Re: [Axiom-math] if-expression and variables

[Ralf Hemmecke]

> > The first questions, when one programs with Axiom usually are:
> > What is my "domain of computation"?
> > (That is basically like with universal algebra. What is the carrier
> > set and what are the operations?)
> > How are the elements of the carrier set represented in terms of
> > already existing (library) types?
> Yes, I think it boils down to second-order logic; in this case a
> category of unevaluated expressions. As above; stored in the tree and
> then brought front and center and evaluated in the tree accessing
> environment.

As I said, it's no problem to implement that in Axiom. Actually, 
InputForm is basically such a domain.

> Going back to the original question. It seems the questioner expects to
> fabricate a template and later to create instances of it with varying
> variables.

Although possible, that is a mindset that belongs to traditional 
(typeless) CAS. I would rather ask the questioner to state the actual 
problem instead of already giving a direction, i.e. using expression trees.

> Sorry if I have taken the discussion drifting; I merely wanted to point
> out the if/else can be a static data structure rather than in-line code.

Well, of course, that's possible. In fact, expression trees is something 
that almost all computer algebra systems rely upon. But Axiom is different.

Take for example 1+1. What is this evaluated?
Three out of infinitely many results.
1) 2
2) 0
3) 1+1

In Axiom (at least in SPAD) there would only be one possible result, 
since the compiler checks types. If it is clear what 1 and + means, it's 
also deterministic what the result is.

Ralf