A little challenge...

[Robert Jacques]

On Thu, 25 Feb 2010 18:57:32 -0500, Norbert Nemec  
<Norbert at nemec-online.de> wrote:
> Hi everybody,
>
> thinking about array expressions, I have stumbled over an interesting  
> challenge for which I still have no idea:
>
> Consider the mathematical sum notation:
>
> 	\sum_i a_i*b_i
>
> here, the variable i is defined only at the scope inside the expression.
>
> A analogous D syntax could be something like
>
> 	sum!(i)(a[i]*b[i])
>
> where sum would have to be some kind of template that takes i as a name  
> parameter and then defines it as variable inside the scope of the second  
> expression.
>
> (Of course, the scalar product is trivial enough to do it in a zillion  
> of other ways, but for more complex sum expressions with potentially  
> more than one variable, this would really be neat to have in an array  
> library.)
>
> Does anyone have an idea how this could be realized in D? Allowing a  
> template to define additional symbols only for the scope of its  
> arguments? Is it possible at all with the current language definion?  
> Does anyone have an idea for an elegant language extension to allows  
> this? It would mean taking lazy evaluation even one step further, all  
> the way to a lazy symbol binding. Seems straighforward enough to me to  
> implement in a compiler. Just the question how exactly to define the  
> semantics.
>
> Greetings,
> Norbert

Well there is std.algorithm's map and reduce. Somehow, I feel slicing,  
ranges/generators and array expressions should be able to handle this. For  
example: \sum_i i*a_i*b_i-1 => sum(iota * a * b[1..$]) But then again I'm  
having trouble thinking of real examples off the top of my head.