final case class WriterT[F[_], W, A](run: F[(W, A)]) { self =>

...

Writer是WriterT的一个F[_] >>> Id特例，那么它的款式也可以被视作这样：

final case class Writer[W, A](run: (W, A)) { self =>

def flatMap[B](f: A => WriterT[F, W, B])(implicit F: Bind[F], s: Semigroup[W]): WriterT[F, W, B] =

flatMapF(f.andThen(_.run))

def flatMapF[B](f: A => F[(W, B)])(implicit F: Bind[F], s: Semigroup[W]): WriterT[F, W, B] =

writerT(F.bind(run){wa =>

val z = f(wa._2)

F.map(z)(wb => (s.append(wa._1, wb._1), wb._2))

})

type StateT[F[_], S, A] = IndexedStateT[F, S, S, A]

type IndexedState[-S1, S2, A] = IndexedStateT[Id, S1, S2, A]

/** A state transition, representing a function `S => (S, A)`. */

type State[S, A] = StateT[Id, S, A]

State是StateT的Id特殊案例，而StateT又是IndexedStateT的S1=S2特殊案例。那我们就从最概括的类型IndexedStateT开始介绍吧。下面是IndexedStateT的定义：scalaz/StateT.scala

trait IndexedStateT[F[_], -S1, S2, A] { self =>

/** Run and return the final value and state in the context of `F` */

def apply(initial: S1): F[(S2, A)]

/** An alias for `apply` */

def run(initial: S1): F[(S2, A)] = apply(initial)

/** Calls `run` using `Monoid[S].zero` as the initial state */

def runZero[S <: S1](implicit S: Monoid[S]): F[(S2, A)] =

run(S.zero)

/** Run, discard the final state, and return the final value in the context of `F` */

def eval(initial: S1)(implicit F: Functor[F]): F[A] =

F.map(apply(initial))(_._2)

/** Calls `eval` using `Monoid[S].zero` as the initial state */

def evalZero[S <: S1](implicit F: Functor[F], S: Monoid[S]): F[A] =

eval(S.zero)

/** Run, discard the final value, and return the final state in the context of `F` */

def exec(initial: S1)(implicit F: Functor[F]): F[S2] =

F.map(apply(initial))(_._1)

/** Calls `exec` using `Monoid[S].zero` as the initial state */

def execZero[S <: S1](implicit F: Functor[F], S: Monoid[S]): F[S2] =

exec(S.zero)

...

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)

})

object IndexedStateT extends StateTInstances with StateTFunctions {

def apply[F[_], S1, S2, A](f: S1 => F[(S2, A)]): IndexedStateT[F, S1, S2, A] = new IndexedStateT[F, S1, S2, A] {

def apply(s: S1) = f(s)

}

}

def state[A](a: A): F[S, A] = bind(init)(s => point(a))

def constantState[A](a: A, s: => S): F[S, A] = bind(put(s))(_ => point(a))

def init: F[S, S]

def get: F[S, S]

def gets[A](f: S => A): F[S, A] = bind(init)(s => point(f(s)))

def put(s: S): F[S, Unit]

def modify(f: S => S): F[S, Unit] = bind(init)(s => put(f(s)))

}

def apply[F[_,_],S](implicit F: MonadState[F, S]) = F

}

private trait StateTMonadState[S, F[_]] extends MonadState[({type f[s, a] = StateT[F, s, a]})#f, S] {

def bind[A, B](fa: StateT[F, S, A])(f: A => StateT[F, S, B]): StateT[F, S, B] = fa.flatMap(f)

def point[A](a: => A): StateT[F, S, A] = {

lazy val aa = a

StateT(s => F.point(s, aa))

}

def init: StateT[F, S, S] = StateT(s => F.point((s, s)))

def get = init

def put(s: S): StateT[F, S, Unit] = StateT(_ => F.point((s, ())))

override def modify(f: S => S): StateT[F, S, Unit] = StateT(s => F.point((f(s), ())))

override def gets[A](f: S => A): StateT[F, S, A] = StateT(s => F.point((s, f(s))))

}

1 type Stack = List[Int]

2 def pop: State[Stack, Int] = State { case h::t => (t,h) }

3 //> pop: => scalaz.State[Exercises.stateT.Stack,Int]

4 def push(a: Int): State[Stack, Unit] = State { xs => (a :: xs, ()) }

5 //> push: (a: Int)scalaz.State[Exercises.stateT.Stack,Unit]

1 val prg = for {

2 _ <- push(1)

3 _ <- push(2)

4 _ <- push(3)

5 a <- pop

6 b <- get

7 _ <- pop

8 _ <- put(List(9))

9 } yield b //> prg : scalaz.IndexedStateT[scalaz.Id.Id,Exercises.stateT.Stack,List[Int],E

10 //| xercises.stateT.Stack] = [email protected]

11 prg.run(List()) //> res2: scalaz.Id.Id[(List[Int], Exercises.stateT.Stack)] = (List(9),List(2,

12 //| 1))

prg只是一段功能描述，因为状态运算函数是个lambda: s => (s,a)。这里s是个未知数，它在for loop里逐层传递下去。运算结果需要通过运行run函数并提供初始状态值List()后才能获取，也就是说真正的运算是在运行run时才开始的。我们称run为程序prg的翻译器（interpreter），这是函数式编程的典型模式，这样可以把具体运算延到最后。

1 val prg = for {

2 _ <- push(1)

3 _ <- push(2)

4 _ <- push(3)

5 a <- pop

6 b <- get //(s,s)

7 c <- gets { s:Stack => s.length} //(s,s.length)

8 _ <- pop

9 _ <- put(List(9)) //(List(9),a)

10 _ <- modify {s:Stack => s ++ List(10) } //(List(9,10),a)

11 } yield c //> prg : scalaz.IndexedStateT[scalaz.Id.Id,Exercises.stateT.Stack,List[Int],I

12 //| nt] = [email protected]

13 prg.run(List()) //> res2: scalaz.Id.Id[(List[Int], Int)] = (List(9, 10),2)

1 val prg1 = for {

2 _ <- push(1)

3 _ <- push(2)

4 _ <- push(3)

5 a <- pop

6 b <- if (a == 3 ) put(List(1,2,3)) else put(List(2,3,4))

7 } yield b //> prg1 : scalaz.IndexedStateT[scalaz.Id.Id,Exercises.stateT.Stack,List[Int],

8 //| Unit] = [email protected]

9 prg1.run(List()) //> res4: scalaz.Id.Id[(List[Int], Unit)] = (List(1, 2, 3),())

def empty[A]: StateT[F, S, A] = liftM[F, A](F.empty[A])

def plus[A](a: StateT[F, S, A], b: => StateT[F, S, A]): StateT[F, S, A] = StateT(s => F.plus(a.run(s), b.run(s)))

}

def liftM[G[_], A](ga: G[A])(implicit G: Monad[G]): StateT[G, S, A] =

StateT(s => G.map(ga)(a => (s, a)))

IndexedStateT还有一个挺有趣的函数lift。在FP风格里lift总是起到搭建OOP到FP通道的作用。我们先来看个例子：

1 def incr: State[Int,Int] = State { s => (s+1,s)}//> incr: => scalaz.State[Int,Int]

2 incr.replicateM(10).evalZero[Int] //> res3: List[Int] = List(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

incr.replicateM(10000).runZero[Int] //> java.lang.StackOverflowError

def lift[M[_]: Applicative]: IndexedStateT[({type λ[α]=M[F[α]]})#λ, S1, S2, A] = new IndexedStateT[({type λ[α]=M[F[α]]})#λ, S1, S2, A] {

def apply(initial: S1): M[F[(S2, A)]] = Applicative[M].point(self(initial))

}

1  import scalaz.Free.Trampoline

2 incr.lift[Trampoline].replicateM(10).evalZero[Int]

3 //> res4: scalaz.Free[Function0,List[Int]] = Gosub()

import scalaz.Free.Trampoline

incr.lift[Trampoline].replicateM(10000).evalZero[Int].run.take(5)

//> res4: List[Int] = List(0, 1, 2, 3, 4)

1 def zipIndex[A](xs: List[A]): List[(A, Int)] =

2 xs.foldLeft(State.state[Int,List[(A,Int)]](List()))(

3 (acc, a) => for {

4 xn <- acc

5 n <- get[Int]

6 _ <- put[Int](n+1)

7 } yield (a,n) :: xn).evalZero.reverse //> zipIndex: [A](xs: List[A])List[(A, Int)]

8

9 zipIndex(1 |-> 5) //> res5: List[(Int, Int)] = List((1,0), (2,1), (3,2), (4,3), (5,4))

1 def zipIndex[A](xs: List[A]): List[(A, Int)] =

2 xs.foldLeft(State.state[Int,List[(A,Int)]](List()))(

3 (acc, a) => for {

4 xn <- acc

5 n <- get[Int]

6 _ <- put[Int](n+1)

7 } yield (a,n) :: xn).lift[Trampoline].evalZero.run.reverse.take(10)

8 //> zipIndex: [A](xs: List[A])List[(A, Int)]

9

10 zipIndex(1 |-> 1000) //> res5: List[(Int, Int)] = List((1,0), (2,1), (3,2), (4,3), (5,4), (6,5), (7,

11 //| 6), (8,7), (9,8), (10,9))

object StateTUsage extends App {

import StateT._

def f[M[_]: Functor] {

Functor[({type l[a] = StateT[M, Int, a]})#l]

}

Applicative[({type l[a] = StateT[M, Int, a]})#l]

Monad[({type l[a] = StateT[M, Int, a]})#l]

