In programming and mathematics, a functional form is an operator or function

Function (mathematics)

In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

 that can either be applied to other operators (i.e. one or more of its operand

Operand

In mathematics, an operand is the object of a mathematical operation, a quantity on which an operation is performed.-Example :The following arithmetic expression shows an example of operators and operands:3 + 6 = 9\;...

s or argument

Argument

In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...

s are itself operators) or yield operators as result, or both. It is, thus, essentially the same as a higher-order function

Higher-order function

In mathematics and computer science, higher-order functions, functional forms, or functionals are functions which do at least one of the following:*take one or more functions as an input*output a function...

, although the syntax may be more reminiscent of (pre-, post-, or infix) operators applied to operands, rather than function application in the lambda calculus

Lambda calculus

In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...

 tradition. Examples of functional forms are function composition

Function composition

In mathematics, function composition is the application of one function to the results of another. For instance, the functions and can be composed by computing the output of g when it has an argument of f instead of x...

, construction

Construction

In the fields of architecture and civil engineering, construction is a process that consists of the building or assembling of infrastructure. Far from being a single activity, large scale construction is a feat of human multitasking...

, and apply-to-all

Map (higher-order function)

In many programming languages, map is the name of a higher-order function that applies a given function to each element of a list, returning a list of results. They are examples of both catamorphisms and anamorphisms...

, but there are numerous others.