状態遷移のシーケンスストリームとして記述されたプログラムをscalaz-streamに置き換えるにはどうすればよいですか？

以前は状態遷移のシーケンスとして作成したプログラムを再編成する方法を理解しようとしています。

私はいくつかのビジネスロジックを持っています：

type In = Long
type Count = Int 
type Out = Count
type S = Map[Int, Count]

val inputToIn: String => Option[In] 
  = s => try Some(s.toLong) catch { case _ : Throwable => None } 

def transition(in: In): S => (S, Out) 
  = s => { val n = s.getOrElse(in, 0); (s + (in -> n+1), n+1) }

val ZeroOut: Out = 0
val InitialState: S = Map.empty 

これらを使用して、初期状態（空のマップ）を渡し、stdinから入力を読み取り、に変換しIn、状態遷移を実行して現在の状態Sと出力Outをstdoutに出力するプログラムを作成したいと思います。

以前は、次のようなことをしていました。

val runOnce = StateT[IO, S, Out](s => IO.readLn.map(inputToIn) flatMap { 
  case None     => IO((s, ZeroOut))
  case Some(in) => val (t, o) = transition(in)(s)
                   IO.putStrLn(t.toString) |+| IO.putStrLn(o.toString) >| IO((t, o))   
})

Stream.continually(runOnce).sequenceU.eval(InitialState)

ただし、このアプローチ（状態遷移のストリーム）をscalaz-streamに接続する方法を見つけるのに本当に苦労しています。私はこれから始めました：

type Transition = S => (S, Out)
val NoTransition: Transition = s => (s, 0)

io.stdInLines.map(inputToIn).map(_.fold(NoTransition)(transition))

これはタイプです：Process[Task, Transition]。そこからどこへ行けばいいのかよくわかりません。

1. 自分を「パスイン」してInitialStateプログラムを実行し、S各ステップの出力をS次のステップへの入力としてスレッド化するにはどうすればよいですか？
2. 各ステップでSとの値を取得し、Outそれらをstdoutに出力するにはどうすればよいですか（文字列に変換できると仮定）？

単一の理解のために使用しようとすると、私は同様に行き詰まります：

for {
  i <- Process.eval(Task.now(InitialState))
  l <- io.stdInLines.map(inputToIn)
...

どんな助けでも大歓迎です！

もう少し先になりました。

type In_ = (S, Option[In])
type Out_ = (S, Out) 

val input: Process[Task, In_] 
  = for  {
      i <- Process.emit(InitialState) 
      o <- io.stdInLines.map(inputToIn)
   } yield (i, o)

val prog =
  input.pipe(process1.collect[In_, Out_]) {
    case (s, Some(in)) => transition(in)(s)
  }).to(io.stdOutLines.contramap[Out_](_.toString))

次に

prog.run.run

動作しません：状態がストリームにスレッド化されていないようです。むしろ、各段階で、初期状態が渡されます。

ポール・チウサノは、のアプローチを使用することを提案しましたprocess1.scan。だから今私はこれを行います：

type In_  = In
type Out_ = (S, Out)

val InitialOut_ = (InitialState, ZeroOut)

val program =
  io.stdInLines.collect(Function.unlift(inputToIn)).pipe(
    process1.scan[In_, Out_](InitialOut_) {
      case ((s, _), in) => transition(in)(s)
    }).to(io.stdOutLines.contramap[Out_](_.shows))

ここに問題があります。この特定の例では、私のOutタイプはモノイドであるため、そのIDを使用して初期状態を作成できますが、通常はそうではない可能性があります。それなら私は何をしますか？（私は使用できると思いますOptionが、これは不要のようです。）

import io.FilePath

import scalaz.stream._
import Process._
import scalaz.concurrent.Task
import Task._
import scalaz.{Show, Reducer, Monoid}
import scalaz.std.list._
import scalaz.syntax.foldable._
import scalaz.syntax.bind._
import scalaz.stream._
import io._
import scalaz.stream.text._
import Processes._
import process1.lift
import control.Functions._

/**
 * A Fold[T] can be used to pass over a Process[Task, T].
 * 
 * It has:
 *
 *  - accumulation, with an initial state, of type S, a fold action and an action to perform with the last state
 *  
 *  - side-effects with a Sink[Task, (T, S)] to write to a file for example, using the current element in the Process
 *    and the current accumulated state
 *
 * This covers many of the needs of iterating over a Scalaz stream and is composable because there is a Monoid
 * instance for Folds
 * 
 */
trait Fold[T] {
  type S

  def prepare: Task[Unit]
  def sink: Sink[Task, (T, S)]
  def fold: (T, S) => S
  def init: S
  def last(s: S): Task[Unit]

  /** create a Process1 returning the state values */
  def foldState1: Process1[T, S] =
    Processes.foldState1(fold)(init)

  /** create a Process1 returning the folded elements and the state values */
  def zipWithState1: Process1[T, (T, S)] =
    Processes.zipWithState1(fold)(init)

