rename Cartesian to Semigroupal

core/src/main/scala/cats/Apply.scala

@@ -8,7 +8,7 @@ import simulacrum.typeclass
  * Must obey the laws defined in cats.laws.ApplyLaws.
  */
 @typeclass(excludeParents = List("ApplyArityFunctions"))
-trait Apply[F[_]] extends Functor[F] with Cartesian[F] with ApplyArityFunctions[F] { self =>
+trait Apply[F[_]] extends Functor[F] with Semigroupal[F] with ApplyArityFunctions[F] { self =>
 
   /**
    * Given a value and a function in the Apply context, applies the

core/src/main/scala/cats/Composed.scala

@@ -113,8 +113,8 @@ private[cats] trait ComposedContravariantCovariant[F[_], G[_]] extends Contravar
     F.contramap(fga)(gb => G.map(gb)(f))
 }
 
-private[cats] trait ComposedCartesian[F[_], G[_]] extends ContravariantCartesian[λ[α => F[G[α]]]] with ComposedContravariantCovariant[F, G] { outer =>
-  def F: ContravariantCartesian[F]
+private[cats] trait ComposedSemigroupal[F[_], G[_]] extends ContravariantSemigroupal[λ[α => F[G[α]]]] with ComposedContravariantCovariant[F, G] { outer =>
+  def F: ContravariantSemigroupal[F]
   def G: Functor[G]
 
   def product[A, B](fa: F[G[A]], fb: F[G[B]]): F[G[(A, B)]] =

core/src/main/scala/cats/ContravariantCartesian.scala

@@ -3,12 +3,12 @@ package cats
 import simulacrum.typeclass
 
 /**
- * [[ContravariantCartesian]] is nothing more than something both contravariant
- * and Cartesian. It comes up enough to be useful, and composes well
+ * [[ContravariantSemigroupal]] is nothing more than something both contravariant
+ * and Semigroupal. It comes up enough to be useful, and composes well
  */
-@typeclass trait ContravariantCartesian[F[_]] extends Cartesian[F] with Contravariant[F] { self =>
-  override def composeFunctor[G[_]: Functor]: ContravariantCartesian[λ[α => F[G[α]]]] =
-    new ComposedCartesian[F, G] {
+@typeclass trait ContravariantSemigroupal[F[_]] extends Semigroupal[F] with Contravariant[F] { self =>
+  override def composeFunctor[G[_]: Functor]: ContravariantSemigroupal[λ[α => F[G[α]]]] =
+    new ComposedSemigroupal[F, G] {
       def F = self
       def G = Functor[G]
     }

core/src/main/scala/cats/InvariantMonoidal.scala

@@ -7,6 +7,6 @@ import simulacrum.typeclass
  *
  * Must obey the laws defined in cats.laws.InvariantMonoidalLaws.
  */
-@typeclass trait InvariantMonoidal[F[_]] extends Invariant[F] with Cartesian[F] {
+@typeclass trait InvariantMonoidal[F[_]] extends Invariant[F] with Semigroupal[F] {
   def pure[A](a: A): F[A]
 }

core/src/main/scala/cats/Cartesian.scala → core/src/main/scala/cats/Semigroupal.scala

@@ -3,17 +3,17 @@ package cats
 import simulacrum.typeclass
 
 /**
- * [[Cartesian]] captures the idea of composing independent effectful values.
+ * [[Semigroupal]] captures the idea of composing independent effectful values.
  * It is of particular interest when taken together with [[Functor]] - where [[Functor]]
  * captures the idea of applying a unary pure function to an effectful value,
  * calling `product` with `map` allows one to apply a function of arbitrary arity to multiple
  * independent effectful values.
  *
  * That same idea is also manifested in the form of [[Apply]], and indeed [[Apply]] extends both
- * [[Cartesian]] and [[Functor]] to illustrate this.
+ * [[Semigroupal]] and [[Functor]] to illustrate this.
  */
-@typeclass trait Cartesian[F[_]] {
+@typeclass trait Semigroupal[F[_]] {
   def product[A, B](fa: F[A], fb: F[B]): F[(A, B)]
 }
 
-object Cartesian extends CartesianArityFunctions
+object Semigroupal extends SemigroupalArityFunctions

core/src/main/scala/cats/instances/eq.scala

@@ -2,8 +2,8 @@ package cats
 package instances
 
 trait EqInstances {
-  implicit val catsContravariantCartesianForEq: ContravariantCartesian[Eq] =
-    new ContravariantCartesian[Eq] {
+  implicit val catsContravariantSemigroupalForEq: ContravariantSemigroupal[Eq] =
+    new ContravariantSemigroupal[Eq] {
       def contramap[A, B](fa: Eq[A])(fn: B => A): Eq[B] =
         fa.on(fn)
       def product[A, B](fa: Eq[A], fb: Eq[B]): Eq[(A, B)] =

core/src/main/scala/cats/instances/equiv.scala

@@ -2,8 +2,8 @@ package cats
 package instances
 
 trait EquivInstances {
-  implicit val catsContravariantCartesianEquiv: ContravariantCartesian[Equiv] =
-    new ContravariantCartesian[Equiv] {
+  implicit val catsContravariantSemigroupalEquiv: ContravariantSemigroupal[Equiv] =
+    new ContravariantSemigroupal[Equiv] {
       def contramap[A, B](fa: Equiv[A])(f: B => A): Equiv[B] =
         new Equiv[B] {
           def equiv(x: B, y: B): Boolean = fa.equiv(f(x), f(y))

core/src/main/scala/cats/instances/order.scala

@@ -3,8 +3,8 @@ package instances
 
 trait OrderInstances extends cats.kernel.OrderToOrderingConversion {
 
-  implicit val catsContravariantCartesianForOrder: ContravariantCartesian[Order] =
-    new ContravariantCartesian[Order] {
+  implicit val catsContravariantSemigroupalForOrder: ContravariantSemigroupal[Order] =
+    new ContravariantSemigroupal[Order] {
       /** Derive an `Order` for `B` given an `Order[A]` and a function `B => A`.
        *
        * Note: resulting instances are law-abiding only when the functions used are injective (represent a one-to-one mapping)

core/src/main/scala/cats/instances/ordering.scala

@@ -3,8 +3,8 @@ package instances
 
 trait OrderingInstances {
 
-  implicit val catsContravariantCartesianForOrdering: ContravariantCartesian[Ordering] =
-    new ContravariantCartesian[Ordering] {
+  implicit val catsContravariantSemigroupalForOrdering: ContravariantSemigroupal[Ordering] =
+    new ContravariantSemigroupal[Ordering] {
       /** Derive an `Ordering` for `B` given an `Ordering[A]` and a function `B => A`.
        *
        * Note: resulting instances are law-abiding only when the functions used are injective (represent a one-to-one mapping)

core/src/main/scala/cats/instances/partialOrder.scala

@@ -2,8 +2,8 @@ package cats
 package instances
 
 trait PartialOrderInstances {
-  implicit val catsContravariantCartesianForPartialOrder: ContravariantCartesian[PartialOrder] =
-    new ContravariantCartesian[PartialOrder] {
+  implicit val catsContravariantSemigroupalForPartialOrder: ContravariantSemigroupal[PartialOrder] =
+    new ContravariantSemigroupal[PartialOrder] {
       /** Derive a `PartialOrder` for `B` given a `PartialOrder[A]` and a function `B => A`.
        *
        * Note: resulting instances are law-abiding only when the functions used are injective (represent a one-to-one mapping)

core/src/main/scala/cats/instances/partialOrdering.scala

@@ -2,8 +2,8 @@ package cats
 package instances
 
 trait PartialOrderingInstances {
-  implicit val catsContravariantCartesianForPartialOrdering: ContravariantCartesian[PartialOrdering] =
-    new ContravariantCartesian[PartialOrdering] {
+  implicit val catsContravariantSemigroupalForPartialOrdering: ContravariantSemigroupal[PartialOrdering] =
+    new ContravariantSemigroupal[PartialOrdering] {
       /** Derive a `PartialOrdering` for `B` given a `PartialOrdering[A]` and a function `B => A`.
        *
        * Note: resulting instances are law-abiding only when the functions used are injective (represent a one-to-one mapping)

core/src/main/scala/cats/package.scala

@@ -90,4 +90,7 @@ package object cats {
   val Semigroup = cats.kernel.Semigroup
   val Monoid = cats.kernel.Monoid
   val Group = cats.kernel.Group
+
+  @deprecated("renamed to Semigroupal", "1.0.0-RC1")
+  type Cartesian[F[_]] = Semigroupal[F]
 }

core/src/main/scala/cats/syntax/all.scala

@@ -10,7 +10,7 @@ trait AllSyntax
     with BifunctorSyntax
     with BifoldableSyntax
     with BitraverseSyntax
-    with CartesianSyntax
+    with SemigroupalSyntax
     with CoflatMapSyntax
     with ComonadSyntax
     with ComposeSyntax

core/src/main/scala/cats/syntax/apply.scala

@@ -1,7 +1,7 @@
 package cats
 package syntax
 
-trait ApplySyntax extends TupleCartesianSyntax {
+trait ApplySyntax extends TupleSemigroupalSyntax {
   implicit final def catsSyntaxApply[F[_], A](fa: F[A])(implicit F: Apply[F]): Apply.Ops[F, A] =
     new Apply.Ops[F, A] {
       type TypeClassType = Apply[F]

core/src/main/scala/cats/syntax/package.scala

@@ -10,7 +10,8 @@ package object syntax {
   object bifunctor extends BifunctorSyntax
   object bifoldable extends BifoldableSyntax
   object bitraverse extends BitraverseSyntax
-  object cartesian extends CartesianSyntax
+  @deprecated("use cats.syntax.semigroupal instead", "1.0.0-RC1") 
+  object cartesian extends SemigroupalSyntax
   object coflatMap extends CoflatMapSyntax
   object eitherK extends EitherKSyntax
   object comonad extends ComonadSyntax
@@ -34,6 +35,7 @@ package object syntax {
   object profunctor extends ProfunctorSyntax
   object reducible extends ReducibleSyntax
   object semigroup extends SemigroupSyntax
+  object semigroupal extends SemigroupalSyntax
   object semigroupk extends SemigroupKSyntax
   object show extends ShowSyntax
   object strong extends StrongSyntax

core/src/main/scala/cats/syntax/semigroupal.scala

@@ -0,0 +1,20 @@
+package cats
+package syntax
+
+trait SemigroupalSyntax {
+  implicit final def catsSyntaxSemigroupal[F[_], A](fa: F[A])(implicit F: Semigroupal[F]): SemigroupalOps[F, A] =
+    new SemigroupalOps[F, A] {
+      type TypeClassType = Semigroupal[F]
+
+      val self = fa
+      val typeClassInstance = F
+    }
+}
+
+abstract class SemigroupalOps[F[_], A] extends Semigroupal.Ops[F, A] {
+
+  @deprecated("Replaced by an apply syntax, e.g. instead of (a |@| b).map(...) use (a, b).mapN(...)", "1.0.0-MF")
+  final def |@|[B](fb: F[B]): SemigroupalBuilder[F]#SemigroupalBuilder2[A, B] =
+    new SemigroupalBuilder[F] |@| self |@| fb
+
+}

docs/src/main/tut/datatypes/validated.md

@@ -522,7 +522,7 @@ implicit def validatedApplicative[E : Semigroup]: Applicative[Validated[E, ?]] =
 ```
 
 Awesome! And now we also get access to all the goodness of `Applicative`, which includes `map{2-22}`, as well as the
-`Cartesian` tuple syntax.
+`Semigroupal` tuple syntax.
 
 We can now easily ask for several bits of configuration and get any and all errors returned back.
 

docs/src/main/tut/typeclasses/invariantmonoidal.md

@@ -43,7 +43,7 @@ def product[A, B](fa: Semigroup[A], fb: Semigroup[B]): Semigroup[(A, B)] =
   }
 ```
 
