Cats（1）－ 从Free开始，Free cats

cats是scala的一个新的函数式编程工具库，其设计原理基本继承了scalaz：大家都是haskell typeclass的scala版实现。当然，cats在scalaz的基础上从实现细节、库组织结构和调用方式上进行了一些优化，所以对用户来说：cats的基础数据类型、数据结构在功能上与scalaz是大致相同的，可能有一些语法上的变化。与scalaz著名抽象、复杂的语法表现形式相比，cats的语法可能更形象、简单直白。在scalaz的学习过程中，我们了解到所谓函数式编程就是monadic Programming：即用monad这样的数据类型来构建程序。而实际可行的monadic programming就是用Free-Monad编程了。因为Free-Monad程序是真正可运行的，或者说是可以实现安全运行的，因为它可以保证在固定的堆栈内实现无限运算。我们知道：函数式编程模式的运行方式以递归算法为主，flatMap函数本身就是一种递归算法。这就预示着monadic programming很容易造成堆栈溢出问题（StackOverflowError）。当我们把普通的泛函类型F[A]升格成Free-Monad后就能充分利用Free-Monad安全运算能力来构建实际可运行的程序了。由于我们在前面已经详细的了解了scalaz的大部分typeclass，包括Free，对cats的讨论就从Free开始，聚焦在cats.Free编程模式方面。同时，我们可以在使用cats.Free的过程中对cats的其它数据类型进行补充了解。

cats.Free的类型款式如下：

sealed abstract class Free[S[_], A] extends Product with Serializable {...}

S是个高阶类，就是一种函数式运算。值得注意的是：现在S不需要是个Functor了。因为Free的一个实例Suspend类型是这样的：

/** Suspend the computation with the given suspension. */
  private final case class Suspend[S[_], A](a: S[A]) extends Free[S, A]

我们不需要map就可以把F[A]升格成Free

/**
   * Suspend a value within a functor lifting it to a Free.
   */
  def liftF[F[_], A](value: F[A]): Free[F, A] = Suspend(value)

我们在scalaz.Free的讨论中并没能详尽地分析在什么情况下S[_]必须是个Functor。下面我们需要用一些篇幅来解析。

Free程序的特点是算式（description）／算法（implementation）关注分离（separation of concern）：我们用一组数据类型来模拟一种编程语句ADT（algebraic data type），这一组ADT就形成了一种定制的编程语言DSL（domain specific language）。Free的编程部分就是用DSL来描述程序功能（description of purpose），即算式了。算法即用DSL描述的功能的具体实现，可以有多种的功能实现方式。我们先看个简单的DSL：

 import cats.free._
 import cats.Functor
 object catsFree {
   object ADTs {
     sealed trait Interact[+A]
     object Interact {
       case class Ask(prompt: String) extends Interact[String]
       case class Tell(msg: String) extends Interact[Unit]

       def ask(prompt: String): Free[Interact,String] = Free.liftF(Ask(prompt))
       def tell(msg: String): Free[Interact,Unit] = Free.liftF(Tell(msg))

       implicit object interactFunctor extends Functor[Interact]  {
         def map[A,B](ia: Interact[A])(f: A => B): Interact[B] = ???
       /*   ia match {
            case Ask(p) => ???
            case Tell(m) => ???
         } */
       }
     }
   }
   object DSLs {
     import ADTs._
     import Interact._
     val prg: Free[Interact,Unit] = for {
       first <- ask("What's your first name?")
       last <- ask("What's your last name?")
       _ <- tell(s"Hello $first $last")
     } yield()
   }

