Partial revert of #1289

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.
    *
    * 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/Foldable.scala

@@ -207,7 +207,7 @@ 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 `scala.util.Either`
    *
    * {{{
    * scala> import cats.implicits._
@@ -251,7 +251,7 @@ 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 `scala.util.Either`
    *
    * {{{
    * scala> import cats.implicits._

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

@@ -1,6 +1,7 @@
 package cats
 package arrow
 
+import cats.data.Xor
 import simulacrum.typeclass
 
 @typeclass trait Choice[F[_, _]] extends Category[F] {
@@ -11,35 +12,37 @@ 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: Xor[Boolean, 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: (Xor[Int, 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.{Coproduct, Xor}
 
 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/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 [[cats.data.Xor]].
  *
- * @param run The underlying [[scala.util.Either]].
+ * @param run The underlying [[cats.data.Xor]].
  */
-final case class Coproduct[F[_], G[_], A](run: Either[F[A], G[A]]) {
+final case class Coproduct[F[_], G[_], A](run: Xor[F[A], 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[Xor[F[A], 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, ?]] =

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

@@ -393,7 +393,7 @@ private[data] trait EitherTMonadError[F[_], L] extends MonadError[EitherT[F, L,
       case r @ Right(_) => F.pure(r)
     })
   def raiseError[A](e: L): EitherT[F, L, A] = EitherT.left(F.pure(e))
-  override def attempt[A](fla: EitherT[F, L, A]): EitherT[F, L, Either[L, A]] = EitherT.right(fla.value)
+  override def attempt[A](fla: EitherT[F, L, A]): EitherT[F, L, Xor[L, A]] = EitherT.right(F.map(fla.value)(_.toXor))
   override def recover[A](fla: EitherT[F, L, A])(pf: PartialFunction[L, A]): EitherT[F, L, A] =
     fla.recover(pf)
   override def recoverWith[A](fla: EitherT[F, L, A])(pf: PartialFunction[L, EitherT[F, L, A]]): EitherT[F, L, A] =

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

@@ -11,14 +11,14 @@ import scala.annotation.tailrec
  *  - `[[Ior.Right Right]][B]`
  *  - `[[Ior.Both Both]][A, B]`
  *
- * `A [[Ior]] B` is similar to `Either[A, B]`, except that it can represent the simultaneous presence of
+ * `A [[Ior]] B` is similar to `Xor[A, B]`, except that it can represent the simultaneous presence of
  * an `A` and a `B`. It is right-biased so methods such as `map` and `flatMap` operate on the
  * `B` value. Some methods, like `flatMap`, handle the presence of two [[Ior.Both Both]] values using a
- * `[[Semigroup]][A]`, while other methods, like [[toEither]], ignore the `A` value in a [[Ior.Both Both]].
+ * `[[Semigroup]][A]`, while other methods, like [[toXor]], ignore the `A` value in a [[Ior.Both Both]].
  *
- * `A [[Ior]] B` is isomorphic to `Either[Either[A, B], (A, B)]`, but provides methods biased toward `B`
+ * `A [[Ior]] B` is isomorphic to `Xor[Xor[A, B], (A, B)]`, but provides methods biased toward `B`
  * values, regardless of whether the `B` values appear in a [[Ior.Right Right]] or a [[Ior.Both Both]].
- * The isomorphic [[scala.util.Either]] form can be accessed via the [[unwrap]] method.
+ * The isomorphic [[cats.data.Xor]] form can be accessed via the [[unwrap]] method.
  */
 sealed abstract class Ior[+A, +B] extends Product with Serializable {
 
@@ -36,10 +36,10 @@ sealed abstract class Ior[+A, +B] extends Product with Serializable {
   final def right: Option[B] = fold(_ => None, b => Some(b), (_, b) => Some(b))
   final def onlyLeft: Option[A] = fold(a => Some(a), _ => None, (_, _) => None)
   final def onlyRight: Option[B] = fold(_ => None, b => Some(b), (_, _) => None)
-  final def onlyLeftOrRight: Option[Either[A, B]] = fold(a => Some(Left(a)), b => Some(Right(b)), (_, _) => None)
+  final def onlyLeftOrRight: Option[Xor[A, B]] = fold(a => Some(Xor.Left(a)), b => Some(Xor.Right(b)), (_, _) => None)
   final def onlyBoth: Option[(A, B)] = fold(_ => None, _ => None, (a, b) => Some((a, b)))
   final def pad: (Option[A], Option[B]) = fold(a => (Some(a), None), b => (None, Some(b)), (a, b) => (Some(a), Some(b)))
-  final def unwrap: Either[Either[A, B], (A, B)] = fold(a => Left(Left(a)), b => Left(Right(b)), (a, b) => Right((a, b)))
+  final def unwrap: Xor[Xor[A, B], (A, B)] = fold(a => Xor.Left(Xor.Left(a)), b => Xor.Left(Xor.Right(b)), (a, b) => Xor.Right((a, b)))
 
   final def toXor: A Xor B = fold(Xor.left, Xor.right, (_, b) => Xor.right(b))
   final def toEither: Either[A, B] = fold(Left(_), Right(_), (_, b) => Right(b))

