Add Bifoldable, fixes #94

Also:
- Add MonadCombine separate
- Add serializability check for Bifunctor[Xor]

core/src/main/scala/cats/Bifoldable.scala

@@ -0,0 +1,23 @@
+package cats
+
+/**
+ * A type class abstracting over types that give rise to two independent [[cats.Foldable]]s.
+ */
+trait Bifoldable[F[_, _]] extends Serializable {
+  /** Collapse the structure with a left-associative function */
+  def bifoldLeft[A, B, C](fab: F[A, B], c: C)(f: (C, A) => C, g: (C, B) => C): C
+
+  /** Collapse the structure with a right-associative function */
+  def bifoldRight[A, B, C](fab: F[A, B], c: Eval[C])(f: (A, Eval[C]) => Eval[C], g: (B, Eval[C]) => Eval[C]): Eval[C]
+
+  /** Collapse the structure by mapping each element to an element of a type that has a [[cats.Monoid]] */
+  def bifoldMap[A, B, C](fab: F[A, B])(f: A => C)(g: B => C)(implicit C: Monoid[C]): C =
+    bifoldLeft(fab, C.empty)(
+      (c: C, a: A) => C.combine(c, f(a)),
+      (c: C, b: B) => C.combine(c, g(b))
+    )
+}
+
+object Bifoldable {
+  def apply[F[_, _]](implicit F: Bifoldable[F]): Bifoldable[F] = F
+}

core/src/main/scala/cats/MonadCombine.scala

@@ -18,4 +18,11 @@ import simulacrum.typeclass
     flatMap(fga) { ga =>
       G.foldLeft(ga, empty[A])((acc, a) => combineK(acc, pure(a)))
     }
+
+  /** Separate the inner foldable values into the "lefts" and "rights" */
+  def separate[G[_, _], A, B](fgab: F[G[A, B]])(implicit G: Bifoldable[G]): (F[A], F[B]) = {
+    val as = flatMap(fgab)(gab => G.bifoldMap(gab)(pure)(_ => empty[A])(algebra[A]))
+    val bs = flatMap(fgab)(gab => G.bifoldMap(gab)(_ => empty[B])(pure)(algebra[B]))
+    (as, bs)
+  }
 }

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

@@ -166,9 +166,19 @@ 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] =
-    new Bifunctor[Xor] {
+  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)
+      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)
+          case Xor.Right(b) => g(b, c)
+        }
     }
 
   implicit def xorInstances[A]: Traverse[A Xor ?] with MonadError[Xor[A, ?], A] =

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

@@ -15,3 +15,4 @@ trait AllInstances
   with    BigIntInstances
   with    BigDecimalInstances
   with    FutureInstances
+  with    TupleInstances

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

@@ -2,6 +2,20 @@ package cats
 package std
 
 trait EitherInstances extends EitherInstances1 {
+  implicit val eitherBifoldable: Bifoldable[Either] =
+    new Bifoldable[Either] {
+      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)
+          case Right(b) => g(b, c)
+        }
+    }
+
   implicit def eitherInstances[A]: Monad[Either[A, ?]] with Traverse[Either[A, ?]] =
     new Monad[Either[A, ?]] with Traverse[Either[A, ?]] {
       def pure[B](b: B): Either[A, B] = Right(b)

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

@@ -27,4 +27,6 @@ package object std {
 
   object bigInt     extends BigIntInstances
   object bigDecimal extends BigDecimalInstances
+
+  object tuple      extends TupleInstances
 }

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

@@ -0,0 +1,15 @@
+package cats
+package std
+
+trait TupleInstances extends Tuple2Instances
+
+sealed trait Tuple2Instances {
+  implicit val tuple2Bifoldable: Bifoldable[Tuple2] =
+    new Bifoldable[Tuple2] {
+      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)
+
+      def bifoldRight[A, B, C](fab: (A, B), c: Eval[C])(f: (A, Eval[C]) => Eval[C], g: (B, Eval[C]) => Eval[C]): Eval[C] =
+        g(fab._2, f(fab._1, c))
+    }
+}

