书单。我书架上涵盖这些主题的一些书：Simon Thompson 的《Type Theory and Functional Programming》（随手搜一下就能找到 PDF）、Rob Nederpelt 和 Herman Geuvers 写的《Type Theory and Formal Proof》前 120 页。至于 dependent types 的早期内容（上述书里也涵盖了），……
Books. Some books on my shelf covering these topics: "Type Theory and Functional Programming" by Simon Thompson (PDF available via quick search) First 120 pages of "Type Theory and Formal Proof" by Rob Nederpelt / Herman Geuvers For some early stuff on dependent types (also covered in the above),…
……先学归纳构造演算（calculus of inductive constructions，形式化机制跟 MLTT 类似），然后再学写代码。不然的话一切看起来都会像魔法一样。不过，这个主题倒是有几本好书：* Type Theory and Functional Programming (http://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) * Programming in Martin-Lof type theory (http://www.cse.chalmers.se/research/group/logic/book/)
…calculus of inductive constructions, which is a similar formalism to MLTT) first, and learn to write code later. Otherwise everything will seem like a magic. There are however, good books on the topic: * Type Theory and Functional Programming (http://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) * Programming in Martin-Lof type theory (http://www.cse.chalmers.se/research/group/logic/book/)
……可能会证明某些类型论的东西，比如类型保持性）。另外类型论的书也有一大堆，因为这个领域横跨了纯逻辑到编程语言，所以你能找到像 Thompson 写的《Type Theory and Functional Programming》这种很早就详细讲解 dependent types 等概念的书。
…might prove some type-theoretic thing like type preservation). There's also a range of type theory books because it's a field that spans pure logic to programming languages, so you can find books like Type Theory and Functional Programming by Thompson that elaborate things like dependent types early on.
……直到我拿起了《Type Theory and Formal Proof》。这本书我大概看了 100 到 200 页才开始懵圈。他们讲遍了整个 lambda cube。但紧接着我就能重新开始看 Thompson 的《Type Theory and Functional Programming》了，而且很明显我开始理解其中的大半内容了。如果你也跟我一样喜欢老书的情怀，那就去搞一本 Per Martin-Löf 编辑的《Intuitionistic Type Theory》原版吧。
…until picking up Type Theory and Formal Proof. This one took me somewhere between 100 to 200 pages before getting lost. They cover the entire lambda cube. But then I was able to re-start Thompson's "Type Theory and Functional Programming" and it was clear that I started to understand a lot of it. If you enjoy the nostalgia of older books like me, then pick up an original copy of "Intuitionistic Type Theory" edited by Per Martin-Löf.
…univalent foundations it sounds like they are adding magic sauce to make this possible, and so I follow it closely (but don't understand it all yet). The interesting path I spoke of earlier: I'm now learning type theory and functional programming just so that I can make sense of this branch of computer science that I originally didn't know existed.
确实，这篇文章的措辞甚至让我联想到了类型论和函数式编程。> 例如，一个通了电的水壶可以充当构造函数（constructor），执行烧水的任务。kettle power_supply water : (water * heat) > 你只需说明创建……的任务
Indeed, the wording of the article even made me think of type theory and functional programming. > For instance, a kettle with a power supply can serve as a constructor that can perform the task of heating water. kettle power_supply water : (water * heat) > You simply say that the task of creating…
书单。我书架上涵盖这些主题的一些书：Simon Thompson 的《Type Theory and Functional Programming》（随手搜一下就能找到 PDF）、Rob Nederpelt 和 Herman Geuvers 写的《Type Theory and Formal Proof》前 120 页。至于 dependent types 的早期内容（上述书里也涵盖了），……
Books. Some books on my shelf covering these topics: "Type Theory and Functional Programming" by Simon Thompson (PDF available via quick search) First 120 pages of "Type Theory and Formal Proof" by Rob Nederpelt / Herman Geuvers For some early stuff on dependent types (also covered in the above),…
……先学归纳构造演算（calculus of inductive constructions，形式化机制跟 MLTT 类似），然后再学写代码。不然的话一切看起来都会像魔法一样。不过，这个主题倒是有几本好书：* Type Theory and Functional Programming (http://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) * Programming in Martin-Lof type theory (http://www.cse.chalmers.se/research/group/logic/book/)
…calculus of inductive constructions, which is a similar formalism to MLTT) first, and learn to write code later. Otherwise everything will seem like a magic. There are however, good books on the topic: * Type Theory and Functional Programming (http://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) * Programming in Martin-Lof type theory (http://www.cse.chalmers.se/research/group/logic/book/)
……可能会证明某些类型论的东西，比如类型保持性）。另外类型论的书也有一大堆，因为这个领域横跨了纯逻辑到编程语言，所以你能找到像 Thompson 写的《Type Theory and Functional Programming》这种很早就详细讲解 dependent types 等概念的书。
…might prove some type-theoretic thing like type preservation). There's also a range of type theory books because it's a field that spans pure logic to programming languages, so you can find books like Type Theory and Functional Programming by Thompson that elaborate things like dependent types early on.
……直到我拿起了《Type Theory and Formal Proof》。这本书我大概看了 100 到 200 页才开始懵圈。他们讲遍了整个 lambda cube。但紧接着我就能重新开始看 Thompson 的《Type Theory and Functional Programming》了，而且很明显我开始理解其中的大半内容了。如果你也跟我一样喜欢老书的情怀，那就去搞一本 Per Martin-Löf 编辑的《Intuitionistic Type Theory》原版吧。
…until picking up Type Theory and Formal Proof. This one took me somewhere between 100 to 200 pages before getting lost. They cover the entire lambda cube. But then I was able to re-start Thompson's "Type Theory and Functional Programming" and it was clear that I started to understand a lot of it. If you enjoy the nostalgia of older books like me, then pick up an original copy of "Intuitionistic Type Theory" edited by Per Martin-Löf.
……univalent foundations，听上去他们就像加了独门秘制酱料才搞定这事的，所以我一直在密切关注（虽然还没全看懂）。我之前提到的那条有趣的路径：我现在正在学习类型论（type theory）和函数式编程（functional programming），纯粹就是为了搞懂这门我原本都不知道存在的计算机科学分支。
…univalent foundations it sounds like they are adding magic sauce to make this possible, and so I follow it closely (but don't understand it all yet). The interesting path I spoke of earlier: I'm now learning type theory and functional programming just so that I can make sense of this branch of computer science that I originally didn't know existed.
确实，这篇文章的措辞甚至让我联想到了类型论和函数式编程。> 例如，一个通了电的水壶可以充当构造函数（constructor），执行烧水的任务。kettle power_supply water : (water * heat) > 你只需说明创建……的任务
Indeed, the wording of the article even made me think of type theory and functional programming. > For instance, a kettle with a power supply can serve as a constructor that can perform the task of heating water. kettle power_supply water : (water * heat) > You simply say that the task of creating…