# Re: [isabelle] Notation for series coefficients

Hm, I think the usual option is to just go with a new $ notation. Maybe
using context/private notation tricks?
Alternatively, you could also try to use the coercion from 'a egf to 'a
fps, and then introduce a output abbreviation:
f $_fps x == fps_of_egf f $ x
- Johannes
Am Mittwoch, den 16.09.2015, 10:53 +0200 schrieb Manuel Eberl:
> Hallo,
>
> I am currently thinking about introducing a type 'a egf for exponential
> generating functions, derived from formal power series ('a fps).
>
> I was wondering how to best express the n-th coefficient of an egf. For
> polynomials, only the rather unwieldy notation "coeff f n" exists. For
> formal power series, "f $ n" exists.
>
> I considered overloading the $ notation so that it works for
> polynomials, formal power series, and exponential generating functions.
> However:
> â introducing a typeclass does not work, because this would be a
> higher-order typeclass.
> â Vanilla âoverloadingâ works, but the type of "op $" must then be 'a â
> nat â 'b, which means that type inference cannot deduce the result type
> of "f $ 0" even when the type of "f" is known, requiring type
> annotations everywhere.
> â Adhoc overloading would probably work, but that is somewhatâ ad-hoc.
>
> Does anybody have other ideas?
>
>
> Manuel
>

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