On Tue, Nov 08, 2011 at 03:51:59PM -0500, Bill Page wrote:
> On Tue, Nov 8, 2011 at 1:15 PM, Serge D. Mechveliani wrote:
> > [..]
> > dependent types
> > [..]
> Yes in general they really do work in Aldor and SPAD but there are
> limitations. Do you have specific examples?
1. The domain D(r, m, n) = (CommutativeRing r => Matrix(r, n, m))
of matrices n x m depends on the values n, m, which often need
to be computed at run-time, in a loop.
If n == m then D(r, m, n) must have the instance of
MultiplicativeSemigoup,
otherwise, it must not. Because so is required by algebra.
2. The residue domain R = Integer/(m) must be a Field, if and only
if m is prime. And only in this case the polynomial domain R[x] has
a sensible gcd operation.
And m is often computed at run-time, in a loop.
3. The domain R = Rational[xs, ppo] of polynomials has a sensible
Euclidean division only if xs = [x] -- a singleton variable.
And the finite set xs = {x_1...x_n}
is often computed at run-time, in a loop.
And the value parameters ppo defining the power product ordering
for R also need sometimes to be computed at run-time.
4. And so on.
> > History
> > -------
> > The DoCon library started in about 1995. In 2000 I got tired and
> > stopped it.
> > [..]
> I have read about DoCon with some interest especially in connection
> with category theory but I did not have sufficient time to learn how
> to install and use even simple examples.
Installation and introductory examples are there in manual.pdf,
(manual.lat, manual.ps).
Category theory
---------------
DoCon has almost nothing to do with the category theory.
I expect, the same is with Haskell, Axiom, and Aldor.
The interrelation with the category theory is only in that they provide
in their library certain particular classes which correspond to
certain fixed finite set of categories used in classical algebra
(a finite set of special cases and examples of categories):
Semigroup, Group, Ring, and several others.
The categorical approach in this software means only simething like
object programming, despite that Axiom calls a class a `category'.
And the category theory is something different
(see any introductory theoretic book this),
this software does not provide any support for this theory.
BTW, in 1970-s I took part in a seminar on the category theory,
for 3 years! And since this time cannot recall anything useful from
there, anything that could help to solve any scientific problem.
My impression is: it is not a theory, but only a language.
Because it provides no methods to solve problems, instead it provides a
certain language to reformulate things.
> Are you planning to revive this project?
I doubt. I have another project, in which I feel less expertize that in
CA. Do not know how long it will last, may be 2 months, may be 3 years.
Now, suppose that I enthusiastically continue DoCon.
Its methods is 3% of Axiom. After another 5 years it will become say 5%
-- a big deal. The real question is: why others do not use this
architecture to continue it.
I am going to write here my verdict about the ways to continue the
Axiom effort.
Thank you for your notes.
Regards,
------
Sergei
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/fricas-devel?hl=en.
