Remove FlatMapRec make all FlatMap implement tailRecM

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

@@ -295,8 +295,8 @@ object Eval extends EvalInstances {
 
 private[cats] trait EvalInstances extends EvalInstances0 {
 
-  implicit val catsBimonadForEval: Bimonad[Eval] with MonadRec[Eval] =
-    new Bimonad[Eval] with MonadRec[Eval] {
+  implicit val catsBimonadForEval: Bimonad[Eval] with Monad[Eval] with RecursiveTailRecM[Eval] =
+    new Bimonad[Eval] with Monad[Eval] with RecursiveTailRecM[Eval] {
       override def map[A, B](fa: Eval[A])(f: A => B): Eval[B] = fa.map(f)
       def pure[A](a: A): Eval[A] = Now(a)
       def flatMap[A, B](fa: Eval[A])(f: A => Eval[B]): Eval[B] = fa.flatMap(f)

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

@@ -1,5 +1,6 @@
 package cats
 
+import cats.data.Xor
 import simulacrum.typeclass
 
 /**
@@ -90,4 +91,20 @@ import simulacrum.typeclass
    */
   def ifM[B](fa: F[Boolean])(ifTrue: => F[B], ifFalse: => F[B]): F[B] =
     flatMap(fa)(if (_) ifTrue else ifFalse)
+
+  /**
+   * Keeps calling `f` until a `[[cats.data.Xor.Right Right]][B]` is returned.
+   *
+   * Based on Phil Freeman's
+   * [[http://functorial.com/stack-safety-for-free/index.pdf Stack Safety for Free]].
+   *
+   * Implementations of this method should ideally use constant stack space. If
+   * it is constant stack space, an instance of `RecursiveTailRecM[F]` should
+   * be made available.
+   *
+   * Note, Monad subclasses can call `defaultTailRecM(a)(f)` to get an implementation
+   * 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[A Xor B]): F[B]
 }

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

@@ -1,5 +1,6 @@
 package cats
 
+import cats.data.Xor
 import simulacrum.typeclass
 
 /**
@@ -14,4 +15,16 @@ import simulacrum.typeclass
 @typeclass trait Monad[F[_]] extends FlatMap[F] with Applicative[F] {
   override def map[A, B](fa: F[A])(f: A => B): F[B] =
     flatMap(fa)(a => pure(f(a)))
+
+  /**
+   * This is not stack safe if the monad is not trampolined, but it
+   * is always lawful. It it better if you can find a stack safe way
+   * 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[A Xor B]): F[B] =
+    flatMap(fn(a)) {
+      case Xor.Right(b) => pure(b)
+      case Xor.Left(nextA) => defaultTailRecM(nextA)(fn)
+    }
 }

core/src/main/scala/cats/RecursiveTailRecM.scala

@@ -0,0 +1,24 @@
+package cats
+
+import java.io.Serializable
+/**
+ * This is a marker type that promises that the method
+ * .tailRecM for this type is stack-safe for arbitrary recursion.
+ */
+trait RecursiveTailRecM[F[_]] extends Serializable {
+  /*
+   * you can call RecusiveTailRecM[F].sameType(Monad[F]).tailRec
+   * to have a static check that the types agree
+   * for safer usage of tailRecM
+   */
+  final def sameType[M[_[_]]](m: M[F]): M[F] = m
+}
+
+object RecursiveTailRecM {
+  private[this] val singleton: RecursiveTailRecM[Id] = new RecursiveTailRecM[Id] { }
+
+  def apply[F[_]](implicit r: RecursiveTailRecM[F]): RecursiveTailRecM[F] = r
+
+  def create[F[_]]: RecursiveTailRecM[F] =
+    singleton.asInstanceOf[RecursiveTailRecM[F]]
+}

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

@@ -4,6 +4,7 @@ package data
 import cats.arrow.{Arrow, Split}
 import cats.functor.{Contravariant, Profunctor}
 import cats.{CoflatMap, Comonad, Functor, Monad}
+import scala.annotation.tailrec
 
 /**
  * Represents a function `F[A] => B`.
@@ -47,7 +48,7 @@ private[data] sealed abstract class CokleisliInstances extends CokleisliInstance
   implicit def catsDataArrowForCokleisli[F[_]](implicit ev: Comonad[F]): Arrow[Cokleisli[F, ?, ?]] =
     new CokleisliArrow[F] { def F: Comonad[F] = ev }
 
