Cats－ 从Free开始，Free cats
Posted 雪川大虫
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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：
1 import cats.free._
2 import cats.Functor
3 object catsFree {
4 object ADTs {
5 sealed trait Interact[+A]
6 object Interact {
7 case class Ask(prompt: String) extends Interact[String]
8 case class Tell(msg: String) extends Interact[Unit]
9
10 def ask(prompt: String): Free[Interact,String] = Free.liftF(Ask(prompt))
11 def tell(msg: String): Free[Interact,Unit] = Free.liftF(Tell(msg))
12
13
14 implicit object interactFunctor extends Functor[Interact] {
15 def map[A,B](ia: Interact[A])(f: A => B): Interact[B] = ???
16 /* ia match {
17 case Ask(p) => ???
18 case Tell(m) => ???
19 } */
20 }
21 }
22 }
23 object DSLs {
24 import ADTs._
25 import Interact._
26 val prg: Free[Interact,Unit] = for {
27 first <- ask("What‘s your first name?")
28 last <- ask("What‘s your last name?")
29 _ <- tell(s"Hello $first $last")
30 } yield()
31 }
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：
1 implicit object interactFunctor extends Functor[Interact] {
2 def map[A,B](ia: Interact[A])(f: A => B): Interact[B] = ia match {
3 case Ask(p) => ???
4 case Tell(m) => ???
5 }
6 }
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：
1 sealed trait FunInteract[NS]
2 object FunInteract {
3 case class FunAsk[NS](prompt: String, onInput: String => NS) extends FunInteract[NS]
4 case class FunTell[NS](msg: String, ns: NS) extends FunInteract[NS]
5
6 def funAsk(prompt: String): Free[FunInteract,String] = Free.liftF(FunAsk(prompt,identity))
7 def funAskInt(prompt: String): Free[FunInteract,Int] = Free.liftF(FunAsk(prompt,_.toInt))
8 def funTell(msg: String): Free[FunInteract,Unit] = Free.liftF(FunTell(msg,()))
9
10 implicit object funInteract extends Functor[FunInteract] {
11 def map[A,NS](fa: FunInteract[A])(f: A => NS) = fa match {
12 case FunAsk(prompt,input) => FunAsk(prompt,input andThen f)
13 case FunTell(msg,ns) => FunTell(msg,f(ns))
14 }
15 }
16 }
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）：
1 import ADTs._
2 object iconsole extends (Interact ~> Id) {
3 def apply[A](ia: Interact[A]): Id[A] = ia match {
4 case Ask(p) => {println(p); readLine}
5 case Tell(m) => println(m)
6 }
7 }
8 }
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：
1 type Prompt = String
2 type Reply = String
3 type Message = String
4 type Tester[A] = Map[Prompt,Reply] => (List[Message],A)
5 object tester extends (Interact ~> Tester) {
6 def apply[A](ia: Interact[A]): Tester[A] = ia match {
7 case Ask(p) => { m => (List(), m(p)) }
8 case Tell(m) => { _ => (List(m), ()) }
9 }
10 }
11 import cats.Monad
12 implicit val testerMonad = new Monad[Tester] {
13 override def pure[A](a: A): Tester[A] = _ => (List(),a)
14 override def flatMap[A,B](ta: Tester[A])(f: A => Tester[B]): Tester[B] = m => {
15 val (o1,a1) = ta(m)
16 val (o2,a2) = f(a1)(m)
17 (o1 ++ o2, a2)
18 }
19 override def tailRecM[A,B](a: A)(f: A => Tester[Either[A,B]]): Tester[B] =
20 defaultTailRecM(a)(f)
21 }
22 }
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：
1 import cats.data.WriterT
2 type WF[A] = Map[Prompt,Reply] => A
3 type WriterTester[A] = WriterT[WF,List[Message],A]
