说道FP,我们马上会联想到Monad。我们说过Monad的代表函数flatMap可以把两个运算F[A],F[B]连续起来，这样就可以从程序的意义上形成一种串型的流程（workflow）。更直白的讲法是：任何类型只要实现了flatMap就可以用for-comprehension, for{...}yield。在这个for{...}里我们可以好像OOP一样编写程序。这个for就是一种运算模式，它规范了在for{...}里指令的行为。我们正从OOP风格走入FP编程模式，希望有个最基本的FP编程模式使我们能够沿用OOP编程风格的语法和思维。Monad应该就是最合适的泛函数据类型了。我们先从最基本的开始：假如我们有一段行令程序：
/*
val a = e1
val b = e2(a)
val c = e3(a,b)
val d = e2(c)
*/
通过这些函数e1,e2,e3最后计算出d值。如果是用FP风格来编这段程序的话，首先我们必须把函数的结果d放入F[d]的F里。F就是上面所说的运算模式，在这里可以用大家熟悉的context（上下文）来表示。F必须是个Monad，F[]相当于for{...}yield。我们先试试用Id，虽然Id[A]对A不做任何处理，直接返回，好像没什么意义，但这种类型具备了map和flatMap，应该可以用for-comprehension：
1 import scalaz._
2 import Scalaz._
3 def e1:Id[Int] = 10 //> e1: => scalaz.Scalaz.Id[Int]
4 def e2(a: Int): Id[Int] = a + 1 //> e2: (a: Int)scalaz.Scalaz.Id[Int]
5 def e3(a: Int, b: Int): Id[Int] = a + b //> e3: (a: Int, b: Int)scalaz.Scalaz.Id[Int]
6 for {
7 a <- e1
8 b <- e2(a)
9 c <- e3(a,b)
10 d <- e2(c)
11 } yield d //> res0: scalaz.Scalaz.Id[Int] = 22
可以看到，在for-loop里就是OOP的行令程序。不过如果觉着这个Id没什么意义，可以试试Option看：
1 import scalaz._
2 import Scalaz._
3 def e1:Option[Int] = 10.some //> e1: => Option[Int]
4 def e2(a: Int): Option[Int] = (a + 1).some //> e2: (a: Int)Option[Int]
5 def e3(a: Int, b: Int): Option[Int] = (a + b).some//> e3: (a: Int, b: Int)Option[Int]
6 for {
7 a <- e1
8 b <- e2(a)
9 c <- e3(a,b)
10 d <- e2(c)
11 } yield d //> res0: Option[Int] = Some(22)
看，虽然换了个壳子（context）, 但for-loop里的程序没有变化。换一句话讲就是for-loop里的程序根本不理会包裹的context。
Reader也是一种Monad，用它又怎样呢：
1 import scalaz._
2 import Scalaz._
3 def e1:Reader[Int,Int] = Reader[Int,Int](a => a) //> e1: => scalaz.Reader[Int,Int]
4 def e2(a: Int): Reader[Int,Int] = Reader[Int,Int](_ => a + 1)
5 //> e2: (a: Int)scalaz.Reader[Int,Int]
6 def e3(a: Int, b: Int): Reader[Int, Int] = Reader[Int,Int](_ => a+b)
7 //> e3: (a: Int, b: Int)scalaz.Reader[Int,Int]
8 val prg = for {
9 a <- e1
10 b <- e2(a)
11 c <- e3(a,b)
12 d <- e2(c)
13 } yield d //> prg : scalaz.Kleisli[scalaz.Id.Id,Int,Int] = Kleisli(<function1>)
14 prg.run(10) //> res0: scalaz.Id.Id[Int] = 22
虽然在语法上有些蹩脚，但还是证明了for-loop里的程序是不理会外面context的。那么我们可不可以说这个prg就是一个简单的FP编程语言。它把运算结果放在context里，直至运行了某种interpreter才能取得实际的运算值（用run(10)得到22）。当然，一段程序，它的运算行为受制于单一种类型的context可能有些弱了。如果需要获得一种可用的FP编程语言，我们可能还是要探讨如何把单一类型context组合成多类型混合的context。
我们发现在scalaz里有些type class的名称是以T结束的如：ReaderT,WriterT,StateT等等。这个T指的是变形器Transformer，意思是用它可以堆砌（stacking）context。看看StateT，简单定义应该是这样的:
case class StateT[F[_],S,A](run: S => F[(S,A)])
我们可以把F类堆砌在State上。实践证明如果这个F实现了flatMap，那么堆砌成的类型也能实现flatMap。好，scalaz的Option是实现了flatMap的，那么能不能把它和State堆砌在一起呢？堆砌而成的context会有什么效果呢？我们先看看单一Option和State作为一种context的效果：
1 for {
2 a <- 3.some
3 b <- (None: Option[Int])
4 c <- 4.some
5 } yield c //> res1: Option[Int] = None
