Roll-back typelevel#1301 and typelevel#1289 to allow 0.7.0 release.

Due to a communications error we merged some PRs which we had been
planning to keep out of master until after 0.7.0. Since one of them
(typelevel#1289) was large and long-running, it was difficult to undo this
merge in an automated way.

This commit represents the following:

 1. Downloaded patches for PRs 1301 and 1289 from Github
 2. Tried to reverse-apply them (-R)
 3. Fixed rejections/failures manually
 4. Got code compiling and tests passing

The code is now different than it was before the PRs were merged,
but things *seem* to be in a reasonable state. I'm keeping all these
changes in one commit so that it will be easier to "reverse" this
once 0.7.0 is relaesed.

core/src/main/scala/cats/ApplicativeError.scala

@@ -1,6 +1,6 @@
 package cats
 
-import cats.data.EitherT
+import cats.data.{Xor, XorT}
 import scala.util.{ Failure, Success, Try }
 import scala.util.control.NonFatal
 
@@ -37,21 +37,21 @@ trait ApplicativeError[F[_], E] extends Applicative[F] {
   def handleError[A](fa: F[A])(f: E => A): F[A] = handleErrorWith(fa)(f andThen pure)
 
   /**
-   * Handle errors by turning them into [[scala.util.Either]] values.
+   * Handle errors by turning them into [[cats.data.Xor]] values.
    *
-   * If there is no error, then an `scala.util.Right` value will be returned instead.
+   * If there is no error, then an [[cats.data.Xor.Right]] value will be returned instead.
    *
    * All non-fatal errors should be handled by this method.
    */
-  def attempt[A](fa: F[A]): F[Either[E, A]] = handleErrorWith(
-    map(fa)(Right(_): Either[E, A])
-  )(e => pure(Left(e)))
+  def attempt[A](fa: F[A]): F[Xor[E, A]] = handleErrorWith(
+    map(fa)(Xor.Right(_): Xor[E, A])
+  )(e => pure(Xor.Left(e)))
 
   /**
-   * Similar to [[attempt]], but wraps the result in a [[cats.data.EitherT]] for
+   * Similar to [[attempt]], but wraps the result in a [[cats.data.XorT]] for
    * convenience.
    */
-  def attemptT[A](fa: F[A]): EitherT[F, E, A] = EitherT(attempt(fa))
+  def attemptT[A](fa: F[A]): XorT[F, E, A] = XorT(attempt(fa))
 
   /**
    * Recover from certain errors by mapping them to an `A` value.

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

@@ -17,23 +17,24 @@ import simulacrum.typeclass
    *
    * Example:
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
    *
-   * scala> val rightSome: Either[Option[String], Option[Int]] = Either.right(Some(3))
+   * scala> val rightSome: Option[String] Xor Option[Int] = Xor.right(Some(3))
    * scala> rightSome.bisequence
-   * res0: Option[Either[String, Int]] = Some(Right(3))
+   * res0: Option[String Xor Int] = Some(Right(3))
    *
-   * scala> val rightNone: Either[Option[String], Option[Int]] = Either.right(None)
+   * scala> val rightNone: Option[String] Xor Option[Int] = Xor.right(None)
    * scala> rightNone.bisequence
-   * res1: Option[Either[String, Int]] = None
+   * res1: Option[String Xor Int] = None
    *
-   * scala> val leftSome: Either[Option[String], Option[Int]] = Either.left(Some("foo"))
+   * scala> val leftSome: Option[String] Xor Option[Int] = Xor.left(Some("foo"))
    * scala> leftSome.bisequence
-   * res2: Option[Either[String, Int]] = Some(Left(foo))
+   * res2: Option[String Xor Int] = Some(Left(foo))
    *
-   * scala> val leftNone: Either[Option[String], Option[Int]] = Either.left(None)
+   * scala> val leftNone: Option[String] Xor Option[Int] = Xor.left(None)
    * scala> leftNone.bisequence
-   * res3: Option[Either[String, Int]] = None
+   * res3: Option[String Xor Int] = None
    * }}}
    */
   def bisequence[G[_]: Applicative, A, B](fab: F[G[A], G[B]]): G[F[A, B]] =