-  implicit def catsDataMonadForCokleisli[F[_], A]: Monad[Cokleisli[F, A, ?]] = new Monad[Cokleisli[F, A, ?]] {
+  implicit def catsDataMonadForCokleisli[F[_], A]: Monad[Cokleisli[F, A, ?]] with RecursiveTailRecM[Cokleisli[F, A, ?]] = new Monad[Cokleisli[F, A, ?]] with RecursiveTailRecM[Cokleisli[F, A, ?]] {
     def pure[B](x: B): Cokleisli[F, A, B] =
       Cokleisli.pure(x)
 
@@ -56,6 +57,16 @@ 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, B Xor C]): Cokleisli[F, A, C] =
+      Cokleisli({ (fa: F[A]) =>
+        @tailrec
+        def loop(c: Cokleisli[F, A, B Xor C]): C = c.run(fa) match {
+          case Xor.Right(c) => c
+          case Xor.Left(bb) => loop(fn(bb))
+        }
+        loop(fn(b))
+      })
   }
 
   implicit def catsDataMonoidKForCokleisli[F[_]](implicit ev: Comonad[F]): MonoidK[λ[α => Cokleisli[F, α, α]]] =

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

@@ -50,6 +50,9 @@ private[data] sealed trait IdTMonad[F[_]] extends Monad[IdT[F, ?]] {
 
   def flatMap[A, B](fa: IdT[F, A])(f: A => IdT[F, B]): IdT[F, B] =
     fa.flatMap(f)
+
+  def tailRecM[A, B](a: A)(f: A => IdT[F, A Xor B]): IdT[F, B] =
+    IdT(F0.tailRecM(a)(f(_).value))
 }
 
 private[data] sealed trait IdTFoldable[F[_]] extends Foldable[IdT[F, ?]] {
@@ -83,6 +86,9 @@ private[data] sealed abstract class IdTInstances0 extends IdTInstances1 {
       implicit val F0: Monad[F] = F
     }
 
+  implicit def catsDataRecursiveTailRecMForIdT[F[_]: RecursiveTailRecM]: RecursiveTailRecM[IdT[F, ?]] =
+    RecursiveTailRecM.create[IdT[F, ?]]
+
   implicit def catsDataFoldableForIdT[F[_]](implicit F: Foldable[F]): Foldable[IdT[F, ?]] =
     new IdTFoldable[F] {
       implicit val F0: Foldable[F] = F

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

@@ -2,6 +2,7 @@ package cats
 package data
 
 import cats.functor.Bifunctor
+import scala.annotation.tailrec
 
 /** Represents a right-biased disjunction that is either an `A`, or a `B`, or both an `A` and a `B`.
  *
@@ -140,9 +141,25 @@ private[data] sealed abstract class IorInstances extends IorInstances0 {
     def show(f: A Ior B): String = f.show
   }
 
-  implicit def catsDataMonadForIor[A: Semigroup]: Monad[A Ior ?] = new Monad[A Ior ?] {
+  implicit def catsDataMonadForIor[A: Semigroup]: Monad[A Ior ?] with RecursiveTailRecM[A Ior ?] = new Monad[A Ior ?] with RecursiveTailRecM[A Ior ?] {
     def pure[B](b: B): A Ior B = Ior.right(b)
     def flatMap[B, C](fa: A Ior B)(f: B => A Ior C): A Ior C = fa.flatMap(f)
+    def tailRecM[B, C](b: B)(fn: B => Ior[A, Xor[B, C]]): A Ior C = {
+      @tailrec
+      def loop(v: Ior[A, Xor[B, C]]): A Ior C = v match {
+        case Ior.Left(a) => Ior.left(a)
+        case Ior.Right(Xor.Right(c)) => Ior.right(c)
+        case Ior.Both(a, Xor.Right(c)) => Ior.both(a, c)
+        case Ior.Right(Xor.Left(b)) => loop(fn(b))
+        case Ior.Both(a, Xor.Left(b)) =>
+          fn(b) match {
+            case Ior.Left(aa) => Ior.left(Semigroup[A].combine(a, aa))
+            case Ior.Both(aa, x) => loop(Ior.both(Semigroup[A].combine(a, aa), x))
+            case Ior.Right(x) => loop(Ior.both(a, x))
+          }
+      }
+      loop(fn(b))
+    }
   }
 