4 def testerToWriter[A](f: Map[Prompt,Reply] => (List[Message],A)) =
5 WriterT[WF,List[Message],A](f)
6 object testWriter extends (Interact ~> WriterTester) {
7 import Interact._
8 def apply[A](ia: Interact[A]): WriterTester[A] = ia match {
9 case Ask(p) => testerToWriter(m => (List(),m(p)))
10 case Tell(m) => testerToWriter(_ => (List(m),()))
11 }
12 }
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：
1 import cats.Monad
2 implicit val testerMonad = new Monad[Tester] with RecursiveTailRecM[Tester]{
3 override def pure[A](a: A): Tester[A] = _ => (List(),a)
4 override def flatMap[A,B](ta: Tester[A])(f: A => Tester[B]): Tester[B] = m => {
5 val (o1,a1) = ta(m)
6 val (o2,a2) = f(a1)(m)
7 (o1 ++ o2, a2)
8 }
9 override def tailRecM[A,B](a: A)(f: A => Tester[Either[A,B]]): Tester[B] =
10 defaultTailRecM(a)(f)
11 }
然后我们制造一些测试数据：
1 val testData = Map("What‘s your first name?" -> "Tiger",
2 "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：
1 import ADTs._,DSLs._,IMPLs._
2 val testData = Map("What‘s your first name?" -> "Tiger",
3 "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)
4 val prgRunner = prg.foldMap(tester) ?//> prgRunner : demo.ws.catsFree.IMPLs.Tester[Unit] = <function1>
5 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：
1 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：
1 implicit val testWriterRecT = new RecursiveTailRecM[WriterTester]{}
2 ?//> testWriterRecT : cats.RecursiveTailRecM[demo.ws.catsFree.IMPLs.WriterTester] = [email protected]
3 val prgRunner = prg.foldMap(testWriter) //> prgRunner : demo.ws.catsFree.IMPLs.WriterTester[Unit] = WriterT(<function1>)
4 prgRunner.run(testData)._1.map(println) //> Hello Tiger Chan
5 //| 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：
1 object ADTs {
2 sealed trait KVStoreA[+A]
3 case class Put[T](key: String, value: T) extends KVStoreA[Unit]
4 case class Get[T](key: String) extends KVStoreA[Option[T]]
5 case class Del(key: String) extends KVStoreA[Unit]
6 }
对应的模拟功能函数设计如下：
1 type KVStore[A] = Free[KVStoreA,A]
2 object KVStoreA {
3 def put[T](key: String, value: T): KVStore[Unit] =
4 Free.liftF[KVStoreA,Unit](Put[T](key,value))
5 def get[T](key: String): KVStore[Option[T]] =
6 Free.liftF[KVStoreA,Option[T]](Get[T](key))
7 def del(key: String): KVStore[Unit] =
8 Free.liftF[KVStoreA,Unit](Del(key))
9 def mod[T](key: String, f: T => T): KVStore[Unit] =
10 for {
11 opt <- get[T](key)
12 _ <- opt.map {t => put[T](key,f(t))}.getOrElse(Free.pure(()))
13 } yield()
14 }
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：
1 object DSLs { 2 import ADTs._ 3 import KVStoreA._ 4 def prg: KVStore[Option[Int]] = 5 for { 6 _ <- put[Int]("wild-cats", 2) 7 _ <- mod[Int]("wild-cats", (_ + 12)) 8 _ <- put[Int]("tame-cats", 5) 9 n <- get[Int]("wild-cats") 10 _ <- del("tame-cats") 11 } yield n 12 }
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：
1 object IMPLs {
2 import ADTs._
3 import cats.{~>}
4 import cats.data.State
5
6 type KVStoreState[A] = State[Map[String, Any], A]
7 val kvsToState: KVStoreA ~> KVStoreState = new (KVStoreA ~> KVStoreState) {
8 def apply[A](fa: KVStoreA[A]): KVStoreState[A] =
9 fa match {
10 case Put(key, value) => State { (s:Map[String, Any]) =>
