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
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