Function Repository Resource:

ExtractDownValues

Source Notebook

Extract all DownValues that match the input

Contributed by: Carl Woll

ResourceFunction["ExtractDownValues"][expr]

finds all DownValues that match expr, in the order in which they would be applied by the pattern matcher.

ResourceFunction["ExtractDownValues"][head,args]

finds all DownValues of head that match head[args].

Details and Options

Unless one of the DownValues uses Condition, the first DownValues should be the one that is used by the pattern matcher.

Examples

Basic Examples (3)

Define a function:

In[1]:=

$abs[c_Complex] := Sqrt[Re[c]^2 + Im[c]^2] abs[n_Real] := Sign[n] n abs[n_?NumericQ] /; MemberQ[{-1, 0, 1}, Sign[n]] := Sign[n] n abs[x_] := x$

Find the DownValues that match abs[23.1]:

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Use the two-argument version to find the DownValues that match abs[c] where c=2+I:

In[3]:=

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Applications (6)

Find a spoken string:

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Suppose you want to use "where" instead of "slash dot" in this spoken string. Use TracePrint to find the arguments to the internal function SpokenStringDump`SSText used to form the spoken string:

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The internal function used by SpokenString has many DownValues:

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ExtractDownValues can find the first downvalue that matches:

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Modify this downvalue:

In[8]:=

SpokenStringDump`SSText[a_ /. b_] := SpokenStringDump`SpeakQuantity[a, ReplaceAll, True] ~~ " where " ~~ If[ListQ[Unevaluated[b]], SpokenStringDump`SpeakListContents[b], SpokenStringDump`SpeakQuantity[b, ReplaceAll, True]]

Check the new output:

In[9]:=

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Properties and Relations (2)

When matching patterns, evaluation leaks can occur. Here is a function that has a side effect:

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Using ExtractDownValues causes the condition to be evaluated:

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Publisher

Version History

1.0.0 – 22 October 2019

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License