Functional programming is a highly developed and deeply integrated core feature of the Wolfram Language, made dramatically richer and more convenient through the symbolic nature of the language. Treating expressions likef[x] as both symbolic data and the application of a functionf provides a uniquely powerful way to integrate structure and function—and an efficient, elegant representation of many common computations.

Function (&)— specify a pure function (e.g.(#+1)&)

#,##,#name— slots for variables in a pure function

Applying Functions to Lists»

Map (/@)— map across a list:f/@{x,y,z}⟶{f[x],f[y],f[z]}

Apply (@@)— apply to a list:f@@{x,y,z}⟶f[x,y,z]

MapApply (@@@)— apply to a list:f@@@{x,y,z}⟶{f@@x,f@@y,f@@z}

MapIndexed— map with index information:{f[x,{1}],f[y,{2}],f[z,{3}]}

MapThread  ▪ MapAt  ▪ MapAll  ▪ Scan  ▪ BlockMap  ▪ SubsetMap  ▪ ...

Applying Lists of Functions to Arguments

Comap— comap into a list:Comap[{f,g,h},x]⟶{f[x],g[x],h[x]}

ComapApply— use multivariate heads:ComapApply[{f,g,…},x]⟶{f@@x,g@@x,…}

Iteratively Applying Functions»

Nest,NestList,NestGraph— nest a function:f[f[f[x]]] etc.

Fold,FoldList— fold in a list of values:f[f[f[x,1],2],3] etc.

SequenceFold  ▪ SequenceFoldList  ▪ FoldPair  ▪ FoldWhile  ▪ ...

FixedPoint,FixedPointList— repeatedly nest until a fixed point

NestWhile  ▪ NestWhileList  ▪ TakeWhile  ▪ LengthWhile  ▪ ...

List-Oriented Functions»

Select— select from a list according to a function

Array— create an array from a function

SortBy  ▪ MaximalBy  ▪ SplitBy  ▪ GatherBy  ▪ ...

Association-Oriented Functions»

AssociationMap— create an association from a function

KeySortBy  ▪ CountsBy  ▪ GroupBy  ▪ ...

Functional Composition»

Identity  ▪ Composition  ▪ ReverseApplied  ▪ Operate  ▪ Through  ▪ ...

"Curried" Operator Forms»

OperatorApplied— make a function be applied in operator form

CurryApplied  ▪ Select  ▪ Cases  ▪ Append  ▪ Map  ▪ Position  ▪ ...

Related Tech Notes

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• Pure Functions
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• Variables in Pure Functions and Rules
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• Applying Functions to Lists and Other Expressions
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• Applying Functions to Parts of Expressions
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• Applying Functions Repeatedly
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• Selecting Parts of Expressions with Functions
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• Working with Operators

Related Guides

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• List Manipulation
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• Rule-Based Programming
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• Expressions