Covariance & 之间的区别逆变 [英] Difference between Covariance & Contra-variance

问题描述

我无法理解协方差和逆变之间的区别.

I am having trouble understanding the difference between covariance and contravariance.

推荐答案

问题是协变和逆变有什么区别?"

The question is "what is the difference between covariance and contravariance?"

协方差和逆变是映射函数的属性，该函数将集合的一个成员与另一个成员相关联.更具体地说，相对于该集合上的关系，映射可以是协变的或逆变的.

Covariance and contravariance are properties of a mapping function that associates one member of a set with another. More specifically, a mapping can be covariant or contravariant with respect to a relation on that set.

考虑所有 C# 类型集合的以下两个子集.第一:

Consider the following two subsets of the set of all C# types. First:

{ Animal, 
  Tiger, 
  Fruit, 
  Banana }.

其次，这个明显相关的集合:

And second, this clearly related set:

{ IEnumerable<Animal>, 
  IEnumerable<Tiger>, 
  IEnumerable<Fruit>, 
  IEnumerable<Banana> }

从第一组到第二组有一个映射操作.也就是说，对于第一组中的每个T，第二组中的对应类型是IEnumerable.或者，简而言之，映射是T → IE.请注意，这是一个细箭头".

There is a mapping operation from the first set to the second set. That is, for each T in the first set, the corresponding type in the second set is IEnumerable<T>. Or, in short form, the mapping is T → IE<T>. Notice that this is a "thin arrow".

到目前为止和我在一起吗?

With me so far?

现在让我们考虑一个关系.第一组中的类型对之间存在赋值兼容关系.Tiger 类型的值可以分配给 Animal 类型的变量，因此这些类型被称为赋值兼容".让我们以较短的形式编写X 类型的值可以分配给 Y 类型的变量":X ⇒ Y.请注意，这是一个粗箭头".

Now let's consider a relation. There is an assignment compatibility relationship between pairs of types in the first set. A value of type Tiger can be assigned to a variable of type Animal, so these types are said to be "assignment compatible". Let's write "a value of type X can be assigned to a variable of type Y" in a shorter form: X ⇒ Y. Notice that this is a "fat arrow".

所以在我们的第一个子集中，这里是所有的分配兼容性关系:

So in our first subset, here are all the assignment compatibility relationships:

Tiger  ⇒ Tiger
Tiger  ⇒ Animal
Animal ⇒ Animal
Banana ⇒ Banana
Banana ⇒ Fruit
Fruit  ⇒ Fruit

在支持某些接口协变赋值兼容性的C#4中，第二组类型对之间存在赋值兼容性关系:

In C# 4, which supports covariant assignment compatibility of certain interfaces, there is an assignment compatibility relationship between pairs of types in the second set:

IE<Tiger>  ⇒ IE<Tiger>
IE<Tiger>  ⇒ IE<Animal>
IE<Animal> ⇒ IE<Animal>
IE<Banana> ⇒ IE<Banana>
IE<Banana> ⇒ IE<Fruit>
IE<Fruit>  ⇒ IE<Fruit>

注意映射T → IE 保留了赋值兼容性的存在和方向.也就是说，如果 X ⇒ Y，那么 IE 也成立.⇒ IE.

Notice that the mapping T → IE<T> preserves the existence and direction of assignment compatibility. That is, if X ⇒ Y, then it is also true that IE<X> ⇒ IE<Y>.

如果我们在粗箭头的两边有两个东西，那么我们可以用相应的细箭头右侧的东西替换两边.

If we have two things on either side of a fat arrow, then we can replace both sides with something on the right hand side of a corresponding thin arrow.

对于特定关系具有此属性的映射称为协变映射".这应该是有道理的:可以在需要一系列 Animals 的地方使用 Tigers 序列，但反之则不然.在需要老虎序列的地方不一定使用动物序列.

A mapping which has this property with respect to a particular relation is called a "covariant mapping". This should make sense: a sequence of Tigers can be used where a sequence of Animals is needed, but the opposite is not true. A sequence of animals cannot necessarily be used where a sequence of Tigers is needed.

这就是协方差.现在考虑所有类型集合的这个子集:

That's covariance. Now consider this subset of the set of all types:

{ IComparable<Tiger>, 
  IComparable<Animal>, 
  IComparable<Fruit>, 
  IComparable<Banana> }

现在我们有了从第一组到第三组的映射T → IC.

now we have the mapping from the first set to the third set T → IC<T>.

在 C# 4 中:

IC<Tiger>  ⇒ IC<Tiger>
IC<Animal> ⇒ IC<Tiger>     Backwards!
IC<Animal> ⇒ IC<Animal>
IC<Banana> ⇒ IC<Banana>
IC<Fruit>  ⇒ IC<Banana>     Backwards!
IC<Fruit>  ⇒ IC<Fruit>

也就是说，映射T → IC保留了存在但反转了分配兼容性的方向.也就是说，如果 X ⇒ Y，则 IC⇐ IC.

That is, the mapping T → IC<T> has preserved the existence but reversed the direction of assignment compatibility. That is, if X ⇒ Y, then IC<X> ⇐ IC<Y>.

保留但反转关系的映射称为逆变映射.

同样，这应该是正确的.可以比较两只动物的设备也可以比较两只老虎，但是可以比较两只老虎的设备不一定可以比较任意两只动物.

Again, this should be clearly correct. A device which can compare two Animals can also compare two Tigers, but a device which can compare two Tigers cannot necessarily compare any two Animals.

这就是 C# 4 中协变和逆变之间的区别.协变保留可赋值的方向.逆变反转它.

So that's the difference between covariance and contravariance in C# 4. Covariance preserves the direction of assignability. Contravariance reverses it.

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