《证明与类型》封面

证明与类型

Proofs and types

Jean-Yves Girard · 初版 1989 年

6人推荐
10位读者提及
14次提及

为什么值得读

  • 虽风格特立独行,但内容极富启发性
  • 向更高阶的程序分析与定理证明进阶的必读作
  • 作者开放了免费在线阅读资源

Hacker News 上怎么说

  • ……过去几个月我自己也在研读类型论(type theory)文献(坦白说,更多是从数学角度而不是编程角度),市面上确实很缺优秀的入门资料。吉拉德(Girard)的《Proofs and Types》是一本神作,但读起来并不轻松,而且对程序员来说没有太多直接相关性。如果其他人感兴趣的话(merijnv,我猜这些你都浏览过了),我有……

    …type theory literature myself over the last couple of months (admittedly more from a mathematical angle than a programming one), and there is definitely a dearth of good introductory material. Girard's Proofs and Types is a great book, but it's not easy going and doesn't have a huge amount of direct relevance to programmers. In case anyone else is interested (merijnv, I assume you've glanced at all of these) I have…

  • ……Fitting写的《Automated Theorem Proving》是一本不错的教材。就我个人而言,我认为应该从Huth & Ryan入手。逻辑学就是计算机科学(CS)的微积分。然后通过Pierce的《TAPL》或者Girard的《Proofs and Types》这样的书进阶到类型论。接着,根据你的兴趣,你可以继续深入到模型检测(model checking)、程序分析和定理证明。前两个方向的经典著作分别是Katoen以及Nielson & Nielson。

    …Automated Theorem Proving by Fitting is a good text. Personally, I think the place to start from is Huth & Ryan. Logic is the calculus of CS. Then progress to type theory using a book like TAPL by Pierce or Proofs and Types by Girard. Then, depending on your interests, you can proceed to model checking, program analysis and theorem proving. For the first two, the classics are Katoen and Nielson & Nielson, respectively.

  • 哪种资源合适取决于你的背景。如果你喜欢看书,Girard、Lafont和Taylor合著的《Proofs and Types》[1]是一本非常棒的读物,尽管风格很独特。[1] http://www.paultaylor.eu/stable/prot.pdf

    What's a suitable resource depends on your background. If you like books, "Proofs and Types" by Girard, Lafont, Taylor [1] is a great read, albeit idiosyncratic. [1] http://www.paultaylor.eu/stable/prot.pdf

  • ……论文('LOCUS SOLUM'的附录A)(https://girard.perso.math.cnrs.fr/0.pdf)。我可以随便翻到他‘附录’的任意一页,然后就沉浸其中。他关于该主题的一部优秀的入门之作是《PROOFS AND TYPES》(https://people.mpi-sws.org/~dreyer/ats/papers/girard.pdf)。

    …paper' (Appendix A of 'LOCUS SOLUM') (https://girard.perso.math.cnrs.fr/0.pdf). I could flip to a random page of his 'appendix' and just sink in. A fine introductory work of his to the subject would be 'PROOFS AND TYPES' (https://people.mpi-sws.org/~dreyer/ats/papers/girard.pdf).

  • 我强烈推荐《Proofs and Types》(http://www.PaulTaylor.EU/stable/Proofs%2BTypes.html),它还有一个额外的优势:是免费的。

    I strongly recommend "Proofs and Types" (http://www.PaulTaylor.EU/stable/Proofs%2BTypes.html), which has the added advantage of being free.

  • 我记得我很喜欢他的《Proofs and Types》这本书,在费劲啃完马丁-洛夫(Martin-Löf)的著作之后读它简直让人豁然开朗。关注这些理论的一个成果就是 Clean,一种速度快得惊人的函数式编程语言(FPL),它提供了更现代的 Haskell/ML 风格语法。……

    I remember really liking his book Proofs and Types which was a revelation after struggling with Martin-Löf’s writings. One outcome of that attention was a nice and blazingly fast for an FPL called Clean which offered a more modern Haskell/MLish syntax.…

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