Finish adding mapK

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

@@ -16,6 +16,12 @@ final case class EitherK[F[_], G[_], A](run: Either[F[A], G[A]]) {
   def map[B](f: A => B)(implicit F: Functor[F], G: Functor[G]): EitherK[F, G, B] =
     EitherK(run.bimap(F.lift(f), G.lift(f)))
 
+  /**
+   * Modify the right side context `G` using transformation `f`.
+   */
+  def mapK[H[_]](f: G ~> H): EitherK[F, H, A] =
+    EitherK(run.map(f.apply))
+
   def coflatMap[B](f: EitherK[F, G, A] => B)(implicit F: CoflatMap[F], G: CoflatMap[G]): EitherK[F, G, B] =
     EitherK(
       run.bimap(a => F.coflatMap(a)(x => f(leftc(x))), a => G.coflatMap(a)(x => f(rightc(x))))
@@ -234,4 +240,3 @@ private[data] trait EitherKComonad[F[_], G[_]] extends Comonad[EitherK[F, G, ?]]
   def extract[A](p: EitherK[F, G, A]): A =
     p.extract
 }
-

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

@@ -91,6 +91,11 @@ final case class EitherT[F[_], A, B](value: F[Either[A, B]]) {
 
   def map[D](f: B => D)(implicit F: Functor[F]): EitherT[F, A, D] = bimap(identity, f)
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): EitherT[G, A, B] = EitherT[G, A, B](f(value))
+
   def semiflatMap[D](f: B => F[D])(implicit F: Monad[F]): EitherT[F, A, D] =
     flatMap(b => EitherT.right(f(b)))
 

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

@@ -12,6 +12,12 @@ sealed abstract class Func[F[_], A, B] { self =>
   def run: A => F[B]
   def map[C](f: B => C)(implicit FF: Functor[F]): Func[F, A, C] =
     Func.func(a => FF.map(self.run(a))(f))
+
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): Func[G, A, B] =
+    Func.func(run andThen f.apply)
 }
 
 object Func extends FuncInstances {

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

@@ -9,6 +9,12 @@ final case class IdT[F[_], A](value: F[A]) {
   def map[B](f: A => B)(implicit F: Functor[F]): IdT[F, B] =
     IdT(F.map(value)(f))
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): IdT[G, A] =
+    IdT[G, A](f(value))
+
   def flatMap[B](f: A => IdT[F, B])(implicit F: FlatMap[F]): IdT[F, B] =
     IdT(F.flatMap(value)(f.andThen(_.value)))
 

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

@@ -52,6 +52,13 @@ final class IndexedReaderWriterStateT[F[_], E, L, SA, SB, A](val runF: F[(E, SA)
   def map[B](f: A => B)(implicit F: Functor[F]): IndexedReaderWriterStateT[F, E, L, SA, SB, B] =
     transform { (l, s, a) => (l, s, f(a)) }
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G)(implicit F: Functor[F]): IndexedReaderWriterStateT[G, E, L, SA, SB, A] =
+    IndexedReaderWriterStateT.applyF(
+      f(F.map(runF)(rwsa => (e, sa) => f(rwsa(e, sa)))))
+
   /**
    * Modify the resulting state using `f` and the resulting value using `g`.
    */

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

@@ -39,6 +39,13 @@ final class IndexedStateT[F[_], SA, SB, A](val runF: F[SA => F[(SB, A)]]) extend
   def map[B](f: A => B)(implicit F: Functor[F]): IndexedStateT[F, SA, SB, B] =
     transform { case (s, a) => (s, f(a)) }
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G)(implicit F: Functor[F]): IndexedStateT[G, SA, SB, A] =
+    IndexedStateT.applyF(
+      f(F.map(runF)(_.andThen(fsa => f(fsa)))))
+
   def contramap[S0](f: S0 => SA)(implicit F: Functor[F]): IndexedStateT[F, S0, SB, A] =
     IndexedStateT.applyF {
       F.map(runF) { safsba =>

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

@@ -21,6 +21,12 @@ final case class Kleisli[F[_], A, B](run: A => F[B]) { self =>
   def mapF[N[_], C](f: F[B] => N[C]): Kleisli[N, A, C] =
     Kleisli(run andThen f)
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): Kleisli[G, A, B] =
+    Kleisli[G, A, B](run andThen f.apply)
+
   def flatMap[C](f: B => Kleisli[F, A, C])(implicit F: FlatMap[F]): Kleisli[F, A, C] =
     Kleisli((r: A) => F.flatMap[B, C](run(r))((b: B) => f(b).run(r)))
 
