FreeT stack-safe transformer

docs/src/main/tut/freemonad.md

@@ -493,6 +493,79 @@ As the sequence of operations becomes longer, the slower a `flatMap`
 "through" the structure will be. With `FlatMapped`, `Free` becomes a
 right-associated structure not subject to quadratic complexity.
 
+## FreeT
+
+Often times we want to interleave the syntax tree when building a Free monad 
+with some other effect not declared as part of the ADT. 
+FreeT solves this problem by allowing us to mix building steps of the AST 
+with calling action in other base monad.
+
+In the following example a basic console application is shown.
+When the user inputs some text we use a separate `State` monad to track what the user
+typed.
+
+As we can observe in this case `FreeT` offers us a the alternative to delegate denotations to `State`
+monad with stronger equational guarantees than if we were emulating the `State` ops in our own ADT.
+
+```tut:book
+import cats.free._
+import cats._
+import cats.data._
+
+/* A base ADT for the user interaction without state semantics */
+sealed abstract class Teletype[A] extends Product with Serializable
+final case class WriteLine(line : String) extends Teletype[Unit]
+final case class ReadLine(prompt : String) extends Teletype[String]
+
+type TeletypeT[M[_], A] = FreeT[Teletype, M, A]
+type Log = List[String]
+
+/** Smart constructors, notice we are abstracting over any MonadState instance
+ *  to potentially support other types beside State 
+ */
+class TeletypeOps[M[_]](implicit MS : MonadState[M, Log]) {
+  def writeLine(line : String) : TeletypeT[M, Unit] =
+	FreeT.liftF[Teletype, M, Unit](WriteLine(line))
+  def readLine(prompt : String) : TeletypeT[M, String] =
+	FreeT.liftF[Teletype, M, String](ReadLine(prompt))
+  def log(s : String) : TeletypeT[M, Unit] =
+	FreeT.liftT[Teletype, M, Unit](MS.modify(s :: _))
+}
+
+object TeletypeOps {
+  implicit def teleTypeOpsInstance[M[_]](implicit MS : MonadState[M, Log]) : TeletypeOps[M] = new TeletypeOps
+}
+
+type TeletypeState[A] = State[List[String], A]
+
+def program(implicit TO : TeletypeOps[TeletypeState]) : TeletypeT[TeletypeState, Unit] = {
+  for {
+	userSaid <- TO.readLine("what's up?!")
+	_ <- TO.log(s"user said : $userSaid")
+	_ <- TO.writeLine("thanks, see you soon!")
+  } yield () 
+}
+
+def interpreter = new (Teletype ~> TeletypeState) {
+  def apply[A](fa : Teletype[A]) : TeletypeState[A] = {  
+	fa match {
+	  case ReadLine(prompt) =>
+		println(prompt)
+		val userInput = "hanging in here" //scala.io.StdIn.readLine()
+		StateT.pure[Eval, List[String], A](userInput)
+	  case WriteLine(line) =>
+		StateT.pure[Eval, List[String], A](println(line))
+	}
+  }
+}
+
+import TeletypeOps._
+
+val state = program.foldMap(interpreter)
+val initialState = Nil
+val (stored, _) = state.run(initialState).value
+```
+
 ## Future Work (TODO)
 
 There are many remarkable uses of `Free[_]`. In the future, we will

free/src/main/scala/cats/free/FreeT.scala

@@ -0,0 +1,254 @@
+package cats
+package free
+
+import scala.annotation.tailrec
+
+import cats.data.Xor
+
+/** FreeT is a monad transformer for Free monads over a Functor S
+  */
+sealed abstract class FreeT[S[_], M[_], A] extends Product with Serializable {
+
+  import FreeT._
+
+  final def map[B](f: A => B)(implicit M: Applicative[M]): FreeT[S, M, B] =
+    flatMap(a => pure(f(a)))
+
+  /** Binds the given continuation to the result of this computation. */
+  final def flatMap[B](f: A => FreeT[S, M, B]): FreeT[S, M, B] =
+    Gosub(this, f)
+
+  /**
+   * Changes the underlying `Monad` for this `FreeT`, ie.