在这个例子里Interact并不是一个Functor，因为我们无法获取Interact Functor实例的map函数。先让我们分析一下Functor的map：

      implicit object interactFunctor extends Functor[Interact]  {
         def map[A,B](ia: Interact[A])(f: A => B): Interact[B] = ia match {
            case Ask(p) => ???
            case Tell(m) => ???
         }
       }

map的作用是用一个函数A => B把F[A]转成F[B]。也就是把语句状态从F[A]转成F[B]，但在Interact的情况里F[B]已经是明确的Interact[Unit]和Interact[String]两种状态，而map的f是A => B，在上面的示范里我们该如何施用f来获取这个Interact[B]呢？从上面的示范里我们观察可以得出Ask和Tell这两个ADT纯粹是为了模拟ask和tell这两个函数。ask和tell分别返回Free版本的String,Unit结果。可以说：Interact并没有转换到下一个状态的要求。那么假如我们把ADT调整成下面这样呢：

       sealed trait FunInteract[NS]
       object FunInteract {
         case class FunAsk[NS](prompt: String, onInput: String =>  NS) extends FunInteract[NS]
         case class FunTell[NS](msg: String, ns: NS) extends FunInteract[NS]

         def funAsk(prompt: String): Free[FunInteract,String] = Free.liftF(FunAsk(prompt,identity))
         def funAskInt(prompt: String): Free[FunInteract,Int] = Free.liftF(FunAsk(prompt,_.toInt))
         def funTell(msg: String): Free[FunInteract,Unit] = Free.liftF(FunTell(msg,()))

         implicit object funInteract extends Functor[FunInteract] {
            def map[A,NS](fa: FunInteract[A])(f: A => NS) = fa match {
               case FunAsk(prompt,input) => FunAsk(prompt,input andThen f)
               case FunTell(msg,ns) => FunTell(msg,f(ns))
            }
         }
       }

现在这两个ADT是有类型参数NS的了：FunAsk[NS],FunTell[NS]。NS代表了ADT当前类型，如FunAsk[Int]、FunTell[String]...，现在这两个ADT都通过类型参数NS变成了可map的对象了，如FunAsk[String] >>> FunAsk[String], FunAsk[String] >>> FunAsk[Int]...。所以我们可以很顺利的实现object funInteract的map函数。但是，一个有趣的现象是：为了实现这种状态转换，如果ADT需要返回操作结果，就必须具备一个引领状态转换的机制，如FunAsk类型里的onInput: String => NS：它代表funAsk函数返回的结果可以指向下一个状态。新增函数funAskInt是个很好的示范：通过返回的String结果将状态转换到FunAsk[Int]状态。函数funTell不返回结果，所以FunTell没有状态转换机制。scalaz旧版本Free.Suspend的类型款式是：Suspend[F[Free,A]]，这是一个递归类型，内部的Free代表下一个状态。由于我们必须用F.map才能取出下一个状态，所以F必须是个Functor。我们应该注意到如果ADT是Functor的话会造成Free程序的冗余代码。既然cats.Free对F[A]没有设置Functor门槛，那么我们应该尽量避免使用Functor。

得出对ADT类型要求结论后，我们接着示范cats的Free编程。下面是Free程序的功能实现interpret部分（implementation）：

     import ADTs._
     object iconsole extends (Interact ~> Id) {
       def apply[A](ia: Interact[A]): Id[A] = ia match {
          case Ask(p) => {println(p); readLine}
          case Tell(m) => println(m)
       }
     }
   }

DSL程序的功能实现就是把ADT F[A]对应到实际的指令集G[A]，在Free编程里用NaturalTransformation ～>来实现。注意G[A]必须是个Monad。在上面的例子里对应关系是：Interact～>Id，代表直接对应到运算指令println和readLine。我们也可以实现另一个版本：

     type Prompt = String
     type Reply = String
     type Message = String
     type Tester[A] = Map[Prompt,Reply] => (List[Message],A)
     object tester extends (Interact ~> Tester) {
       def apply[A](ia: Interact[A]): Tester[A] = ia match {
         case Ask(p) => { m => (List(), m(p)) }
         case Tell(m) => { _ => (List(m), ()) }
       }
     }
     import cats.Monad
     implicit val testerMonad = new Monad[Tester] {
       override def pure[A](a: A): Tester[A] = _ => (List(),a)
       override def flatMap[A,B](ta: Tester[A])(f: A => Tester[B]): Tester[B] = m => {
         val (o1,a1) = ta(m)
         val (o2,a2) = f(a1)(m)
         (o1 ++ o2, a2)
       }
       override def tailRecM[A,B](a: A)(f: A => Tester[Either[A,B]]): Tester[B] =
          defaultTailRecM(a)(f)
     }
   }

