Re: [Axiom-developer] Why did Axiom fail in the 1990s?

[Ralf Hemmecke]

> I could be that as an experiment, the failure of Axiom as a viable
> computer algebra system shows that there is something wrong with the
> concepts of strong typing and object-orientation when it comes to the
> design of computer algebra systems. After all most mathematics is not
> conducted in anywhere near a rigorously typed manner as required by
> even the simplest Axiom program.

I think it is clear to everyone that there are two things to achieve 
with Axiom

1) write a good an maintainable library
2) call that library (being an ordinary mathematician)

I agree that 1) is hard, but without types that will end up in code 
nobody understands. Look at today's Maple and Mathematica languages, 
they add type information and check that at runtime. I think the 
direction is pretty clear and Aldor is still miles ahead of the big M's.

Point 2) is a hard nut. I agree that if a mathematician (or however 
wants to use Axiom) tries to understand his own field with the help of a 
 CAS doesn't want to be bothered with types. It should be possible to 
add them, but initially it might not be very clear to the user. Think of 
someone exploring a completely new field where perhaps no algorithm is 
known to achieve some task. It is usually impossible to give a type.

However, I don't think it is a hard task to implement ExpressionTrees in 
Aldor/SPAD as they exist in other CAS. With that domain everything is 
basically typeless. The next task then would be to add properties to 
things like "+", "*", "diff", "int", etc. That can be done as in Maple.

The biggest problem is to connect the typeless and the typed worlds. 
That I consider as a research project.

Ralf