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Consider some example definitions:

abba["1"] = 1;
abba["2"] = 2;

For some reason, I do not want to introduce the other form of representation such as associations.

Is it possible at all to extract keys for which abba takes the predefined values (i.e., "1","2")?

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    $\begingroup$ lookUp = ReplaceAll[ Merge[Identity] @ Map[Reverse] @ ReleaseHold[ DownValues[#] /. {RuleDelayed -> Rule, #[x_] :> x}]] &; Use as lookUp[abba]@{1, 2}, lookUp[abba]@2 etc $\endgroup$
    – kglr
    May 17 at 11:07

1 Answer 1

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Keys[DownValues[abba]][[All, 1, 1]]
(* {"1", "2"} *)
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