[Axiom-developer] strict vs. fuzzy Axiom

[Ralf Hemmecke]

> C Y wrote:

> > I guarantee that making Axiom too strict in a correctness sense
> > without providing a way to get things done will lose it much of its
> > audience in the unit game, since physicists as a rule are not
> > overly concerned with mathematical rigor. (Compared to
> > mathematicians, anyway ;-)  I think allowing both strict mode and
> > fuzzy mode is a good idea, which allows for both full correctness
> > if needed and a more practical working environment if desired.  I
> > invite comment on this, since I might have just stomped Axiom
> > philosophy into the carpet :-/.

> Being "fuzzy" is certainly against the philosophy of Axiom, but I
> suppose as long as it is clearly pointed out, there is no reason not
> to allow it. Martin has a "guessing" program for sequences, and it is
> very useful. So go ahead. I agree that Axiom suffered commercial
> failure for its inflexibility.

As some of you might know Aldor's intermediate name was A# (A-sharp). I 
once heard of a project which was called B-flat and if I am not wrong it 
did exactly address the "problem" that Axiom was to complicated for a 
wider audience. (Please correct me if I am wrong.) In my opinion, the 
idea should be that internally Axiom/Aldor is strict and that should 
NEVER change. However, I couln't say anything against another layer (I 
my eyes that could be the work of a user interface) which tries hard to 
guess what the user had in mind. The user input would be equipped with 
all the necessary type information to run a strict program internally. 
One cannot expect everyone to know all the hairy details of the 
algorithms. How many people bother to understand the Risch algorithm 
just to solve an intergral. If they have a CAS at hand which translates 
their input and gives a reasonable output _and_ is able to tell what the 
output actually means (that may depend on the an ambiguous 
interpretation of the input).

So I would vote for a two-layered AXIOM.
1) internal libraries (strict)
2) user interface (fuzzy)
and I would like to see these layers being separate things.
A user should however always be allowed to just use the strict mode if 
he is knowledgable enough. And other people should be encouraged to 
provide enough information.

One approach could be like that...
http://www-sop.inria.fr/cafe/Manuel.Bronstein/sumit/sumitdoc/node628.html

Best regards
Ralf