11 (s.updated(key, value),()) }
12 case Get(key) => State { (s:Map[String, Any]) =>
13 (s,s.get(key).asInstanceOf[A]) }
14 case Del(key) => State { (s:Map[String, Any]) =>
15 (s - key, (())) }
16 }
17 }
18 }
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：
1 import ADTs._,DSLs._,IMPLs._
2 val prgRunner = prg.foldMap(kvsToState) //> prgRunner : demo.ws.catsFreeKVS.IMPLs.KVStoreState[Option[Int]] = [email protected]
3 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：
1 import cats.{Monad,RecursiveTailRecM}
2 implicitly[Monad[KVStoreState]] //> res1: cats.Monad[demo.ws.catsFreeKVS.IMPLs.KVStoreState] = cats.data.StateT [email protected]
3 implicitly[RecursiveTailRecM[KVStoreState]] //> res2: cats.RecursiveTailRecM[demo.ws.catsFreeKVS.IMPLs.KVStoreState] = [email protected]
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:
1 import cats.free._ 2 import cats.{Functor, RecursiveTailRecM} 3 object catsFree { 4 object ADTs { 5 sealed trait Interact[+A] 6 object Interact { 7 case class Ask(prompt: String) extends Interact[String] 8 case class Tell(msg: String) extends Interact[Unit] 9 10 def ask(prompt: String): Free[Interact,String] = Free.liftF(Ask(prompt)) 11 def tell(msg: String): Free[Interact,Unit] = Free.liftF(Tell(msg)) 12 13 14 implicit object interactFunctor extends Functor[Interact] { 15 def map[A,B](ia: Interact[A])(f: A => B): Interact[B] = ??? 16 /* ia match { 17 case Ask(p) => ??? 18 case Tell(m) => ??? 19 } */ 20 } 21 22 sealed trait FunInteract[NS] 23 object FunInteract { 24 case class FunAsk[NS](prompt: String, onInput: String => NS) extends FunInteract[NS] 25 case class FunTell[NS](msg: String, ns: NS) extends FunInteract[NS] 26 27 def funAsk(prompt: String): Free[FunInteract,String] = Free.liftF(FunAsk(prompt,identity)) 28 def funAskInt(prompt: String): Free[FunInteract,Int] = Free.liftF(FunAsk(prompt,_.toInt)) 29 def funTell(msg: String): Free[FunInteract,Unit] = Free.liftF(FunTell(msg,())) 30 31 implicit object funInteract extends Functor[FunInteract] { 32 def map[A,NS](fa: FunInteract[A])(f: A => NS) = fa match { 33 case FunAsk(prompt,input) => FunAsk(prompt,input andThen f) 34 case FunTell(msg,ns) => FunTell(msg,f(ns)) 35 } 36 } 37 } 38 } 39 } 40 object DSLs { 41 import ADTs._ 42 import Interact._ 43 val prg: Free[Interact,Unit] = for { 44 first <- ask("What‘s your first name?") 45 last <- ask("What‘s your last name?") 46 _ <- tell(s"Hello $first $last") 47 } yield() 48 } 49 object IMPLs { 50 import cats.{Id,~>} 51 import ADTs._ 52 import Interact._ 53 object iconsole extends (Interact ~> Id) { 54 def apply[A](ia: Interact[A]): Id[A] = ia match { 55 case Ask(p) => {println(p); readLine} 56 case Tell(m) => println(m) 57 } 58 } 59 60 type Prompt = String 61 type Reply = String 62 type Message = String 63 type Tester[A] = Map[Prompt,Reply] => (List[Message],A) 64 object tester extends (Interact ~> Tester) { 65 def apply[A](ia: Interact[A]): Tester[A] = ia match { 66 case Ask(p) => { m => (List(), m(p)) } 67 case Tell(m) => { _ => (List(m), ()) } 68 } 69 } 70 import cats.Monad 71 implicit val testerMonad = new Monad[Tester] with RecursiveTailRecM[Tester]{ 72 override def pure[A](a: A): Tester[A] = _ => (List(),a) 73 override def