Add foldMap/compile FunctionK to Free companion (#1411)

* Add foldMap/compile FunctionK to Free companion

* Rename interpret and replace ~> (#1433)

* Use FunctionK instead of ~> alias in FreeT

* Rename interpret in FreeT to compile for consistency with Free

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

@@ -174,6 +174,21 @@ object Free {
   def suspend[F[_], A](value: => Free[F, A]): Free[F, A] =
     pure(()).flatMap(_ => value)
 
+  /**
+   * a FunctionK, suitable for composition, which calls compile
+   */
+  def compile[F[_], G[_]](fk: FunctionK[F, G]): FunctionK[Free[F, ?], Free[G, ?]] =
+    new FunctionK[Free[F, ?], Free[G, ?]] {
+      def apply[A](f: Free[F, A]): Free[G, A] = f.compile(fk)
+    }
+  /**
+   * a FunctionK, suitable for composition, which calls foldMap
+   */
+  def foldMap[F[_], M[_]: Monad](fk: FunctionK[F, M]): FunctionK[Free[F, ?], M] =
+    new FunctionK[Free[F, ?], M] {
+      def apply[A](f: Free[F, A]): M[A] = f.foldMap(fk)
+    }
+
   /**
    * This method is used to defer the application of an Inject[F, G]
    * instance. The actual work happens in

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

@@ -3,6 +3,8 @@ package free
 
 import scala.annotation.tailrec
 
+import cats.arrow.FunctionK
+
 /**
  * FreeT is a monad transformer for Free monads over a Functor S
  *
@@ -27,19 +29,22 @@ sealed abstract class FreeT[S[_], M[_], A] extends Product with Serializable {
    * 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] =
+  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))
     }
 
+  @deprecated("Use compile", "0.8.0")
+  def interpret[T[_]](st: FunctionK[S, T])(implicit M: Functor[M]): FreeT[T, M, A] = compile(st)
+
   /** Change the base functor `S` for a `FreeT` action. */
-  def interpret[T[_]](st: S ~> T)(implicit M: Functor[M]): FreeT[T, M, A] =
+  def compile[T[_]](st: FunctionK[S, T])(implicit M: Functor[M]): FreeT[T, M, A] =
     step match {
       case e @ FlatMapped(_, _) =>
-        FlatMapped(e.a.interpret(st), e.f.andThen(_.interpret(st)))
+        FlatMapped(e.a.compile(st), e.f.andThen(_.compile(st)))
       case Suspend(m) =>
         Suspend(M.map(m)(_.left.map(s => st(s))))
     }
@@ -48,7 +53,7 @@ sealed abstract class FreeT[S[_], M[_], A] extends Product with Serializable {
    * 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 M: Monad[M]): M[A] = {
+  def foldMap(f: FunctionK[S, M])(implicit M: Monad[M]): M[A] = {
     def go(ft: FreeT[S, M, A]): M[Either[FreeT[S, M, A], A]] =
       ft match {
         case Suspend(ma) => M.flatMap(ma) {
@@ -170,6 +175,15 @@ object FreeT extends FreeTInstances {
   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)
 
+  def compile[S[_], T[_], M[_]: Functor](st: FunctionK[S, T]): FunctionK[FreeT[S, M, ?], FreeT[T, M, ?]] =
+    new FunctionK[FreeT[S, M, ?], FreeT[T, M, ?]] {
+     def apply[A](f: FreeT[S, M, A]) = f.compile(st)
+    }
+
+  def foldMap[S[_], M[_]: Monad](fk: FunctionK[S, M]): FunctionK[FreeT[S, M, ?], M] =
+    new FunctionK[FreeT[S, M, ?], M] {
+     def apply[A](f: FreeT[S, M, A]) = f.foldMap(fk)
+    }
 }
 
 private[free] sealed trait FreeTInstances3 {

free/src/test/scala/cats/free/FreeTTests.scala

@@ -101,25 +101,29 @@ class FreeTTests extends CatsSuite {
     val d: FreeT[JustFunctor, JustFunctor, Int] = transLiftInstance.liftT[JustFunctor, Int](JustFunctor(1))
   }
 
-  test("interpret to universal id equivalent to original instance") {
+  test("compile to universal id equivalent to original instance") {
     forAll { a: FreeTOption[Int] =>
-      val b = a.interpret(FunctionK.id)
+      val b = a.compile(FunctionK.id)
       Eq[FreeTOption[Int]].eqv(a, b) should ===(true)
+      val fk = FreeT.compile[Option, Option, Option](FunctionK.id)
+      a should === (fk(a))
     }
   }
 
-  test("interpret stack-safety") {
+  test("compile stack-safety") {
     val a = (0 until 50000).foldLeft(Applicative[FreeTOption].pure(()))(
       (fu, i) => fu.flatMap(u => Applicative[FreeTOption].pure(u))
     )
-    val b = a.interpret(FunctionK.id) // used to overflow
+    val b = a.compile(FunctionK.id) // used to overflow
   }
 
   test("foldMap consistent with runM") {
     forAll { a: FreeTOption[Int] =>
       val x = a.runM(identity)
       val y = a.foldMap(FunctionK.id)
+      val fk = FreeT.foldMap[Option, Option](FunctionK.id)
       Eq[Option[Int]].eqv(x, y) should ===(true)
+      y should === (fk(a))
     }
   }
 

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

@@ -26,6 +26,8 @@ class FreeTests extends CatsSuite {
   test("compile id"){
     forAll { x: Free[List, Int] =>
       x.compile(FunctionK.id[List]) should === (x)
+      val fk = Free.compile(FunctionK.id[List])
+      fk(x) === x
     }
   }
 
@@ -46,6 +48,9 @@ class FreeTests extends CatsSuite {
       val mapped = x.compile(headOptionU)
       val folded = mapped.foldMap(FunctionK.id[Option])
       folded should === (x.foldMap(headOptionU))
+
+      val fk = Free.foldMap(headOptionU)
+      folded should === (fk(x))
     }
   }