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Re: [Axiom-developer] Curiosities with Axiom mathematical structures
From: |
Ralf Hemmecke |
Subject: |
Re: [Axiom-developer] Curiosities with Axiom mathematical structures |
Date: |
Wed, 08 Mar 2006 23:24:42 +0100 |
User-agent: |
Thunderbird 1.5 (X11/20051201) |
Do you mean that passing operations to the categories would be a feasible
approach? I.e., being allowed to say something like
Monoid(m:(%,%)->%): Category == with
square: % -> %
add
square a == m(a,a)
Martin, stop writing in SPAD. I thought you also agreed that new things
have to be written in Aldor. And there you would to write the default
implementation with "default" and not with "add". Otherwise there would
be an anonymous domain "add {square ...}" inside a with clause.
Of course, one would have to rethink this several times, the suggested notation
here is clearly not yet perfect. One might object that this notation violates
the possibility of creating anonymous categories, but I suspect that this
wouldn't make sense anyway.
Yes, one has to rethink that quite a lot. The problem with your
suggestion is the following
1) You cannot simply ask
Integer has Monoid
because you have to give a parameter.
2) If you say something like
MyMonoid(T: Type, m: (T, T) -> T): Category == with {
square: T-> T;
default {square(t: T): T == m(t, t)}
}
then it is perfect Aldor.
Then, however, you ask
Integer has MyMonoid(Integer, *)
and it will return true only if you have said
extend Integer: MyMonoid(Integer, *) == add;
somewhere.
(But probably you had something else in mind.)
Although I don't really like that an AbelianMonoid is not a Monoid, and
although I think that renaming during inheritance would be nearer to
mathematics... after all the discussion here, I somehow think that the
design in Axiom is not really bad. The reason is that I have not seen a
clear case where renaming would be over-advantageous.
I'd like to say
Integer has Monoid
instead of
Integer has Monoid(*, 1);
Integer has Monoid(+, 0);
Simply think of a category Foo with hundreds of exported function, would
you like to write
Dom has Foo(f1, f2, ..., f100)
??? That is not really handy.
Maybe we should open up a page on AxiomWiki and list some cases where
one could really benefit from renaming. I guess the list would be quite
short and not comparable with the effort such an Aldor extension would cost.
Ralf
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, (continued)
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, William Sit, 2006/03/02
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/02
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/04
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/03
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, William Sit, 2006/03/04
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/07
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, William Sit, 2006/03/07
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/08
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures,
Ralf Hemmecke <=
- Re: [Axiom-developer] Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/09
- [Axiom-developer] BINGO, Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/09
- Re: [Axiom-developer] BINGO,Curiosities with Axiom mathematical structures, William Sit, 2006/03/09
- Re: [Axiom-developer] BINGO, Curiosities with Axiom mathematical structures, Ralf Hemmecke, 2006/03/10
- Re: [Axiom-developer] BINGO,Curiosities with Axiom mathematical structures, William Sit, 2006/03/10
- Re: [Axiom-developer] BINGO, Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/13
- RE: [Axiom-developer] BINGO, Curiosities with Axiom mathematical structures, Bill Page, 2006/03/09
- Re: [Axiom-developer] BINGO,Curiosities with Axiom mathematical structures, William Sit, 2006/03/10
- Re: [Axiom-developer] BINGO, Curiosities with Axiom mathematical structures, Gabriel Dos Reis, 2006/03/13
- [Axiom-developer] Re: BINGO, Curiosities with Axiom mathematical structures, Martin Rubey, 2006/03/10