with a little more tolerance in interpretation of "context":

IIRC some operands and builtins only work in special contexts, some even throw (threw?) warnings if not used properly.

> > There ought to be a repository of common expressions and how they behave in each context
> The perl documentation does that, doesn't it?

Well I once meditated over this, unfortunately POD doesn't have a standard notation for a brief definition for the interface of a term.

If it had, they could not only automatically be compiled into cheat sheets, but also into tool tips for IDEs or grammatical rules for syntax checkers.

There are various alternative sources for such abstracts, which get hopelessly fast outdated

For instance emacs's cperl-mode has tool-tips hardcoded which are far from being up-to-date.

Another advantage of such an hypothetical POD-extension could be the definition of use cases for snippet-expansion within an IDE, like for yasnippet in emacs or more detailed error-texts for diagnostics.

Of course some (all?) of this could be achieved with a special =FOR :format-paragraph, but there is no standard notation yet. (maybe Perl6 signatures could be a good start)