Add Bitraverse, fixes #800

core/src/main/scala/cats/Bitraverse.scala

@@ -0,0 +1,45 @@
+package cats
+
+import cats.functor.Bifunctor
+
+/**
+ *  A type class abstracting over types that give rise to two independent [[cats.Traverse]]s.
+ */
+trait Bitraverse[F[_, _]] extends Bifoldable[F] with Bifunctor[F] { self =>
+  /** Traverse each side of the structure with the given functions */
+  def bitraverse[G[_]: Applicative, A, B, C, D](fab: F[A, B])(f: A => G[C], g: B => G[D]): G[F[C, D]]
+
+  /** Sequence each side of the structure with the given functions */
+  def bisequence[G[_]: Applicative, A, B](fab: F[G[A], G[B]]): G[F[A, B]] =
+    bitraverse(fab)(identity, identity)
+
+  /** If F and G are both [[cats.Bitraverse]] then so is their composition F[G[_, _], G[_, _]] */
+  def compose[G[_, _]](implicit ev: Bitraverse[G]): Bifoldable[Lambda[(A, B) => F[G[A, B], G[A, B]]]] =
+    new CompositeBitraverse[F, G] {
+      val F = self
+      val G = ev
+    }
+
+  override def bimap[A, B, C, D](fab: F[A, B])(f: A => C, g: B => D): F[C, D] =
+    bitraverse[Id, A, B, C, D](fab)(f, g)
+}
+
+object Bitraverse {
+  def apply[F[_, _]](implicit F: Bitraverse[F]): Bitraverse[F] = F
+}
+
+trait CompositeBitraverse[F[_, _], G[_, _]]
+    extends Bitraverse[Lambda[(A, B) => F[G[A, B], G[A, B]]]]
+    with    CompositeBifoldable[F, G] {
+  def F: Bitraverse[F]
+  def G: Bitraverse[G]
+
+  def bitraverse[H[_]: Applicative, A, B, C, D](
+    fab: F[G[A, B], G[A, B]])(
+    f: A => H[C], g: B => H[D]
+  ): H[F[G[C, D], G[C, D]]] =
+    F.bitraverse(fab)(
+      gab => G.bitraverse(gab)(f, g),
+      gab => G.bitraverse(gab)(f, g)
+    )
+}

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

@@ -166,14 +166,20 @@ private[data] sealed abstract class XorInstances extends XorInstances1 {
       def combine(x: A Xor B, y: A Xor B): A Xor B = x combine y
     }
 
-  implicit def xorBifunctor: Bifunctor[Xor] with Bifoldable[Xor] =
-    new Bifunctor[Xor] with Bifoldable[Xor]{
-      override def bimap[A, B, C, D](fab: A Xor B)(f: A => C, g: B => D): C Xor D = fab.bimap(f, g)
+  implicit def xorBifunctor: Bitraverse[Xor] =
+    new Bitraverse[Xor] {
+      def bitraverse[G[_], A, B, C, D](fab: Xor[A, B])(f: A => G[C], g: B => G[D])(implicit G: Applicative[G]): G[Xor[C, D]] =
+        fab match {
+          case Xor.Left(a) => G.map(f(a))(Xor.left)
+          case Xor.Right(b) => G.map(g(b))(Xor.right)
+        }
+
       def bifoldLeft[A, B, C](fab: Xor[A, B], c: C)(f: (C, A) => C, g: (C, B) => C): C =
         fab match {
           case Xor.Left(a) => f(c, a)
           case Xor.Right(b) => g(c, b)
         }
+
       def bifoldRight[A, B, C](fab: Xor[A, B], c: Eval[C])(f: (A, Eval[C]) => Eval[C], g: (B, Eval[C]) => Eval[C]): Eval[C] =
         fab match {
           case Xor.Left(a) => f(a, c)

