Too Elegant For September

Being on sabbatical has given me a bit of experience with other systems and languages. Also, my kids are now old enough to “mess around” with programming. Learning from both of these, I’d like to hazard a bit of HtDP heresy: students should learn for i = 1 to 10 before they learn

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(define (sum lon)
  (cond [(empty? lon) 0]
        [else (+ (first lon) (sum (rest lon)))]))

To many of you, this may seem obvious. I’m not writing to you. Or maybe you folks can just read along and nod sagely.

HtDP takes this small and very lovely thing—recursive traversals over inductively defined data—and shows how it covers a huge piece of real estate. Really, if students could just understand how to write this class of programs effectively, they would have a vastly easier time with much of the rest of their programming careers, to say nothing of the remainder of their undergraduate tenure. Throw a few twists in there—a bit of mutation for efficiency, some memoization, some dynamic programming—and you’re pretty much done with the programming part of your first four years.

The sad thing is that many, many students make it through an entire four-year curriculum without ever really figuring out how to write a simple recursive traversal of an inductively defined data structure. This makes professors sad.

Among the Very Simple applications of this nice idea is that of “indexes.” That is, the natural numbers can be regarded as an inductively defined set, where a natural number is either 0 or the successor of a natural number. This allows you to regard any kind of indexing loop as simply a special case of … a recursive traversal of an inductively defined data structure.

So here’s the problem: in September, you face a bunch of bright-eyed, enthusiastic, deeply forgiving first-year college students. And you give them the recursive traversal of the inductively defined data structure. A very small number of them get it, and they’re off to the races. The rest of them struggle, and struggle, and finally get their teammates to help them write the code, and really wish they’d taken some other class.

NB: the rest of this makes less sense… even to me. Not finished.

However, another big part of the problem is … well, monads are like burritos.

Let me take a step back.

The notion of repeated action is a visceral and easily-understood one. Here’s what I mean. “A human can multiply a pair of 32-bit integers in about a minute. A computer can multiply 32-bit integers at a rate of several billion per second, or about a hundred billion times as fast as a person.” That’s an easily-understood claim: we understand what it means to the same thing a whole bunch of times really fast.

So, when I write

for i=[1..100] multiply_two_numbers();

It’s pretty easy to understand that I’m doing something one hundred times.