Add rethrowT method to EitherT

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

@@ -44,6 +44,12 @@ final case class EitherT[F[_], A, B](value: F[Either[A, B]]) {
       case other                        => F.pure(other)
     })
 
+  /**
+   * Inverse of `MonadError#attemptT`
+   */
+  def rethrowT(implicit F: MonadError[F, A]): F[B] =
+    F.rethrow(value)
+
   def valueOr[BB >: B](f: A => BB)(implicit F: Functor[F]): F[BB] = fold(f, identity)
 
   def valueOrF[BB >: B](f: A => F[BB])(implicit F: Monad[F]): F[BB] =

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

@@ -18,10 +18,12 @@ final class MonadErrorOps[F[_], E, A](private val fa: F[A]) extends AnyVal {
   def ensureOr(error: A => E)(predicate: A => Boolean)(implicit F: MonadError[F, E]): F[A] =
     F.ensureOr(fa)(error)(predicate)
 
+  /**
+   * Turns a successful value into the error returned by a given partial function if it is
+   * in the partial function's domain.
+   */
   def reject(pf: PartialFunction[A, E])(implicit F: MonadError[F, E]): F[A] =
-    F.flatMap(fa) { a =>
-      pf.andThen(F.raiseError[A]).applyOrElse(a, (_: A) => fa)
-    }
+    F.flatMap(fa)(pf.andThen(F.raiseError[A]).applyOrElse(_, (_: A) => fa))
 
   def adaptError(pf: PartialFunction[E, E])(implicit F: MonadError[F, E]): F[A] =
     F.adaptError(fa)(pf)

tests/src/test/scala/cats/tests/EitherTSuite.scala

@@ -7,6 +7,7 @@ import cats.data.EitherT
 import cats.laws.discipline._
 import cats.laws.discipline.arbitrary._
 import cats.kernel.laws.discipline.{EqTests, MonoidTests, OrderTests, PartialOrderTests, SemigroupTests}
+import scala.util.{Failure, Success, Try}
 
 class EitherTSuite extends CatsSuite {
   implicit val iso = SemigroupalTests.Isomorphisms
@@ -270,6 +271,20 @@ class EitherTSuite extends CatsSuite {
     eithert.recoverWith { case "noteithert" => EitherT.pure[Id, String](5) } should ===(eithert)
   }
 
+  test("rethrowT is inverse of attemptT when applied to a successful value") {
+    implicit val eqThrow: Eq[Throwable] = Eq.fromUniversalEquals
+    val success: Try[Int] = Success(42)
+
+    success.attemptT.rethrowT should ===(success)
+  }
+
+  test("rethrowT is inverse of attemptT when applied to a failed value") {
+    implicit val eqThrow: Eq[Throwable] = Eq.fromUniversalEquals
+    val failed: Try[Int] = Failure(new IllegalArgumentException("error"))
+
+    failed.attemptT.rethrowT should ===(failed)
+  }
+
   test("transform consistent with value.map") {
     forAll { (eithert: EitherT[List, String, Int], f: Either[String, Int] => Either[Long, Double]) =>
       eithert.transform(f) should ===(EitherT(eithert.value.map(f)))

tests/src/test/scala/cats/tests/MonadErrorSuite.scala

@@ -38,22 +38,29 @@ class MonadErrorSuite extends CatsSuite {
     failed.ensureOr(_ => otherValue)(_ => true) should ===(failed)
   }
 
-  test("ensureP returns the successful value if the partial function is not defined") {
+  test("reject returns the successful value if the partial function is not defined") {
     successful.reject {
       case i if i < 0 => failedValue
     } should ===(successful)
   }
 
-  test("ensureP returns the original failure, when applied to a failure") {
+  test("reject returns the original failure, when applied to a failure") {
     failed.reject {
       case i if i < 0 => otherValue
     } should ===(failed)
   }
 
-  test("ensureP raises an error if the partial function is defined") {
+  test("reject raises an error if the partial function is defined") {
     successful.reject {
       case i if i > 0 => failedValue
     } should ===(failed)
   }
 
+  test("rethrow returns the failure, when applied to a Left of a failure") {
+    failed.attempt.rethrow should ===(failed)
+  }
+
+  test("rethrow returns the successful value, when applied to a Right of a successful value") {
+    successful.attempt.rethrow should ===(successful)
+  }
 }