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

From: Robby Findler (robby at eecs.northwestern.edu)
Date: Tue Jun 7 10:27:16 EDT 2011

Put the call to eval outside and add the wrapper `(lambda (x y)
,code-with-x-and-y-free). Then just call that function each time,
instead of calling eval each time.


On Tue, Jun 7, 2011 at 7:19 AM, Stephen Bloch <sbloch at adelphi.edu> wrote:
> 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)
>        eval-ns))
> 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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