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

[ I think Matthias probably meant to lift

  (generate-expression (sub1 i))

out of the (lambda (x y) ...). ]

Robby

On Tue, Jun 7, 2011 at 8:31 AM, Matthias Felleisen <matthias at ccs.neu.edu> wrote:
>
> Why don't you teach them how closure compilers work:
>
> #|
>                 EXPR = x |
>                        y |
>                        (,sinpi EXPR) |
>                        (,cospi EXPR) |
>                        (,* EXPR EXPR) |
>                        (,avg EXPR EXPR)
> |#
>
> ;; N -> EXPR
> ;; generate an expression of depth i
> (define (generate-expression i)
>  (local ((define select (random 6)))
>    (cond
>      [(= select 0) (lambda (x y) x)]
>      [(= select 1) (lambda (x y) y)]
>      [(= select 2) (lambda (x y) (sin ((generate-expression (sub1 i)) x y)))]
>      [(= select 3) (lambda (x y) (cos ((generate-expression (sub1 i)) x y)))]
>      [(= select 4) (lambda (x y)
>                      (* ((generate-expression (sub1 i)) x y)
>                         ((generate-expression (sub1 i)) x y)))]
>      [(= select 5) (lambda (x y)
>                      (avg ((generate-expression (sub1 i)) x y)
>                           ((generate-expression (sub1 i)) x y)))])))
>
> (define (avg x y)
>  (/ (+ x y)
>     2))
>
>
> ((generate-expression i) -1.0 +1.0)
>
> You may have to fix the details. -- Matthias
>
>
>
> On Jun 7, 2011, at 10:19 AM, Stephen Bloch 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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