Clojure Changing My Mind

As good as Processing is, it’s still java. I’ve slowly been learning clojure, and trying to use it with Processing, via clj-processing. While the clojure docs and the book are both good, I’m still in that flounder-around stage, trying out tiny experiments to understand how things work.

I wanted a function to make saw-step sequences: (1 2 3 2 1 2 3 2 …). You give it the low bound, the high bound, and the step-size. For example:

  • (saw-step 1 4 1) gives (1 2 3 4 3 2 1 2 3 4 3 ...)
  • (saw-step 0 15 5) gives (0 5 10 15 10 5 0 5 ...)
  • (saw-step 0 5 2) gives (0 2 4 5 3 1 0 2 4 5 ...)

I’ve coded this kind of thing up in ruby, javascript, or java a dozen times, though it’s usually inside a loop, not returning a list. Something like this:

var min = 3;
var max = 7;
var step = 2;

var n = min;
while(shouldContinue()) {
    n += step;
    if (n+step > max || n-step < min) {
        step *= -1;  // turn around

My first try in clojure took a similar tack. I never got it right, but it was something like this:

(defn saw-step
  [min max step-size]
    (let [step (ref step-size)]
       (fn [x]
         (if (or ( min (- x @step)))
           (dosync (alter step -)))
         (+ @step x))

It’s a disaster — the parentheses don’t even match — but you get the gist. I was trying to cram the same imperative algorithm into clojure: keep some mutable state, add step to it, and when you reach the edges, mutate step to change direction. I kept getting bugs where it would go one step beyond the edge, or it would start working its way back from one edge, only to turn around again, and bounce against the edge forever.

I gave up and went to bed, but a few days later, I had better luck.

(defn saw-step
  [min max step]
      (into (vec (range min max step)) ; vec, so (into) adds to end
	    (for [x
		  (iterate #(- % step) max)
		  :while (> x min)] x))))

The first not-entirely-wrong step I made was to try breaking the list of numbers I wanted into two parts: the going-up numbers, and the coming-down numbers. (0 2 4 5 3 1) is just (0 2 4) + (5 3 1). The (range min max step) part gives you the going-ups, and the (for [x (iterate ...) stuff is the going-downs, as a list comprehension.

(One mistake I made was trying (range max min step) for the going-downs, which yields an empty list; another was using (iterate dec max), which never ends, because it keeps decrementing into the negatives. I found my way out with the list comprehension, but I bet there’s a better way.)

Once you have those two lists, you can use into to add each item from the second list to the first, giving you (0 2 4 5 3 1). That goes into cycle for a lazy, infinite sequence.

The solution’s not too bad: a saw-step is a cycle of the going-ups, followed by the going-downs. The code looks about that way.

(It occurred to me after that I could always use a default step of 1, and pipe the result through a scaling map. That would give me the bounds I wanted, with the extra benefit of evenly-spaced steps. Maybe I’ll remove step later.)

Alan Perlis said, “A language that doesn’t affect the way you think about programming, is not worth knowing.” He also said, “The only difference(!) between Shakespeare and you was the size of his idiom list – not the size of his vocabulary.”  Clojure’s changing my mind, a bit at a time.