一句话：重新审视面向对象方法参数的协变/逆变特化，论证二者可在同一语言中共存，并以实例讲解进阶类型系统概念与实现技巧。
本文重新审视作者二十年前关于协变与逆变特化的文章。该文曾指出，面向对象编程中方法参数的协变与逆变特化目的不同，因此不仅能够、而且应当在同一语言中共存。作者结合子类型理论及编程语言的最新进展，对这一旧问题给出新视角；但文章更主要的目的是以简单术语和示例，向本科生及愿意学习的函数式程序员解释复杂的类型论概念。文章还借此机会描述了一些鲜为人知的类型系统实现高级技术，这些技术原先只见于少数深入编译器源码的内行。因而，即使资深语言设计者和实现者也可能从中获益。
Twenty years ago, in an article titled "Covariance and contravariance: conflict without a cause", I argued that covariant and contravariant specialization of method parameters in object-oriented programming had different purposes and deduced that, not only they could, but actually they should both coexist in the same language. In this work I reexamine the result of that article in the light of recent advances in (sub-)typing theory and programming languages, taking a fresh look at this old issue. Actually, the revamping of this problem is just an excuse for writing an essay that aims at explaining sophisticated type-theoretic concepts, in simple terms and by examples, to undergraduate computer science students and/or willing functional programmers. Finally, I took advantage of this opportunity to describe some undocumented advanced techniques of type-systems implementation that are known only to few insiders that dug in the code of some compilers: therefore, even expert language designers and implementers may find this work worth of reading.Comment: This is a corrected version of the paper arXiv:1809.01427v7 published originally on Feb. 13, 2020
@article{paperbot1722,
title = {Covariance and Controvariance: a fresh look at an old issue (a primer in advanced type systems for learning functional programmers)},
author = {Giuseppe Castagna},
journal = {Logical Methods in Computer Science},
volume = {Volume 16, Issue 1},
year = {2022},
doi = {10.23638/lmcs-16(1:15)2020}
}