6 val statePrg = for {
7 a <- get[Int]
8 b <- State[Int,Int](s => (s, s + a))
9 _ <- put(9)
10 } yield b //> statePrg : scalaz.IndexedStateT[scalaz.Id.Id,Int,Int,Int] = scalaz.IndexedS
11 //| tateT$$anon$10@15ff3e9e
12 statePrg.run(3) //> res2: scalaz.Id.Id[(Int, Int)] = (9,6)
依我来看，Option主要效果是在遇到None值时立即退出。而State的主要作用是在运算同时可以维护一个状态。那么如果把Option和State叠加起来就会同时具备这两种类型的特点了吧？也就是既能维护状态又能在遇到None值时立即终止运算退出了。首先验证一下用Option的flatMap来实现叠加context的flatMap:
case class OptionState[S,A](run: S => Option[(S,A)]) {
def map[B](f: A => B): OptionState[S,B] =
OptionState {
s => run(s) map { case (s1,a1) => (s1,f(a1)) }
}
def flatMap[B](f: A => OptionState[S,B]): OptionState[S,B] =
OptionState {
s => run(s) flatMap { case (s1,a1) => f(a1).run(s1) }
}
}
是的，我们可以用Option的map和flatMap来实现OptionState的map和flatMap。当然，如果我们想在一个for-comprehension里同时使用Option和State就必须把它们升格成OptionState类型：
def liftOption[S,A](oa: Option[A]): OptionState[S,A] = oa match {
case Some(a) => OptionState {s => (s,a).some }
case None => OptionState {_ => none}
}
def liftState[S,A](sa: State[S,A]): OptionState[S,A] =
OptionState {s => sa(s).some}
现在试试用叠加效果的for-comprehension：
1 val osprg: OptionState[Int,Int] = for {
2 a <- liftOption(3.some)
3 b <- liftState(put(a))
4 c <- liftState(get[Int])
5 d <- liftState(State[Int,Int](s => (s+c, s+a)))
6 } yield c //> osprg : Exercises.rws.OptionState[Int,Int] = OptionState(<function1>)
7 osprg.run(2) //> res3: Option[(Int, Int)] = Some((6,3))
8 val osprg1: OptionState[Int,Int] = for {
9 a <- liftOption(3.some)
10 b <- liftState(put(a))
11 _ <- liftOption((None: Option[Int]))
12 c <- liftState(get[Int])
13 d <- liftState(State[Int,Int](s => (s+c, s+a)))
14 } yield c //> osprg1 : Exercises.rws.OptionState[Int,Int] = OptionState(<function1>)
15 osprg1.run(2) //> res4: Option[(Int, Int)] = None
看，既可以维护状态又具备None处理机制。
好了，scalaz里有个ReaderWriterState这么个type class，就是一个Reader+Writer+State堆砌的Monad。相信scalaz特别提供了这么个type class应该有它的用意。我的猜想是这个Monad是个功能比较完整的组合Monad。作为for-comprehension的context应该能提供比较全面的效果。从字意上解释就是在由它形成的Monadic编程语言里可以同时提供运算（compute）、跟踪(logging)和状态维护功能。它的基础类型是IndexedReaderWriterStateT：scalaz/package.scala
type ReaderWriterStateT[F[_], -R, W, S, A] = IndexedReaderWriterStateT[F, R, W, S, S, A]
object ReaderWriterStateT extends ReaderWriterStateTInstances with ReaderWriterStateTFunctions {
def apply[F[_], R, W, S, A](f: (R, S) => F[(W, A, S)]): ReaderWriterStateT[F, R, W, S, A] = IndexedReaderWriterStateT[F, R, W, S, S, A] { (r: R, s: S) => f(r, s) }
}
type IndexedReaderWriterState[-R, W, -S1, S2, A] = IndexedReaderWriterStateT[Id, R, W, S1, S2, A]
object IndexedReaderWriterState extends ReaderWriterStateTInstances with ReaderWriterStateTFunctions {
