主要来自 Scala 语言发明人 Martin Odersky 教授的 Coursera 课程 《Functional Programming Principles in Scala》。
3. Data and Abstraction
3.1 Class Hierarchies
这一集字幕不同步-,-，听得有点费力！
类的概念和其他语言里面很相似，基类，子类，父类啥的叫法差不多。在 Scala 中，所有用户自定义的类都是另外一个类的子类，如果没有显式给定父类，java 里面默认继承 java.lang，scala 里面是 Object。无论基类中的方法有没有具体实现，子类都可以用 override 重新定义，回想起之前强大的 toString 了吗？
举一个二叉树的例子：
package week3
object insets {
val t1 = new NonEmpty(, Empty, Empty) //> t1 : week3.NonEmpty = {.3.}
val t2 = t1 incl //> t2 : week3.IntSet = {.3{.4.}}
val t3 = new NonEmpty(, Empty, Empty) //> t3 : week3.NonEmpty = {.5.}
t2 union t3 //> res0: week3.IntSet = {{{.3.}4.}5.}
}
abstract class IntSet { // 抽象类作为基类，无法实例化，定义了三个接口
def contains(x: Int): Boolean // 查找是否包含 x
def incl(x: Int): IntSet // 如果 x 不存在，将 x 放入二叉树中
def union(x: IntSet): IntSet // 两棵树融合
}
object Empty extends IntSet { // Empty 是 IntSet 的 subclass，`object` 表示单例模式，所有空节点都可以用一个对象来表示
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 = "." // 空节点打印"."
}
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 =
// 实际上创建了一个新树，新树和旧树共用未改变的子树
// 这个叫 persistent data structure,是把函数式编程扩展到 collections 的关键之一
// 反正他是这么说的 `-,-`
if (x < elem) new NonEmpty(elem, left incl x, right) // 一重一重地复制节点
else if (x > elem) new NonEmpty(elem, left, right incl x)
else this
def union(other: IntSet): IntSet =
((left union right) union other) incl elem //
override def toString = "{" + left + elem + right + "}" //强大的递归啊
}
3.2 How Classes Are Organized
没学过 java，估计和 java 中 package 管理一样。
在源码最顶端写上 package week3 表示这个文件的 object 或者 class 属于这个包。要使用某一个类，可以在源码中用全名 week3.classA，也可以像 python 一样在最开始 import，源码中间用类名：
- import week3.classA：导入类 classA
- import week3.{classA, classB}：导入两个类
- import week3._ ：导入包所有（通配符导入方法）
除了从包导入，还可以从 object 导入。所有 Scala 程序默认导入一些 entities，比如 scala 中的 Int，java.lang 中的 Object，scala.Predef 中的断言等。更多信息可以查看 scala 的标准库。
在 java 和 scala 中，一个类只能有一个父类（单继承），如何实现多继承，scala 中采用 traits。trait 像 java 里面的接口，偏抽象，但是更强大，可以包含 field 和具体方法，但是不能有value参数。子类可只能继承一个父类，但是可以继承任意多个 traits，例如：class Square extends Shape with Planar with Moveble。
scala 类型结构如下，实线表示继承，虚线表示隐式转化。
-
Any是所有类型的基本类，包含的方法有：‘==’，‘!=’，‘equals’，‘hashCode’，‘toString’ -
AnyVal是数值类型的基本类。 -
AnyRef是所有引用类型的基本类，也是 java.lang.Object 的别名。 -
Nothing是所有类的子类型。主要作用是异常类与collection中的一个空元素。 -
Null是所有类的子类型。但是与 AnyVal 的子类型不兼容。
Q：if (true) 1 else False 的返回类型是什么？
A：int 和 boolean 类型，返回父类 AnyVal。
3.3 Polymorphism
Polymorphism 意味着函数可以以多种类型出现。一张 PPT 总结 Polymorphism：
假设我们要建立一个 list 类，它可能包含了不同的数据类型（整数，布尔，list自身类型等），例子如下：
这时需要用泛型来表示。新建一个package叫week4,在其中新建一个 trait。它的两个‘子类’分别为 Cons 和 Nil，分别表示含有元素的节点和空节点。
package week4
// [T] 是类型参数，比如int，double之类。是泛型编程的基础
trait List[T] {
def isEmpty: Boolean
def head: T
def tail: List[T]
}
class Cons[T](val head: T, val tail: List[T]) extends List[T] {
def isEmpty = false
// head 和 tail 已经在初始化中实现
}
class Nil[T] extends List[T] {
def isEmpty = true
def head: Nothing = throw new NoSuchElementException("Nil.head")
// Nothing 是任何类型的子类，所以也是 T 的子类
def tail: Nothing = throw new NoSuchElementException("Nil.tail")
}
在 week4 中新建一个 scala worksheet，测试一下上述代码：
package week4
import week4._
object nth {
// 创建一个含有一个元素的 list
def singleton[T](elem: T) = new Cons(elem, new Nil)
//> singleton: [T](elem: T)week4.Cons[T]
singleton[Int](3) //> res0: week4.Cons[Int] = week4.Cons@71be98f5
singleton(3) // 编译器可以从 3 推到出 T 是 Int
// 寻找 list 中的第 n 个元素
def nth[T](n: Int, xs: List[T]): T =
if (xs.isEmpty) throw new IndexOutOfBoundsException
else if (n == 0) xs.head
else nth(n - 1, xs.tail) //> nth: [T](n: Int, xs: week4.List[T])T
// 创建一个 list = [1, 2, 3]
val list = new Cons(1, new Cons(2, new Cons(3, new Nil)))
nth(2, list) //> res2: Int = 3
}
小记
这里是课程前四次的大概内容，因为第一次课是教你怎么安装，所以实际内容只有三次课，后面还有四次课。总体来说，函数式编程给人很多启发，但是如果不是真正需要用，也不宜占用太多时间去学习。暑假要去实习了，等下学期再学吧。
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