-Given an instance of `InvariantMonoidal` for `Semigroup`, we are able to combine existing `Semigroup` instances to form a new `Semigroup` by using the `Cartesian` syntax:
+Given an instance of `InvariantMonoidal` for `Semigroup`, we are able to combine existing `Semigroup` instances to form a new `Semigroup` by using the `Semigroupal` syntax:
 
 ```tut:silent
 import cats.implicits._

free/src/test/scala/cats/free/CofreeTests.scala

@@ -2,7 +2,7 @@ package cats
 package free
 
 import cats.data.{NonEmptyList, OptionT}
-import cats.laws.discipline.{CartesianTests, ComonadTests, ReducibleTests, SerializableTests, TraverseTests}
+import cats.laws.discipline.{SemigroupalTests, ComonadTests, ReducibleTests, SerializableTests, TraverseTests}
 import cats.syntax.list._
 import cats.tests.{CatsSuite, Spooky}
 import org.scalacheck.{Arbitrary, Cogen, Gen}
@@ -11,7 +11,7 @@ class CofreeTests extends CatsSuite {
 
   import CofreeTests._
 
-  implicit val iso = CartesianTests.Isomorphisms.invariant[Cofree[Option, ?]]
+  implicit val iso = SemigroupalTests.Isomorphisms.invariant[Cofree[Option, ?]]
 
   checkAll("Cofree[Option, ?]", ComonadTests[Cofree[Option, ?]].comonad[Int, Int, Int])
   locally {

free/src/test/scala/cats/free/FreeApplicativeTests.scala

@@ -3,15 +3,15 @@ package free
 
 import cats.tests.CatsSuite
 import cats.arrow.FunctionK
-import cats.laws.discipline.{CartesianTests, ApplicativeTests, SerializableTests}
+import cats.laws.discipline.{SemigroupalTests, ApplicativeTests, SerializableTests}
 import cats.data.State
 
 import org.scalacheck.{Arbitrary, Gen}
 
 class FreeApplicativeTests extends CatsSuite {
   import FreeApplicativeTests._
 
-  implicit val iso = CartesianTests.Isomorphisms.invariant[FreeApplicative[Option, ?]]
+  implicit val iso = SemigroupalTests.Isomorphisms.invariant[FreeApplicative[Option, ?]]
 
   checkAll("FreeApplicative[Option, ?]", ApplicativeTests[FreeApplicative[Option, ?]].applicative[Int, Int, Int])
   checkAll("Applicative[FreeApplicative[Option, ?]]", SerializableTests.serializable(Applicative[FreeApplicative[Option, ?]]))

free/src/test/scala/cats/free/FreeInvariantMonoidalTests.scala

@@ -4,7 +4,7 @@ package tests
 import cats.arrow.FunctionK
 import cats.free.FreeInvariantMonoidal
 import cats.laws.discipline.{InvariantMonoidalTests, SerializableTests}
-import cats.laws.discipline.CartesianTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.{Arbitrary, Gen}
 import cats.tests.CsvCodecInvariantMonoidalTests._
 

free/src/test/scala/cats/free/FreeTTests.scala

@@ -173,17 +173,17 @@ trait FreeTTestsInstances {
   import IndexedStateT._
   import cats.kernel.instances.option._
   import cats.tests.IndexedStateTTests._
-  import CartesianTests._
+  import SemigroupalTests._
 
   type IntState[A] = State[Int, A]
   type FreeTOption[A] = FreeT[Option, Option, A]
   type FreeTState[A] = FreeT[IntState, IntState, A]
 
   case class JustFunctor[A](a: A)
 
-  implicit val ftlWIso: Isomorphisms[FreeTOption] = CartesianTests.Isomorphisms.invariant[FreeTOption]
+  implicit val ftlWIso: Isomorphisms[FreeTOption] = SemigroupalTests.Isomorphisms.invariant[FreeTOption]
 
-  implicit val ftlSIso: Isomorphisms[FreeTState] = CartesianTests.Isomorphisms.invariant[FreeTState]
+  implicit val ftlSIso: Isomorphisms[FreeTState] = SemigroupalTests.Isomorphisms.invariant[FreeTState]
 