core/src/main/scala/cats/std/either.scala

@@ -2,13 +2,20 @@ package cats
 package std
 
 trait EitherInstances extends EitherInstances1 {
-  implicit val eitherBifoldable: Bifoldable[Either] =
-    new Bifoldable[Either] {
+  implicit val eitherBitraverse: Bitraverse[Either] =
+    new Bitraverse[Either] {
+      def bitraverse[G[_], A, B, C, D](fab: Either[A, B])(f: A => G[C], g: B => G[D])(implicit G: Applicative[G]): G[Either[C, D]] =
+        fab match {
+          case Left(a) => G.map(f(a))(Left(_))
+          case Right(b) => G.map(g(b))(Right(_))
+        }
+
       def bifoldLeft[A, B, C](fab: Either[A, B], c: C)(f: (C, A) => C, g: (C, B) => C): C =
         fab match {
           case Left(a) => f(c, a)
           case Right(b) => g(c, b)
         }
+
       def bifoldRight[A, B, C](fab: Either[A, B], c: Eval[C])(f: (A, Eval[C]) => Eval[C], g: (B, Eval[C]) => Eval[C]): Eval[C] =
         fab match {
           case Left(a) => f(a, c)

core/src/main/scala/cats/std/tuple.scala

@@ -4,8 +4,11 @@ package std
 trait TupleInstances extends Tuple2Instances
 
 sealed trait Tuple2Instances {
-  implicit val tuple2Bifoldable: Bifoldable[Tuple2] =
-    new Bifoldable[Tuple2] {
+  implicit val tuple2Bitraverse: Bitraverse[Tuple2] =
+    new Bitraverse[Tuple2] {
+      def bitraverse[G[_]: Applicative, A, B, C, D](fab: (A, B))(f: A => G[C], g: B => G[D]): G[(C, D)] =
+        Applicative[G].tuple2(f(fab._1), g(fab._2))
+
       def bifoldLeft[A, B, C](fab: (A, B), c: C)(f: (C, A) => C, g: (C, B) => C): C =
         g(f(c, fab._1), fab._2)
 

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

@@ -6,6 +6,7 @@ trait AllSyntax
     with ApplySyntax
     with BifunctorSyntax
     with BifoldableSyntax
+    with BitraverseSyntax
     with CartesianSyntax
     with CoflatMapSyntax
     with ComonadSyntax

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

@@ -0,0 +1,22 @@
+package cats
+package syntax
+
+trait BitraverseSyntax extends BitraverseSyntax1 {
+  implicit def bitraverseSyntax[F[_, _]: Bitraverse, A, B](fab: F[A, B]): BitraverseOps[F, A, B] =
+    new BitraverseOps[F, A, B](fab)
+}
+
+private[syntax] trait BitraverseSyntax1 {
+  implicit def nestedBitraverseSyntax[F[_, _]: Bitraverse, G[_], A, B](fgagb: F[G[A], G[B]]): NestedBitraverseOps[F, G, A, B] =
+    new NestedBitraverseOps[F, G, A, B](fgagb)
+}
+
+final class BitraverseOps[F[_, _], A, B](fab: F[A, B])(implicit F: Bitraverse[F]) {
+  def bitraverse[G[_]: Applicative, C, D](f: A => G[C], g: B => G[D]): G[F[C, D]] =
+    F.bitraverse(fab)(f, g)
+}
+
+final class NestedBitraverseOps[F[_, _], G[_], A, B](fgagb: F[G[A], G[B]])(implicit F: Bitraverse[F]) {
+  def bisequence(implicit G: Applicative[G]): G[F[A, B]] =
+    F.bisequence(fgagb)
+}

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

@@ -6,6 +6,7 @@ package object syntax {
   object apply extends ApplySyntax
   object bifunctor extends BifunctorSyntax
   object bifoldable extends BifoldableSyntax
+  object bitraverse extends BitraverseSyntax
   object cartesian extends CartesianSyntax
   object coflatMap extends CoflatMapSyntax
   object coproduct extends CoproductSyntax