core/src/main/scala/cats/Eval.scala

@@ -1,6 +1,7 @@
 package cats
 
 import scala.annotation.tailrec
+import cats.data.Xor
 import cats.syntax.all._
 
 /**
@@ -301,7 +302,11 @@ private[cats] trait EvalInstances extends EvalInstances0 {
       def flatMap[A, B](fa: Eval[A])(f: A => Eval[B]): Eval[B] = fa.flatMap(f)
       def extract[A](la: Eval[A]): A = la.value
       def coflatMap[A, B](fa: Eval[A])(f: Eval[A] => B): Eval[B] = Later(f(fa))
-      def tailRecM[A, B](a: A)(f: A => Eval[Either[A, B]]): Eval[B] = defaultTailRecM(a)(f)
+      def tailRecM[A, B](a: A)(f: A => Eval[Xor[A, B]]): Eval[B] =
+        f(a).flatMap(_ match {
+          case Xor.Left(a1) => tailRecM(a1)(f) // recursion OK here, since flatMap is lazy
+          case Xor.Right(b) => Eval.now(b)
+        })
     }
 
   implicit def catsOrderForEval[A: Order]: Order[Eval[A]] =

core/src/main/scala/cats/FlatMap.scala

@@ -2,6 +2,8 @@ package cats
 
 import simulacrum.typeclass
 
+import cats.data.Xor
+
 /**
  * FlatMap type class gives us flatMap, which allows us to have a value
  * in a context (F[A]) and then feed that into a function that takes
@@ -92,7 +94,7 @@ import simulacrum.typeclass
     flatMap(fa)(if (_) ifTrue else ifFalse)
 
   /**
-   * Keeps calling `f` until a `scala.util.Right[B]` is returned.
+   * Keeps calling `f` until a `[[Right]][B]` is returned.
    *
    * Based on Phil Freeman's
    * [[http://functorial.com/stack-safety-for-free/index.pdf Stack Safety for Free]].
@@ -105,5 +107,5 @@ import simulacrum.typeclass
    * using recursive flatMap. Such an implementation will only be stack safe if
    * the Monad is trampolined.
    */
-  def tailRecM[A, B](a: A)(f: A => F[Either[A, B]]): F[B]
+  def tailRecM[A, B](a: A)(f: A => F[Xor[A, B]]): F[B]
 }

