Hi!
I'm working through the early examples of the "Stratified Design" paper[1] and I've run (almost immediately!) into something that doesn't seem to work.
They describe an average-damp function that given a function, returns a new function that averages the value with the result of the function:
(define (average)
(div (apply 'add (args)) (length (args))))
(define (average-damp f)
(fn (x)
(average x (f x))))
You might use it like this: ((average-damp (fn (y) (+ 2 y))) 3)
And expect to get 4 (the average of 3 and the result of adding 2 to 3). However, instead I get this:
ERR: invalid function : (f x)
called from user defined function average
I assume that this is happening because the function f, that is passed to average-damp is not lexically closed in the new function that's returned, because NewLisp is not doing that sort of thing.
I have looked through the "Functions as Data" section of the Code Patterns and those examples didn't seem to help. I tried both "expand" and "letex" and they didn't seem to help.
So, is it possible to implement something like average-damp in NewLisp, and how would you do it?
Thanks!
[1] See http://dspace.mit.edu/bitstream/handle/1721.1/6064/AIM-986.pdf?sequence=2
You are correct that the reliance on lexical scope is causing the problem. In the manual, Lutz talks about what you should do in this case. From http://www.newlisp.org/downloads/newlisp_manual.html#letex.
Quote
In the second example a function make-adder is defined for making adder functions:
(define (make-adder n)
(letex (c n) (lambda (x) (+ x c))))
(define add3 (make-adder 3)) → (lambda (x) (+ x 3))
(add3 10) → 13
letex evaluates n to the constant 3 and replaces c with it in the lambda expression.
So your definition of average-damp in this case might be:
> (define (average-damp f)
(letex ([f] f)
(fn (x) (average x ([f] x)))))
> ((average-damp (fn (y) (+ 2 y))) 3)
4
Hope that helps.
(define (average)
(div (apply add (args)) (length (args))))
(define (average-damp f)
(apply average (append (map f (args)) (args))))
I assume a dampening factor has to be applied to every argument, as in the second example
> (average-damp (fn (x) (+ 2 x)) 3)
4
> (average-damp (fn (x) (+ 2 x)) 3 4 5 6)
5.5
>
Note, that the x is not a free variable in (fn (x)...) and is protected so the following won't harm:
> (set 'x 3)
3
> (average-damp (fn (x) (+ 2 x)) x (+ x 1) (+ x 2) (+ x 3))
5.5
>
also: fn is just a shorter writing for lambda
:-) I just see, rickyboy and I posted at the same time, but two different solutions
the function passed doesn't need to be anonymous:
> (define (my-damp x) (+ 2 x))
(lambda (x) (+ 2 x))
> (average-damp my-damp 3)
4
> (average-damp my-damp 3 4 5 6)
5.5
>
Very nice, Lutz!