@@ -48,8 +54,9 @@ final case class Kleisli[F[_], A, B](run: A => F[B]) { self =>
   def local[AA](f: AA => A): Kleisli[F, AA, B] =
     Kleisli(f.andThen(run))
 
+  @deprecated("Use mapK", "1.0.0")
   def transform[G[_]](f: FunctionK[F, G]): Kleisli[G, A, B] =
-    Kleisli(a => f(run(a)))
+    mapK(f)
 
   def lower(implicit F: Applicative[F]): Kleisli[F, A, F[B]] =
     Kleisli(a => F.pure(run(a)))
@@ -148,10 +155,10 @@ private[data] sealed abstract class KleisliInstances1 extends KleisliInstances2
     def monad: Monad[Kleisli[M, A, ?]] = catsDataMonadForKleisli
 
     def sequential: Kleisli[F, A, ?] ~> Kleisli[M, A, ?] =
-      λ[Kleisli[F, A, ?] ~> Kleisli[M, A, ?]](_.transform(P.sequential))
+      λ[Kleisli[F, A, ?] ~> Kleisli[M, A, ?]](_.mapK(P.sequential))
 
     def parallel: Kleisli[M, A, ?] ~> Kleisli[F, A, ?] =
-      λ[Kleisli[M, A, ?] ~> Kleisli[F, A, ?]](_.transform(P.parallel))
+      λ[Kleisli[M, A, ?] ~> Kleisli[F, A, ?]](_.mapK(P.parallel))
   }
 }
 

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

@@ -23,7 +23,15 @@ package data
  * res1: List[Option[String]] = List(Some(2), None)
  * }}}
  */
-final case class Nested[F[_], G[_], A](value: F[G[A]])
+final case class Nested[F[_], G[_], A](value: F[G[A]]) {
+
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[H[_]](f: F ~> H): Nested[H, G, A] =
+    Nested(f(value))
+
+}
 
 object Nested extends NestedInstances
 

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

@@ -76,6 +76,12 @@ final case class OneAnd[F[_], A](head: A, tail: F[A]) {
   def map[B](f: A => B)(implicit F: Functor[F]): OneAnd[F, B] =
     OneAnd(f(head), F.map(tail)(f))
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): OneAnd[G, A] =
+    OneAnd(head, f(tail))
+
   /**
    * Typesafe equality operator.
    *

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

@@ -28,6 +28,11 @@ final case class OptionT[F[_], A](value: F[Option[A]]) {
   def map[B](f: A => B)(implicit F: Functor[F]): OptionT[F, B] =
     OptionT(F.map(value)(_.map(f)))
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): OptionT[G, A] = OptionT[G, A](f(value))
+
   def semiflatMap[B](f: A => F[B])(implicit F: Monad[F]): OptionT[F, B] =
     flatMap(a => OptionT.liftF(f(a)))
 

core/src/main/scala/cats/data/Tuple2K.scala

@@ -8,7 +8,15 @@ import cats.Contravariant
  *
  * See: [[https://www.cs.ox.ac.uk/jeremy.gibbons/publications/iterator.pdf The Essence of the Iterator Pattern]]
  */
-final case class Tuple2K[F[_], G[_], A](first: F[A], second: G[A])
+final case class Tuple2K[F[_], G[_], A](first: F[A], second: G[A]) {
+
+  /**
+   * Modify the context `G` of `second` using transformation `f`.
+   */
+  def mapK[H[_]](f: G ~> H): Tuple2K[F, H, A] =
+    Tuple2K(first, f(second))
+
+}
 
 object Tuple2K extends Tuple2KInstances
 

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

@@ -27,6 +27,12 @@ final case class WriterT[F[_], L, V](run: F[(L, V)]) {
       functorF.map(run) { z => (z._1, fn(z._2)) }
     }
 
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): WriterT[G, L, V] =
+    WriterT[G, L, V](f(run))
+
   def contramap[Z](fn: Z => V)(implicit F: Contravariant[F]): WriterT[F, L, Z] =
     WriterT {
       F.contramap(run) { z => (z._1, fn(z._2)) }

free/src/main/scala/cats/free/Coyoneda.scala

@@ -46,9 +46,16 @@ sealed abstract class Coyoneda[F[_], A] extends Serializable { self =>
   final def map[B](f: A => B): Aux[F, B, Pivot] =
     unsafeApply(fi)(f.asInstanceOf[Any => Any] :: ks)
 