core/src/main/scala/cats/Foldable.scala

@@ -186,8 +186,9 @@ import simulacrum.typeclass
    * For example:
    *
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
-   * scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
+   * scala> def parseInt(s: String): Option[Int] = Xor.catchOnly[NumberFormatException](s.toInt).toOption
    * scala> val F = Foldable[List]
    * scala> F.traverse_(List("333", "444"))(parseInt)
    * res0: Option[Unit] = Some(())
@@ -207,18 +208,19 @@ import simulacrum.typeclass
   /**
    * Behaves like traverse_, but uses [[Unapply]] to find the
    * [[Applicative]] instance for `G` - used when `G` is a
-   * type constructor with two or more parameters such as [[scala.util.Either]]
+   * type constructor with two or more parameters such as [[cats.data.Xor]]
    *
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
-   * scala> def parseInt(s: String): Either[String, Int] =
-   *      |   try { Right(s.toInt) }
-   *      |   catch { case _: NumberFormatException => Left("boo") }
+   * scala> def parseInt(s: String): Xor[String, Int] =
+   *      |   try { Xor.Right(s.toInt) }
+   *      |   catch { case _: NumberFormatException => Xor.Left("boo") }
    * scala> val F = Foldable[List]
    * scala> F.traverseU_(List("333", "444"))(parseInt)
-   * res0: Either[String, Unit] = Right(())
+   * res0: Xor[String, Unit] = Right(())
    * scala> F.traverseU_(List("333", "zzz"))(parseInt)
-   * res1: Either[String, Unit] = Left(boo)
+   * res1: Xor[String, Unit] = Left(boo)
    * }}}
    *
    * Note that using `traverse_` instead of `traverseU_` would not compile without
@@ -251,15 +253,16 @@ import simulacrum.typeclass
   /**
    * Behaves like sequence_, but uses [[Unapply]] to find the
    * [[Applicative]] instance for `G` - used when `G` is a
-   * type constructor with two or more parameters such as [[scala.util.Either]]
+   * type constructor with two or more parameters such as [[cats.data.Xor]]
    *
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
    * scala> val F = Foldable[List]
-   * scala> F.sequenceU_(List(Either.right[String, Int](333), Right(444)))
-   * res0: Either[String, Unit] = Right(())
-   * scala> F.sequenceU_(List(Either.right[String, Int](333), Left("boo")))
-   * res1: Either[String, Unit] = Left(boo)
+   * scala> F.sequenceU_(List(Xor.right[String, Int](333), Xor.Right(444)))
+   * res0: Xor[String, Unit] = Right(())
+   * scala> F.sequenceU_(List(Xor.right[String, Int](333), Xor.Left("boo")))
+   * res1: Xor[String, Unit] = Left(boo)
    * }}}
    *
    * Note that using `sequence_` instead of `sequenceU_` would not compile without

core/src/main/scala/cats/Monad.scala

@@ -2,6 +2,8 @@ package cats
 
 import simulacrum.typeclass
 
+import cats.data.Xor
+
 /**
  * Monad.
  *
@@ -21,9 +23,9 @@ import simulacrum.typeclass
    * to write this method (all cats types have a stack safe version
    * of this). When this method is safe you can find an `implicit r: RecursiveTailRecM`.
    */
-  protected def defaultTailRecM[A, B](a: A)(fn: A => F[Either[A, B]]): F[B] =
+  protected def defaultTailRecM[A, B](a: A)(fn: A => F[Xor[A, B]]): F[B] =
     flatMap(fn(a)) {
-      case Right(b) => pure(b)
-      case Left(nextA) => defaultTailRecM(nextA)(fn)
+      case Xor.Right(b) => pure(b)
+      case Xor.Left(nextA) => defaultTailRecM(nextA)(fn)
     }
 }

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

@@ -11,7 +11,7 @@ import simulacrum.typeclass
    * Fold over the inner structure to combine all of the values with
    * our combine method inherited from MonoidK. The result is for us
    * to accumulate all of the "interesting" values of the inner G, so
-   * if G is Option, we collect all the Some values, if G is Either,
+   * if G is Option, we collect all the Some values, if G is Xor,
    * we collect all the Right values, etc.
    */
   def unite[G[_], A](fga: F[G[A]])(implicit G: Foldable[G]): F[A] =