+   * turning this `FreeT[S, M, A]` into a `FreeT[S, N, A]`.
+   */
+  def hoist[N[_]](mn: M ~> N): FreeT[S, N, A] =
+    step match {
+      case e @ Gosub(_, _) =>
+        Gosub(e.a.hoist(mn), e.f.andThen(_.hoist(mn)))
+      case Suspend(m) =>
+        Suspend(mn(m))
+    }
+
+  /** Change the base functor `S` for a `FreeT` action. */
+  def interpret[T[_]](st: S ~> T)(implicit M: Functor[M]): FreeT[T, M, A] =
+    step match {
+      case e @ Gosub(_, _) =>
+        Gosub(e.a.interpret(st), e.f.andThen(_.interpret(st)))
+      case Suspend(m) =>
+        Suspend(M.map(m)(_.map(s => st(s))))
+    }
+
+  /**
+    * Runs to completion, mapping the suspension with the given transformation
+    * at each step and accumulating into the monad `M`.
+    */
+  def foldMap(f: S ~> M)(implicit MR: MonadRec[M]): M[A] = {
+    def go(ft: FreeT[S, M, A]): M[FreeT[S, M, A] Xor A] =
+      ft match {
+        case Suspend(ma) => MR.flatMap(ma) {
+          case Xor.Left(a) => MR.pure(Xor.Right(a))
+          case Xor.Right(sa) => MR.map(f(sa))(Xor.right)
+        }
+        case g @ Gosub(_, _) => g.a match {
+          case Suspend(mx) => MR.flatMap(mx) {
+            case Xor.Left(x) => MR.pure(Xor.left(g.f(x)))
+            case Xor.Right(sx) => MR.map(f(sx))(g.f andThen Xor.left)
+          }
+          case g0 @ Gosub(_, _) => MR.pure(Xor.left(g0.a.flatMap(g0.f(_).flatMap(g.f))))
+        }
+      }
+
+    MR.tailRecM(this)(go)
+  }
+
+  /** Evaluates a single layer of the free monad */
+  def resume(implicit S: Functor[S], MR: MonadRec[M]): M[A Xor S[FreeT[S, M, A]]] = {
+    def go(ft: FreeT[S, M, A]): M[FreeT[S, M, A] Xor (A Xor S[FreeT[S, M, A]])] =
+      ft match {
+        case Suspend(f) => MR.map(f)(as => Xor.right(as.map(S.map(_)(pure(_)))))
+        case g1 @ Gosub(_, _) => g1.a match {
+          case Suspend(m1) => MR.map(m1) {
+            case Xor.Left(a) => Xor.left(g1.f(a))
+            case Xor.Right(fc) => Xor.right(Xor.right(S.map(fc)(g1.f(_))))
+          }
+          case g2 @ Gosub(_, _) => MR.pure(Xor.left(g2.a.flatMap(g2.f(_).flatMap(g1.f))))
+        }
+      }
+
+    MR.tailRecM(this)(go)
+  }
+
+  /**
+    * Runs to completion, using a function that maps the resumption from `S` to a monad `M`.
+    */
+  def runM(interp: S[FreeT[S, M, A]] => M[FreeT[S, M, A]])(implicit S: Functor[S], MR: MonadRec[M]): M[A] = {
+    def runM2(ft: FreeT[S, M, A]): M[FreeT[S, M, A] Xor A] =
+      MR.flatMap(ft.resume) {
+        case Xor.Left(a) => MR.pure(Xor.right(a))
+        case Xor.Right(fc) => MR.map(interp(fc))(Xor.left)
+      }
+    MR.tailRecM(this)(runM2)
+  }
+
+  /**
+   * Finds the first `M` instance, `m`, and maps it to contain the rest
+   * of the computation. Since only `map` is used on `m`, its structure
+   * is preserved.
