Dear Robert,
On Sat, Feb 14, 2009 at 03:57:07PM -0800, Robert Bradshaw wrote:
> ...
> > Would it be possible to add the following functionality (with whatever
> > appropriate syntax):
> >
> > declare_conversion(source, target, morphism)
> >
> > which would adds the morphism from source to target to the conversion
> > list (and probably similarly for coercions). Having some restrictions
> > on it (like making sure it's called before any coercion/conversion is
> > attempted) is no problem.
> >
> > This functionality will make it possible for each category to
> > automatically declare the relevant morphisms, independently of the
> > other categories (like if A is in Algebras(K), then this category will
> > declare the natural morphism from K to A).
>
> This functionality is certainly possible, but the decision was made a
> long time ago that Parents are supposed to be immutable. One problem
> is that asserting embeddings can drastically change how things
> operate globally, and one of the goals of coercion is to be stateless
> (from the user's point of view, of course it caches things for speed)
> and consistent. However, I can see how a command like this could be
> very useful. The restriction that it be called before any coercion
> take place seems very reasonable to me (and I'm less worried about
> conversions, but better safe than sorry). I'd like to have feedback
> from other people too though--I remember last time this came up there
> was concern over the problems Magma's "assert embedding" caused.
For the record, we had no trouble with this with MuPAD, despite a
really non-trivial coercion graph (but we also had no advanced
coercion attempts like pushouts computations).
How much time would it take you to write a quick draft of function
like this? It would be great if I could experiment with it in the
short term, and see how it feels (and decide how strong or not I'll
push forward its use).
> Another thing that we talked about way back, but never got around to
> implementing, was contextual coercions, e.g.
>
> with embedding(...):
> do stuff using that coercion
> # coercion doesn't work anymore here
Again for the record, I never had a use for this myself; but this
doesn't say anything about others!
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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