[racket] "compiling" evaluation of an arbitrary s-expression

From: Stephen Bloch (sbloch at adelphi.edu)
Date: Tue Jun 7 10:19:16 EDT 2011

I was looking at <a href="http://nifty.stanford.edu/2009/stone-random-art/">this Nifty Assignment</a>, which of course lends itself very nicely to my picturing-programs teachpack.

The random-expression generator to produce random trees over the algebra
	EXPR = x |
			y |
			(sinpi EXPR) |
			(cospi EXPR) |
			(* EXPR EXPR) |
			(avg EXPR EXPR)
is an easy student exercise.  (Note that each of these functions maps [-1,1] to [-1,1], so composing them at random makes sense.)

If I copy-and-paste the random expressions thus generated into the body of a function definition, I (or my students) can produce cool graphics like the ones at the Nifty Assignment web page, reasonably efficiently (e.g. a 300x300 pixel image, each pixel of which requires 26 trig functions, in 1.5 seconds).  But that requires manual intervention to copy-and-paste the expressions into a definition and then re-"Run".

Or I can take the random expression as a parameter and "eval" it (or more precisely, insert it into a backquoted expression to bind "x" and "y", and "eval" that).  Much more elegant, not to mention scriptable, than doing the copy-and-paste... but it takes c. 200 times longer to run, presumably because the expression is being rebuilt and re-parsed for each pixel.

(define (eval-with-x-y x y fmla)
  (eval `(let ((x ,x)  (y ,y)) ,fmla)

Is there a way I can get the best of both worlds?  I'd like to take an arbitrary s-expression (containing the free variables "x" and "y" as well as a limited set of function names) and "compile" it into a function of x and y that can be called efficiently on each of tens of thousands of pixels.

Assuming the answer is "yes" (this IS Racket, after all :-)), the next challenge is to package it so it's accessible from student programs in *SL.

Stephen Bloch
sbloch at adelphi.edu

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