MonadRec instances for Id, Option, OptionT, Either, Xor, XorT, Free, …

…List.

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

@@ -132,7 +132,7 @@ object OptionT extends OptionTInstances {
   def liftF[F[_], A](fa: F[A])(implicit F: Functor[F]): OptionT[F, A] = OptionT(F.map(fa)(Some(_)))
 }
 
-private[data] sealed trait OptionTInstances1 {
+private[data] sealed trait OptionTInstances2 {
   implicit def optionTFunctor[F[_]:Functor]: Functor[OptionT[F, ?]] =
     new Functor[OptionT[F, ?]] {
       override def map[A, B](fa: OptionT[F, A])(f: A => B): OptionT[F, B] =
@@ -148,22 +148,41 @@ private[data] sealed trait OptionTInstances1 {
     }
 }
 
-private[data] sealed trait OptionTInstances extends OptionTInstances1 {
-
-  implicit def optionTMonad[F[_]](implicit F: Monad[F]): Monad[OptionT[F, ?]] =
-    new Monad[OptionT[F, ?]] {
-      def pure[A](a: A): OptionT[F, A] = OptionT.pure(a)
-
-      def flatMap[A, B](fa: OptionT[F, A])(f: A => OptionT[F, B]): OptionT[F, B] =
-        fa.flatMap(f)
+private[data] sealed trait OptionTInstances1 extends OptionTInstances2 {
+  implicit def optionTMonad[F[_]](implicit F0: Monad[F]): Monad[OptionT[F, ?]] =
+    new OptionTMonad[F] { implicit val F = F0 }
+}
 
-      override def map[A, B](fa: OptionT[F, A])(f: A => B): OptionT[F, B] =
-        fa.map(f)
-    }
+private[data] sealed trait OptionTInstances extends OptionTInstances1 {
+  implicit def optionTMonadRec[F[_]](implicit F0: MonadRec[F]): MonadRec[OptionT[F, ?]] =
+    new OptionTMonadRec[F] { implicit val F = F0 }
 
   implicit def optionTEq[F[_], A](implicit FA: Eq[F[Option[A]]]): Eq[OptionT[F, A]] =
     FA.on(_.value)
 
   implicit def optionTShow[F[_], A](implicit F: Show[F[Option[A]]]): Show[OptionT[F, A]] =
     functor.Contravariant[Show].contramap(F)(_.value)
 }
+
+private[data] trait OptionTMonad[F[_]] extends Monad[OptionT[F, ?]] {
+  implicit val F: Monad[F]
+
+  def pure[A](a: A): OptionT[F, A] = OptionT.pure(a)
+
+  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 val 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){
+      case None => Xor.Right(None)
+      case Some(Xor.Left(a1)) => Xor.Left(a1)
+      case Some(Xor.Right(b)) => Xor.Right(Some(b))
+    }))
+}

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

@@ -1,6 +1,7 @@
 package cats
 package data
 
+import scala.annotation.tailrec
 import scala.reflect.ClassTag
 import scala.util.{Failure, Success, Try}
 
@@ -203,13 +204,19 @@ private[data] sealed abstract class XorInstances extends XorInstances1 {
         }
     }
 
