The symbolic structure of the Wolfram Language makes it easy to create "operators" that can be composed and manipulated symbolically—forming "pipelines" of operations—and then applied to arguments. Some built-in functions also directly support a "curried" form, in which they can immediately be given as symbolic operators.

f@x — function application f[x]

Composition or f@*g — left-to-right composition f[g[_]]

x//f — function application f[x]

RightComposition or f/*g — right-to-left composition g[f[_]]

ApplyTo or x//=f — x=f[x]

Construct — construct an expression from its head and arguments

Function — turn any expression into a pure function that can be applied

Identity — identity function

InverseFunction — symbolic inverse function

Inactive — a function made inactive

OperatorApplied — turn a function into one to be applied as an operator form

CurryApplied — general "curried" operator form

ReverseApplied — turn a function into one to be applied to reversed arguments

Functions with Operator Forms

Select — represent a selection operator to apply to expressions

Map   ▪ Apply   ▪ MapApply   ▪ Comap   ▪ ComapApply

Append   ▪ Prepend   ▪ Insert   ▪ ReplacePart

SelectFirst   ▪ FirstCase   ▪ Cases   ▪ DeleteCases

Position   ▪ Extract   ▪ Delete

AnyTrue   ▪ AllTrue   ▪ NoneTrue

SortBy   ▪ MaximalBy   ▪ MinimalBy   ▪ DeleteDuplicatesBy

Rearranging Functional Forms

Operate — form p[f][x] from p and f[x]

Through — form {f[x],g[x]} from {f,g}[x]

Distribute — distribute one symbolic function over another

Key — operator to extract a value from an association