上面是个模拟测试：我们用个Map[K,V]来模拟互动，K模拟问prompt，V模拟获取回答Input。测试方式是个Function1，输入测试数据Map，在List[Message]里返回所有Tell产生的信息。上面提到过Tester[A]必须是个Monad，所以我们实现了Tester的Monad实例testMonad。实际上 m=>(List,a)就是个writer函数。所谓的Writer就是包嵌一个对值pair(L,V)的Monad，L代表Log，V代表运算值。Writer的特性就是log所有V的运算过程。我们又可以用Writer来实现这个tester：

    import cats.data.WriterT
     type WF[A] = Map[Prompt,Reply] => A
     type WriterTester[A] = WriterT[WF,List[Message],A]
     def testerToWriter[A](f: Map[Prompt,Reply] => (List[Message],A)) =
     WriterT[WF,List[Message],A](f)
     object testWriter extends (Interact ~> WriterTester) {
       import Interact._
       def apply[A](ia: Interact[A]): WriterTester[A] = ia match {
         case Ask(p) => testerToWriter(m => (List(),m(p)))
         case Tell(m) => testerToWriter(_ => (List(m),()))
       }
     }

如果我们用Writer来实现Interact，实际上就是把Ask和Tell都升格成Writer类型。

我们再来看看在cats里是如何运算Free DSL程序的。相对scalaz而言，cats的运算函数简单的多，就一个foldMap，我们来看看它的定义：

/**
   * Catamorphism for `Free`.
   *
   * Run to completion, mapping the suspension with the given
   * transformation at each step and accumulating into the monad `M`.
   *
   * This method uses `tailRecM` to provide stack-safety.
   */
  final def foldMap[M[_]](f: FunctionK[S, M])(implicit M: Monad[M], r: RecursiveTailRecM[M]): M[A] =
    r.sameType(M).tailRecM(this)(_.step match {
      case Pure(a) => M.pure(Right(a))
      case Suspend(sa) => M.map(f(sa))(Right(_))
      case FlatMapped(c, g) => M.map(c.foldMap(f))(cc => Left(g(cc)))
    })

除了要求M是个Monad之外，cats还要求M的RecursiveTailRecM隐式实例。那么什么是RecursiveTailRecM呢：

/**
 * 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 RecursiveTailRecM[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
}

我们用RecursiveTailRecM来保证这个Monad类型与tailRecM是匹配的，这是一种运算安全措施，所以在foldMap函数里r.sameType(M).tailRecM保证了tailRecM不会造成StackOverflowError。cats.Free里还有一种不需要类型安全检验的函数foldMapUnsafe：

/**
   * Same as foldMap but without a guarantee of stack safety. If the recursion is shallow
   * enough, this will work
   */
  final def foldMapUnsafe[M[_]](f: FunctionK[S, M])(implicit M: Monad[M]): M[A] =
    foldMap[M](f)(M, RecursiveTailRecM.create)

这个函数不需要RecursiveTailRecM。下面我们选择能保证运算安全的方法来运算tester：首先我们需要Tester类型的Monad和RecursiveTailRecM实例：

     import cats.Monad
     implicit val testerMonad = new Monad[Tester] with RecursiveTailRecM[Tester]{
       override def pure[A](a: A): Tester[A] = _ => (List(),a)
       override def flatMap[A,B](ta: Tester[A])(f: A => Tester[B]): Tester[B] = m => {
         val (o1,a1) = ta(m)
         val (o2,a2) = f(a1)(m)
         (o1 ++ o2, a2)
       }
       override def tailRecM[A,B](a: A)(f: A => Tester[Either[A,B]]): Tester[B] =
         defaultTailRecM(a)(f)
     }

然后我们制造一些测试数据：

   val testData = Map("What's your first name?" -> "Tiger",
   "What's your last name?" -> "Chan")             //> testData  : scala.collection.immutable.Map[String,String] = Map(What's your first name? -> Tiger, What's your last name? -> Chan)