-  implicit def xorInstances[A]: Traverse[A Xor ?] with MonadError[Xor[A, ?], A] =
-    new Traverse[A Xor ?] with MonadError[Xor[A, ?], A] {
+  implicit def xorInstances[A]: Traverse[A Xor ?] with MonadRec[A Xor ?] with MonadError[Xor[A, ?], A] =
+    new Traverse[A Xor ?] with MonadRec[A Xor ?] with MonadError[Xor[A, ?], A] {
       def traverse[F[_]: Applicative, B, C](fa: A Xor B)(f: B => F[C]): F[A Xor C] = fa.traverse(f)
       def foldLeft[B, C](fa: A Xor B, c: C)(f: (C, B) => C): C = fa.foldLeft(c)(f)
       def foldRight[B, C](fa: A Xor B, lc: Eval[C])(f: (B, Eval[C]) => Eval[C]): Eval[C] = fa.foldRight(lc)(f)
       def flatMap[B, C](fa: A Xor B)(f: B => A Xor C): A Xor C = fa.flatMap(f)
       def pure[B](b: B): A Xor B = Xor.right(b)
+      @tailrec def tailRecM[B, C](b: B)(f: B => A Xor (B Xor C)): A Xor C =
+        f(b) match {
+          case Xor.Left(a) => Xor.Left(a)
+          case Xor.Right(Xor.Left(b1)) => tailRecM(b1)(f)
+          case Xor.Right(Xor.Right(c)) => Xor.Right(c)
+        }
       def handleErrorWith[B](fea: Xor[A, B])(f: A => Xor[A, B]): Xor[A, B] =
         fea match {
           case Xor.Left(e) => f(e)

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

@@ -241,6 +241,11 @@ private[data] abstract class XorTInstances1 extends XorTInstances2 {
 }
 
 private[data] abstract class XorTInstances2 extends XorTInstances3 {
+  implicit def xorTMonadRec[F[_], L](implicit F0: MonadRec[F]): MonadRec[XorT[F, L, ?]] =
+    new XorTMonadRec[F, L] { implicit val F = F0 }
+}
+
+private[data] abstract class XorTInstances3 extends XorTInstances4 {
   implicit def xorTMonadError[F[_], L](implicit F: Monad[F]): MonadError[XorT[F, L, ?], L] = {
     implicit val F0 = F
     new XorTMonadError[F, L] { implicit val F = F0 }
@@ -261,7 +266,7 @@ private[data] abstract class XorTInstances2 extends XorTInstances3 {
     }
 }
 
-private[data] abstract class XorTInstances3 {
+private[data] abstract class XorTInstances4 {
   implicit def xorTFunctor[F[_], L](implicit F: Functor[F]): Functor[XorT[F, L, ?]] = {
     implicit val F0 = F
     new XorTFunctor[F, L] { implicit val F = F0 }
@@ -273,10 +278,13 @@ private[data] trait XorTFunctor[F[_], L] extends Functor[XorT[F, L, ?]] {
   override def map[A, B](fa: XorT[F, L, A])(f: A => B): XorT[F, L, B] = fa map f
 }
 
-private[data] trait XorTMonadError[F[_], L] extends MonadError[XorT[F, L, ?], L] with XorTFunctor[F, L] {
+private[data] trait XorTMonad[F[_], L] extends Monad[XorT[F, L, ?]] with XorTFunctor[F, L] {
   implicit val F: Monad[F]
   def pure[A](a: A): XorT[F, L, A] = XorT.pure[F, L, A](a)
   def flatMap[A, B](fa: XorT[F, L, A])(f: A => XorT[F, L, B]): XorT[F, L, B] = fa flatMap f
+}
+
+private[data] trait XorTMonadError[F[_], L] extends MonadError[XorT[F, L, ?], L] with XorTMonad[F, L] {
   def handleErrorWith[A](fea: XorT[F, L, A])(f: L => XorT[F, L, A]): XorT[F, L, A] =
     XorT(F.flatMap(fea.value) {
       case Xor.Left(e) => f(e).value
@@ -295,6 +303,16 @@ private[data] trait XorTMonadError[F[_], L] extends MonadError[XorT[F, L, ?], L]
     fla.recoverWith(pf)
 }
 
