Re: [Axiom-developer] How to do generic sum using aldor?

[Ralf Hemmecke]

> I read the excellent aldor user's guide and neglected the fact, that
> it is written for the standalone version of aldor rather than the axiom 
> version. Is there a similar manual for axiom+aldor other than
> http://www.aldor.org/docs/HTML/chap18.html ?
> Is this the right mailing list anyways?

Since you want to work with Axiom, I guess you are right here.

[snip]

> Now to the real questions.
> I was aware of reduce but did not use it because I actually wanted to 
> write a "generic" sum function for "all" possible structures, including 
> finite streams etc. on which reduce does not work.
> The only way I found in axiom was
>
>   last complete scan(0,+,somestream)
>
> which looks rather insatisfactory.

I currently rather rely on what is provided in LibAldor+LibAlgebra and 
don't take things from LibAxiom, but that is personal taste.

It seems that you want

---BEGIN sum.as
#include "axiom"
macro {
        MyAdditiveMonoid == with {
                0: %;
                +: (%, %) -> %;
        }
}
SumPackage(M: MyAdditiveMonoid): with {
    sum: Generator M -> M;
} == add {
     sum(g: Generator M): M == {
         m: M := 0;
         for x in g repeat m := m+x;
         return m;
     }
}
---END sum.as

You would call that via

l: List Integer := [2,3,4]
sum generator l

You have probably read that "Generator" abstracts from the actual 
underlying datastructure and only relies on the fact that the elements 
are delivered in a linear fashion. The bad thing is: "Generator" is not 
available in an Axiom Session. And even worse, no Axiom domain provides 
a "generator" function for its elements.
You always have to hide it inside an Aldor program. So your problem is 
probably not easily solvable. But that would be my Aldor approach.

> What could be axiom equivalents of AdditiveType and 
> BoundedFiniteDataStructureType?

I don't know of any "Bounded..." category in Axiom.

> Then SumPackage(L:BoundedFiniteDataStructureType,R:AdditiveType)
> with essentially the same code would do just any possible case.

Yep. But sorry to say: Axiom is weak in that respect (at least to my 
knowledge).

Ralf