I wrote:
>
> Gabriel Dos Reis wrote:
> >
> > Waldek Hebisch <hebi...@math.uni.wroc.pl> writes:
<snip>
> > |
> > | new : (NonNegativeInteger, S) -> %
> > |
> > | So the first argument to 'new' must be 'NonNegativeInteger' and the
> > | second must be '%'.
> >
> > 1. new, expects its second *argument* to be of type %. It does not
> > require that there be no implicit coercion between the argument
> > as lexically written in the source code, and the actual code
> > generated for that argument. If one thinks that the mere presence of
> > the parameter "Rep" indicates that is the representation domain,
> > therefore the implicit coercion from Rep to % is OK, then 0@Rep is
> > a good viable candidate.
> >
> > 2. Fortunately, in this case, 0@% is also defined explicitly to be
> > 0$Rep, but there is no requirement that be the case. And when
> > it is not, we get a problem.
>
> Actually 13.6 says that '%' take precedence over 'Rep', so this one
> is excluded.
>
> > 3. ModMonic(R,Rep) satisfies UnivariatePolynomialCategory(R), so that
> > means that there is alsoanother implicit coercion that turns
> > 0@R into a legitimate value of type %.
> >
> > 4. Similar reasoning holds for 0@Integer because % satisfies Ring,
> > and there is an implicit coercion from Integer to any domain that
> > satisfies Ring.
> >
> > 5. Since NonNegativeInteger is a subdomain of Integer, it also
> > provides an implicit coercion.
> >
> > So, in fact if one thinks that the mere presense of the parameter Rep is
> > sufficient to indicate representation domain and therefore implicit
> > coercions, then we have a legitimate case of ambiguity.
>
> OK, if you think about exact operations used to produce 0, then
> there is really ambiguity. However, IMO coercions are supposed
> to be homomorphims, so each of ways should lead to 0 in '%'.
>
A little correction: when checking if selected modemap
is applicable compiler tries to coerce obtained result
to requested type. AFAICS compiler only will succeed
coercing '%' to '%' and 'Rep' to '%'. I am not sure if
hacks to prefer '%' over 'Rep' work in this case. If yes
then there is no ambiguity in choice of operations.
If no, maybe we should fix compiler to choose '%' (given that
this preference is documented).
Also, if chooses representation which has 0 different than
0 in %, then it is probably better not to specify Rep at
all.
--
Waldek Hebisch
hebi...@math.uni.wroc.pl
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