Function Repository Resource:

MapAtEvaluate

Source Notebook

A version of MapAt that evaluates even within held expressions

Contributed by: Nikolay Murzin

ResourceFunction["MapAtEvaluate"][f,expr,pos]

maps function f at position pos of the expression expr with evaluation.

ResourceFunction["MapAtEvaluate"][f,expr,pos,patt]

specifies a pattern to delete after evaluation.

ResourceFunction["MapAtEvaluate"][f,pos]

represents an operator form that can be applied to an expression.

Details

In ResourceFunction["MapAtEvaluate"][f,expr,pos,patt], patt is taken to be Unevaluated by default.

Examples

Basic Examples (2)

Map a function at a single position of an expression and evaluate in-place:

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Map at multiple positions:

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Scope (8)

Use All and Span to map over multiple subexpression parts:

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Prevent evaluation of the function output with Unevaluated:

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The Unevaluated is not present in the result:

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Specify a different subexpression to delete after evaluation:

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Prevent evaluation of subexpressions using a function with held arguments:

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Evaluate subexpressions:

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Map at a held Sequence:

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Map at a held Evaluate:

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Unevaluated function evaluates at each position:

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Properties and Relations (4)

MapAt does not evaluate the function it is mapping inside held arguments:

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MapAtEvaluate does:

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MapAt fails if any position is invalid:

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MapAtEvaluate silently ignores invalid positions:

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The resource function ReplaceAt with a _/;True condition can achieve the same results:

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$ResourceFunction[ ResourceObject[<|"Name" -> "ReplaceAt", "ShortName" -> "ReplaceAt", "UUID" -> "73d6853d-88b7-41b6-89f3-2e4d88b8984f", "ResourceType" -> "Function", "Version" -> "1.0.0", "Description" -> "Replace parts of an expression using replacement rules and a part specification", "RepositoryLocation" -> URL[ "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"], "SymbolName" -> "FunctionRepository`$afcb7bc0f2404e26ad4460411122e0e8`ReplaceAt", "FunctionLocation" -> CloudObject[ "https://www.wolframcloud.com/obj/d36a0ff8-6751-427d-92ec-4c39a5f79557"]|>, {ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"}]][Hold[1, 2, 3], x_ :> With[{y = x + 10}, y /; True], {All}]$

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With MapAtEvaluate, one can control which subexpressions not to evaluate without producing an additional wrapper:

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The resource function MapCases with the option "EvaluateCases"→True has similar behavior to MapAtEvaluate, except that it takes patterns instead of positions:

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