Question

有人可以向我解释方法union在此代码中的确切作用吗？我可以看到它在功能中呼唤自己，但除此之外，我不知道它做了什么。打印t2 union t3会产生{{{.-1.}2.}3{{.4.}5{.7.}}}。

object Mp6 {  
  def main(args: Array[String]): Unit = {
    val t1 = Empty
    val t2 = t1 incl 3 incl 5 incl 4 incl 7
    val t3 = t2 incl 2 incl 4 incl -1

    println(t1)
    println(t2)
    println(t1 contains 5)
    println(t2 contains 5)
    println(t2 contains 5)

    println(t2 union t3)
  }
}

abstract class IntSet {
  def incl(x: Int): IntSet
  def contains(x: Int): Boolean
  def union(other: IntSet): IntSet
}

object Empty extends IntSet {
  def contains(x: Int): Boolean = false
  def incl(x: Int): IntSet = new NonEmpty(x, Empty, Empty)  
  def union(other: IntSet): IntSet = other
  override def toString = "."
}

class NonEmpty(elem: Int, left: IntSet, right: IntSet) extends IntSet {
  def contains(x: Int): Boolean =
    if (x < elem) left contains x
    else if (x > elem) right contains x
    else true

  def incl(x: Int): IntSet =
    if (x < elem) new NonEmpty(elem, left incl x, right)
    else if (x > elem) new NonEmpty(elem, left, right incl x)
    else this

  def union(other: IntSet): IntSet = {
    val set = left.union(right.union(other))
    set.incl(elem)
  }

  override def toString = "{" + left + elem + right + "}"
}

Answer 1

好吧，你基本上要求解释评估的替换模型是如何工作的。如上面的评论中所述，您的代码段非常类似于Martin Odersky（Scala的创建者）编写的IntSets的实现，因此我将使用其课程笔记中的符号。我假设您已经快速阅读了替换模型规则。如果没有，Functional Programming Principles in Scala和Scala by Example是开始的好地方。

我会给你一个提示：为了方便起见，假设val t1 = new NonEmpty(1, Empty, Empty)和val t2 = new NonEmpty(2, Empty, new NonEmpty(3, Empty, Empty))。这意味着t1: NonEmpty = {.1.}和t2: NonEmpty = {.2{.3.}}。现在让我们评估表达式t1 union t2。

t1 union t2 = new NonEmpty(1, Empty, Empty) union new NonEmpty(2, Empty, new NonEmpty(3, Empty, Empty))
            → [1/elem, Empty/left, Empty/right] [new NonEmpty(2, Empty, new NonEmpty(3, Empty, Empty))/other] [new NonEmpty(1, Empty, Empty)/this] (left union (right union other)) incl elem 
            = (Empty union (Empty union new NonEmpty(2, Empty, new NonEmpty(3, Empty, Empty)))) incl 1
            ...

您现在可以完成评估吗？

Answer 2

它是一个排序整数集的实现，它通过使用不添加重复项的二进制排序树进行备份来工作。因此，union只执行一个集合理论联合，其中整数的顺序被保留。

Scala中的类和替换

2 个答案: