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ddevienne wrote:
> How does one get this list? 

There is no public API.  If you use the amalgamation then you can add
code to dig it out of the SQLite internals (a hash table amongst other
things).  Look for functionSearch and sqlite3FindFunction

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

They read this page http://sqlite.org/lang_corefunc.html

> 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?

Note that there can be multiple implementations of the same function
taking different numbers of arguments.  For example the builtin lower()
takes one argument, and ICU adds a variant taking two (the second
argument is the locale).

If this is still important to you, then I suggest writing the code that
returns all functions via a pragma or something similar and contribute
it back http://sqlite.org/contrib  - if your code is small enough then
you have a case to make it a standard part of SQLite.

In any event I recommend you create a bug ticket (type enhancement) so
that your issue is not forgotten.  Include your use case so others can
judge how valuable it would be if implemented.

Roger
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