+private[data] trait XorTMonadRec[F[_], L] extends MonadRec[XorT[F, L, ?]] with XorTMonad[F, L] {
+  implicit val F: MonadRec[F]
+  def tailRecM[A, B](a: A)(f: A => XorT[F, L, A Xor B]): XorT[F, L, B] =
+    XorT(F.tailRecM(a)(a0 => F.map(f(a0).value){
+      case Xor.Left(l) => Xor.Right(Xor.Left(l))
+      case Xor.Right(Xor.Left(a1)) => Xor.Left(a1)
+      case Xor.Right(Xor.Right(b)) => Xor.Right(Xor.Right(b))
+    }))
+}
+
 private[data] trait XorTMonadFilter[F[_], L] extends MonadFilter[XorT[F, L, ?]] with XorTMonadError[F, L] {
   implicit val F: Monad[F]
   implicit val L: Monoid[L]

core/src/main/scala/cats/package.scala

@@ -1,3 +1,6 @@
+import scala.annotation.tailrec
+import cats.data.Xor
+
 /**
  * Symbolic aliases for various types are defined here.
  */
@@ -26,12 +29,16 @@ package object cats {
  * encodes pure unary function application.
  */
   type Id[A] = A
-  implicit val idInstances: Bimonad[Id] with Traverse[Id] =
-    new Bimonad[Id] with Traverse[Id] {
+  implicit val idInstances: Bimonad[Id] with MonadRec[Id] with Traverse[Id] =
+    new Bimonad[Id] with MonadRec[Id] with Traverse[Id] {
       def pure[A](a: A): A = a
       def extract[A](a: A): A = a
       def flatMap[A, B](a: A)(f: A => B): B = f(a)
       def coflatMap[A, B](a: A)(f: A => B): B = f(a)
+      @tailrec def tailRecM[A, B](a: A)(f: A => A Xor B): B = f(a) match {
+        case Xor.Left(a1) => tailRecM(a1)(f)
+        case Xor.Right(b) => b
+      }
       override def map[A, B](fa: A)(f: A => B): B = f(fa)
       override def ap[A, B](ff: A => B)(fa: A): B = ff(fa)
       override def flatten[A](ffa: A): A = ffa

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

@@ -1,6 +1,9 @@
 package cats
 package std
 
+import scala.annotation.tailrec
+import cats.data.Xor
+
 trait EitherInstances extends EitherInstances1 {
   implicit val eitherBitraverse: Bitraverse[Either] =
     new Bitraverse[Either] {
@@ -23,8 +26,8 @@ trait EitherInstances extends EitherInstances1 {
         }
     }
 
-  implicit def eitherInstances[A]: Monad[Either[A, ?]] with Traverse[Either[A, ?]] =
-    new Monad[Either[A, ?]] with Traverse[Either[A, ?]] {
+  implicit def eitherInstances[A]: MonadRec[Either[A, ?]] with Traverse[Either[A, ?]] =
+    new MonadRec[Either[A, ?]] with Traverse[Either[A, ?]] {
       def pure[B](b: B): Either[A, B] = Right(b)
 
       def flatMap[B, C](fa: Either[A, B])(f: B => Either[A, C]): Either[A, C] =
@@ -33,6 +36,14 @@ trait EitherInstances extends EitherInstances1 {
       override def map[B, C](fa: Either[A, B])(f: B => C): Either[A, C] =
         fa.right.map(f)
 
+      @tailrec
+      def tailRecM[B, C](b: B)(f: B => Either[A, B Xor C]): Either[A, C] =
+        f(b) match {
+          case Left(a) => Left(a)
+          case Right(Xor.Left(b1)) => tailRecM(b1)(f)
+          case Right(Xor.Right(c)) => Right(c)
+        }
+
       override def map2Eval[B, C, Z](fb: Either[A, B], fc: Eval[Either[A, C]])(f: (B, C) => Z): Eval[Either[A, Z]] =
         fb match {
           // This should be safe, but we are forced to use `asInstanceOf`,

core/src/main/scala/cats/std/list.scala

@@ -6,10 +6,12 @@ import cats.syntax.show._
 import scala.annotation.tailrec
 import scala.collection.mutable.ListBuffer
 
+import cats.data.Xor
+
 trait ListInstances extends cats.kernel.std.ListInstances {
 