   implicit val jfFunctor: Functor[JustFunctor] = new Functor[JustFunctor] {
     override def map[A, B](fa: JustFunctor[A])(f: A => B): JustFunctor[B] = JustFunctor(f(fa.a))

free/src/test/scala/cats/free/FreeTests.scala

@@ -3,7 +3,7 @@ package free
 
 import cats.arrow.FunctionK
 import cats.data.EitherK
-import cats.laws.discipline.{CartesianTests, FoldableTests, MonadTests, SerializableTests, TraverseTests}
+import cats.laws.discipline.{SemigroupalTests, FoldableTests, MonadTests, SerializableTests, TraverseTests}
 import cats.laws.discipline.arbitrary.catsLawsArbitraryForFn0
 import cats.tests.CatsSuite
 
@@ -13,7 +13,7 @@ import Arbitrary.arbFunction1
 class FreeTests extends CatsSuite {
   import FreeTests._
 
-  implicit val iso = CartesianTests.Isomorphisms.invariant[Free[Option, ?]]
+  implicit val iso = SemigroupalTests.Isomorphisms.invariant[Free[Option, ?]]
 
   checkAll("Free[Option, ?]", MonadTests[Free[Option, ?]].monad[Int, Int, Int])
   checkAll("Monad[Free[Option, ?]]", SerializableTests.serializable(Monad[Free[Option, ?]]))

laws/src/main/scala/cats/laws/ApplicativeLaws.scala

@@ -39,7 +39,7 @@ trait ApplicativeLaws[F[_]] extends ApplyLaws[F] {
     F.unit.map(_ => a) <-> F.pure(a)
 
   // The following are the lax monoidal functor identity laws - the associativity law is covered by
-  // Cartesian's associativity law.
+  // Semigroupal's associativity law.
 
   def monoidalLeftIdentity[A](fa: F[A]): (F[(Unit, A)], F[A]) =
     (F.product(F.pure(()), fa), fa)

laws/src/main/scala/cats/laws/ApplyLaws.scala

@@ -7,7 +7,7 @@ import cats.syntax.functor._
 /**
  * Laws that must be obeyed by any `Apply`.
  */
-trait ApplyLaws[F[_]] extends FunctorLaws[F] with CartesianLaws[F] {
+trait ApplyLaws[F[_]] extends FunctorLaws[F] with SemigroupalLaws[F] {
   implicit override def F: Apply[F]
 
   def applyComposition[A, B, C](fa: F[A], fab: F[A => B], fbc: F[B => C]): IsEq[F[C]] = {

laws/src/main/scala/cats/laws/InvariantMonoidalLaws.scala

@@ -4,9 +4,9 @@ package laws
 /**
  * Laws that must be obeyed by any `cats.InvariantMonoidal`.
  */
-trait InvariantMonoidalLaws[F[_]] extends InvariantLaws[F] with CartesianLaws[F] {
+trait InvariantMonoidalLaws[F[_]] extends InvariantLaws[F] with SemigroupalLaws[F] {
   override implicit def F: InvariantMonoidal[F]
-  import cats.syntax.cartesian._
+  import cats.syntax.semigroupal._
   import cats.syntax.invariant._
 
   def invariantMonoidalLeftIdentity[A, B](fa: F[A], b: B): IsEq[F[A]] =

laws/src/main/scala/cats/laws/SemigroupalLaws.scala

@@ -0,0 +1,17 @@
+package cats
+package laws
+
+/**
+ * Laws that must be obeyed by any `cats.Semigroupal`.
+ */
+trait SemigroupalLaws[F[_]] {
+  implicit def F: Semigroupal[F]
+
+  def semigroupalAssociativity[A, B, C](fa: F[A], fb: F[B], fc: F[C]): (F[(A, (B, C))], F[((A, B), C)]) =
+    (F.product(fa, F.product(fb, fc)), F.product(F.product(fa, fb), fc))
+}
+
+object SemigroupalLaws {
+  def apply[F[_]](implicit ev: Semigroupal[F]): SemigroupalLaws[F] =
+    new SemigroupalLaws[F] { val F = ev }
+}

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

@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.CartesianTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.{Arbitrary, Cogen, Prop}
 import Prop._