Scala函数的泛型特性——逆变与协变

deltamaster posted @ Jun 17, 2014 10:22:10 PM in Scala with tags scala 函数 泛型 Functional Programming Liskov 协变 逆变 , 9194 阅读

在Scala(以及其他许多编程语言)中,函数也是对象,可以使用、定义其他对象的地方,也可以使用、定义函数。Scala中的函数,具有apply方法的类的实例,就可以当做函数来使用。其中apply接受的参数就是函数的参数,而apply的返回值就是函数的返回值。

首先给出一个接受一个参数的函数的泛型定义。

trait Function1[-T, +U] {
  def apply(x: T): U
}

这种函数接受一个参数,参数类型为泛型类型T,返回类型为泛型类型U。和其他支持泛型的语言一样,实际定义函数时T和U的类型会被确定下来,不过需要注意的是,这边的T之前有一个“-”,而U之前有一个“+”。

在这里引入关于这个符号的说明,在声明Scala的泛型类型时,“+”表示协变,而“-”表示逆变。

  • C[+T]:如果A是B的子类,那么C[A]是C[B]的子类。
  • C[-T]:如果A是B的子类,那么C[B]是C[A]的子类。
  • C[T]:无论A和B是什么关系,C[A]和C[B]没有从属关系。

根据Liskov替换原则,如果A是B的子类,那么能适用于B的所有操作,都适用于A。让我们看看这边Function1的定义,是否满足这样的条件。假设Bird是Animal的子类,那么看看下面两个函数之间是什么关系:

def f1(x: Bird): Animal // instance of Function1[Bird, Animal]
def f2(x: Animal): Bird // instance of Function1[Animal, Bird]

在这里f2的类型是f1的类型的子类。为什么?

我们先看一下参数类型,根据Liskov替换原则,f1能够接受的参数,f2也能接受。在这里f1接受的Bird类型,f2显然可以接受,因为Bird对象可以被当做其父类Animal的对象来使用。

再看返回类型,f1的返回值可以被当做Animal的实例使用,f2的返回值可以被当做Bird的实例使用,当然也可以被当做Animal的实例使用。

所以我们说,函数的参数类型是逆变的,而函数的返回类型是协变的。

那么我们在定义Scala类的时候,是不是可以随便指定泛型类型为协变或者逆变呢?答案是否定的。通过上面的例子可以看出,如果将Function1的参数类型定义为协变,或者返回类型定义为逆变,都会违反Liskov替换原则,因此,Scala规定,协变类型只能作为方法的返回类型,而逆变类型只能作为方法的参数类型。类比函数的行为,结合Liskov替换原则,就能发现这样的规定是非常合理的。

这种函数的泛型特性对于函数式编程非常有用。尽管C++的泛型在语法层面上不支持协变与逆变,但在C++11的function<U(T)>中,返回类型U和参数类型T也同样遵循与Scala相同的协变与逆变规则。

* 本文在CC BY-SA(署名-相同方式共享)协议下发布。
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