Scalaz（28）－ ST Monad ：FP方式适用变量

    函数式编程模式强调纯代码（pure code），主要实现方式是使用不可变数据结构，目的是函数组合（composability）最终实现函数组件的重复使用。但是，如果我们在一个函数p内部使用了可变量（mutable variables），如果函数的输入参数e是纯代码，那么表达式p(e)同样是纯代码的，因为函数的调用者是无法接触到函数内部申明的这些可变量的。不过，这样的做法会造成函数的臃肿代码，因为在函数内部是无法实现函数组合的，无法重复使用函数组件，实际上又违背了FP的宗旨。Scalaz提供了专门解决可变量使用问题的方法，能保证即使在并行运算的环境内各线程无法影响相互间的可变量，即ST Monad。

Scalaz的可变量分两种：一个内存地址STRef或一个可变数组STArray。我们先看看它们在源代码中的定义：effect/ST.scala

/**Mutable variable in state thread S containing a value of type A. [[http://research.microsoft.com/en-us/um/people/simonpj/papers/lazy-functional-state-threads.ps.Z]] */
sealed trait STRef[S, A] {
  protected var value: A

  /**Reads the value pointed at by this reference. */
  def read: ST[S, A] = returnST(value)

  /**Modifies the value at this reference with the given function. */
  def mod[B](f: A => A): ST[S, STRef[S, A]] = st((s: Tower[S]) => {
    value = f(value);
    (s, this)
  })

  /**Associates this reference with the given value. */
  def write(a: => A): ST[S, STRef[S, A]] = st((s: Tower[S]) => {
    value = a;
    (s, this)
  })

  /**Synonym for write*/
  def |=(a: => A): ST[S, STRef[S, A]] =
    write(a)

  /**Swap the value at this reference with the value at another. */
  def swap(that: STRef[S, A]): ST[S, Unit] = for {
    v1 <- this.read
    v2 <- that.read
    _ <- this write v2
    _ <- that write v1
  } yield ()
}
...
/**Mutable array in state thread S containing values of type A. */
sealed trait STArray[S, A] {
  def size: Int
  def z: A
  implicit def manifest: Manifest[A]

  private lazy val value: Array[A] = Array.fill(size)(z)

  import ST._

  /**Reads the value at the given index. */
  def read(i: Int): ST[S, A] = returnST(value(i))

  /**Writes the given value to the array, at the given offset. */
  def write(i: Int, a: A): ST[S, STArray[S, A]] = st(s => {
    value(i) = a;
    (s, this)
  })

  /**Turns a mutable array into an immutable one which is safe to return. */
  def freeze: ST[S, ImmutableArray[A]] = st(s => (s, ImmutableArray.fromArray(value)))

  /**Fill this array from the given association list. */
  def fill[B](f: (A, B) => A, xs: Traversable[(Int, B)]): ST[S, Unit] = xs match {
    case Nil             => returnST(())
    case ((i, v) :: ivs) => for {
      _ <- update(f, i, v)
      _ <- fill(f, ivs)
    } yield ()
  }

  /**Combine the given value with the value at the given index, using the given function. */
  def update[B](f: (A, B) => A, i: Int, v: B) = for {
    x <- read(i)
    _ <- write(i, f(x, v))
  } yield ()
}

我们看到STRef和STArray都定义了write,mod,update这样有副作用的操作函数，它们都返回了ST[S,STRef[S,A]]类型的结果。ST是个Monad，我们可以从源代码中证实： 

/**
 * Purely functional mutable state threads.
 * Based on JL and SPJ's paper "Lazy Functional State Threads"
 */
sealed trait ST[S, A] {
  private[effect] def apply(s: Tower[S]): (Tower[S], A)

  import ST._

  def flatMap[B](g: A => ST[S, B]): ST[S, B] =
    st(s => apply(s) match {
      case (ns, a) => g(a)(ns)
    })

  def map[B](g: A => B): ST[S, B] =
    st(s => apply(s) match {
      case (ns, a) => (ns, g(a))
    })
}

 1 import scalaz._
 2 import Scalaz._
 3 import effect._
 4 import ST._
 5 object st {
 6 def e1[S] = for {
 7   r <- newVar[S](3)
 8   x <- r.mod {_ + 2}
 9 } yield x                                         //> e1: [S]=> scalaz.effect.ST[S,scalaz.effect.STRef[S,Int]]
10 
11 def e2[S] = for {
12   r <- newVar[S](3)
13   x <- r.mod {_ + 2}
14   y <- x.read
15 } yield y                                         //> e2: [S]=> scalaz.effect.ST[S,Int]
16 
17 def e3[S] = for {
18   arr <- newArr[S,Int](5,0)
19   _ <- arr.write(0,3)
20   _ <- arr.write(1,2)
21   _ <- arr.update ((a: Int,b: Int) => a + b, 2, 4)
22   r <- arr.freeze
23 } yield r                                         //> e3: [S]=> scalaz.effect.ST[S,scalaz.ImmutableArray[Int]]

newVar[S](3)以状态S新建一个Int存放地址并存入值3。mod操作返回ST[S,STRef[S,Int]]，返回的是个地址（reference），而read返回的是ST[S,Int]，则是个值。首先注意e1[S],e2[S],e3[S]它们都附带了独立状态标签S。

1 runST(new Forall[({type l[x] = ST[x, Int]})#l]{def apply[S] = e2[S]})
2                                                   //> res0: Int = 5
3 //runST(new Forall[({type l[x] = ST[x, Int]})#l]{def apply[S] = e1[S]})   
4 //type mismatch;  found   : scalaz.effect.ST[S,scalaz.effect.STRef[S,Int]]  required: scalaz.effect.ST[S,Int]  

/** A universally quantified value */
trait Forall[P[_]] {
  def apply[A]: P[A]
}

1 type ForallST[A] = Forall[({type l[x] = ST[x,A]})#l]
2 runST(new ForallST[Int]{ def apply[S] = e2[S] })  //> res0: Int = 5
3 //runST(new ForallST[Int]{def apply[S] = e1[S]})
4 //type mismatch;  found   : scalaz.effect.ST[S,scalaz.effect.STRef[S,Int]]  required: scalaz.effect.ST[S,Int]

 /**Run a state thread */
  def runST[A](f: Forall[({type λ[S] = ST[S, A]})#λ]): A =
    f.apply.apply(ivoryTower)._2