测试运算：

 import ADTs._,DSLs._,IMPLs._
    val testData = Map("What's your first name?" -> "Tiger",
   "What's your last name?" -> "Chan")    //> testData  : scala.collection.immutable.Map[String,String] = Map(What's your first name? -> Tiger, What's your last name? -> Chan)
   val prgRunner = prg.foldMap(tester)    //> prgRunner  : demo.ws.catsFree.IMPLs.Tester[Unit] = <function1>
   prgRunner(testData)                    //> res0: (List[demo.ws.catsFree.IMPLs.Message], Unit) = (List(Hello Tiger Chan),())

那么如果运算testWriter呢？我们先取得WriterT的Monad实例：

    implicit val testWriterMonad =  WriterT.catsDataMonadWriterForWriterT[WF,List[Message]]

然后构建一个RecursiveTailRecM实例后再用同样的测试数据来运算：

  implicit val testWriterRecT = new RecursiveTailRecM[WriterTester]{}
            //> testWriterRecT  : cats.RecursiveTailRecM[demo.ws.catsFree.IMPLs.WriterTester] = demo.ws.catsFree$$anonfun$main$1$$anon$2@6093dd95
   val prgRunner = prg.foldMap(testWriter)         //> prgRunner  : demo.ws.catsFree.IMPLs.WriterTester[Unit] = WriterT(<function1>)
   prgRunner.run(testData)._1.map(println)         //> Hello Tiger Chan
                                                   //| res0: List[Unit] = List(())

运算结果一致。

我们再示范一下cats官方文件里关于free monad例子：模拟一个KVStore的put,get,delete功能。ADT设计如下：

   object ADTs {
     sealed trait KVStoreA[+A]
     case class Put[T](key: String, value: T) extends KVStoreA[Unit]
     case class Get[T](key: String) extends KVStoreA[Option[T]]
     case class Del(key: String) extends KVStoreA[Unit]
   }

对应的模拟功能函数设计如下：

     type KVStore[A] = Free[KVStoreA,A]
     object KVStoreA {
       def put[T](key: String, value: T): KVStore[Unit] =
         Free.liftF[KVStoreA,Unit](Put[T](key,value))
       def get[T](key: String): KVStore[Option[T]] =
         Free.liftF[KVStoreA,Option[T]](Get[T](key))
       def del(key: String): KVStore[Unit] =
         Free.liftF[KVStoreA,Unit](Del(key))
       def mod[T](key: String, f: T => T): KVStore[Unit] =
         for {
           opt <- get[T](key)
           _ <- opt.map {t => put[T](key,f(t))}.getOrElse(Free.pure(()))
         } yield()
     }

注意一下mod函数：它是由基础函数get和put组合而成。我们要求所有在for内的类型为Free[KVStoreA,?]，所以当f函数施用后如果opt变成None时就返回结果Free.pure(())，它的类型是：Free[Nothing,Unit]，Nothing是KVStoreA的子类。

现在我们可以用这个DSL来编制KVS程序了：

  object DSLs {
     import ADTs._
     import KVStoreA._
     def prg: KVStore[Option[Int]] =
     for {
       _ <- put[Int]("wild-cats", )
       _ <- mod[Int]("wild-cats", (_ + ))
       _ <- put[Int]("tame-cats", )
       n <- get[Int]("wild-cats")
       _ <- del("tame-cats")
     } yield n
   }

我们可以通过State数据结纯代码（pure code）方式来实现用immutable map的KVStore：

  object IMPLs {
     import ADTs._
     import cats.{~>}
     import cats.data.State

     type KVStoreState[A] = State[Map[String, Any], A]
     val kvsToState: KVStoreA ~> KVStoreState = new (KVStoreA ~> KVStoreState) {
       def apply[A](fa: KVStoreA[A]): KVStoreState[A] =
         fa match {
           case Put(key, value) => State { (s:Map[String, Any]) =>
              (s.updated(key, value),()) }
           case Get(key) => State { (s:Map[String, Any]) =>
             (s,s.get(key).asInstanceOf[A]) }
           case Del(key) => State { (s:Map[String, Any]) =>
               (s - key, (())) }
         }
     }
   }

