Functional (C++)

In the context of the C++ programming language, functional refers to a header file that is part of the C++ Standard Library and provides a number of predefined class templates for function objects, including arithmetic operations, comparisons, and logical operations. Instances of these class templates are C++ classes that define a function call operator, and the instances of these classes can be called as if they were functions. It is possible to perform very sophisticated operations without actually writing a new function object, simply by combining predefined function objects and function object adaptors.

The class template std::function provided by C++11 is a general-purpose polymorphic function wrapper. Instances of std::function can store, copy, and invoke any callable target—functions, lambda expressions (expressions defining anonymous functions), bind expressions (instances of function adapters that transform functions to other functions of smaller arity by providing values for some of the arguments), or other function objects.

Functional

Functional may refer to:

In mathematics,

In computer science, software engineering

Functional programming

In computer science, functional programming is a programming paradigm—a style of building the structure and elements of computer programs—that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data. It is a declarative programming paradigm, which means programming is done with expressions. In functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f(x) each time. Eliminating side effects, i.e. changes in state that do not depend on the function inputs, can make it much easier to understand and predict the behavior of a program, which is one of the key motivations for the development of functional programming.

Functional programming has its roots in lambda calculus, a formal system developed in the 1930s to investigate computability, the Entscheidungsproblem, function definition, function application, and recursion. Many functional programming languages can be viewed as elaborations on the lambda calculus. Another well-known declarative programming paradigm, logic programming, is based on relations.

Functional (mathematics)

In mathematics, and particularly in functional analysis and the calculus of variations, a functional is a function from a vector space into its underlying scalar field, or a set of functions of the real numbers. In other words, it is a function that takes a vector as its input argument, and returns a scalar. Commonly the vector space is a space of functions, thus the functional takes a function for its input argument, then it is sometimes considered a function of a function (a higher-order function). Its use originates in the calculus of variations where one searches for a function that minimizes a certain functional. A particularly important application in physics is searching for a state of a system that minimizes the energy functional.

Functional details

Duality

The mapping

is a function, where x₀ is an argument of a function f. At the same time, the mapping of a function to the value of the function at a point

is a functional, here x₀ is a parameter.

Provided that f is a linear function from a linear vector space to the underlying scalar field, the above linear maps are dual to each other, and in functional analysis both are called linear functionals.