Scalaz（36）－ Free ：实践－Free In Action

  在上面几期讨论中我们连续介绍了Free Monad。因为FP是纯函数编程，也既是纯函数的组合集成，要求把纯代码和副作用代码可以分离开来。Free Monad的程序描述（AST）和程序实现（Interpretation）关注分离（separation of concern）模式恰恰能满足FP要求。我们可以用一些代数数据类型（ADT Algebraic Data Type）来模拟功能，再把这些ADT组合起来形成AST（Abstract Syntax Tree）。AST既是对程序功能的描述，它的组成过程也就是Monadic Programming了。在另外一个过程中，我们可以按需要去实现各种Interpreter，从而达到实际运算的目的。我认为既然FP也被称为Monadic Programming，那么Free Monad应该是FP里最重要的数据结构，它的应用模式代表了主流FP，应该有个规范的具体使用方式。在本次讨论中我们将会集中对Free Monad的应用模式进行示范体验。

 我们在这次示范中模拟一个针对键值存储（Key Value Store）的操作例子：

 1、ADT设计

sealed trait KVS[+Next]
object KVS {
 case class Get[Next](key: String, onValue: String => Next) extends KVS[Next]
 case class Put[Next](key: String, value: String, n: Next) extends KVS[Next]
 case class Del[Next](key: String, n: Next) extends KVS[Next]

 KVS[+Next]就是一种F[A]类型。从Suspend[F[Free[F,A]]可以得出A类型即Free类型，那么Next就是一个Free类，代表Free的下一个状态。如果需要使用Next，F[_]必须是个Functor, 这样才能通过F.map(A=>B)来获取F[B]，B==另一个Free。 Put,Del模拟了无返回结果指令，那么如果需要链接到下一个Free状态的话就直接把一个Free放人Next位置。Get返回一个String，onValue函数接过这个返回值再连接到下一个Free状态。

2、获取Functor实例

  implicit val kvsFunctor = new Functor[KVS] {
     def map[A,B](kvs: KVS[A])(f: A => B): KVS[B] = kvs match {
       case Get(key, onResult) => Get(key, onResult andThen f)
       case Put(key, value, next) => Put(key,value,f(next))
       case Del(key,next) => Del(key,f(next))
     }
  }

把A转换成B就是把Free[KVS,A]转成Free[KVS,B]，其实就是map over Next，对Next进行转换。对于函数C=>Next，map就是函数组合了：(C=>Next) andThen (Next=>B)。

3、类型升格，lift to Free

implicit def kvsToFree[A](ka: KVS[A]): Free[KVS,A] = Free.liftF(ka)
 def put(key: String , value: String): Free[KVS,Unit] = Free.liftF(Put(key,value,()))
 def get(key: String): Free[KVS,String] = Free.liftF(Get(key,identity))
 def del(key: String): Free[KVS,Unit] = Free.liftF(Del(key,()))

包括隐式类型转换kvsToFree，可以把任何KVS[A]升格成Free[KVS,A]。独立指令升格put,get,del，因为不涉及下一个状态所以使用了()和identity。

4、Composition，Free Monad组合

import KVS._
def modify(key: String, f: String => String): Free[KVS,Unit] =
  for {
   v <- Get(key,identity)
   _ <- Put(key,f(v), ())
  } yield()              //> modify: (key: String, f: String => String)scalaz.Free[Exercises.freeExamples.KVS,Unit]

通过隐式函数kvsToFree把ADT Get,Put升格成Free[KVS,A]，然后实现函数组合。

5、功能描述，AST设计

val script = for {
  _ <- put("USA","United States Of America")
  _ <- put("CHN","China")
  _ <- put("PIL","Pilipines")
  _ <- put("JPN","Japan")
  _ <- modify("CHN",_ =>"People's Republic Of China")
  _ <- del("PIL")
  chn <- get("CHN")
} yield chn              //> script  : scalaz.Free[Exercises.freeExamples.KVS,String] = Gosub()

使用的是独立直接升格指令函数。函数直接返回了Free类型。就像是在for-loop里进行我们熟悉的行令编程：逐条指令编写。

6、功能实现，Interpretation

a、尾递归编译，tail-recursive interpretation

def foldScript(kvs: Free[KVS,String],table: Map[String,String] = Map.empty): Map[String,String] =
  kvs.resume.fold (
  {
    case Get(key,onResult) => foldScript(onResult(table(key)), table)
    case Put(key,value, next) => foldScript(next, table + (key -> value))
    case Del(key,next) => foldScript(next, table - key)
  },
  _ => table
 )              //> foldScript: (kvs: scalaz.Free[Exercises.freeExamples.KVS,String], table: Map[String,String])Map[String,String]
 foldScript(script,Map.empty)     //> res0: Map[String,String] = Map(USA -> United States Of America, CHN -> People's Republic Of China, JPN -> Japan)