我们把KVStoreA ADT模拟成对State结构的S转换（mutation），返回State{S=>(S,A)}。KVStoreState[A]类型的S参数为immutable.Map[String, Any]，所以我们在S转换操作时用immutable map的操作函数来构建新的map返回，典型的pure code。我们来运算一下KVStoreA程序：

   import ADTs._,DSLs._,IMPLs._
   val prgRunner = prg.foldMap(kvsToState)    //> prgRunner  : demo.ws.catsFreeKVS.IMPLs.KVStoreState[Option[Int]] = cats.data.StateT@2cfb4a64
   prgRunner.run(Map.empty).value       //> res0: (Map[String,Any], Option[Int]) = (Map(wild-cats -> 14),Some(14))

但是难道不需要Monad、RecursiveTailRecM实例了吗？实际上cats已经提供了State的Monad和RecursiveTailRecM实例：

   import cats.{Monad,RecursiveTailRecM}
   implicitly[Monad[KVStoreState]]      //> res1: cats.Monad[demo.ws.catsFreeKVS.IMPLs.KVStoreState] = cats.data.StateT Instances$$anon$2@71bbf57e
   implicitly[RecursiveTailRecM[KVStoreState]]     //> res2: cats.RecursiveTailRecM[demo.ws.catsFreeKVS.IMPLs.KVStoreState] = cats.RecursiveTailRecM$$anon$1@7f13d6e

在cats的StateT.scala里可以找到这段代码：

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 }
}

我把上面两个示范的源代码提供在下面：

Interact:

 import cats.free._
 import cats.{Functor, RecursiveTailRecM}
 object catsFree {
   object ADTs {
     sealed trait Interact[+A]
     object Interact {
       case class Ask(prompt: String) extends Interact[String]
       case class Tell(msg: String) extends Interact[Unit]

       def ask(prompt: String): Free[Interact,String] = Free.liftF(Ask(prompt))
       def tell(msg: String): Free[Interact,Unit] = Free.liftF(Tell(msg))

       implicit object interactFunctor extends Functor[Interact]  {
         def map[A,B](ia: Interact[A])(f: A => B): Interact[B] = ???
         /*   ia match {
              case Ask(p) => ???
              case Tell(m) => ???
           } */
       }

       sealed trait FunInteract[NS]
       object FunInteract {
         case class FunAsk[NS](prompt: String, onInput: String =>  NS) extends FunInteract[NS]
         case class FunTell[NS](msg: String, ns: NS) extends FunInteract[NS]

         def funAsk(prompt: String): Free[FunInteract,String] = Free.liftF(FunAsk(prompt,identity))
         def funAskInt(prompt: String): Free[FunInteract,Int] = Free.liftF(FunAsk(prompt,_.toInt))
         def funTell(msg: String): Free[FunInteract,Unit] = Free.liftF(FunTell(msg,()))

         implicit object funInteract extends Functor[FunInteract] {
           def map[A,NS](fa: FunInteract[A])(f: A => NS) = fa match {
             case FunAsk(prompt,input) => FunAsk(prompt,input andThen f)
             case FunTell(msg,ns) => FunTell(msg,f(ns))
           }
         }
       }
     }
   }
   object DSLs {
     import ADTs._
     import Interact._
     val prg: Free[Interact,Unit] = for {
       first <- ask("What's your first name?")
       last <- ask("What's your last name?")
       _ <- tell(s"Hello $first $last")
     } yield()
   }
   object IMPLs {
     import cats.{Id,~>}
     import ADTs._
     import Interact._
     object iconsole extends (Interact ~> Id) {
       def apply[A](ia: Interact[A]): Id[A] = ia match {
         case Ask(p) => {println(p); readLine}
         case Tell(m) => println(m)
       }
     }

