Function Repository Resource:

SubexpressionPositions

Source Notebook

Find subexpressions together with their positions

Contributed by: Nikolay Murzin

ResourceFunction["SubexpressionPositions"][expr,opts]

returns an association with position and subexpression of expr that match certain criteria provided in opts.

ResourceFunction["SubexpressionPositions"][expr,levelspec, opts]

finds only subexpressions that appear on the levels specified by levelspec.

ResourceFunction["SubexpressionPositions"][expr,levelspec, n, opts]

return only first n results.

ResourceFunction["SubexpressionPositions"][expr,positions, opts]

select from a given list of positions.

Details and Options

ResourceFunction["SubexpressionPositions"] takes the following options:

"OuterMatch"

_→_

outer expressions matching criteria

"InnerMatch"

_→_

inner expressions matching criteria

"OuterMode"

"Any"

"Any" or All

"InnerMode"

"Any"

"Any" or All

"Complement"

False

take a complement of an overall criteria

Heads

True

whether to include expression heads

"OuterMatch" and "InnerMatch" are both assumed to be of the form subExpr→pos (read as "at"), a pair of patterns that would be matched against a subexpression and a relative position under consideration.

Relative positions on the right-hand side of matching patterns are always of the form {i₁,i₂,…} with non-negative integers i_k. Examples of position patterns include {} for exact position of matched subexpression, _ for any relative position, {___,0} for heads and so on.

"OuterMode" and "InnerMode" allow for matching criteria to match either any or all of the corresponding subexpressions.

Patterns may come in form of a constraint specified using Except.

Examples

Basic Examples (13)

Find all subexpressions:

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Specify level:

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Use explicit positions:

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Find subexpressions that match a pattern:

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Find subexpressions with any inner expression matching a specified pattern:

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Find subexpressions with any outer expression matching a pattern:

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Find subexpressions that have any inner expression matching a specified pattern and relative position:

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Find subexpressions that have any outer expression matching a specified pattern and are positioned at given relative position to it:

In[9]:=

$ResourceFunction["SubexpressionPositions"][f[x, g[y, x], g[x, y]], "OuterMatch" -> _g -> {2}]$

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Find subexpressions with any inner subexpression not matching a specified pattern:

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Find subexpressions with all inner subexpressions not matching a specified pattern:

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Find subexpressions with all outer expressions matching a specified pattern:

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Find subexpressions with combined outer and inner matching patterns:

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$ResourceFunction[ "SubexpressionPositions"][{f[x, g[y]], f[a, b], f[h[1], 2], g[x, y], f[a, c[b]]}, "OuterMatch" -> _f -> {2}, "InnerMatch" -> _ -> {1}]$

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Find specific heads:

In[14]:=

$ResourceFunction[ "SubexpressionPositions"][{f[x, g[y]], f[a, b], f[h[1], 2], g[x, y], f[a, c[b]]}, "OuterMatch" -> _g -> {___, 0}]$

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Scope (3)

Use Unevaluated to delay evaluation:

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Specify an explicit list of positions with use of All and Span with UpTo:

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Return only given number of subexpressions:

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Options (6)

OuterMode (2)

Find subexpressions with all outer expressions matching a given pattern. Positions {1} and {1,1} corresponding to g[x] and x are not present due to having an outer expression matching _g:

In[18]:=

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Find subexpressions matching outer expression with relative position. Positions {2} and {2,2} corresponding to g[y,z] and z are not present because they both have relative position {2}:

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$ResourceFunction["SubexpressionPositions"][f[x, g[y, z]], "OuterMatch" -> Except[_ -> {2}], "OuterMode" -> All]$

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InnerMode (2)

Find subexpressions having all inner expressions matching a given pattern. Positions {2} and {2, 1} of expressions g[y] and y, respectively, are not present due to both having an inner expression matching y:

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Find subexpressions having all inner expressions matching any but the given pattern and relative position. Position {2} corresponding to g[y,z] is not present because it has the inner expression matching y at relative position {1}:

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Complement (1)

Take a complement to the provided criteria:

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Heads (1)

Ignore heads:

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Applications (2)

Ignore subexpressions of patterns, conditions and pattern tests, except pattern variables themselves:

In[24]:=

$ResourceFunction["SubexpressionPositions"][f[x_?p, y_ /; q[y]], "OuterMatch" -> Except[((_Pattern | _Condition) -> {__}) | (_PatternTest -> {Except[ 1], ___})], "OuterMode" -> All, Heads -> False]$

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Find subexpressions of list elements together with labeled elements:

In[25]:=

$ResourceFunction[ "SubexpressionPositions"][{Labeled[x, "x"], y, f[x], {g[x, y], Labeled[z, "z"]}}, "OuterMatch" -> (_List -> {_}) | (_Labeled -> {1}), "InnerMatch" -> Except[_Labeled | _List -> {}], "InnerMode" -> All, Heads -> False]$

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Properties and Relations (1)

SubexpressionPositions combines Position and Extract in a convenient way to filter results by relative subexpression positions:

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$ResourceFunction["SubexpressionPositions"][{f[x], y, f[z, a], b, f[]}, "OuterMatch" -> _f -> {1}]$

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In[27]:=

$With[{expr = {f[x], y, f[z, a], b, f[]}}, KeyMap[Append[1]]@ DeleteMissing@ Map[Quiet@Check[Extract[#, {1}], Missing[]] &]@ Select[MatchQ[_f]]@ AssociationMap[First@Extract[expr, {#}] &, Position[expr, _]] ]$

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Version History

1.2.0 – 13 May 2022
1.1.0 – 28 March 2022
1.0.0 – 21 December 2021

Related Resources

License Information

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