    new CommutativeApplyLaws[F] { def F: CommutativeApply[F] = ev }
+}

laws/src/main/scala/cats/laws/CommutativeFlatMapLaws.scala

@@ -4,7 +4,7 @@ package laws
 /**
  * Laws that must be obeyed by any `CommutativeFlatMap`.
  */
-trait CommutativeFlatMapLaws[F[_]] extends FlatMapLaws[F] {
+trait CommutativeFlatMapLaws[F[_]] extends CommutativeApplyLaws[F] with FlatMapLaws[F] {
   implicit override def F: CommutativeFlatMap[F]
 
   def flatmapCommutative[A, B, C](fa: F[A], fb: F[B], g: (A, B) => F[C]): IsEq[F[C]] =

laws/src/main/scala/cats/laws/CommutativeMonadLaws.scala

@@ -4,7 +4,7 @@ package laws
 /**
  * Laws that must be obeyed by any `CommutativeMonad`.
  */
-trait CommutativeMonadLaws[F[_]] extends MonadLaws[F] with CommutativeFlatMapLaws[F] {
+trait CommutativeMonadLaws[F[_]] extends MonadLaws[F] with CommutativeFlatMapLaws[F] with CommutativeApplicativeLaws[F] {
   implicit override def F: CommutativeMonad[F]
 }
 

laws/src/main/scala/cats/laws/discipline/CommutativeApplicativeTests.scala

@@ -0,0 +1,42 @@
+package cats
+package laws
+package discipline
+
+import cats.laws.discipline.CartesianTests.Isomorphisms
+import org.scalacheck.{Arbitrary, Cogen, Prop}
+
+trait CommutativeApplicativeTests[F[_]] extends CommutativeApplyTests[F] with ApplicativeTests[F] {
+
+  def laws: CommutativeApplicativeLaws[F]
+
+  def commutativeApplicative[A: Arbitrary: Eq, B: Arbitrary: Eq, C: Arbitrary: Eq](implicit
+    ArbFA: Arbitrary[F[A]],
+    ArbFB: Arbitrary[F[B]],
+    ArbFC: Arbitrary[F[C]],
+    ArbFAtoB: Arbitrary[F[A => B]],
+    ArbFBtoC: Arbitrary[F[B => C]],
+    CogenA: Cogen[A],
+    CogenB: Cogen[B],
+    CogenC: Cogen[C],
+    EqFA: Eq[F[A]],
+    EqFB: Eq[F[B]],
+    EqFC: Eq[F[C]],
+    EqFABC: Eq[F[(A, B, C)]],
+    EqFInt: Eq[F[Int]],
+    iso: Isomorphisms[F]
+  ): RuleSet = {
+    new RuleSet {
+      def name: String = "commutative applicative"
+      def bases: Seq[(String, RuleSet)] = Nil
+      def parents: Seq[RuleSet] = Seq(applicative[A, B, C], commutativeApply[A, B, C])
+      def props: Seq[(String, Prop)] = Nil
+    }
+  }
+}
+
+object CommutativeApplicativeTests {
+  def apply[F[_]:  CommutativeApplicative]: CommutativeApplicativeTests[F] =
+    new CommutativeApplicativeTests[F] {
+      def laws: CommutativeApplicativeLaws[F] = CommutativeApplicativeLaws[F]
+    }
+}