laws/src/main/scala/cats/laws/BitraverseLaws.scala

@@ -0,0 +1,38 @@
+package cats
+package laws
+
+trait BitraverseLaws[F[_, _]] extends BifoldableLaws[F] with BifunctorLaws[F] {
+  implicit override def F: Bitraverse[F]
+
+  def bitraverseIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]] =
+    fab <-> F.bitraverse[Id, A, B, A, B](fab)(identity, identity)
+
+  def bitraverseCompose[G[_], A, B, C, D, E, H](
+    fab: F[A, B],
+    f: A => G[C],
+    g: B => G[D],
+    h: C => G[E],
+    i: D => G[H]
+  )(implicit
+    G: Applicative[G]
+  ): IsEq[G[G[F[E, H]]]] = {
+    val fg = F.bitraverse(fab)(f, g)
+    val hi = G.map(fg)(f => F.bitraverse(f)(h, i))
+
+    type GCompose[X] = G[G[X]]
+    val GCompose = G.compose[G]
+
+    val c =
+      F.bitraverse[GCompose, A, B, E, H](fab)(
+        a => G.map(f(a))(h),
+        b => G.map(g(b))(i)
+      )(GCompose)
+
+    hi <-> c
+  }
+}
+
+object BitraverseLaws {
+  def apply[F[_, _]](implicit ev: Bitraverse[F]): BitraverseLaws[F] =
+    new BitraverseLaws[F] { def F: Bitraverse[F] = ev }
+}

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

@@ -0,0 +1,47 @@
+package cats
+package laws
+package discipline
+
+import org.scalacheck.Arbitrary
+import org.scalacheck.Prop.forAll
+
+trait BitraverseTests[F[_, _]] extends BifoldableTests[F] with BifunctorTests[F] {
+  def laws: BitraverseLaws[F]
+
+  def bitraverse[G[_], A, B, C, D, E, H](implicit
+    G: Applicative[G],
+    C: Monoid[C],
+    ArbFAB: Arbitrary[F[A, B]],
+    ArbFAD: Arbitrary[F[A, D]],
+    ArbGC: Arbitrary[G[C]],
+    ArbGD: Arbitrary[G[D]],
+    ArbGE: Arbitrary[G[E]],
+    ArbGH: Arbitrary[G[H]],
+    ArbA: Arbitrary[A],
+    ArbB: Arbitrary[B],
+    ArbC: Arbitrary[C],
+    ArbE: Arbitrary[E],
+    ArbH: Arbitrary[H],
+    EqFAB: Eq[F[A, B]],
+    EqFAD: Eq[F[A, D]],
+    EqFAH: Eq[F[A, H]],
+    EqFCD: Eq[F[C, D]],
+    EqFCH: Eq[F[C, H]],
+    EqGGFEH: Eq[G[G[F[E, H]]]],
+    EqC: Eq[C]
+  ): RuleSet =
+    new RuleSet {
+      val name = "bitraverse"
+      val parents = Seq(bifoldable[A, B, C], bifunctor[A, B, C, D, E, H])
+      val bases = Seq.empty
+      val props = Seq(
+        "bitraverse identity" -> forAll(laws.bitraverseIdentity[A, B] _),
+        "bitraverse composition" -> forAll(laws.bitraverseCompose[G, A, B, C, D, E, H] _)
+      )
+    }
+}
+
+object BitraverseTests {
+  def apply[F[_, _]: Bitraverse]: BitraverseTests[F] =
+    new BitraverseTests[F] { def laws: BitraverseLaws[F] = BitraverseLaws[F] }
+}

tests/src/test/scala/cats/tests/EitherTests.scala

@@ -1,7 +1,7 @@
 package cats
 package tests
 
-import cats.laws.discipline.{BifoldableTests, TraverseTests, MonadTests, SerializableTests, CartesianTests}
+import cats.laws.discipline.{BitraverseTests, TraverseTests, MonadTests, SerializableTests, CartesianTests}
 import cats.laws.discipline.eq._
 import algebra.laws.OrderLaws
 
@@ -18,8 +18,8 @@ class EitherTests extends CatsSuite {
   checkAll("Either[Int, Int] with Option", TraverseTests[Either[Int, ?]].traverse[Int, Int, Int, Int, Option, Option])
   checkAll("Traverse[Either[Int, ?]", SerializableTests.serializable(Traverse[Either[Int, ?]]))
 