def apply[R, W, S1, S2, A](f: (R, S1) => (W, A, S2)): IndexedReaderWriterState[R, W, S1, S2, A] = IndexedReaderWriterStateT[Id, R, W, S1, S2, A] { (r: R, s: S1) => f(r, s) }
}
type ReaderWriterState[-R, W, S, A] = ReaderWriterStateT[Id, R, W, S, A]
object ReaderWriterState extends ReaderWriterStateTInstances with ReaderWriterStateTFunctions {
def apply[R, W, S, A](f: (R, S) => (W, A, S)): ReaderWriterState[R, W, S, A] = IndexedReaderWriterStateT[Id, R, W, S, S, A] { (r: R, s: S) => f(r, s) }
}
type IRWST[F[_], -R, W, -S1, S2, A] = IndexedReaderWriterStateT[F, R, W, S1, S2, A]
val IRWST: IndexedReaderWriterStateT.type = IndexedReaderWriterStateT
type IRWS[-R, W, -S1, S2, A] = IndexedReaderWriterState[R, W, S1, S2, A]
val IRWS: IndexedReaderWriterState.type = IndexedReaderWriterState
type RWST[F[_], -R, W, S, A] = ReaderWriterStateT[F, R, W, S, A]
val RWST: ReaderWriterStateT.type = ReaderWriterStateT
type RWS[-R, W, S, A] = ReaderWriterState[R, W, S, A]
val RWS: ReaderWriterState.type = ReaderWriterState
如果把Reader,Writer,State款式分开来对比分析的话：
case class Reader[R, A](f: R => A) //传入R，返回A后不理会R
case class Writer[W, A](w: (W, A)) //直接返回W,A
case class State[S, A](f: S => (A, S)) //传入S, 返回A和S
那么把以上三个结合起来后它的款式应该是这样的了吧：
case class ReaderWriterState[R, W, S, A](
run: (R, S) => (W, A, S) //传入R,S 返回W,A,S
)
case class ReaderWriterStateT[F[_],R, W, S, A](
run: (R, S) => F[(W, A, S)] //传入R,S 返回W,A,S。只是包在了F内
)
传入的和返回的类型是匹配的。在scalaz里是这样定义的：scalaz/ReaderWriterStateT.scala
/** A monad transformer stack yielding `(R, S1) => F[(W, A, S2)]`. */
sealed abstract class IndexedReaderWriterStateT[F[_], -R, W, -S1, S2, A] {
self =>
def run(r: R, s: S1): F[(W, A, S2)]
/** Discards the writer component. */
def state(r: R)(implicit F: Functor[F]): IndexedStateT[F, S1, S2, A] =
IndexedStateT((s: S1) => F.map(run(r, s)) {
case (w, a, s1) => (s1, a)
})
/** Calls `run` using `Monoid[S].zero` as the initial state */
def runZero[S <: S1](r: R)(implicit S: Monoid[S]): F[(W, A, S2)] =
run(r, S.zero)
/** Run, discard the final state, and return the final value in the context of `F` */
def eval(r: R, s: S1)(implicit F: Functor[F]): F[(W, A)] =
F.map(run(r,s)) { case (w,a,s2) => (w,a) }
/** Calls `eval` using `Monoid[S].zero` as the initial state */
def evalZero[S <: S1](r:R)(implicit F: Functor[F], S: Monoid[S]): F[(W,A)] =
eval(r,S.zero)
/** Run, discard the final value, and return the final state in the context of `F` */
def exec(r: R, s: S1)(implicit F: Functor[F]): F[(W,S2)] =
F.map(run(r,s)){case (w,a,s2) => (w,s2)}
/** Calls `exec` using `Monoid[S].zero` as the initial state */
def execZero[S <: S1](r:R)(implicit F: Functor[F], S: Monoid[S]): F[(W,S2)] =
exec(r,S.zero)
...