注意，fold其实是Either.fold。foldScript是个尾递归函数。这时候Next就成为下一步递归的链接了。

b、foldMap，高阶类型转换，Natural Transformation，F[A]～>G[A]

type KVState[A] = State[Map[String,String],A]
 object KvsToMap extends (KVS ~> KVState) {
   def apply[A](kvs: KVS[A]): KVState[A] = kvs match {
      case Get(key,onResult) => State { m => (m, onResult(m(key))) }
      case Put(key,value,next) => State { m => (m + (key -> value), next) }
      case Del(key,next) => State { m => (m - key, next) }
   }
 }
 script.foldMap(KvsToMap).run(Map.empty)          //> res1: scalaz.Id.Id[(Map[String,String], String)] = (Map(USA -> United States Of America, CHN -> People's Republic Of China, JPN -> Japan),People's Republic Of China)

c、mutable实现方法：

def goScript(kvs: Free[KVS,String],table: scala.collection.mutable.Map[String,String]):Unit =
   kvs.go {
     case Get(key,onResult) => onResult(table(key))
     case Put(key,value,next) => table += (key -> value); next
     case Del(key,next) => table -= key; next
   }                  //> goScript: (kvs: scalaz.Free[Exercises.freeExamples.KVS,String], table: scala.collection.mutable.Map[String,String])Unit
 val mutableMap = scala.collection.mutable.Map[String,String]()
                      //> mutableMap  : scala.collection.mutable.Map[String,String] = Map()
 goScript(script,mutableMap)
 println(mutableMap)  //> Map(JPN -> Japan, CHN -> People's Republic Of China, USA -> United States Of America)

把完整的示范源代码提供给大家：

package Exercises
import scalaz._
import Scalaz._
import scala.language.higherKinds
import scala.language.implicitConversions
object freeExamples {
sealed trait KVS[+Next]
object KVS {
 case class Get[Next](key: String, onValue: String => Next) extends KVS[Next]
 case class Put[Next](key: String, value: String, n: Next) extends KVS[Next]
 case class Del[Next](key: String, n: Next) extends KVS[Next]
  implicit val kvsFunctor = new Functor[KVS] {
     def map[A,B](kvs: KVS[A])(f: A => B): KVS[B] = kvs match {
       case Get(key, onResult) => Get(key, onResult andThen f)
       case Put(key, value, next) => Put(key,value,f(next))
       case Del(key,next) => Del(key,f(next))
     }
  }
 implicit def kvsToFree[A](ka: KVS[A]): Free[KVS,A] = Free.liftF(ka)
 def put(key: String , value: String): Free[KVS,Unit] = Free.liftF(Put(key,value,()))
 def get(key: String): Free[KVS,String] = Free.liftF(Get(key,identity))
 def del(key: String): Free[KVS,Unit] = Free.liftF(Del(key,()))
}
import KVS._
def modify(key: String, f: String => String): Free[KVS,Unit] =
  for {
   v <- Get(key,identity)
   _ <- Put(key,f(v), ())
  } yield()
val script = for {
  _ <- put("USA","United States Of America")
  _ <- put("CHN","China")
  _ <- put("PIL","Pilipines")
  _ <- put("JPN","Japan")
  _ <- modify("CHN",_ =>"People's Republic Of China")
  _ <- del("PIL")
  chn <- get("CHN")
} yield chn

def foldScript(kvs: Free[KVS,String],table: Map[String,String] = Map.empty): Map[String,String] =
  kvs.resume.fold (
  {
    case Get(key,onResult) => foldScript(onResult(table(key)), table)
    case Put(key,value, next) => foldScript(next, table + (key -> value))
    case Del(key,next) => foldScript(next, table - key)
  },
  _ => table
 )
 foldScript(script,Map.empty)

 type KVState[A] = State[Map[String,String],A]
 object KvsToMap extends (KVS ~> KVState) {
   def apply[A](kvs: KVS[A]): KVState[A] = kvs match {
      case Get(key,onResult) => State { m => (m, onResult(m(key))) }
      case Put(key,value,next) => State { m => (m + (key -> value), next) }
      case Del(key,next) => State { m => (m - key, next) }
   }
 }
 script.foldMap(KvsToMap).run(Map.empty)
 
 def goScript(kvs: Free[KVS,String],table: scala.collection.mutable.Map[String,String]):Unit =
   kvs.go {
     case Get(key,onResult) => onResult(table(key))
     case Put(key,value,next) => table += (key -> value); next
     case Del(key,next) => table -= key; next
   }
 val mutableMap = scala.collection.mutable.Map[String,String]()
 goScript(script,mutableMap)
 println(mutableMap)
}