Oops. Thanks. In addition to a closure pass, you can also ask to generate two values: a symbolic representation, ready for printing, and a closure. It's just a couple of lines extra. In plain Racket, I'd use values to do dit. In *SL you have to use lists of pairs.
This is indeed a nice example of using lambda for *representation* and not for abstraction. Good idea. On Jun 7, 2011, at 11:41 AM, Robby Findler wrote: > [ 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 <matth...@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 >>> sbl...@adelphi.edu >>> >>> >>> _________________________________________________ >>> For list-related administrative tasks: >>> http://lists.racket-lang.org/listinfo/users >> >> >> _________________________________________________ >> For list-related administrative tasks: >> http://lists.racket-lang.org/listinfo/users >> _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/users