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

@@ -101,7 +101,7 @@ private[data] sealed abstract class KleisliInstances extends KleisliInstances0 {
     new Choice[Kleisli[F, ?, ?]] {
       def id[A]: Kleisli[F, A, A] = Kleisli(ev.pure(_))
 
-      def choice[A, B, C](f: Kleisli[F, A, C], g: Kleisli[F, B, C]): Kleisli[F, Either[A, B], C] =
+      def choice[A, B, C](f: Kleisli[F, A, C], g: Kleisli[F, B, C]): Kleisli[F, Xor[A, B], C] =
         Kleisli(_.fold(f.run, g.run))
 
       def compose[A, B, C](f: Kleisli[F, B, C], g: Kleisli[F, A, B]): Kleisli[F, A, C] =

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

@@ -86,11 +86,11 @@ final case class OptionT[F[_], A](value: F[Option[A]]) {
         case None => default
       })
 
-  def toRight[L](left: => L)(implicit F: Functor[F]): EitherT[F, L, A] =
-    EitherT(cata(Left(left), Right.apply))
+  def toRight[L](left: => L)(implicit F: Functor[F]): XorT[F, L, A] =
+    XorT(cata(Xor.Left(left), Xor.Right.apply))
 
-  def toLeft[R](right: => R)(implicit F: Functor[F]): EitherT[F, A, R] =
-    EitherT(cata(Right(right), Left.apply))
+  def toLeft[R](right: => R)(implicit F: Functor[F]): XorT[F, A, R] =
+    XorT(cata(Xor.Right(right), Xor.Left.apply))
 
   def show(implicit F: Show[F[Option[A]]]): String = F.show(value)
 

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

@@ -80,11 +80,11 @@ sealed abstract class Validated[+E, +A] extends Product with Serializable {
   def toXor: Xor[E, A] = fold(Xor.Left.apply, Xor.Right.apply)
 
   /**
-   * Convert to an Either, apply a function, convert back.  This is handy
-   * when you want to use the Monadic properties of the Either type.
+   * Convert to an Xor, apply a function, convert back.  This is handy
+   * when you want to use the Monadic properties of the Xor type.
    */
-  def withEither[EE, B](f: Either[E, A] => Either[EE, B]): Validated[EE, B] =
-    Validated.fromEither(f(toEither))
+  def withXor[EE, B](f: Xor[E, A] => Xor[EE, B]): Validated[EE, B] =
+    Validated.fromXor(f(toXor))
 
   /**
    * Validated is a [[functor.Bifunctor]], this method applies one of the
@@ -391,6 +391,11 @@ trait ValidatedFunctions {
    */
   def fromEither[A, B](e: Either[A, B]): Validated[A, B] = e.fold(invalid, valid)
 
+  /**
+   * Converts an `Xor[A, B]` to an `Validated[A, B]`.
+   */
+  def fromXor[A, B](e: Xor[A, B]): Validated[A, B] = e.fold(invalid, valid)
+
   /**
    * Converts an `Option[B]` to an `Validated[A, B]`, where the provided `ifNone` values is returned on
    * the invalid of the `Validated` when the specified `Option` is `None`.

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

@@ -278,7 +278,7 @@ private[data] sealed abstract class XorInstances extends XorInstances1 {
       override def map[B, C](fa: A Xor B)(f: B => C): A Xor C = fa.map(f)
       override def map2Eval[B, C, Z](fb: A Xor B, fc: Eval[A Xor C])(f: (B, C) => Z): Eval[A Xor Z] =
         fb.map2Eval(fc)(f)
-      override def attempt[B](fab: A Xor B): A Xor (Either[A, B]) = Xor.right(fab.toEither)
+      override def attempt[B](fab: A Xor B): A Xor (Xor[A, B]) = Xor.right(fab)
       override def recover[B](fab: A Xor B)(pf: PartialFunction[A, B]): A Xor B =
         fab recover pf
       override def recoverWith[B](fab: A Xor B)(pf: PartialFunction[A, A Xor B]): A Xor B =

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

@@ -403,7 +403,7 @@ private[data] trait XorTMonadError[F[_], L] extends MonadError[XorT[F, L, ?], L]
       case r @ Xor.Right(_) => F.pure(r)
     })
   def raiseError[A](e: L): XorT[F, L, A] = XorT.left(F.pure(e))
-  override def attempt[A](fla: XorT[F, L, A]): XorT[F, L, Either[L, A]] = XorT.right(fla.toEither)
+  override def attempt[A](fla: XorT[F, L, A]): XorT[F, L, Xor[L, A]] = XorT.right(fla.value)
   override def recover[A](fla: XorT[F, L, A])(pf: PartialFunction[L, A]): XorT[F, L, A] =
     fla.recover(pf)
   override def recoverWith[A](fla: XorT[F, L, A])(pf: PartialFunction[L, XorT[F, L, A]]): XorT[F, L, A] =

