2016-06-16 09:57:07 UTC
it appears that the infix operator $ is used both for the n-th component
of a vector and the n-th coefficient of a Formal Power Series.
Since I now use both Multivariate_Analysis and Formal_Power_Series, I
get lots of syntax ambiguity warnings all the time. We should probably
do something about this.
I see the following three options:
1. Rename one of the operators. Since Formal_Power_Series is used less
than vectors, this is probably the one to change in this case. I am not
sure, however, what it could be renamed to. The standard mathematical
notation is something like "[X^n] f", so I suppose we could go for
"⟨X^n⟩ f", but I'm not sure if that's a good idea.
2. Disable the "$" notation completely outside the FPS theory, or put it
in a locale that has to be interpreted every time one wants to use the
notation. On the down side, one still runs into problems when one wants
to use the $ notation for FPSs but has Multivariate_Analysis loaded as
well. I guess one could put both of them in locales, but I don't know if
we want that.
3. Use ad-hoc Overloading, similar to what is done for monads. One could
then also use $ e.g. for the n-th coefficient of a polynomial, or
perhaps even unify the notation with the n-th element of lists and
arrays etc. at some point. The down side of this is that when there are
ambiguities/type errors, the error messages get a bit confusing.
Note that "normal" overloading does not work, since the constant would
have to have the type "'a => nat => 'b", and that means one has to write
type annotations everywhere.
Any opinions? Whatever the outcome is, I will take care of implementing it.