   implicit def catsDataBifunctorForIor: Bifunctor[Ior] =

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

@@ -144,7 +144,12 @@ private[data] sealed abstract class KleisliInstances0 extends KleisliInstances1
 
     def map[B, C](fa: Kleisli[F, A, B])(f: B => C): Kleisli[F, A, C] =
       fa.map(f)
+
+    def tailRecM[B, C](b: B)(f: B => Kleisli[F, A, B Xor C]): Kleisli[F, A, C] =
+      Kleisli[F, A, C]({ a => FlatMap[F].tailRecM(b) { f(_).run(a) } })
   }
+  implicit def catsDataRecursiveTailRecMForKleisli[F[_]: RecursiveTailRecM, A]: RecursiveTailRecM[Kleisli[F, A, ?]] =
+    RecursiveTailRecM.create[Kleisli[F, A, ?]]
 
   implicit def catsDataSemigroupForKleisli[F[_], A, B](implicit M: Semigroup[F[B]]): Semigroup[Kleisli[F, A, B]] =
     new KleisliSemigroup[F, A, B] { def FB: Semigroup[F[B]] = M }
@@ -194,6 +199,9 @@ private[data] sealed abstract class KleisliInstances4 {
 
       def local[B](f: A => A)(fa: Kleisli[F, A, B]): Kleisli[F, A, B] =
         Kleisli(f.andThen(fa.run))
+
+      def tailRecM[B, C](b: B)(f: B => Kleisli[F, A, B Xor C]): Kleisli[F, A, C] =
+        Kleisli[F, A, C]({ a => FlatMap[F].tailRecM(b) { f(_).run(a) } })
     }
 }
 

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

@@ -146,9 +146,9 @@ object NonEmptyList extends NonEmptyListInstances {
 private[data] sealed trait NonEmptyListInstances extends NonEmptyListInstances0 {
 
   implicit val catsDataInstancesForNonEmptyList: SemigroupK[NonEmptyList] with Reducible[NonEmptyList]
-      with Comonad[NonEmptyList] with Traverse[NonEmptyList] with MonadRec[NonEmptyList] =
-    new NonEmptyReducible[NonEmptyList, List] with SemigroupK[NonEmptyList]
-        with Comonad[NonEmptyList] with Traverse[NonEmptyList] with MonadRec[NonEmptyList] {
+      with Comonad[NonEmptyList] with Traverse[NonEmptyList] with Monad[NonEmptyList] with RecursiveTailRecM[NonEmptyList] =
+    new NonEmptyReducible[NonEmptyList, List] with SemigroupK[NonEmptyList] with Comonad[NonEmptyList]
+      with Traverse[NonEmptyList] with Monad[NonEmptyList] with RecursiveTailRecM[NonEmptyList] {
 
       def combineK[A](a: NonEmptyList[A], b: NonEmptyList[A]): NonEmptyList[A] =
         a concat b

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

@@ -135,9 +135,9 @@ final class NonEmptyVector[A] private (val toVector: Vector[A]) extends AnyVal {
 private[data] sealed trait NonEmptyVectorInstances {
 
   implicit val catsDataInstancesForNonEmptyVector: SemigroupK[NonEmptyVector] with Reducible[NonEmptyVector]
-      with Comonad[NonEmptyVector] with Traverse[NonEmptyVector] with MonadRec[NonEmptyVector] =
-    new NonEmptyReducible[NonEmptyVector, Vector] with SemigroupK[NonEmptyVector]
-        with Comonad[NonEmptyVector] with Traverse[NonEmptyVector] with MonadRec[NonEmptyVector] {
+    with Comonad[NonEmptyVector] with Traverse[NonEmptyVector] with Monad[NonEmptyVector] with RecursiveTailRecM[NonEmptyVector] =
+    new NonEmptyReducible[NonEmptyVector, Vector] with SemigroupK[NonEmptyVector] with Comonad[NonEmptyVector]
+      with Traverse[NonEmptyVector] with Monad[NonEmptyVector] with RecursiveTailRecM[NonEmptyVector] {
 
       def combineK[A](a: NonEmptyVector[A], b: NonEmptyVector[A]): NonEmptyVector[A] =
         a concatNev b

