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Oct 28, 2023

I’m working on what feels like my lispiest Mathematica project. One of the pieces I wanted was to be able to search a list of associations by pattern, like:

• Fetch by ID: findAll[db, {"id" -> 42}] should return the full record, like {<|"id" → 42, "value" -> "A"|>}
• Return a custom expression using the values captured by the search pattern: findAll[db, {"id" -> id_, "value" -> "A"} :> id] should return all the IDs of records whose value is “A”, like {42, 99, 67}.

It turns out to be pretty simple to make a little API like that because pattern-matching is common in Mathematica so all the necessary pieces are right there, waiting to be assembled:

(* Plain search *)
findAll[o_, {pattern__}] := 
  Cases[o, <|OrderlessPatternSequence[PatternSequence[pattern], ___]|>];

(* Search and map *)
findAll[o_, {pattern__} :> replacement_] := 
  Cases[o, <|
     OrderlessPatternSequence[PatternSequence[pattern], ___]|> :> 
    replacement];