-  final def transform[G[_]](f: FunctionK[F, G]): Aux[G, A, Pivot] =
+  /**
+    * Modify the context `F` using transformation `f`.
+    */
+  final def mapK[G[_]](f: F ~> G): Aux[G, A, Pivot] =
     unsafeApply(f(fi))(ks)
 
+  @deprecated("Use mapK", "1.0.0")
+  final def transform[G[_]](f: FunctionK[F, G]): Aux[G, A, Pivot] =
+    mapK(f)
+
 }
 
 object Coyoneda {

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

@@ -17,6 +17,21 @@ sealed abstract class Free[S[_], A] extends Product with Serializable {
   final def map[B](f: A => B): Free[S, B] =
     flatMap(a => Pure(f(a)))
 
+  /**
+   * Modify the functor context `S` using transformation `f`.
+   *
+   * This is effectively compiling your free monad into another
+   * language by changing the suspension functor using the given
+   * natural transformation `f`.
+   *
+   * If your natural transformation is effectful, be careful. These
+   * effects will be applied by `mapK`.
+   */
+  final def mapK[T[_]](f: S ~> T): Free[T, A] =
+    foldMap[Free[T, ?]] { // this is safe because Free is stack safe
+      λ[FunctionK[S, Free[T, ?]]](fa => Suspend(f(fa)))
+    }(Free.catsFreeMonadForFree)
+
   /**
    * Bind the given continuation to the result of this computation.
    * All left-associated binds are reassociated to the right.
@@ -147,11 +162,8 @@ sealed abstract class Free[S[_], A] extends Product with Serializable {
    *
    * If your natural transformation is effectful, be careful. These
    * effects will be applied by `compile`.
-   */
-  final def compile[T[_]](f: FunctionK[S, T]): Free[T, A] =
-    foldMap[Free[T, ?]] { // this is safe because Free is stack safe
-      λ[FunctionK[S, Free[T, ?]]](fa => Suspend(f(fa)))
-    }(Free.catsFreeMonadForFree)
+    */
+  final def compile[T[_]](f: FunctionK[S, T]): Free[T, A] = mapK(f)
 
   /**
    * Lift into `G` (typically a `EitherK`) given `InjectK`. Analogous
@@ -169,7 +181,7 @@ sealed abstract class Free[S[_], A] extends Product with Serializable {
    *}}}
    */
   final def inject[G[_]](implicit ev: InjectK[S, G]): Free[G, A] =
-    compile(λ[S ~> G](ev.inj(_)))
+    mapK(λ[S ~> G](ev.inj(_)))
 
   override def toString: String =
     "Free(...)"
@@ -217,11 +229,17 @@ object Free extends FreeInstances {
   def defer[F[_], A](value: => Free[F, A]): Free[F, A] =
     pure(()).flatMap(_ => value)
 
+  /**
+   * a FunctionK, suitable for composition, which calls mapK
+   */
+  def mapK[F[_], G[_]](fk: FunctionK[F, G]): FunctionK[Free[F, ?], Free[G, ?]] =
+    λ[FunctionK[Free[F, ?], Free[G, ?]]](f => f.mapK(fk))
+
   /**
    * a FunctionK, suitable for composition, which calls compile
    */
   def compile[F[_], G[_]](fk: FunctionK[F, G]): FunctionK[Free[F, ?], Free[G, ?]] =
-    λ[FunctionK[Free[F, ?], Free[G, ?]]](f => f.compile(fk))
+    mapK(fk)
 
   /**
    * a FunctionK, suitable for composition, which calls foldMap

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

@@ -21,21 +21,27 @@ sealed abstract class FreeT[S[_], M[_], A] extends Product with Serializable {
   final def map[B](f: A => B)(implicit M: Applicative[M]): FreeT[S, M, B] =
     flatMap(a => pure(f(a)))
 
+  /**
+    * Modify the context `M` using transformation `mn`.
+    */
+  def mapK[N[_]](mn: M ~> N): FreeT[S, N, A] =
+    step match {
+      case e @ FlatMapped(_, _) =>
+        FlatMapped(e.a.mapK(mn), e.f.andThen(_.mapK(mn)))
+      case Suspend(m) =>
+        Suspend(mn(m))
+    }
+
   /** Binds the given continuation to the result of this computation. */
   final def flatMap[B](f: A => FreeT[S, M, B]): FreeT[S, M, B] =
     FlatMapped(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: FunctionK[M, N]): FreeT[S, N, A] =
-    step match {
-      case e @ FlatMapped(_, _) =>
-        FlatMapped(e.a.hoist(mn), e.f.andThen(_.hoist(mn)))
-      case Suspend(m) =>
-        Suspend(mn(m))
-    }
+    mapK(mn)
 