flatMap[A,B](ta: Tester[A])(f: A => Tester[B]): Tester[B] = m => { 74 val (o1,a1) = ta(m) 75 val (o2,a2) = f(a1)(m) 76 (o1 ++ o2, a2) 77 } 78 override def tailRecM[A,B](a: A)(f: A => Tester[Either[A,B]]): Tester[B] = 79 defaultTailRecM(a)(f) 80 } 81 import cats.data.WriterT 82 import cats.instances.all._ 83 type WF[A] = Map[Prompt,Reply] => A 84 type WriterTester[A] = WriterT[WF,List[Message],A] 85 def testerToWriter[A](f: Map[Prompt,Reply] => (List[Message],A)) = 86 WriterT[WF,List[Message],A](f) 87 implicit val testWriterMonad = WriterT.catsDataMonadWriterForWriterT[WF,List[Message]] 88 object testWriter extends (Interact ~> WriterTester) { 89 import Interact._ 90 def apply[A](ia: Interact[A]): WriterTester[A] = ia match { 91 case Ask(p) => testerToWriter(m => (List(),m(p))) 92 case Tell(m) => testerToWriter(_ => (List(m),())) 93 } 94 } 95 } 96 97 import ADTs._,DSLs._,IMPLs._ 98 val testData = Map("What‘s your first name?" -> "Tiger", 99 "What‘s your last name?" -> "Chan") 100 //val prgRunner = prg.foldMap(tester) 101 //prgRunner(testData) 102 implicit val testWriterRecT = new RecursiveTailRecM[WriterTester]{} 103 val prgRunner = prg.foldMap(testWriter) 104 prgRunner.run(testData)._1.map(println) 105 }
KVStore：
1 import cats.free._ 2 import cats.instances.all._ 3 object catsFreeKVS { 4 object ADTs { 5 sealed trait KVStoreA[+A] 6 case class Put[T](key: String, value: T) extends KVStoreA[Unit] 7 case class Get[T](key: String) extends KVStoreA[Option[T]] 8 case class Del(key: String) extends KVStoreA[Unit] 9 type KVStore[A] = Free[KVStoreA,A] 10 object KVStoreA { 11 def put[T](key: String, value: T): KVStore[Unit] = 12 Free.liftF[KVStoreA,Unit](Put[T](key,value)) 13 def get[T](key: String): KVStore[Option[T]] = 14 Free.liftF[KVStoreA,Option[T]](Get[T](key)) 15 def del(key: String): KVStore[Unit] = 16 Free.liftF[KVStoreA,Unit](Del(key)) 17 def mod[T](key: String, f: T => T): KVStore[Unit] = 18 for { 19 opt <- get[T](key) 20 _ <- opt.map {t => put[T](key,f(t))}.getOrElse(Free.pure(())) 21 } yield() 22 } 23 } 24 object DSLs { 25 import ADTs._ 26 import KVStoreA._ 27 def prg: KVStore[Option[Int]] = 28 for { 29 _ <- put[Int]("wild-cats", 2) 30 _ <- mod[Int]("wild-cats", (_ + 12)) 31 _ <- put[Int]("tame-cats", 5) 32 n <- get[Int]("wild-cats") 33 _ <- del("tame-cats") 34 } yield n 35 } 36 object IMPLs { 37 import ADTs._ 38 import cats.{~>} 39 import cats.data.State 40 41 type KVStoreState[A] = State[Map[String, Any], A] 42 val kvsToState: KVStoreA ~> KVStoreState = new (KVStoreA ~> KVStoreState) { 43 def apply[A](fa: KVStoreA[A]): KVStoreState[A] = 44 fa match { 45 case Put(key, value) => State { (s:Map[String, Any]) => 46 (s.updated(key, value),()) } 47 case Get(key) => State { (s:Map[String, Any]) => 48 (s,s.get(key).asInstanceOf[A]) } 49 case Del(key) => State { (s:Map[String, Any]) => 50 (s - key, (())) } 51 } 52 } 53 } 54 import ADTs._,DSLs._,IMPLs._ 55 val prgRunner = prg.foldMap(kvsToState) 56 prgRunner.run(Map.empty).value 57 58 import cats.{Monad,RecursiveTailRecM} 59 implicitly[Monad[KVStoreState]] 60 implicitly[RecursiveTailRecM[KVStoreState]] 61 }
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Cats－ Free语法组合，Coproduct-ADT composition