-  implicit val listInstance: Traverse[List] with MonadCombine[List] with CoflatMap[List] =
-    new Traverse[List] with MonadCombine[List] with CoflatMap[List] {
+  implicit val listInstance: Traverse[List] with MonadCombine[List] with MonadRec[List] with CoflatMap[List] =
+    new Traverse[List] with MonadCombine[List] with MonadRec[List] with CoflatMap[List] {
 
       def empty[A]: List[A] = Nil
 
@@ -26,6 +28,20 @@ trait ListInstances extends cats.kernel.std.ListInstances {
       override def map2[A, B, Z](fa: List[A], fb: List[B])(f: (A, B) => Z): List[Z] =
         fa.flatMap(a => fb.map(b => f(a, b)))
 
+      def tailRecM[A, B](a: A)(f: A => List[A Xor B]): List[B] = {
+        val buf = List.newBuilder[B]
+        @tailrec def go(lists: List[List[A Xor B]]): Unit = lists match {
+          case (ab :: abs) :: tail => ab match {
+            case Xor.Right(b) => buf += b; go(abs :: tail)
+            case Xor.Left(a) => go(f(a) :: abs :: tail)
+          }
+          case Nil :: tail => go(tail)
+          case Nil => ()
+        }
+        go(f(a) :: Nil)
+        buf.result
+      }
+
       def coflatMap[A, B](fa: List[A])(f: List[A] => B): List[B] = {
         @tailrec def loop(buf: ListBuffer[B], as: List[A]): List[B] =
           as match {

core/src/main/scala/cats/std/option.scala

@@ -1,10 +1,13 @@
 package cats
 package std
 
+import scala.annotation.tailrec
+import cats.data.Xor
+
 trait OptionInstances extends cats.kernel.std.OptionInstances {
 
-  implicit val optionInstance: Traverse[Option] with MonadError[Option, Unit] with MonadCombine[Option] with CoflatMap[Option] with Alternative[Option] =
-    new Traverse[Option] with MonadError[Option, Unit]  with MonadCombine[Option] with CoflatMap[Option] with Alternative[Option] {
+  implicit val optionInstance: Traverse[Option] with MonadError[Option, Unit] with MonadCombine[Option] with MonadRec[Option] with CoflatMap[Option] with Alternative[Option] =
+    new Traverse[Option] with MonadError[Option, Unit]  with MonadCombine[Option] with MonadRec[Option] with CoflatMap[Option] with Alternative[Option] {
 
       def empty[A]: Option[A] = None
 
@@ -18,6 +21,14 @@ trait OptionInstances extends cats.kernel.std.OptionInstances {
       def flatMap[A, B](fa: Option[A])(f: A => Option[B]): Option[B] =
         fa.flatMap(f)
 
+      @tailrec
+      def tailRecM[A, B](a: A)(f: A => Option[A Xor B]): Option[B] =
+        f(a) match {
+          case None => None
+          case Some(Xor.Left(a1)) => tailRecM(a1)(f)
+          case Some(Xor.Right(b)) => Some(b)
+        }
+
       override def map2[A, B, Z](fa: Option[A], fb: Option[B])(f: (A, B) => Z): Option[Z] =
         fa.flatMap(a => fb.map(b => f(a, b)))
 

free/src/main/scala/cats/free/Free.scala

@@ -40,11 +40,16 @@ object Free {
   /**
    * `Free[S, ?]` has a monad for any type constructor `S[_]`.
    */
-  implicit def freeMonad[S[_]]: Monad[Free[S, ?]] =
-    new Monad[Free[S, ?]] {
+  implicit def freeMonad[S[_]]: MonadRec[Free[S, ?]] =
+    new MonadRec[Free[S, ?]] {
       def pure[A](a: A): Free[S, A] = Free.pure(a)
       override def map[A, B](fa: Free[S, A])(f: A => B): Free[S, B] = fa.map(f)
       def flatMap[A, B](a: Free[S, A])(f: A => Free[S, B]): Free[S, B] = a.flatMap(f)
+      def tailRecM[A, B](a: A)(f: A => Free[S, A Xor B]): Free[S, B] =
+        f(a).flatMap(_ match {
+          case Xor.Left(a1) => tailRecM(a1)(f) // recursion OK here, since Free is lazy
+          case Xor.Right(b) => pure(b)
+        })
     }
 }
 