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

@@ -136,7 +136,42 @@ private[data] sealed trait OneAndInstances extends OneAndLowPriority2 {
         val fst = f(fa.head)
         OneAnd(fst.head, monad.combineK(fst.tail, end))
       }
+
+      def tailRecM[A, B](a: A)(fn: A => OneAnd[F, A Xor B]): OneAnd[F, B] = {
+        def stepF(a: A): F[A Xor B] = {
+          val oneAnd = fn(a)
+          monad.combineK(monad.pure(oneAnd.head), oneAnd.tail)
+        }
+        def toFB(in: A Xor B): F[B] = in match {
+          case Xor.Right(b) => monad.pure(b)
+          case Xor.Left(a) => monad.tailRecM(a)(stepF)
+        }
+
+        // This could probably be in SemigroupK to perform well
+        @tailrec
+        def combineAll(items: List[F[B]]): F[B] = items match {
+          case Nil => monad.empty
+          case h :: Nil => h
+          case h1 :: h2 :: tail => combineAll(monad.combineK(h1, h2) :: tail)
+        }
+
+        @tailrec
+        def go(in: A, rest: List[F[B]]): OneAnd[F, B] =
+          fn(in) match {
+            case OneAnd(Xor.Right(b), tail) =>
+              val fbs = monad.flatMap(tail)(toFB)
+              OneAnd(b, combineAll(fbs :: rest))
+            case OneAnd(Xor.Left(a), tail) =>
+              val fbs = monad.flatMap(tail)(toFB)
+              go(a, fbs :: rest)
+          }
+
+        go(a, Nil)
+      }
     }
+
+    implicit def catsDataOneAnd[F[_]: RecursiveTailRecM]: RecursiveTailRecM[OneAnd[F, ?]] =
+      RecursiveTailRecM.create[OneAnd[F, ?]]
 }
 
 private[data] trait OneAndLowPriority0 {

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

@@ -175,8 +175,8 @@ object OptionT extends OptionTInstances {
 }
 
 private[data] sealed trait OptionTInstances extends OptionTInstances0 {
-  implicit def catsDataMonadRecForOptionT[F[_]](implicit F0: MonadRec[F]): MonadRec[OptionT[F, ?]] =
-    new OptionTMonadRec[F] { implicit val F = F0 }
+  implicit def catsDataMonadForOptionT[F[_]](implicit F0: Monad[F]): Monad[OptionT[F, ?]] =
+    new OptionTMonad[F] { implicit val F = F0 }
 
   implicit def catsDataFoldableForOptionT[F[_]](implicit F0: Foldable[F]): Foldable[OptionT[F, ?]] =
     new OptionTFoldable[F] { implicit val F = F0 }
@@ -195,6 +195,8 @@ private[data] sealed trait OptionTInstances0 extends OptionTInstances1 {
   implicit def catsDataMonadErrorForOptionT[F[_], E](implicit F0: MonadError[F, E]): MonadError[OptionT[F, ?], E] =
     new OptionTMonadError[F, E] { implicit val F = F0 }
 
+  implicit def catsDataRecursiveTailRecM[F[_]](implicit F: RecursiveTailRecM[F]): RecursiveTailRecM[OptionT[F, ?]] = RecursiveTailRecM.create[OptionT[F, ?]]
+
   implicit def catsDataSemigroupKForOptionT[F[_]](implicit F0: Monad[F]): SemigroupK[OptionT[F, ?]] =
     new OptionTSemigroupK[F] { implicit val F = F0 }
 
