[isabelle] Operator clash for $


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 "âX^nâ 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.



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