Return definition that would be applied to an expression

Question

Say I have an expression that has multiple subvalues how do I return the definition that would be applied to it.

Say I define for example:

fun[y_][x_] := {x, y};
fun[3][x_] := 2;

Then I would like findSubValue[fun[3][5]] to return HoldPattern[fun[3][x_]] :> 2.

score 5 · Answer 1 · answered Apr 14 '22 at 14:25

How about something like this:

SetAttributes[FindMatchingSubValue, HoldAll];
FindMatchingSubValue[sym_, expr_] := 
  SelectFirst[SubValues[sym], MatchQ[Unevaluated[expr], First@#] &]

Testing:

FindMatchingSubValue[fun, fun[3][5]]
(*HoldPattern[fun[3][x_]] :> 2*)
FindMatchingSubValue[fun, fun[4][5]]
(HoldPattern[fun[y_][x_]] :> {x, y})

score 0 · Answer 2 · answered Apr 14 '22 at 13:07

I think the following works because SubValues are automatically sorted (according to specificity, see https://mathematica.stackexchange.com/a/106093/45020) in the list returned by SubValues (or DownValues etc...):

SetAttributes[outermostHeadHeld,HoldAllComplete];
outermostHeadHeld[expr_]:=ReleaseHold[Hold[expr]//.Hold[h_[___]]:>Hold[h]];
SetAttributes[findSubValue,HoldAll];
findSubValue[expr_]:= Module[{subvals},
    subvals=SubValues[Evaluate[outermostHeadHeld[expr]]];
    SelectFirst[subvals,MatchQ[Hold[expr],Hold[Evaluate[#[[1]]]]]&]
]

The same idea should also work for DownValues.

Return definition that would be applied to an expression

2 Answers2