编程与软件工程byorgey.wordpress.com
与六岁孩子聊函数式编程
Conversations with a six-year-old on functional programming
2018 — 2020，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
这篇文章记录了作者 Brent Yorgey 与他六岁儿子关于函数式编程的对话，用“函数机器”等比喻向孩子解释 lambda 演算、常量函数乃至自由定理（free theorem）等抽象概念。文中既有孩子天真的误解，也有令人意外的领悟，展现了如何用平实的语言把抽象思想讲给孩子听。
为什么经久不衰：它既是一份温暖的教育实践记录，也巧妙揭示了函数式编程的核心直觉，对程序员和父母都同样耐读。
HN 评论精选
盛赞作者的教学能力，并推荐他的教学文章和 CIS 194 课程资源。
Brent 是我遇到过的最好的老师之一。我曾上过他的课（也给他教的其他课当过助教），每次都惊叹于他的热情和分享概念的能力。他还有一篇关于教学法的精彩文章。如果你想学习函数式编程的美丽基础，我强烈推荐他 Penn CIS 194 课程的讲义和作业。
zwass查看英文原文
Brent is one of the greatest teachers I've ever experienced. I used to take classes from him (and TA some others he taught) and was consistently blown away by his enthusiasm and capacity for sharing concepts. He has a great essay on pedagogy as well (https://byorgey.wordpress.com/2009/01/12/abstraction-intuition-and-the-monad-tutorial-fallacy/) If you're interested in learning some of the beautiful foundations of functional programming, I highly recommend checking out the lecture notes and assignments from his Penn CIS 194 class (http://www.cis.upenn.edu/~cis194/spring13/lectures.html)
常量函数对六岁孩子和大学生都同样反直觉，说明人的直觉偏向线性类型。
文中说 \lambda x.\, 6 这个常量函数让孩子很难猜（虽然他最终猜对了）。我觉得他只是卡在了“函数一定要对输入做某种算术运算”这个想法上，很难想出什么算术过程能无论输入什么都得到 6！他根本没想到机器可能完全不关心输入。（有趣的是，我这学期函数式编程课上很多学生在学 lambda 演算时也被常量函数搞糊涂了；他们特别想把输入代入某个地方，对绑定变量根本不出现在函数体里感到困惑。）这说明我们的直觉是基于线性类型的。
ummonk查看英文原文
>\lambda x.\, 6 was also surprisingly difficult for him to guess (though he did get it right eventually). I think he was just stuck on the idea of the function doing something arithmetical to the input, and was having trouble coming up with some sort of arithmetic procedure which would result in 6 no matter what you put in! It simply hadn’t occurred to him that the machine might not care about the input. (Interestingly, many students in my functional programming class this semester were also confused by constant functions when we were learning about the lambda calculus; they really wanted to substitute the input somewhere and were upset/confused by the fact that the bound variable did not occur in the body at all!) Just goes to show, our intuition works on linear types.
用“臭味探测器”的趣事说明：孩子（和很多人）会默认系统一定在利用输入，正如常量函数让人困惑。
“\lambda x.\, 6 让孩子很难猜……他根本没想到机器可能完全不关心输入。”有一年圣诞节全家聚会，我做了个“臭味探测器”，就是一个装在密封袋里的 USB 线。侄子们可以把任何人的袜子放进袋子，然后在界面上输入一些参数（比如袜子颜色、多久没洗，以及最关键的是袜子主人的名字）。界面背后是一个 grep 引擎，检查一个白名单里的名字和称呼（当然包括“叔叔”），给这些名字分配最低的臭味值；而侄子们自然会被保证得到高分。结果再经过随机数生成器，生成一个带噪声的正态分布显示在屏幕上。他们花了很长时间调整参数，想搞清楚这些参数如何影响“分析”结果，最后才发现一切都是由名字决定的。
dmlorenzetti查看英文原文
\lambda x. 6 was also surprisingly difficult for him to guess... It simply hadn’t occurred to him that the machine might not care about the input. One Christmas when my whole family got together, I made a "stink detector" which consisted of a USB cable stuck inside a ziplock bag. My nephews were invited to put anybody's sock in the bag, then enter some parameters (like sock color, how long since it was washed, and, crucially, the name of the sock's owner) in a GUI. Under the hood of the GUI was a grep engine that checked for a whitelist of names and titles ("uncle" among them to be sure), and assigned those names the lowest possible stink number. Whereas my nephews of course were guaranteed to get a high value. That result was fed through a random number generator, to produce a fuzzed-up normal distribution for display on the screen. They spent a long time varying the parameters, trying to figure out how they affected the "analysis" before figuring out it was all driven by the name.
文章开头“直接如实回答”才是关键：诚实对待孩子的问题，也能反过来加深自己的理解。
最关键的一点就在开头：“我决定直接如实回答。”这会在你和孩子的互动以及他们认识世界的方式上产生巨大差别。太多问题源于父母对孩子不够诚实。要直接，无论解释起来多尴尬。避免居高临下的简化，别说“你长大就懂了”。如果他们理解不了或不想听，他们就会停止提问。另外，提升自己对某件事理解的最好方法之一就是试着向别人解释，而还有谁比孩子更合适呢？如果他们说某个传统很蠢很傻，也许它确实如此！如果你无法向他们辩护它，那你为什么还要遵循它？谁知道呢，也许你还会意外收获一个分享兴趣的朋友。
Scapeghost查看英文原文
The most key point of this is right at the start: "I decided to just answer straightforwardly" That can make all the difference in your interactions with your child and how they learn about this world. Too many problems are caused by parents not being honest with their kids. Be straightforward, no matter how awkward the explanations may be. Avoid patronizing simplifications and saying things like "you'll understand when you're older". If they're not able to understand or decide they don't want to, they'll stop asking. and also one of the best ways of improving your own understanding of something is to try explaining it to someone else, and who better than a child? If they say some tradition is stupid or silly, maybe it is! If you can't defend it to them, why do you follow it? Who knows, maybe you'll even make an unexpected friend to share your interests with. :)
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