variance 变型

[towry]

• https://doc.rust-lang.org/nomicon/subtyping.html

The core problem is that this rule, naively applied, will lead to meowing Dogs. That is, we can convince someone that a Dog is actually a Cat. This completely destroys the fabric of our static type system, making it worse than useless (and leading to Undefined Behaviour).

Clearly, we need a more robust system than "find and replace". That system is variance, which is a set of rules governing how subtyping should compose. Most importantly, variance defines situations where subtyping should be disabled.

[towry]

We can also see why UnsafeCell and all the other interior mutability types must be invariant: they make &T work like &mut T!

[towry]

???

https://doc.rust-lang.org/nomicon/lifetimes.html

However this is not at all how Rust reasons that this program is bad. Rust doesn't understand that x is a reference to a subpath of data. It doesn't understand Vec at all. What it does see is that x has to live for 'b to be printed. The signature of Index::index subsequently demands that the reference we take to data has to survive for 'b. When we try to call push, it then sees us try to make an &'c mut data. Rust knows that 'c is contained within 'b, and rejects our program because the &'b data must still be live!

[towry]

术语

• Variance 变型
• Covariant 协变
• Contravariant 逆变
• Invariant 不变

要理解这些术语，一个关键词是 类型构造器。
类型构造器，学习 Haskell 语言的应该知道是什么，对于我们这些没学过 Haskell 或者 Type Theory 的同学们，可以
简单将其理解为一个函数，接受一个类型，生成另一个类型。比如 String 类型 和由 String 类型构造出来的 String[] 数组类型。

因此我们可以有这样的类型构造器：T[]，某些支持范型的语言有 List<T> 是类型构造器（你可以理解为基本类型 T 和 [] 或者 List 构造了新的复杂类型）。

因而，可变（Variance）可以看作 类型构造器 的一个属性，这个属性的作用是用来指明，这个类型构造器的输出类型（构造出来的新的类型，比如 Animal[]）之间的子类型关系（即 Dog[] 和 Animal[]之间的子类型关系）是如何被输入类型的子类型关系（即 Dog 和 Animal 的子类型关系）所影响的。

如果我们定义两个类型，Dog 和 Animal，并且 Dog 继承 Animal 是 Animal 的子类型。那么 Dog[] 一定就是 Animal[] 的子类型吗？答案是不一定！最终决定权就在于这个 类型构造器的Variance 是 “协变”，还是“逆变”，或者是“不变（没有任何父子继承关系）”。

• 如果 Dog[] 是 Animal[] 的子类型，记作：Dog[] -> Animal[]，即和 Dog -> Animal 的关系保持一致，就是协变。
• 如果相反，Animal[] 是 Dog[] 的子类型，Dog 是 Animal 的子类型，就是逆变。
• 如果没有任何父子关系，就是不变。