MonadState[({type f[s, a] = StateT[M, s, a]})#f, Int]

}

def state() {

val state: State[String, Int] = State((x: String) => (x + 1, 0))

val eval: Int = state.eval("")

state.flatMap(_ => state)

}

}

import Scalaz._

import scala.language.higherKinds

def f[M[_]: Functor] {

Functor[({type l[a] = StateT[M, Int, a]})#l]

} //> f: [M[_]](implicit evidence\$2: scalaz.Functor[M])Unit

Applicative[({type l[a] = StateT[M, Int, a]})#l]

Monad[({type l[a] = StateT[M, Int, a]})#l]

MonadState[({type f[s, a] = StateT[M, s, a]})#f, Int]

} //> m: [M[_]](implicit evidence\$3: scalaz.Monad[M])Unit

def state() {

val state: State[String, Int] = State((x: String) => (x + 1, 0))

val eval: Int = state.eval("")

state.flatMap(_ => state)

} //> state: ()Unit

f[List]

m[List]

state

1 //Functor实例

2 val fs = Functor[({type l[a] = StateT[List, Int, a]})#l]

3 //> fs : scalaz.Functor[[a]scalaz.IndexedStateT[[+A]List[A],Int,Int,a]] = scala

4 //

5 State[Int,Int] {s => (s+1,s)} //> res0: scalaz.State[Int,Int] = [email protected]

6 val st = StateT[List, Int, Int](s => List((s,s)))//> st : scalaz.StateT[List,Int,Int] = [email protected]

7 fs.map(st){a => a + 1}.run(0) //> res1: List[(Int, Int)] = List((0,1))

9 val ms = MonadState[({type f[s, a] = StateT[List, s, a]})#f, Int]

10 //> ms : scalaz.MonadState[[s, a]scalaz.IndexedStateT[[+A]List[A],s,s,a],Int] =

11 //

12 ms.state(1).run(0) //> res2: List[(Int, Int)] = List((0,1))

16 //

17 monad.bind(st){a => StateT(a1 => List((a1,a)))}.run(0)

18 //Applicative实例 //> res3: List[(Int, Int)] = List((0,0))

19 val ap = Applicative[({type l[a] = StateT[List, Int, a]})#l]

20 //> ap : scalaz.Applicative[[a]scalaz.IndexedStateT[[+A]List[A],Int,Int,a]] = s

21 //

22 ap.point(0).run(0) //> res4: List[(Int, Int)] = List((0,0))

1 // def state() {

2 //构建一个State实例。每次它的状态会加个!符号

3 val state: State[String, Int] = State((x: String) => (x + "!", 0))

4 //> state : scalaz.State[String,Int] = [email protected]

5 //运算值不变

6 val eval: Int = state.eval("") //> eval : Int = 0

7 //连续两次运行状态运算函数。加两个!

8 state.flatMap(_ => state).run("haha") //> res0: scalaz.Id.Id[(String, Int)] = (haha!!,0)

9 // }

trait Cache

trait FollowerState

def followerState(user: String, cache: Cache): (Cache, FollowerState) = {

val (c1,ofs) = checkCache(user,cache) //检查cache里有没有user资料

//c1是新cache,更新了hit或miss count

ofs match { //在cache里找到否

case Some(fs) => (c1,fs) //找到就返回fs和新cache c1

case None => retrieve(user,c1) //找不到就从数据库里重新读取

}

}

//检查cache，更新cache hit/miss count

def checkCache(user: String, cache: Cache): (Cache, Option[FollowerState]) = ...

//从数据库读取user资料，更新加入cache

def retrieve(user: String, cache: Cache): (Cache, FollowerState) = ...

def followerState(user: String, cache: Cache): (Cache, FollowerState)

def followerState(user: String)(cache: Cache): (Cache, FollowerState)

def followerState(user: String): Cache => (Cache, FollowerState)

def checkCache(user: String): Cache => (Cache, Option[FollowerState]) = ...

def retrieve(user: String): Cache => (Cache, FollowerState) = ...

def followerState(user: String): Cache => (Cache, FollowerState) = cache => {

val (c1,ofs) = checkCache(user,cache)

ofs match {

case Some(fs) => (c1,fs)

case None => retrieve(user,c1)

}

}

def followerState(user: String): State[Cache,FollowerState] = State {

cache => {

val (c1,ofs) = checkCache(user,cache)

ofs match {

case Some(fs) => (c1,fs)

case None => retrieve(user,c1)

}

}

}

def checkCache(user: String): State[Cache,Option[FollowerState]] = ...

def retrieve(user: String): State[Cache,FollowerState] = ...

def followerState(user: String): State[Cache,FollowerState] = for {

optfs <- checkCache(user)

fs <- optfs match {

case Some(fs) => State{ s => (s, fs) }

case None => retrieve(user)

}

} yield fs

followerState("Johny Depp").eval(emptyCache)

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