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

@@ -1,6 +1,7 @@
 package cats
 package instances
 
+import cats.data.Xor
 import cats.syntax.EitherUtil
 import cats.syntax.either._
 import scala.annotation.tailrec
@@ -71,7 +72,7 @@ trait EitherInstances extends EitherInstances1 {
       def foldRight[B, C](fa: Either[A, B], lc: Eval[C])(f: (B, Eval[C]) => Eval[C]): Eval[C] =
         fa.fold(_ => lc, b => f(b, lc))
 
-      override def attempt[B](fab: Either[A, B]): Either[A, Either[A, B]] = Right(fab)
+      override def attempt[B](fab: Either[A, B]): Either[A, Xor[A, B]] = Right(fab.toXor)
       override def recover[B](fab: Either[A, B])(pf: PartialFunction[A, B]): Either[A, B] =
         fab recover pf
       override def recoverWith[B](fab: Either[A, B])(pf: PartialFunction[A, Either[A, B]]): Either[A, B] =

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

@@ -2,6 +2,7 @@ package cats
 package instances
 
 import cats.arrow.{Arrow, Choice}
+import cats.data.Xor
 import cats.functor.Contravariant
 import annotation.tailrec
 
@@ -70,10 +71,10 @@ private[instances] sealed trait Function1Instances extends Function1Instances0 {
 
   implicit val catsStdInstancesForFunction1: Choice[Function1] with Arrow[Function1] =
     new Choice[Function1] with Arrow[Function1] {
-      def choice[A, B, C](f: A => C, g: B => C): Either[A, B] => C =
+      def choice[A, B, C](f: A => C, g: B => C): Xor[A, B] => C =
         _ match {
-          case Left(a)  => f(a)
-          case Right(b) => g(b)
+          case Xor.Left(a)  => f(a)
+          case Xor.Right(b) => g(b)
         }
 
       def lift[A, B](f: A => B): A => B = f

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

@@ -1,6 +1,7 @@
 package cats
 package instances
 
+import cats.data.Xor
 import scala.util.control.NonFatal
 import scala.concurrent.{ExecutionContext, Future}
 
@@ -27,8 +28,8 @@ trait FutureInstances extends FutureInstances1 {
       def raiseError[A](e: Throwable): Future[A] = Future.failed(e)
       override def handleError[A](fea: Future[A])(f: Throwable => A): Future[A] = fea.recover { case t => f(t) }
 
-      override def attempt[A](fa: Future[A]): Future[Either[Throwable, A]] =
-        (fa.map(a => Right[Throwable, A](a))) recover { case NonFatal(t) => Left(t) }
+      override def attempt[A](fa: Future[A]): Future[Xor[Throwable, A]] =
+        (fa.map(a => Xor.Right(a))) recover { case NonFatal(t) => Xor.Left(t) }
 
       override def recover[A](fa: Future[A])(pf: PartialFunction[Throwable, A]): Future[A] = fa.recover(pf)
 

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

@@ -3,6 +3,7 @@ package instances
 
 import TryInstances.castFailure
 
+import cats.data.Xor
 import scala.util.control.NonFatal
 import scala.util.{Failure, Success, Try}
 import scala.annotation.tailrec
@@ -66,8 +67,8 @@ trait TryInstances extends TryInstances1 {
       override def handleError[A](ta: Try[A])(f: Throwable => A): Try[A] =
         ta.recover { case t => f(t) }
 
-      override def attempt[A](ta: Try[A]): Try[Either[Throwable, A]] =
-        (ta.map(a => Right[Throwable, A](a))) recover { case NonFatal(t) => Left(t) }
+      override def attempt[A](ta: Try[A]): Try[Xor[Throwable, A]] =
+        (ta.map(a => Xor.Right(a))) recover { case NonFatal(t) => Xor.Left(t) }
 
       override def recover[A](ta: Try[A])(pf: PartialFunction[Throwable, A]): Try[A] =
         ta.recover(pf)

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

@@ -1,7 +1,7 @@
 package cats
 package syntax
 
-import cats.data.EitherT
+import cats.data.{Xor, XorT}
 
 trait ApplicativeErrorSyntax {
   implicit def catsSyntaxApplicativeErrorId[E](e: E): ApplicativeErrorIdOps[E] =
@@ -24,10 +24,10 @@ final class ApplicativeErrorOps[F[_], E, A](fa: F[A])(implicit F: ApplicativeErr
   def handleErrorWith(f: E => F[A]): F[A] =
     F.handleErrorWith(fa)(f)
 
-  def attempt: F[Either[E, A]] =
+  def attempt: F[Xor[E, A]] =
     F.attempt(fa)
 
-  def attemptT: EitherT[F, E, A] =
+  def attemptT: XorT[F, E, A] =
     F.attemptT(fa)
 
   def recover(pf: PartialFunction[E, A]): F[A] =