On formal correctness and readability (was: Re: [Maxima] Re: [Axiom-developer] Re: FeynCalc -> MAXIMA)

[David MENTRE]

Hello,

Bertfried Fauser <address@hidden> writes:

> Hence, for challenging problems, ie new math! and phys!, I would _reject_
> the lates goodies programmers can provide and favour to have a stable, as
> simple as possible, if possible provable algorithm.

This is the path followed by the FOC project
(http://www-calfor.lip6.fr/foc/index-en.html). The objective is to make
a provable CAS. They are using free software for that (the OCaml
language and the Coq proof assistant) but unfortunalty, they have chosen
to make the system closed source and proprietary[1].

On the Axiom side, there is a path that can be followed: using ACL2
(http://www.cs.utexas.edu/users/moore/acl2/) to make a similar
system. Both Axiom and ACL2 (and Maxima) run on GCL. But all the hard
work (i.e. proving things) remain to be done.

> New goodies, may be later added (in a separate pamphlet file <grin>,
> also by people who do not fully understand the theory and purpose of
> the program. They can then check against the slow but stable
> code. This method at least led me to stable and reasonable fast code,
> which at the and was relatively complex.

Interesting idea: systematizing the idea of reference
implementation. And formal proofs between the different implementations
are not necessary. We just need a framework to easily redo a fast
computation with a slower but safer implementation. Of course, formal
proof would be a plus, but I doubt that it can be done.

Yours,
david


[1] I wonder when one french reasearcher will understand the power and
    necessity of free software for real research!
-- 
David MENTRE <address@hidden> -- http://www.nongnu.org/axiom/