-  checkAll("Either[?, ?]", BifoldableTests[Either].bifoldable[Int, Int, Int])
-  checkAll("Bifoldable[Either]", SerializableTests.serializable(Bifoldable[Either]))
+  checkAll("Either[?, ?]", BitraverseTests[Either].bitraverse[Option, Int, Int, Int, String, String, String])
+  checkAll("Bitraverse[Either]", SerializableTests.serializable(Bitraverse[Either]))
 
   val partialOrder = eitherPartialOrder[Int, String]
   val order = implicitly[Order[Either[Int, String]]]

tests/src/test/scala/cats/tests/SyntaxTests.scala

@@ -202,6 +202,17 @@ class SyntaxTests extends AllInstances with AllSyntax {
     val d0 = fab.bifoldMap(f2, g2)
   }
 
+  def testBitraverse[F[_, _]: Bitraverse, G[_]: Applicative, A, B, C, D]: Unit = {
+    val f = mock[A => G[C]]
+    val g = mock[B => G[D]]
+
+    val fab = mock[F[A, B]]
+    val gfcd = fab.bitraverse(f, g)
+
+    val fgagb = mock[F[G[A], G[B]]]
+    val gfab = fgagb.bisequence
+  }
+
   def testApplicative[F[_]: Applicative, A]: Unit = {
     val a = mock[A]
     val fa = a.pure[F]

tests/src/test/scala/cats/tests/TupleTests.scala

@@ -1,9 +1,10 @@
 package cats
 package tests
 
-import cats.laws.discipline.{BifoldableTests, SerializableTests}
+import cats.laws.discipline.{BitraverseTests, SerializableTests}
+import cats.laws.discipline.eq.tuple2Eq
 
 class TupleTests extends CatsSuite {
-  checkAll("Tuple2", BifoldableTests[Tuple2].bifoldable[Int, Int, Int])
-  checkAll("Bifoldable[Tuple2]", SerializableTests.serializable(Bifoldable[Tuple2]))
+  checkAll("Tuple2", BitraverseTests[Tuple2].bitraverse[Option, Int, Int, Int, String, String, String])
+  checkAll("Bitraverse[Tuple2]", SerializableTests.serializable(Bitraverse[Tuple2]))
 }

tests/src/test/scala/cats/tests/XorTests.scala

@@ -3,9 +3,8 @@ package tests
 
 import cats.data.{NonEmptyList, Xor, XorT}
 import cats.data.Xor._
-import cats.functor.Bifunctor
 import cats.laws.discipline.arbitrary._
-import cats.laws.discipline.{BifunctorTests, BifoldableTests, TraverseTests, MonadErrorTests, SerializableTests, CartesianTests}
+import cats.laws.discipline.{BitraverseTests, TraverseTests, MonadErrorTests, SerializableTests, CartesianTests}
 import cats.laws.discipline.eq.tuple3Eq
 import algebra.laws.{GroupLaws, OrderLaws}
 import org.scalacheck.{Arbitrary, Gen}
@@ -55,11 +54,8 @@ class XorTests extends CatsSuite {
     } yield xor
   }
 
-  checkAll("? Xor ?", BifunctorTests[Xor].bifunctor[Int, Int, Int, String, String, String])
-  checkAll("Bifunctor[Xor]", SerializableTests.serializable(Bifunctor[Xor]))
-
-  checkAll("? Xor ?", BifoldableTests[Xor].bifoldable[Int, Int, Int])
-  checkAll("Bifoldable[Xor]", SerializableTests.serializable(Bifoldable[Xor]))
+  checkAll("? Xor ?", BitraverseTests[Xor].bitraverse[Option, Int, Int, Int, String, String, String])
+  checkAll("Bitraverse[Xor]", SerializableTests.serializable(Bitraverse[Xor]))
 
   test("catchOnly catches matching exceptions") {
     assert(Xor.catchOnly[NumberFormatException]{ "foo".toInt }.isInstanceOf[Xor.Left[NumberFormatException]])