+   */
+  @tailrec
+  private[cats] final def toM(implicit M: Applicative[M]): M[FreeT[S, M, A]] =
+    this match {
+      case Suspend(m) => M.map(m) {
+        case Xor.Left(a) => pure(a)
+        case Xor.Right(s) => liftF(s)
+      }
+      case g1 @ Gosub(_, _) => g1.a match {
+        case Suspend(m) => M.map(m) {
+          case Xor.Left(a) => g1.f(a)
+          case Xor.Right(s) => liftF[S, M, g1.A](s).flatMap(g1.f)
+        }
+        case g0 @ Gosub(_, _) => g0.a.flatMap(g0.f(_).flatMap(g1.f)).toM
+      }
+    }
+
+  @tailrec
+  private def step: FreeT[S, M, A] =
+    this match {
+      case g @ Gosub(_, _) => g.a match {
+        case g0 @ Gosub(_, _) => g0.a.flatMap(a => g0.f(a).flatMap(g.f)).step
+        case _ => g
+      }
+      case x => x
+    }
+}
+
+
+object FreeT extends FreeTInstances {
+  /** Suspend the computation with the given suspension. */
+  private[free] case class Suspend[S[_], M[_], A](a: M[A Xor S[A]]) extends FreeT[S, M, A]
+
+  /** Call a subroutine and continue with the given function. */
+  private[free] case class Gosub[S[_], M[_], A0, B](a0: FreeT[S, M, A0], f0: A0 => FreeT[S, M, B]) extends FreeT[S, M, B] {
+    type A = A0
+    def a: FreeT[S, M, A] = a0
+    def f: A => FreeT[S, M, B] = f0
+  }
+
+  /** Return the given value in the free monad. */
+  def pure[S[_], M[_], A](value: A)(implicit M: Applicative[M]): FreeT[S, M, A] = Suspend(M.pure(Xor.left(value)))
+
+  def suspend[S[_], M[_], A](a: M[A Xor S[FreeT[S, M, A]]])(implicit M: Applicative[M]): FreeT[S, M, A] =
+    liftT(a).flatMap({
+      case Xor.Left(a) => pure(a)
+      case Xor.Right(s) => roll(s)
+    })
+
+  def tailRecM[S[_], M[_]: Applicative, A, B](a: A)(f: A => FreeT[S, M, A Xor B]): FreeT[S, M, B] =
+    f(a).flatMap {
+      case Xor.Left(a0) => tailRecM(a0)(f)
+      case Xor.Right(b) => pure[S, M, B](b)
+    }
+
+  def liftT[S[_], M[_], A](value: M[A])(implicit M: Functor[M]): FreeT[S, M, A] =
+    Suspend(M.map(value)(Xor.left))
+
+  /** A version of `liftT` that infers the nested type constructor. */
+  def liftTU[S[_], MA](value: MA)(implicit M: Unapply[Functor, MA]): FreeT[S, M.M, M.A] =
+    liftT[S, M.M, M.A](M.subst(value))(M.TC)
+
+  /** Suspends a value within a functor in a single step. Monadic unit for a higher-order monad. */
+  def liftF[S[_], M[_], A](value: S[A])(implicit M: Applicative[M]): FreeT[S, M, A] =
+    Suspend(M.pure(Xor.right(value)))
+
+  def roll[S[_], M[_], A](value: S[FreeT[S, M, A]])(implicit M: Applicative[M]): FreeT[S, M, A] =
+    liftF[S, M, FreeT[S, M, A]](value).flatMap(identity)
+
+}
+
+private[free] sealed trait FreeTInstances3 {
+  implicit def catsFreeMonadStateForFreeT[S[_], M[_], E](implicit M1: MonadState[M, E]): MonadState[FreeT[S, M, ?], E] =
+    new MonadState[FreeT[S, M, ?], E] with FreeTMonad[S, M] {
+      override def M = implicitly
+      override def get =
+        FreeT.liftT(M1.get)
+      override def set(s: E) =
+        FreeT.liftT(M1.set(s))
+    }
+}
+
+private[free] sealed trait FreeTInstances2 extends FreeTInstances3 {
