How to get all the symbols `x` for which `f[x]` is defined?

Question

Assume that definitions like the following are in place:

f[alpha] = "artichoke";
f[bravo] = "beet";
f[charlie] = "celery";
...
f[yankee] = "yam";
f[zulu] = "zucchini";

etc. (Also assume that all the symbols alpha, bravo, charlie, ..., yankee, zulu evaluate to themselves.)

I'm looking for a way to get a list of all the symbols for which f is defined. IOW, given f, I'm looking for a way to get the list of symbols

{alpha, bravo, charlie, ..., yankee, zulu}

(Note that, for the query I'm interested in here, the values associated with the definitions are irrelevant.)

The closest I've found is to somehow scrape the output of Information[f] (or Definition[f]), which strikes me as a horrible prospect.

Is there a more civilized approach?

@Virgil. Nice, but not always equivalent. Try f[alpha]={{beta}}. Then Level[DownValues[f], {4}] returns {alpha, beta}. — Fred Simons, May 01 '15 at 06:49
@Virgil This DownValues[f][[All, 1, 1, 1]] will behave slightly faster for large DownValues. — Rolf Mertig, May 01 '15 at 07:09

score 4 · Accepted Answer · edited Apr 13 '17 at 12:55

4

Barbarism can be avoided through judicious application of DownValues. Using RolfMertig's suggestion, you can get what you want with

f[alpha] = "artichoke";
f[bravo] = "beet";
f[charlie] = "celery";
...
f[yankee] = "yam";
f[zulu] = "zucchini";

DownValues[f][[All, 1, 1, 1]]

(* -> {alpha, bravo, charlie, ..., yankee, zulu} *)

edited Apr 13 '17 at 12:55

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answered May 01 '15 at 23:00

Virgil

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How to get all the symbols `x` for which `f[x]` is defined?

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