free/src/test/scala/cats/free/FreeTests.scala

@@ -3,7 +3,8 @@ package free
 
 import cats.tests.CatsSuite
 import cats.arrow.NaturalTransformation
-import cats.laws.discipline.{CartesianTests, MonadTests, SerializableTests}
+import cats.data.Xor
+import cats.laws.discipline.{CartesianTests, MonadRecTests, SerializableTests}
 import cats.laws.discipline.arbitrary.function0Arbitrary
 
 import org.scalacheck.{Arbitrary, Gen}
@@ -14,8 +15,8 @@ class FreeTests extends CatsSuite {
 
   implicit val iso = CartesianTests.Isomorphisms.invariant[Free[Option, ?]]
 
-  checkAll("Free[Option, ?]", MonadTests[Free[Option, ?]].monad[Int, Int, Int])
-  checkAll("Monad[Free[Option, ?]]", SerializableTests.serializable(Monad[Free[Option, ?]]))
+  checkAll("Free[Option, ?]", MonadRecTests[Free[Option, ?]].monadRec[Int, Int, Int])
+  checkAll("MonadRec[Free[Option, ?]]", SerializableTests.serializable(MonadRec[Free[Option, ?]]))
 
   test("mapSuspension id"){
     forAll { x: Free[List, Int] =>
@@ -43,6 +44,13 @@ class FreeTests extends CatsSuite {
     }
   }
 
+  test("tailRecM is stack safe") {
+    val n = 50000
+    val fa = MonadRec[Free[Option, ?]].tailRecM(0)(i =>
+      Free.pure[Option, Int Xor Int](if(i < n) Xor.Left(i+1) else Xor.Right(i)))
+    fa should === (Free.pure[Option, Int](n))
+  }
+
   ignore("foldMap is stack safe") {
     trait FTestApi[A]
     case class TB(i: Int) extends FTestApi[Int]

laws/src/main/scala/cats/laws/FlatMapRecLaws.scala

@@ -0,0 +1,26 @@
+package cats
+package laws
+
+import cats.data.Xor
+import cats.syntax.flatMap._
+import cats.syntax.functor._
+
+/**
+ * Laws that must be obeyed by any `FlatMapRec`.
+ */
+trait FlatMapRecLaws[F[_]] extends FlatMapLaws[F] {
+  implicit override def F: FlatMapRec[F]
+
+  def tailRecMConsistentFlatMap[A](a: A, f: A => F[A]): IsEq[F[A]] = {
+    val bounce = F.tailRecM[(A, Int), A]((a, 1)) { case (a0, i) =>
+      if(i > 0) f(a0).map(a1 => Xor.left((a1, i-1)))
+      else f(a0).map(Xor.right)
+    }
+    bounce <-> f(a).flatMap(f)
+  }
+}
+
+object FlatMapRecLaws {
+  def apply[F[_]](implicit ev: FlatMapRec[F]): FlatMapRecLaws[F] =
+    new FlatMapRecLaws[F] { def F: FlatMapRec[F] = ev }
+}

laws/src/main/scala/cats/laws/MonadRecLaws.scala

@@ -0,0 +1,14 @@
+package cats
+package laws
+
+/**
+ * Laws that must be obeyed by any `MonadRec`.
+ */
+trait MonadRecLaws[F[_]] extends MonadLaws[F] with FlatMapRecLaws[F] {
+  implicit override def F: MonadRec[F]
+}
+
+object MonadRecLaws {
+  def apply[F[_]](implicit ev: MonadRec[F]): MonadRecLaws[F] =
+    new MonadRecLaws[F] { def F: MonadRec[F] = ev }
+}