This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Functional Programming
Long viewed as an important theoretical idea, functional programming finally became truly convenient and practical with the introduction of Mathematica's symbolic 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)&)
#, ## slots for variables in a pure function
Map (/@) — map across a list: f/@{x, y, z}LongRightArrow{f[x], f[y], f[z]}
Apply (@@, @@@) — apply to a list: f@@{x, y, z}LongRightArrowf[x, y, z]
MapIndexed map with index information: {f[x, {1}], f[y, {2}], f[z, {3}]}
MapThread  ▪ MapAt  ▪ MapAll  ▪ Scan  ▪ ...
Nest, NestList nest a function: f[f[f[x]]] etc.
Fold, FoldList fold in a list of values: f[f[f[x, 1], 2], 3] etc.
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
Sort, Split sort, split according to a function
Functional Composition Operations
Identity  ▪ Composition  ▪ Operate  ▪ Through  ▪ Distribute