core/src/main/scala/cats/Traverse.scala

@@ -22,8 +22,9 @@ import simulacrum.typeclass
    *
    * Example:
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
-   * scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
+   * scala> def parseInt(s: String): Option[Int] = Xor.catchOnly[NumberFormatException](s.toInt).toOption
    * scala> List("1", "2", "3").traverse(parseInt)
    * res0: Option[List[Int]] = Some(List(1, 2, 3))
    * scala> List("1", "two", "3").traverse(parseInt)
@@ -38,13 +39,14 @@ import simulacrum.typeclass
    *
    * Example:
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
-   * scala> def parseInt(s: String): Either[String, Int] = Either.catchOnly[NumberFormatException](s.toInt).leftMap(_ => "no number")
+   * scala> def parseInt(s: String): Xor[String, Int] = Xor.catchOnly[NumberFormatException](s.toInt).leftMap(_ => "no number")
    * scala> val ns = List("1", "2", "3")
    * scala> ns.traverseU(parseInt)
-   * res0: Either[String, List[Int]] = Right(List(1, 2, 3))
-   * scala> ns.traverse[Either[String, ?], Int](parseInt)
-   * res1: Either[String, List[Int]] = Right(List(1, 2, 3))
+   * res0: Xor[String, List[Int]] = Right(List(1, 2, 3))
+   * scala> ns.traverse[Xor[String, ?], Int](parseInt)
+   * res1: Xor[String, List[Int]] = Right(List(1, 2, 3))
    * }}}
    */
   def traverseU[A, GB](fa: F[A])(f: A => GB)(implicit U: Unapply[Applicative, GB]): U.M[F[U.A]] =
@@ -55,8 +57,9 @@ import simulacrum.typeclass
    *
    * Example:
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
-   * scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
+   * scala> def parseInt(s: String): Option[Int] = Xor.catchOnly[NumberFormatException](s.toInt).toOption
    * scala> val x = Option(List("1", "two", "3"))
    * scala> x.traverseM(_.map(parseInt))
    * res0: List[Option[Int]] = List(Some(1), None, Some(3))

core/src/main/scala/cats/arrow/Choice.scala

@@ -1,6 +1,8 @@
 package cats
 package arrow
 
+import cats.data.Xor
+
 import simulacrum.typeclass
 
 @typeclass trait Choice[F[_, _]] extends Category[F] {
@@ -11,35 +13,37 @@ import simulacrum.typeclass
    *
    * Example:
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
    * scala> val b: Boolean => String = _ + " is a boolean"
    * scala> val i: Int => String =  _ + " is an integer"
-   * scala> val f: (Either[Boolean, Int]) => String = Choice[Function1].choice(b, i)
+   * scala> val f: (Boolean Xor Int) => String = Choice[Function1].choice(b, i)
    *
-   * scala> f(Right(3))
+   * scala> f(Xor.right(3))
    * res0: String = 3 is an integer
    *
-   * scala> f(Left(false))
+   * scala> f(Xor.left(false))
    * res0: String = false is a boolean
    * }}}
    */
-  def choice[A, B, C](f: F[A, C], g: F[B, C]): F[Either[A, B], C]
+  def choice[A, B, C](f: F[A, C], g: F[B, C]): F[Xor[A, B], C]
 
   /**
    * An `F` that, given a source `A` on either the right or left side, will
    * return that same `A` object.
    *
    * Example:
    * {{{
+   * scala> import cats.data.Xor
    * scala> import cats.implicits._
-   * scala> val f: (Either[Int, Int]) => Int = Choice[Function1].codiagonal[Int]
+   * scala> val f: (Int Xor Int) => Int = Choice[Function1].codiagonal[Int]
    *
-   * scala> f(Right(3))
+   * scala> f(Xor.right(3))
    * res0: Int = 3
    *
-   * scala> f(Left(3))
+   * scala> f(Xor.left(3))
    * res1: Int = 3
    * }}}
    */
-  def codiagonal[A]: F[Either[A, A], A] = choice(id, id)
+  def codiagonal[A]: F[Xor[A, A], A] = choice(id, id)
 }

core/src/main/scala/cats/arrow/FunctionK.scala

@@ -1,7 +1,7 @@
 package cats
 package arrow
 
-import cats.data. Coproduct
+import cats.data.{Xor, Coproduct}
 
 trait FunctionK[F[_], G[_]] extends Serializable { self =>
   def apply[A](fa: F[A]): G[A]
@@ -17,8 +17,8 @@ trait FunctionK[F[_], G[_]] extends Serializable { self =>
   def or[H[_]](h: FunctionK[H, G]): FunctionK[Coproduct[F, H, ?], G] =
     new FunctionK[Coproduct[F, H, ?], G] {
       def apply[A](fa: Coproduct[F, H, A]): G[A] = fa.run match {
-        case Left(ff) => self(ff)
-        case Right(gg) => h(gg)
+        case Xor.Left(ff) => self(ff)
+        case Xor.Right(gg) => h(gg)
       }
     }
 }