     type Prompt = String
     type Reply = String
     type Message = String
     type Tester[A] = Map[Prompt,Reply] => (List[Message],A)
     object tester extends (Interact ~> Tester) {
       def apply[A](ia: Interact[A]): Tester[A] = ia match {
         case Ask(p) => { m => (List(), m(p)) }
         case Tell(m) => { _ => (List(m), ()) }
       }
     }
     import cats.Monad
     implicit val testerMonad = new Monad[Tester] with RecursiveTailRecM[Tester]{
       override def pure[A](a: A): Tester[A] = _ => (List(),a)
       override def flatMap[A,B](ta: Tester[A])(f: A => Tester[B]): Tester[B] = m => {
         val (o1,a1) = ta(m)
         val (o2,a2) = f(a1)(m)
         (o1 ++ o2, a2)
       }
       override def tailRecM[A,B](a: A)(f: A => Tester[Either[A,B]]): Tester[B] =
         defaultTailRecM(a)(f)
     }
     import cats.data.WriterT
     import cats.instances.all._
     type WF[A] = Map[Prompt,Reply] => A
     type WriterTester[A] = WriterT[WF,List[Message],A]
     def testerToWriter[A](f: Map[Prompt,Reply] => (List[Message],A)) =
       WriterT[WF,List[Message],A](f)
     implicit val testWriterMonad =  WriterT.catsDataMonadWriterForWriterT[WF,List[Message]]
     object testWriter extends (Interact ~> WriterTester) {
       import Interact._
       def apply[A](ia: Interact[A]): WriterTester[A] = ia match {
         case Ask(p) => testerToWriter(m => (List(),m(p)))
         case Tell(m) => testerToWriter(_ => (List(m),()))
       }
     }
   }

   import ADTs._,DSLs._,IMPLs._
    val testData = Map("What's your first name?" -> "Tiger",
   "What's your last name?" -> "Chan")
   //val prgRunner = prg.foldMap(tester)
   //prgRunner(testData)
   implicit val testWriterRecT = new RecursiveTailRecM[WriterTester]{}
   val prgRunner = prg.foldMap(testWriter)
   prgRunner.run(testData)._1.map(println)
 }

KVStore：

 import cats.free._
 import cats.instances.all._
 object catsFreeKVS {
   object ADTs {
     sealed trait KVStoreA[+A]
     case class Put[T](key: String, value: T) extends KVStoreA[Unit]
     case class Get[T](key: String) extends KVStoreA[Option[T]]
     case class Del(key: String) extends KVStoreA[Unit]
     type KVStore[A] = Free[KVStoreA,A]
     object KVStoreA {
       def put[T](key: String, value: T): KVStore[Unit] =
         Free.liftF[KVStoreA,Unit](Put[T](key,value))
       def get[T](key: String): KVStore[Option[T]] =
         Free.liftF[KVStoreA,Option[T]](Get[T](key))
       def del(key: String): KVStore[Unit] =
         Free.liftF[KVStoreA,Unit](Del(key))
       def mod[T](key: String, f: T => T): KVStore[Unit] =
         for {
           opt <- get[T](key)
           _ <- opt.map {t => put[T](key,f(t))}.getOrElse(Free.pure(()))
         } yield()
     }
   }
   object DSLs {
     import ADTs._
     import KVStoreA._
     def prg: KVStore[Option[Int]] =
     for {
       _ <- put[Int]("wild-cats", )
       _ <- mod[Int]("wild-cats", (_ + ))
       _ <- put[Int]("tame-cats", )
       n <- get[Int]("wild-cats")
       _ <- del("tame-cats")
     } yield n
   }
   object IMPLs {
     import ADTs._
     import cats.{~>}
     import cats.data.State

     type KVStoreState[A] = State[Map[String, Any], A]
     val kvsToState: KVStoreA ~> KVStoreState = new (KVStoreA ~> KVStoreState) {
       def apply[A](fa: KVStoreA[A]): KVStoreState[A] =
         fa match {
           case Put(key, value) => State { (s:Map[String, Any]) =>
              (s.updated(key, value),()) }
           case Get(key) => State { (s:Map[String, Any]) =>
             (s,s.get(key).asInstanceOf[A]) }
           case Del(key) => State { (s:Map[String, Any]) =>
               (s - key, (())) }
         }
     }
   }
   import ADTs._,DSLs._,IMPLs._
   val prgRunner = prg.foldMap(kvsToState)
   prgRunner.run(Map.empty).value

   import cats.{Monad,RecursiveTailRecM}
   implicitly[Monad[KVStoreState]]
   implicitly[RecursiveTailRecM[KVStoreState]]
 }