laws/src/main/scala/cats/laws/discipline/CommutativeApplyTests.scala

@@ -0,0 +1,45 @@
+package cats
+package laws
+package discipline
+
+import cats.laws.discipline.CartesianTests.Isomorphisms
+import org.scalacheck.{Arbitrary, Cogen, Prop}
+import Prop._
+
+trait CommutativeApplyTests[F[_]] extends ApplyTests[F] {
+  def laws: CommutativeApplyLaws[F]
+
+  def commutativeApply[A: Arbitrary: Eq, B: Arbitrary: Eq, C: Arbitrary: Eq](implicit
+   ArbFA: Arbitrary[F[A]],
+   ArbFB: Arbitrary[F[B]],
+   ArbFC: Arbitrary[F[C]],
+   ArbFAtoB: Arbitrary[F[A => B]],
+   ArbFBtoC: Arbitrary[F[B => C]],
+   CogenA: Cogen[A],
+   CogenB: Cogen[B],
+   CogenC: Cogen[C],
+   EqFA: Eq[F[A]],
+   EqFB: Eq[F[B]],
+   EqFC: Eq[F[C]],
+   EqFABC: Eq[F[(A, B, C)]],
+   EqFInt: Eq[F[Int]],
+   iso: Isomorphisms[F]
+  ): RuleSet = {
+    new RuleSet {
+      def name: String = "commutative apply"
+      def bases: Seq[(String, RuleSet)] = Nil
+      def parents: Seq[RuleSet] = Seq(apply[A, B, C])
+      def props: Seq[(String, Prop)] = Seq(
+        "apply commutativity" -> forAll(laws.applyCommutative[A, B, C] _)
+      )
+    }
+  }
+
+}
+
+object CommutativeApplyTests {
+  def apply[F[_]:  CommutativeFlatMap]: CommutativeApplyTests[F] =
+    new CommutativeApplyTests[F] {
+      def laws: CommutativeApplyLaws[F] = CommutativeApplyLaws[F]
+    }
+}

laws/src/main/scala/cats/laws/discipline/CommutativeFlatMapTests.scala

@@ -6,7 +6,7 @@ import cats.laws.discipline.CartesianTests.Isomorphisms
 import org.scalacheck.{Arbitrary, Cogen, Prop}
 import Prop._
 
-trait CommutativeFlatMapTests[F[_]] extends FlatMapTests[F] {
+trait CommutativeFlatMapTests[F[_]] extends FlatMapTests[F] with CommutativeApplyTests[F] {
   def laws: CommutativeFlatMapLaws[F]
 
   def commutativeFlatMap[A: Arbitrary: Eq, B: Arbitrary: Eq, C: Arbitrary: Eq](implicit
@@ -28,7 +28,7 @@ trait CommutativeFlatMapTests[F[_]] extends FlatMapTests[F] {
     new RuleSet {
       def name: String = "commutative flatMap"
       def bases: Seq[(String, RuleSet)] = Nil
-      def parents: Seq[RuleSet] = Seq(flatMap[A, B, C])
+      def parents: Seq[RuleSet] = Seq(flatMap[A, B, C], commutativeApply[A, B, C])
       def props: Seq[(String, Prop)] = Seq(
         "flatmap commutativity" -> forAll(laws.flatmapCommutative[A, B, C] _)
       )

laws/src/main/scala/cats/laws/discipline/CommutativeMonadTests.scala

@@ -5,7 +5,7 @@ package discipline
 import cats.laws.discipline.CartesianTests.Isomorphisms
 import org.scalacheck.{Arbitrary, Cogen, Prop}
 
-trait CommutativeMonadTests[F[_]] extends MonadTests[F] with CommutativeFlatMapTests[F] {
+trait CommutativeMonadTests[F[_]] extends MonadTests[F] with CommutativeFlatMapTests[F] with CommutativeApplicativeTests[F] {
   def laws: CommutativeMonadLaws[F]
 
   def commutativeMonad[A: Arbitrary: Eq, B: Arbitrary: Eq, C: Arbitrary: Eq](implicit
@@ -27,7 +27,7 @@ trait CommutativeMonadTests[F[_]] extends MonadTests[F] with CommutativeFlatMapT
     new RuleSet {
       def name: String = "commutative monad"
       def bases: Seq[(String, RuleSet)] = Nil
-      def parents: Seq[RuleSet] = Seq(monad[A, B, C], commutativeFlatMap[A, B, C])
+      def parents: Seq[RuleSet] = Seq(monad[A, B, C], commutativeFlatMap[A, B, C], commutativeApplicative[A, B, C])
       def props: Seq[(String, Prop)] = Nil
     }
   }

tests/src/test/scala/cats/tests/ValidatedTests.scala

@@ -34,6 +34,8 @@ class ValidatedTests extends CatsSuite {
 
   checkAll("Validated[String, NonEmptyList[Int]]", GroupLaws[Validated[String, NonEmptyList[Int]]].semigroup)
 
+  checkAll("Validated[Int, Int]", CommutativeApplicativeTests[Validated[Int, ?]].commutativeApplicative[Int, Int, Int])
+
   {
     implicit val L = ListWrapper.semigroup[String]
     checkAll("Validated[ListWrapper[String], ?]", SemigroupKTests[Validated[ListWrapper[String], ?]].semigroupK[Int])