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}
{f[x], f[y], f[z]}
Apply (
@@,
@@@) — apply to a list:
f@@{x, y, z}f[x, y, z]
MapIndexed — map with index information:
{f[x, {1}], f[y, {2}], f[z, {3}]}
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
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
