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MultiReplace (2.0.0) current version: 2.2.3 »

Source Notebook

Perform replacements and also give positions at which they occur

Contributed by: Nikolay Murzin

ResourceFunction["MultiReplace"][expr, rule]

returns all possible subexpressions of expr after application of rule with information about each replacement.

ResourceFunction["MultiReplace"][expr, {rule₁,rule₂,…}]

returns result after applying a list of rules.

ResourceFunction["MultiReplace"][expr,{x₁,x₂,…}→{y₁,y₂,…}]

use a list of patterns to replace subexpression tuples/subsets.

ResourceFunction["MultiReplace"][expr,rules,level]

specify a level spec.

ResourceFunction["MultiReplace"][expr,rules,level, head]

uses a custom head to specify subexpression tuples/subsets.

Details and Options

ResourceFunction["MultiReplace"] returns an association with keys containing a rule index and list of positions of a tuple/subset of subexpressions where the corresponding rule was applied.

If one rule is given, keys contain positions only.

Association values are results of applying ReplaceList at corresponding positions, so for a given position multiple results of substitution are possible.

The left-hand side of a rule can be a list or a custom head to replace tuples/subsets of subexpressions, similar to SequenceReplace and SubsetReplace but for all positions.

When a tuple is specified as a left-hand side, replacement applies at multiple positions where all elements of a tuple match, meaning each position can be replaced multiple times.

In contrast, with "Subsets"→True option, multiple positions are considered where elements of a subset match, i.e. only disjoint positions are considered.

If a rule returns a list (or a head) of expressions, they are substituted for the corresponding tuple/subset positions on the left-hand side.

ResourceFunction["MultiReplace"] takes the same options as the resource function SubexpressionPositions for subexpression selection.

ResourceFunction["MultiReplace"] takes the following options:

"Subsets"

False

whether to look for tuples or subsets

Method

"Substitution"

substitution strategy to use: "Susbtitution", "Cosubstitution" or "Bisubstitution"

Examples

Basic Examples (3)

Apply a rule at each possible position of an expression:

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Apply multiple rules:

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$ResourceFunction["MultiReplace"][f[x, g[y]], {a_ :> h[a], b_ -> 1}]$

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Apply tuple replacement rule:

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Scope (4)

Tuples replacement is being spliced in the order of matched elements:

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Splicing continues after the last element:

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A single element can be matched more than once:

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Specify a level:

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$ResourceFunction["MultiReplace"][{a, b, f[c]}, x_ :> g[x], {1}]$

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Use a custom head to replace tuples within it:

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Options (4)

Heads (1)

Ignore heads:

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Subsets (1)

Use subsets instead of tuples:

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Method (2)

Three substitution strategies are supported, based on the direction of pattern unification:

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$ResourceFunction["MultiReplace"][{f[a, b], f[y_, x_], f[a, x_]}, f[y_, b] -> c, 1, Method -> "Substitution"]$

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$ResourceFunction["MultiReplace"][{f[a, b], f[y_, x_], f[a, x_]}, f[y_, b] -> c, 1, Method -> "Cosubstitution"]$

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$ResourceFunction["MultiReplace"][{f[a, b], f[y_, x_], f[a, x_]}, f[y_, b] -> c, 1, Method -> "Bisubstitution"]$

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Get all tuple bisubstitutions:

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$ResourceFunction["MultiReplace", ResourceVersion->"2.0.0"][{f[a, x_], f[b, y_], f[c, z_], g[x_, y_, z_]}, {f[y_, 1], f[z_, 2]} -> {y, z}, 1, Method -> "Bisubstitution"]$

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Properties and Relations (2)

Replacement is done in all possible ways similar to ReplaceList but at multiple positions:

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SequenceReplace and SubsetReplace replace all the matches and destroy subexpressions, while MultiReplace does all possible single replacements and preserves subexpressions:

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$SequenceReplace[{a, b, x, x, a, c}, {a, e_} :> f[e]]$