laws/src/main/scala/cats/laws/BifoldableLaws.scala

@@ -0,0 +1,29 @@
+package cats
+package laws
+
+trait BifoldableLaws[F[_, _]] {
+  implicit def F: Bifoldable[F]
+
+  def bifoldLeftConsistentWithBifoldMap[A, B, C](fab: F[A, B], f: A => C, g: B => C)(implicit C: Monoid[C]): IsEq[C] = {
+    val expected = F.bifoldLeft(fab, C.empty)(
+      (c: C, a: A) => C.combine(c, f(a)),
+      (c: C, b: B) => C.combine(c, g(b))
+    )
+    expected <-> F.bifoldMap(fab)(f)(g)
+  }
+
+  def bifoldRightConsistentWithBifoldMap[A, B, C](fab: F[A, B], f: A => C, g: B => C)(implicit C: Monoid[C]): IsEq[C] = {
+    val expected = F.bifoldRight(fab, Later(C.empty))(
+      (a: A, ec: Eval[C]) => ec.map(c => C.combine(f(a), c)),
+      (b: B, ec: Eval[C]) => ec.map(c => C.combine(g(b), c))
+    )
+    expected.value <-> F.bifoldMap(fab)(f)(g)
+  }
+}
+
+object BifoldableLaws {
+  def apply[F[_, _]](implicit ev: Bifoldable[F]): BifoldableLaws[F] =
+    new BifoldableLaws[F] {
+      def F: Bifoldable[F] = ev
+    }
+}

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

@@ -0,0 +1,26 @@
+package cats
+package laws
+package discipline
+
+import org.scalacheck.Arbitrary
+import org.scalacheck.Prop._
+import org.typelevel.discipline.Laws
+
+trait BifoldableTests[F[_, _]] extends Laws {
+  def laws: BifoldableLaws[F]
+
+  def bifoldable[A: Arbitrary, B: Arbitrary, C: Arbitrary: Monoid: Eq](implicit
+    ArbFAB: Arbitrary[F[A, B]]
+  ): RuleSet =
+    new DefaultRuleSet(
+      name = "bifoldable",
+      parent = None,
+      "bifoldLeft consistent with bifoldMap" -> forAll(laws.bifoldLeftConsistentWithBifoldMap[A, B, C] _),
+      "bifoldRight consistent with bifoldMap" -> forAll(laws.bifoldRightConsistentWithBifoldMap[A, B, C] _)
+    )
+}
+
+object BifoldableTests {
+  def apply[F[_, _]: Bifoldable]: BifoldableTests[F] =
+    new BifoldableTests[F] { def laws: BifoldableLaws[F] = BifoldableLaws[F] }
+}

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

@@ -1,7 +1,7 @@
 package cats
 package tests
 
-import cats.laws.discipline.{TraverseTests, MonadTests, SerializableTests, CartesianTests}
+import cats.laws.discipline.{BifoldableTests, TraverseTests, MonadTests, SerializableTests, CartesianTests}
 import cats.laws.discipline.eq._
 import algebra.laws.OrderLaws
 
@@ -18,6 +18,9 @@ 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]))
+
   val partialOrder = eitherPartialOrder[Int, String]
   val order = implicitly[Order[Either[Int, String]]]
   val monad = implicitly[Monad[Either[Int, ?]]]

tests/src/test/scala/cats/tests/MonadCombineTests.scala

@@ -0,0 +1,18 @@
+package cats
+package tests
+
+import cats.data.Xor
+import cats.laws.discipline.arbitrary.xorArbitrary
+import cats.laws.discipline.eq.tuple2Eq
+
+class MonadCombineTest extends CatsSuite {
+  test("separate") {
+    forAll { (list: List[Xor[Int, String]]) =>
+      val ints = list.collect { case Xor.Left(i) => i }
+      val strings = list.collect { case Xor.Right(s) => s }
+      val expected = (ints, strings)
+
+      MonadCombine[List].separate(list) should === (expected)
+    }
+  }
+}

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

@@ -0,0 +1,9 @@
+package cats
+package tests
+
+import cats.laws.discipline.{BifoldableTests, SerializableTests}
+
+class TupleTests extends CatsSuite {
+  checkAll("Tuple2", BifoldableTests[Tuple2].bifoldable[Int, Int, Int])
+  checkAll("Bifoldable[Tuple2]", SerializableTests.serializable(Bifoldable[Tuple2]))
+}

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

@@ -3,8 +3,9 @@ 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, TraverseTests, MonadErrorTests, SerializableTests, CartesianTests}
+import cats.laws.discipline.{BifunctorTests, BifoldableTests, TraverseTests, MonadErrorTests, SerializableTests, CartesianTests}
 import cats.laws.discipline.eq.tuple3Eq
 import algebra.laws.{GroupLaws, OrderLaws}
 import org.scalacheck.{Arbitrary, Gen}
@@ -55,6 +56,10 @@ class XorTests extends CatsSuite {
   }
 
   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]))
 
   test("catchOnly catches matching exceptions") {
     assert(Xor.catchOnly[NumberFormatException]{ "foo".toInt }.isInstanceOf[Xor.Left[NumberFormatException]])