我们看到IndexedReaderWriterStateT已经实现了很多IndexedStateT的运算方法如：eval,exec等。看看它的map和flatMap是怎么实现的：
def map[B](f: A => B)(implicit F: Functor[F]): IndexedStateT[F, S1, S2, B] = IndexedStateT(s => F.map(apply(s)) {
case (s1, a) => (s1, f(a))
})
def flatMap[S3, B](f: A => IndexedStateT[F, S2, S3, B])(implicit F: Bind[F]): IndexedStateT[F, S1, S3, B] = IndexedStateT(s => F.bind(apply(s)) {
case (s1, a) => f(a)(s1)
})
与我们前面所做的OptionState例子一样：如果F能实现map和flatMap则IndexedReaderWriterStateT就能实现map和flatMap。为了省却在for-loop里每行命令都使用lift进行类型升格，IndexedReaderWriterStateT重新实现了大部分操作函数:
private trait ReaderWriterStateTMonad[F[_], R, W, S]
extends MonadReader[({type λ[r, α]=ReaderWriterStateT[F, r, W, S, α]})#λ, R]
with MonadState[({type f[s, α] = ReaderWriterStateT[F, R, W, s, α]})#f, S]
with MonadListen[({type f[w, α] = ReaderWriterStateT[F, R, w, S, α]})#f, W]
with IndexedReaderWriterStateTFunctor[F, R, W, S, S] {
implicit def F: Monad[F]
implicit def W: Monoid[W]
def bind[A, B](fa: ReaderWriterStateT[F, R, W, S, A])(f: A => ReaderWriterStateT[F, R, W, S, B]): ReaderWriterStateT[F, R, W, S, B] = fa flatMap f
def point[A](a: => A): ReaderWriterStateT[F, R, W, S, A] =
ReaderWriterStateT((_, s) => F.point((W.zero, a, s)))
def ask: ReaderWriterStateT[F, R, W, S, R] =
ReaderWriterStateT((r, s) => F.point((W.zero, r, s)))
def local[A](f: R => R)(fa: ReaderWriterStateT[F, R, W, S, A]): ReaderWriterStateT[F, R, W, S, A] =
ReaderWriterStateT((r, s) => fa.run(f(r), s))
override def scope[A](k: R)(fa: ReaderWriterStateT[F, R, W, S, A]): ReaderWriterStateT[F, R, W, S, A] =
ReaderWriterStateT((_, s) => fa.run(k, s))
override def asks[A](f: R => A): ReaderWriterStateT[F, R, W, S, A] =
ReaderWriterStateT((r, s) => F.point((W.zero, f(r), s)))
def init: ReaderWriterStateT[F, R, W, S, S] =
ReaderWriterStateT((_, s) => F.point((W.zero, s, s)))
def get = init
def put(s: S): ReaderWriterStateT[F, R, W, S, Unit] =
ReaderWriterStateT((r, _) => F.point((W.zero, (), s)))
override def modify(f: S => S): ReaderWriterStateT[F, R, W, S, Unit] =
ReaderWriterStateT((r, s) => F.point((W.zero, (), f(s))))
override def gets[A](f: S => A): ReaderWriterStateT[F, R, W, S, A] =
ReaderWriterStateT((_, s) => F.point((W.zero, f(s), s)))
def writer[A](w: W, v: A): ReaderWriterStateT[F, R, W, S, A] =
ReaderWriterStateT((_, s) => F.point((w, v, s)))
override def tell(w: W): ReaderWriterStateT[F, R, W, S, Unit] =
ReaderWriterStateT((_, s) => F.point((w, (), s)))
def listen[A](ma: ReaderWriterStateT[F, R, W, S, A]): ReaderWriterStateT[F, R, W, S, (A, W)] =
ReaderWriterStateT((r, s) => F.map(ma.run(r, s)) { case (w, a, s1) => (w, (a, w), s1)})
}
我们示范用这个ReaderWriterState来写一段程序：模拟一段通讯端口使用程序并把使用情况记录下来。先传入一个端口号，在程序中可以重设使用的端口号：
