I can't find a way to list registered functions (the built-in ones and the
ones added programmatically) via an API call nor via a built-in table like
there is for tables in sqlite_master, which I could query.

How does one get this list? Or asked differently, how would a user know
which SQL functions she can use unless there's a way to list them in SQL?

We have a UI which allows to aggregate rows by selecting a column and an
aggregate function, but we must hard code the list of aggregate functions
instead of introspecting the connection for all available aggregate
functions.

In general, I'd also like to be able to tell the cardinality of the function
as passed as nArg to sqlite3_create_function. Is that also possible?

Thanks, --DD
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