Adding sequenceM method to Traverse

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

@@ -58,11 +58,11 @@ import simulacrum.typeclass
    * scala> import cats.implicits._
    * scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
    * scala> val x = Option(List("1", "two", "3"))
-   * scala> x.traverseM(_.map(parseInt))
+   * scala> x.flatTraverse(_.map(parseInt))
    * res0: List[Option[Int]] = List(Some(1), None, Some(3))
    * }}}
    */
-  def traverseM[G[_], A, B](fa: F[A])(f: A => G[F[B]])(implicit G: Applicative[G], F: FlatMap[F]): G[F[B]] =
+  def flatTraverse[G[_], A, B](fa: F[A])(f: A => G[F[B]])(implicit G: Applicative[G], F: FlatMap[F]): G[F[B]] =
     G.map(traverse(fa)(f))(F.flatten)
 
   /**
@@ -83,6 +83,24 @@ import simulacrum.typeclass
   def sequence[G[_]: Applicative, A](fga: F[G[A]]): G[F[A]] =
     traverse(fga)(ga => ga)
 
+  /**
+   * Thread all the G effects through the F structure and flatten to invert the
+   * structure from F[G[F[A]]] to G[F[A]].
+   *
+   * Example:
+   * {{{
+   * scala> import cats.implicits._
+   * scala> val x: List[Option[List[Int]]] = List(Some(List(1, 2)), Some(List(3)))
+   * scala> val y: List[Option[List[Int]]] = List(None, Some(List(3)))
+   * scala> x.flatSequence
+   * res0: Option[List[Int]] = Some(List(1, 2, 3))
+   * scala> y.flatSequence
+   * res1: Option[List[Int]] = None
+   * }}}
+   */
+  def flatSequence[G[_], A](fgfa: F[G[F[A]]])(implicit G: Applicative[G], F: FlatMap[F]): G[F[A]] =
+    G.map(sequence(fgfa))(F.flatten)
+
   /**
    * Behaves just like sequence, but uses [[Unapply]] to find the
    * Applicative instance for G.

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

@@ -122,7 +122,7 @@ object SyntaxTests extends AllInstances with AllSyntax {
     val gfb: G[F[B]] = fa.traverse(f1)
 
     val f2 = mock[A => G[F[B]]]
-    val gfb2: G[F[B]] = fa.traverseM(f2)
+    val gfb2: G[F[B]] = fa.flatTraverse(f2)
 
     val fga = mock[F[G[A]]]
     val gunit: G[F[A]] = fga.sequence