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

@@ -58,12 +58,12 @@ private[data] sealed abstract class CokleisliInstances extends CokleisliInstance
     override def map[B, C](fa: Cokleisli[F, A, B])(f: B => C): Cokleisli[F, A, C] =
       fa.map(f)
 
-    def tailRecM[B, C](b: B)(fn: B => Cokleisli[F, A, Either[B, C]]): Cokleisli[F, A, C] =
+    def tailRecM[B, C](b: B)(fn: B => Cokleisli[F, A, Xor[B, C]]): Cokleisli[F, A, C] =
       Cokleisli({ (fa: F[A]) =>
         @tailrec
-        def loop(c: Cokleisli[F, A, Either[B, C]]): C = c.run(fa) match {
-          case Right(c) => c
-          case Left(bb) => loop(fn(bb))
+        def loop(c: Cokleisli[F, A, Xor[B, C]]): C = c.run(fa) match {
+          case Xor.Right(c) => c
+          case Xor.Left(bb) => loop(fn(bb))
         }
         loop(fn(b))
       })

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

@@ -3,13 +3,12 @@ package data
 
 import cats.arrow.FunctionK
 import cats.functor.Contravariant
-import cats.syntax.either._
 
-/** `F` on the left and `G` on the right of [[scala.util.Either]].
+/** `F` on the left and `G` on the right of [[Xor]].
  *
- * @param run The underlying [[scala.util.Either]].
+ * @param run The underlying [[Xor]].
  */
-final case class Coproduct[F[_], G[_], A](run: Either[F[A], G[A]]) {
+final case class Coproduct[F[_], G[_], A](run: F[A] Xor G[A]) {
 
   import Coproduct._
 
@@ -87,17 +86,17 @@ final case class Coproduct[F[_], G[_], A](run: Either[F[A], G[A]]) {
 object Coproduct extends CoproductInstances {
 
   def leftc[F[_], G[_], A](x: F[A]): Coproduct[F, G, A] =
-    Coproduct(Left(x))
+    Coproduct(Xor.left(x))
 
   def rightc[F[_], G[_], A](x: G[A]): Coproduct[F, G, A] =
-    Coproduct(Right(x))
+    Coproduct(Xor.right(x))
 
   final class CoproductLeft[G[_]] private[Coproduct] {
-    def apply[F[_], A](fa: F[A]): Coproduct[F, G, A] = Coproduct(Left(fa))
+    def apply[F[_], A](fa: F[A]): Coproduct[F, G, A] = Coproduct(Xor.left(fa))
   }
 
   final class CoproductRight[F[_]] private[Coproduct] {
-    def apply[G[_], A](ga: G[A]): Coproduct[F, G, A] = Coproduct(Right(ga))
+    def apply[G[_], A](ga: G[A]): Coproduct[F, G, A] = Coproduct(Xor.right(ga))
   }
 
   def left[G[_]]: CoproductLeft[G] = new CoproductLeft[G]
@@ -107,7 +106,7 @@ object Coproduct extends CoproductInstances {
 
 private[data] sealed abstract class CoproductInstances3 {
 
-  implicit def catsDataEqForCoproduct[F[_], G[_], A](implicit E: Eq[Either[F[A], G[A]]]): Eq[Coproduct[F, G, A]] =
+  implicit def catsDataEqForCoproduct[F[_], G[_], A](implicit E: Eq[F[A] Xor G[A]]): Eq[Coproduct[F, G, A]] =
     Eq.by(_.run)
 
   implicit def catsDataFunctorForCoproduct[F[_], G[_]](implicit F0: Functor[F], G0: Functor[G]): Functor[Coproduct[F, G, ?]] =