}

/**
 * Fold functions and typeclasses
 */
object Fold {

  /**
   * Create a Fold from a Sink with no accumulation
   */
  def fromSink[T](aSink: Sink[Task, T]) =  new Fold[T] {
    type S = Unit
    lazy val sink: Sink[Task, (T, S)] = aSink.extend[S]

    def prepare = Task.now(())
    def fold = (t: T, u: Unit) => u
    def init = ()
    def last(u: Unit) = Task.now(u)
  }

  /**
   * Transform a simple sink where the written value doesn't depend on the
   * current state into a sink where the current state is passed all the time
   * (and actually ignored)
   * Create a Fold a State function
   */
  def fromState[T, S1](state: (T, S1) => S1)(initial: S1) = new Fold[T] {
    type S = S1
    lazy val sink: Sink[Task, (T, S)] = unitSink[T, S]

    def prepare = Task.now(())
    def fold = state
    def init = initial
    def last(s: S) = Task.now(())
  }

  /**
   * Create a Fold from a side-effecting function
   */
  def fromFunction[T](f: T => Task[Unit]): Fold[T] =
    fromSink(Process.constant(f))

  /**
   * Create a Fold from a Reducer
   */
  def fromReducer[T, S1](reducer: Reducer[T, S1]): Fold[T] = new Fold[T] {
    type S = S1
    lazy val sink: Sink[Task, (T, S)] = unitSink[T, S]

    def prepare = Task.now(())
    def fold = reducer.cons
    def init = reducer.monoid.zero
    def last(s: S) = Task.now(())
  }

  /**
   * Create a Fold from a Reducer and a last action
   */
  def fromReducerAndLast[T, S1](reducer: Reducer[T, S1], lastTask: S1 => Task[Unit]): Fold[T] = new Fold[T] {
    type S = S1
    lazy val sink: Sink[Task, (T, S)] = unitSink[T, S]

    def prepare = Task.now(())
    def fold = reducer.cons
    def init = reducer.monoid.zero
    def last(s: S) = lastTask(s)
  }

  /**
   * This Sink doesn't do anything
   * It can be used to build a Fold that does accumulation only
   */
  def unitSink[T, S]: Sink[Task, (T, S)] =
    channel((tu: (T, S)) => Task.now(()))

  /**
   * Unit Fold with no side-effect or accumulation
   */
  def unit[T] = fromSink(channel((t: T) => Task.now(())))

  /**
   * Unit fold function
   */
  def unitFoldFunction[T]: (T, Unit) => Unit = (t: T, u: Unit) => u

  /** create a fold sink to output lines to a file */
  def showToFilePath[T : Show, S](path: FilePath): Sink[Task, (T, S)] =
    io.fileChunkW(path.path).pipeIn(lift(Show[T].shows) |> utf8Encode).extend[S]

  implicit class FoldOps[T](val fold: Fold[T]) {
  }

  /**
   * Monoid for Folds, where effects are sequenced
   */
  implicit def foldMonoid[T]: Monoid[Fold[T]] = new Monoid[Fold[T]] {
    def append(f1: Fold[T], f2: =>Fold[T]): Fold[T] = f1 >> f2
    lazy val zero = Fold.unit[T]
  }

  /**
   * create a new Fold sequencing the effects of 2 Folds
   */
  implicit class sequenceFolds[T](val fold1: Fold[T]) {
    def >>(fold2: Fold[T]) = new Fold[T] {
      type S = (fold1.S, fold2.S)

      def prepare = fold1.prepare >> fold2.prepare

      def sink = fold1.sink.zipWith(fold2.sink) { (f1: ((T, fold1.S)) => Task[Unit], f2: ((T, fold2.S)) => Task[Unit]) =>
        (ts: (T, S)) => {
          val (t, (s1, s2)) = ts
          (f1((t, s1)) |@| f2((t, s2)))((_,_))
        }
      }

      def fold = (t : T, s12: (fold1.S, fold2.S)) => (fold1.fold(t, s12._1), fold2.fold(t, s12._2))
      def last(s12: (fold1.S, fold2.S)) = (fold1.last(s12._1) |@| fold2.last(s12._2))((_,_))
      def init = (fold1.init, fold2.init)
    }
  }

  /**
   * Run a fold an return the last value
   */
  def runFoldLast[T](process: Process[Task, T], fold: Fold[T]): Task[fold.S] =
    fold.prepare >>
    logged(process |> fold.zipWithState1).drainW(fold.sink).map(_._2).runLastOr(fold.init)

  /**
   * Run a Fold an let it perform a last action with the accumulated state
   */
  def runFold[T](process: Process[Task, T], fold: Fold[T]): Task[Unit] =
    runFoldLast(process, fold).flatMap(fold.last)

  /**
   * Run a list of Folds, sequenced with the Fold Monoid
   */
  def runFolds[T](process: Process[Task, T], folds: List[Fold[T]]): Task[Unit] =
    runFold(process, folds.suml)

}