1 val program: ReaderWriterState[Config, List[String], Int, Int] = for {
2 _ <- log("Start - r: %s, s: %s")
3 res <- invokeService
4 _ <- log("Between - r: %s, s: %s")
5 _ <- setService(8,"Com8")
6 _ <- invokeService
7 _ <- log("Done - r: %s, s: %s")
8 } yield res //> program : scalaz.RWS[Exercises.rws.Config,List[String],Int,Int] = scalaz.I
9 //| ndexedReaderWriterStateT$$anon$5@223191a6
这倒像是一段高级语言写的程序。细节都在几个功能函数里。它们都必须返回ReaderWriterState类型：
1 case class Config(var port: Int, var portName: String)
2 def log[R, S](msg: String): RWS[R, List[String], S, Unit] =
3 ReaderWriterState {
4 case (r, s) => (msg.format(r, s) :: Nil, (), s) //.point[Identity]
5 } //> log: [R, S](msg: String)scalaz.RWS[R,List[String],S,Unit]
6 def invokeService: ReaderWriterState[Config, List[String], Int, Int] =
7 ReaderWriterState {
8 case (cfg, invocationCount) => (
9 List("Invoking service with port: " + cfg.portName),
10 scala.util.Random.nextInt(100),
11 invocationCount + 1
12 ) //.point[Identity]
13 } //> invokeService: => scalaz.ReaderWriterState[Exercises.rws.Config,List[String
14 //| ],Int,Int]
15 def setService(p: Int, n: String): ReaderWriterState[Config, List[String], Int, Int] =
16 ReaderWriterState {
17 case (cfg, invocationCount) => cfg.port=p; cfg.portName=n
18 (List("Changing service port to " + cfg.portName),
19 scala.util.Random.nextInt(100),
20 invocationCount)
21 } //> setService: (p: Int, n: String)scalaz.ReaderWriterState[Exercises.rws.Confi
22 //| g,List[String],Int,Int]
23
24 val program: ReaderWriterState[Config, List[String], Int, Int] = for {
25 _ <- log("Start - r: %s, s: %s")
26 res <- invokeService
27 _ <- log("Between - r: %s, s: %s")
28 _ <- setService(8,"Com8")
29 _ <- invokeService
30 _ <- log("Done - r: %s, s: %s")
31 } yield res //> program : scalaz.RWS[Exercises.rws.Config,List[String],Int,Int] = scalaz.I
32 //| ndexedReaderWriterStateT$$anon$5@223191a6
33 val r = program run (Config(443,"Com3"), 0) //> r : scalaz.Id.Id[(List[String], Int, Int)] = (List(Start - r: Config(443,C
34 //| om3), s: 0, Invoking service with port: Com3, Between - r: Config(443,Com3)
35 //| , s: 1, Changing service port to Com8, Invoking service with port: Com8, Do
36 //| ne - r: Config(88,Com8), s: 2),68,2)
37 println("Result: " + r._2) //> Result: 68
38 println("Service invocations: " + r._3) //> Service invocations: 2
39 println("Log: %n%s".format(r._1.mkString(" ", "%n ".format(), "")))
40 //> Log:
41 //| Start - r: Config(443,Com3), s: 0
42 //| Invoking service with port: Com3
43 //| Between - r: Config(443,Com3), s: 1
44 //| Changing service port to Com8
45 //| Invoking service with port: Com8
46 //| Done - r: Config(88,Com8), s: 2