[ 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