   @deprecated("Use compile", "0.8.0")
   def interpret[T[_]](st: FunctionK[S, T])(implicit M: Functor[M]): FreeT[T, M, A] = compile(st)
@@ -251,4 +257,3 @@ private[free] sealed trait FreeTSemigroupK[S[_], M[_]] extends SemigroupK[FreeT[
   override final def combineK[A](a: FreeT[S, M, A], b: FreeT[S, M, A]): FreeT[S, M, A] =
     FreeT.liftT(M1.combineK(a.toM, b.toM))(M).flatMap(identity)
 }
-

free/src/main/scala/cats/free/Yoneda.scala

@@ -28,6 +28,14 @@ abstract class Yoneda[F[_], A] extends Serializable { self =>
     new Yoneda[F, B] {
       def apply[C](g: B => C): F[C] = self(f andThen g)
     }
+
+  /**
+   * Modify the context `F` using transformation `f`.
+   */
+  def mapK[G[_]](f: F ~> G): Yoneda[G, A] =
+    new Yoneda[G, A] {
+      def apply[B](g: A => B): G[B] = f(self(g))
+    }
 }
 
 object Yoneda {
@@ -48,4 +56,3 @@ object Yoneda {
       def apply[B](f: A => B): F[B] = F.map(fa)(f)
     }
 }
-

free/src/test/scala/cats/free/CoyonedaSuite.scala

@@ -25,11 +25,11 @@ class CoyonedaSuite extends CatsSuite {
     }
   }
 
-  test("transform and run is same as applying natural trans") {
+  test("mapK and run is same as applying natural trans") {
       val nt = λ[FunctionK[Option, List]](_.toList)
       val o = Option("hello")
       val c = Coyoneda.lift(o)
-      c.transform(nt).run should === (nt(o))
+      c.mapK(nt).run should === (nt(o))
   }
 
   test("map order") {

free/src/test/scala/cats/free/FreeTSuite.scala

@@ -76,18 +76,18 @@ class FreeTSuite extends CatsSuite {
     Eq[FreeTOption[Unit]].eqv(expected, result) should ===(true)
   }
 
-  test("hoist to universal id equivalent to original instance") {
+  test("mapK to universal id equivalent to original instance") {
     forAll { a: FreeTOption[Int] =>
-      val b = a.hoist(FunctionK.id)
+      val b = a.mapK(FunctionK.id)
       Eq[FreeTOption[Int]].eqv(a, b) should ===(true)
     }
   }
 
-  test("hoist stack-safety") {
+  test("mapK stack-safety") {
     val a = (0 until 50000).foldLeft(Applicative[FreeTOption].pure(()))(
       (fu, i) => fu.flatMap(u => Applicative[FreeTOption].pure(u))
     )
-    val b = a.hoist(FunctionK.id)
+    val b = a.mapK(FunctionK.id)
   }
 
   test("compile to universal id equivalent to original instance") {

tests/src/test/scala/cats/tests/EitherTSuite.scala

@@ -242,6 +242,13 @@ class EitherTSuite extends CatsSuite {
     }
   }
 
+  test("mapK consistent with f(value)+pure") {
+    val f: List ~> Option = λ[List ~> Option](_.headOption)
+    forAll { (eithert: EitherT[List, String, Int]) =>
+      eithert.mapK(f) should === (EitherT(f(eithert.value)))
+    }
+  }
+
   test("semiflatMap consistent with value.flatMap+f+pure") {
     forAll { (eithert: EitherT[List, String, Int], f: Int => List[String]) =>
       eithert.semiflatMap(f) should === (EitherT(eithert.value.flatMap {

tests/src/test/scala/cats/tests/IdTSuite.scala

@@ -87,4 +87,11 @@ class IdTSuite extends CatsSuite {
     }
   }
 
+  test("mapK consistent with f(value)+pure") {
+    val f: List ~> Option = λ[List ~> Option](_.headOption)
+    forAll { (idT: IdT[List, Int]) =>
+      idT.mapK(f) should === (IdT(f(idT.value)))
+    }
+  }
+
 }