@@ -206,9 +208,6 @@ private[data] sealed trait OptionTInstances0 extends OptionTInstances1 {
 }
 
 private[data] sealed trait OptionTInstances1 extends OptionTInstances2 {
-  implicit def catsDataMonadForOptionT[F[_]](implicit F0: Monad[F]): Monad[OptionT[F, ?]] =
-    new OptionTMonad[F] { implicit val F = F0 }
-
   // do NOT change this to val! I know it looks like it should work, and really I agree, but it doesn't (for... reasons)
   implicit def catsDataTransLiftForOptionT: TransLift.Aux[OptionT, Functor] =
     new TransLift[OptionT] {
@@ -251,10 +250,6 @@ private[data] trait OptionTMonad[F[_]] extends Monad[OptionT[F, ?]] {
   def flatMap[A, B](fa: OptionT[F, A])(f: A => OptionT[F, B]): OptionT[F, B] = fa.flatMap(f)
 
   override def map[A, B](fa: OptionT[F, A])(f: A => B): OptionT[F, B] = fa.map(f)
-}
-
-private[data] trait OptionTMonadRec[F[_]] extends MonadRec[OptionT[F, ?]] with OptionTMonad[F] {
-  implicit def F: MonadRec[F]
 
   def tailRecM[A, B](a: A)(f: A => OptionT[F, A Xor B]): OptionT[F, B] =
     OptionT(F.tailRecM(a)(a0 => F.map(f(a0).value)(

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

@@ -159,19 +159,16 @@ private[data] sealed trait StateTInstances extends StateTInstances1 {
 }
 
 private[data] sealed trait StateTInstances1 extends StateTInstances2 {
-  implicit def catsDataMonadRecForStateT[F[_], S](implicit F0: MonadRec[F]): MonadRec[StateT[F, S, ?]] =
-    new StateTMonadRec[F, S] { implicit def F = F0 }
-}
-
-private[data] sealed trait StateTInstances2 extends StateTInstances3 {
   implicit def catsDataMonadCombineForStateT[F[_], S](implicit F0: MonadCombine[F]): MonadCombine[StateT[F, S, ?]] =
     new StateTMonadCombine[F, S] { implicit def F = F0 }
 }
 
-private[data] sealed trait StateTInstances3 {
+private[data] sealed trait StateTInstances2 {
   implicit def catsDataMonadForStateT[F[_], S](implicit F0: Monad[F]): Monad[StateT[F, S, ?]] =
     new StateTMonad[F, S] { implicit def F = F0 }
 
+  implicit def catsDataRecursiveTailRecMForStateT[F[_]: RecursiveTailRecM, S]: RecursiveTailRecM[StateT[F, S, ?]] = RecursiveTailRecM.create[StateT[F, S, ?]]
+
   implicit def catsDataSemigroupKForStateT[F[_], S](implicit F0: Monad[F], G0: SemigroupK[F]): SemigroupK[StateT[F, S, ?]] =
     new StateTSemigroupK[F, S] { implicit def F = F0; implicit def G = G0 }
 }
@@ -219,6 +216,11 @@ private[data] sealed trait StateTMonad[F[_], S] extends Monad[StateT[F, S, ?]] {
     fa.flatMap(f)
 
   override def map[A, B](fa: StateT[F, S, A])(f: A => B): StateT[F, S, B] = fa.map(f)
+
+  def tailRecM[A, B](a: A)(f: A => StateT[F, S, A Xor B]): StateT[F, S, B] =
+    StateT[F, S, B](s => F.tailRecM[(S, A), (S, B)]((s, a)) {
+      case (s, a) => F.map(f(a).run(s)) { case (s, ab) => ab.bimap((s, _), (s, _)) }
+    })
 }
 
 private[data] sealed trait StateTMonadState[F[_], S] extends MonadState[StateT[F, S, ?], S] with StateTMonad[F, S] {
@@ -227,15 +229,6 @@ private[data] sealed trait StateTMonadState[F[_], S] extends MonadState[StateT[F
   def set(s: S): StateT[F, S, Unit] = StateT(_ => F.pure((s, ())))
 }
 
-private[data] sealed trait StateTMonadRec[F[_], S] extends MonadRec[StateT[F, S, ?]] with StateTMonad[F, S] {
-  override implicit def F: MonadRec[F]
-
-  def tailRecM[A, B](a: A)(f: A => StateT[F, S, A Xor B]): StateT[F, S, B] =
-    StateT[F, S, B](s => F.tailRecM[(S, A), (S, B)]((s, a)) {
-      case (s, a) => F.map(f(a).run(s)) { case (s, ab) => ab.bimap((s, _), (s, _)) }
-    })
-}
-
 private[data] sealed trait StateTTransLift[S] extends TransLift[StateT[?[_], S, ?]] {
   type TC[M[_]] = Applicative[M]