On 11/14/2008 09:00 AM, Martin Rubey wrote:
> I'd like to report on a curious problem I have with SPAD/Aldor, which Python
> does not seem to have.
>
> In Axiom, we currently have the (mostly unused) Categories
>
> CoercibleTo S, RetractableTo S and ConvertibleTo S that provide
>
> coerce: % -> S, coerce: S -> % and retract: % -> S
>
> respectively.
Not quite true.
CoercibleTo(S:Type): Category == with
coerce: % -> S
ConvertibleTo(S:Type): Category == with
convert: % -> S
RetractableTo(S: Type): Category == with
coerce: S -> %
retractIfCan: % -> Union(S,"failed")
retract: % -> S
add
retract(s) ==
(u:=retractIfCan s) case "failed" => error "not retractable"
u
> Very unfortunately, currently in almost all cases the query "has CoercibleTo
> Something" will return false, because the coerce function is not inherited by
> the category.
> Now, I would like that for domains of the same category, say
> UnivariatePolynomialCategory, that differ only in the representation of their
> elements, say sparse or dense, we would have
> A has CoercibleTo B and B has CoercibleTo A
OK, let's say I take AbelianMonoid as a category. For A, I take Integer
and for B, I take String (just let's suppose 0: String is the empty
string and +: (String, String) -> String is concatenation.
One can easily find the homomorphism (of monoids) #: String -> Integer
(the length of the string) in one direction and call it coerce. But the
other direction I find a bit difficult to come up with. ;-)
Looks like your specification of the problem is too imprecise.
Ralf
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