编程与软件工程matt.might.net
把数学翻译成代码：Java、Racket、Haskell、Python 示例（2011）
Translating math into code with examples in Java, Racket, Haskell, Python (2011)
2011 — 2022，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
Matt Might 的经典文章，讲解如何把离散数学中的常见记号（集合、逻辑、函数等）翻译成可执行的代码，并分别用 Java、Racket、Haskell、Python 四种语言给出示例。文章帮助程序员用熟悉的编程思维理解数学表达式的含义。
为什么经久不衰：它把数学记号当作另一种'语言'来翻译，弥合了程序员与数学之间的鸿沟，多年来反复登上首页说明这个需求始终存在。
HN 评论精选
反驳'数学是纯函数式语言'的说法，认为 FP 与数学的相似性被夸大了
> 数学是一门纯函数式语言。它并不是。例如 x ∈ ℕ ∧ x > 2 ∧ x < 5 ∧ x % 2 = 0 可以推出 x = 4，这不是纯函数式语言能直接表达的。数学中大量使用关系（函数只是其特例），即使处理函数，函数式编程语言也不够用，比如 f(t) = t + 1 ∧ x ∈ ℕ ∧ f(x) = 3 等价于 x = 2。而且数学还常用不可计算的对象。这只是困扰函数式编程社区的众多'数学神话'之一：FP 和命令式编程彼此的相似度，都比它们与数学的相似度高。
pron查看英文原文
> Mathematics is a purely functional language. It is not. E.g. x ∈ ℕ ∧ x > 2 ∧ x < 5 ∧ x % 2 = 0 implies x = 4. This is not something pure functional languages can express directly. In math we make common use of relations, of which functions are a special case, but not the common one and certainly not the only one. But even when we do work with functions, a functional PL does not suffice. E.g. writing f(t) = t + 1 ∧ x ∈ ℕ ∧ f(x) = 3 is equivalent to writing x = 2. Also, we commonly employ objects that are not computable. This is just one of the many mathy myths that plague the FP community. Yes, there are some similarities between FP and mathematical notation, but FP and imperative are much closer to one another than either is to mathematics.
程序员的视角：数学记号难学，希望有代码化的数学教学材料
我梦想有这样的材料：用 Python 解释一些（对普通人来说）高深的数学概念。也许因为我写程序比做数学多，数学的'语言'实在太疯狂：到处是单字母变量、没有结构、成千上万种自定义记号。我不是批评它，我知道它存在自有道理，只是我当年太懒没在学校学好。以我 31 岁习惯顺序代码流的大脑，现在学数学相当困难。
dreen查看英文原文
I dream of material that would explain some advanced (for a regular person understanding of the word) math concepts using Python. Maybe it's because I've programmed more in my life than did math, but the "language" we use to write it is absolutely crazy: one letter variables everywhere, no structure, thousands of custom notations etc. I'm not criticising it, I realise it exists this way for a reason and if I wasn't so lazy I would have learnt it in school. But with my 31-year old brain oriented for looking at a sequential flow of code, it's quite difficult to learn math now.
区分'数学描述计算'与'代码描述可执行运算'，两者看似相似但有微妙差异
我认为一个思考得不够充分的问题是：数学通常描述的是计算（calculation），而代码描述的是计算的超集——运算/执行（computation）。我们整天和更大的集合打交道，常常忘了 calculation 表达力更受限。文章里的很多内容，正是关于如何在更受限的框架下工作，以及理解两者看似相似实则暗藏差异与陷阱。
bane查看英文原文
Okay, 94 points and still no comments, I'll bite. I think the difference here is, and I don't think this is a subject that has been thought about quite enough, is that mathematics typically describe calculation, while code describes a superset of calculation, computation. When we spend all our time working with the more expansive set, computation, we sometimes forget that calculation is in many ways less expressive and has fewer ways to express a thing. Many of the ideas in the article seem to be about getting over things we take for granted in computation, and understanding how to operate in the more limited framework offered by calculation, and/or understanding that even if things look kind of alike (what's a good word for this concept? a homoscript?) in computation vs. calculation they can be subtly different with a range of pitfalls.
数学的无副作用特性正是编程中诸多难题的对照
'数学没有副作用'——这可能是对 1970 年以来所有计算机科学问题最简洁的概括。
dvanduzer查看英文原文
"Math has no side effects" might be the most concise explanation of every computer science problem since 1970.
历次讨论
同类还值得读
开源应用架构
The Architecture of Open Source Applications
《开源软件架构》（AOSA）是一本在线免费书，邀请知名开源项目的作者亲自剖析其内部设计，涵盖 SQLAlchemy、LLVM、Audacity、Apache、Bash 等系统。
编程与软件工程上首页 9 次 · 2011–2024aosabook.org编辑精选编程语言简史：简短、不完整且多半错误
A Brief, Incomplete, and Mostly Wrong History of Programming Languages
一篇以戏谑、故意不准确的方式回顾编程语言史的博客文章，用夸张轶事和讽刺定义串起 Lisp、C、C++、Java、JavaScript、PHP 等语言。
编程与软件工程上首页 8 次 · 2009–2021james-iry.blogspot.comSQLite 是如何测试的
How SQLite is tested
SQLite 官方文档页，系统介绍 SQLite 的测试体系：多种测试方法（TCL 测试、模糊测试、回归测试、静态分析等）和海量测试用例，展示了这个小型开源项目如何靠极致测试获得…
编程与软件工程上首页 8 次 · 2009–2025sqlite.org编辑精选高级编程语言（2009）
Advanced programming languages (2009)
Matt Might 的经典文章，按用途推荐“高级编程语言”：如果追求就业就选主流语言，如果追求表达力、学术研究或创业，则推荐 Haskell、OCaml、Scala 等函数式语…
编程与软件工程上首页 8 次 · 2009–2022matt.might.net我的 Forth 与栈机器经历
Yosefk - My history with Forth & stack machines
作者以亲身经历回顾了使用 Forth 语言和栈式机器的历程：既赞叹其简洁优雅、代码量小、可自举的优点，也坦率指出栈操作在实际编程中的痛苦，以及 Forth 社区文化中的问题。
编程与软件工程上首页 8 次 · 2010–2024yosefk.com编辑精选