Implicit/default arguments/notations with differing arities

[Jazzpirate]

e.g. the general linear group of dimension n over a field K is usually just denoted as GL(n), omitting the field. Should we expect users to provide them each time?

Alternatively: Semantic abbreviations (I think sTeX has an \abbrdef, but it's not documented afaik?), possibly with an \implicit macro that signals MMT that an implicit argument occurs here, e.g.
\symdef{gln}[2]{GL(#1,#2)}
\abbrdef{glni}[1]{\gln{\implicit}{#1}}{GL(#1)}
Then MMT can attempt to do type inference and search the context for the most likely value. We can also allow for
local \abbrdefs that explicitly state a fixed argument for the current section, in which case we might want to mark these as not-exported in \includemodules.

[kohlhase]

I suspect that the user of a math paper might be willing to give the explicit argument explicitly, but does not want it to be formatted in the result (alternatively be hidden in the result but available upon request).
I consider this ability of hiding given arities an important capability of sTeX.

[Jazzpirate]

hiding given arguments would be easily achieved by a notation, e.g.:
\notation[hidefield]{gln}[2]{GL(#2)}

[Jazzpirate]

It occurs to me, that (some variant of) \abbrdef might allow us to

1. Turn MMT symbols into sTeX symbols and
2. "Sneak in" logical foundations.

E.g. expanding on #14 and #12, a module PLImplication could extend a face-theory for Implication by assigning \implication to the implication in latin2.
e.g.
\abbrdef{implication}[2]{\OMA{latin:/?Implication?implication}{#1,#2}}{#1 \Rightarrow #2}

(where \OMA would do nothing on the tex-side and represent an OMA/LFApply on the MMT-side...)

...in general I think the "definiens" in an \abbrdef would only matter on the MMT-side, never on the tex-side