Add traverseWithStateM to Traverse

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

@@ -130,4 +130,38 @@ import simulacrum.typeclass
    */
   def zipWithIndex[A](fa: F[A]): F[(A, Int)] =
     mapWithIndex(fa)((a, i) => (a, i))
+
+  /**
+   * Statefully traverse through the structure F while carrying and updating a
+   * value of type S.
+   *
+   * Value `s0` is used as the initial state and function `fs` is used
+   * to update the state after each application of `f` through the structure.
+   *
+   * Function `fs` can update the state using the current traversal value, the
+   * previous state, and the output of the current application of `f`.
+   *
+   * Both the final state value and the traversed result are returned.
+   *
+   * The parameters are grouped in this order for better type inferencing.
+   *
+   * @see [[traverseWithStateMA]] if the final state value isn't needed.
+   */
+  def traverseWithStateM[G[_], A, S, B](fa: F[A])(s0: S)(f: (A, S) => G[B])(fs: (A, S, B) => S)(implicit G: Monad[G]): G[(S, F[B])] =
+    internalTraverseWithStateM(fa)(s0)(f)(fs).run(s0)
+
+  /**
+   * Statefully traverse through the structure F while carrying and updating a
+   * value of type S.
+   *
+   * This is identical to [[traverseWithStateM]] except it does not
+   * include the final state value in the result.
+   */
+  def traverseWithStateMA[G[_], A, S, B](fa: F[A])(s0: S)(f: (A, S) => G[B])(fs: (A, S, B) => S)(implicit G: Monad[G]): G[F[B]] =
+    internalTraverseWithStateM(fa)(s0)(f)(fs).runA(s0)
+
+  private[this] def internalTraverseWithStateM[G[_], A, S, B](
+    fa: F[A])(s0: S)(f: (A, S) => G[B])(fs: (A, S, B) => S)(implicit G: Monad[G]
+  ): StateT[G, S, F[B]] =
+    traverse(fa)(a => StateT[G, S, B](s => G.map(f(a, s))(b => (fs(a, s, b), b))))
 }

tests/src/test/scala/cats/tests/TraverseTests.scala

@@ -28,6 +28,25 @@ abstract class TraverseCheck[F[_]: Traverse](name: String)(implicit ArbFInt: Arb
     }
   }
 
+  test(s"Traverse[$name].traverseWithStateM") {
+    forAll { (fa: F[Int]) =>
+      val left = fa.traverseWithStateM(Set.empty[Int])(
+        (a, s) => if (s.contains(a)) Eval.now("duplicate") else Eval.later(a.toString))(
+        (a, s, _) => s + a)
+      val fal = fa.toList
+      left.value.map(_.toList.filterNot(_ == "duplicate")) should === (fal.toSet -> fal.distinct.map(_.toString))
+    }
+  }
+
+  test(s"Traverse[$name].traverseWithStateMA") {
+    forAll { (fa: F[Int]) =>
+      val left = fa.traverseWithStateMA(Set.empty[Int])(
+        (a, s) => if (s.contains(a)) Eval.now("duplicate") else Eval.later(a.toString))(
+        (a, s, _) => s + a)
+      left.value.toList.filterNot(_ == "duplicate") should === (fa.toList.distinct.map(_.toString))
+    }
+  }
+
 }
 
 object TraverseCheck {