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 like f[x] as both symbolic data and the application of a function f 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   ▪ ...