+  implicit def catsFreeMonadErrorForFreeT[S[_], M[_]: FlatMapRec, E](implicit E: MonadError[M, E]): MonadError[FreeT[S, M, ?], E] =
+    new MonadError[FreeT[S, M, ?], E] with FreeTMonad[S, M] {
+      override def M = implicitly
+      override def handleErrorWith[A](fa: FreeT[S, M, A])(f: E => FreeT[S, M, A]) =
+        FreeT.liftT[S, M, FreeT[S, M, A]](E.handleErrorWith(fa.toM)(f.andThen(_.toM)))(M).flatMap(identity)
+      override def raiseError[A](e: E) =
+        FreeT.liftT(E.raiseError[A](e))(M)
+    }
+}
+
+private[free] sealed trait FreeTInstances1 extends FreeTInstances2 {
+  implicit def catsFreeFlatMapForFreeT[S[_], M[_]](implicit M0: Applicative[M]): FlatMap[FreeT[S, M, ?]] =
+    new FreeTFlatMap[S, M] {
+      implicit def M: Applicative[M] = M0
+    }
+
+  implicit def catsFreeTransLiftForFreeT[S[_]]: TransLift.Aux[FreeT[S, ?[_], ?], Functor] =
+    new TransLift[FreeT[S, ?[_], ?]] {
+
+      type TC[M[_]] = Functor[M]
+
+      override def liftT[M[_]: Functor, A](ma: M[A]): FreeT[S, M, A] =
+        FreeT.liftT(ma)
+    }
+}
+
+private[free] sealed trait FreeTInstances0 extends FreeTInstances1 {
+  implicit def catsFreeMonadForFreeT[S[_], M[_]](implicit M0: Applicative[M]): Monad[FreeT[S, M, ?]] with FlatMapRec[FreeT[S, M, ?]] =
+    new FreeTMonad[S, M] {
+      def M = M0
+    }
+
+  implicit def catsFreeCombineForFreeT[S[_], M[_]: Applicative: FlatMapRec: SemigroupK]: SemigroupK[FreeT[S, M, ?]] =
+    new FreeTCombine[S, M] {
+      override def M = implicitly
+      override def M1 = implicitly
+      override def M2 = implicitly
+    }
+}
+
+private[free] sealed trait FreeTInstances extends FreeTInstances0 {
+  implicit def catsFreeMonadCombineForFreeT[S[_], M[_]: Alternative: FlatMapRec]: MonadCombine[FreeT[S, M, ?]] =
+    new MonadCombine[FreeT[S, M, ?]] with FreeTCombine[S, M] with FreeTMonad[S, M] {
+      override def M = implicitly
+      override def M1 = implicitly
+      override def M2 = implicitly
+
+      override def empty[A] = FreeT.liftT[S, M, A](MonoidK[M].empty[A])(M)
+    }
+}
+
+private[free] sealed trait FreeTFlatMap[S[_], M[_]] extends FlatMap[FreeT[S, M, ?]] {
+  implicit def M: Applicative[M]
+
+  override final def map[A, B](fa: FreeT[S, M, A])(f: A => B): FreeT[S, M, B] = fa.map(f)
+  def flatMap[A, B](fa: FreeT[S, M, A])(f: A => FreeT[S, M, B]): FreeT[S, M, B] = fa.flatMap(f)
+}
+
+private[free] sealed trait FreeTMonad[S[_], M[_]] extends Monad[FreeT[S, M, ?]] with FlatMapRec[FreeT[S, M, ?]] with FreeTFlatMap[S, M] {
+  implicit def M: Applicative[M]
+
+  override final def pure[A](a: A): FreeT[S, M, A]  =
+    FreeT.pure[S, M, A](a)
+  override final def tailRecM[A, B](a: A)(f: A => FreeT[S, M, A Xor B]): FreeT[S, M, B] =
+    FreeT.tailRecM(a)(f)
+}
+
+private[free] sealed trait FreeTCombine[S[_], M[_]] extends SemigroupK[FreeT[S, M, ?]] {
+  implicit def M: Applicative[M]
+  implicit def M1: FlatMapRec[M]
+  def M2: SemigroupK[M]
+  override final def combineK[A](a: FreeT[S, M, A], b: FreeT[S, M, A]): FreeT[S, M, A] =
+    FreeT.liftT(M2.combineK(a.toM, b.toM))(M).flatMap(identity)
+}