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Evaluation of a function on its argument
In mathematics, function application (or evaluation) is the act of taking a function and an input from its domain to obtain the corresponding value from
Function_application
In functional programming
partial application (or partial function application) refers to the process of fixing a number of arguments of a function, producing another function of smaller
Partial_application
Transforming a function in such a way that it only takes a single argument
partial application. The example above can be used to illustrate partial application; it is quite similar. Partial application is the function apply {\displaystyle
Currying
Topics referred to by the same term
tasks Application layer, an abstraction layer that specifies protocols and interface methods used in a communications network Function application, in mathematics
Application
Connection between computers or programs
An application programming interface (API) is a connection between computers or between computer programs. It is a type of software interface, offering
API
Mathematical theory of data types
of inference rules. Type theories which have functions also have the inference rule of function application: if t {\displaystyle t} is a term of type
Type_theory
Programming language feature
first-class functions if it treats functions as first-class citizens. This means the language supports passing functions as arguments to other functions, returning
First-class_function
Mapping arbitrary data to fixed-size values
or the grid method. In these applications, the set of all inputs is some sort of metric space, and the hashing function can be interpreted as a partition
Hash_function
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Special mathematical function defined as sin(x)/x
probability in telecommunication", saying "This function occurs so often in Fourier analysis and its applications that it does seem to merit some notation of
Sinc_function
Logical formalism using combinators instead of variables
{\displaystyle E_{1}E_{2}} are called applications. Applications model function invocation or execution: the function represented by E 1 {\displaystyle E_{1}}
Combinatory_logic
Basic notion of sameness in mathematics
century by Giuseppe Peano. Other properties like substitution and function application weren't formally stated until the development of symbolic logic.
Equality_(mathematics)
Hash function that is suitable for use in cryptography
practice, a hash-function that is only second pre-image resistant is considered insecure and is therefore not recommended for real applications. Informally
Cryptographic_hash_function
Compile-time transformation
only finitely many function abstractions, so that each can be assigned and replaced by a unique identifier. Every function application within the program
Defunctionalization
Type of programming language
denote functions, and the juxtaposition of expressions denotes function composition. Concatenative programming replaces function application, which is
Concatenative programming language
Concatenative_programming_language
Mathematical formalism
of a lambda term is simply a variable, a lambda abstraction, or a function application, but a formal presentation can be somewhat lengthy. The focus of
Lambda_calculus_definition
Mathematical-logic system
λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus
Lambda_calculus
Any computer program for end-user use
media players, and mobile applications used in daily tasks. An application (app, application program, software application) is any program that can be
Application_software
Sigmoid shape special function
many applications, the function argument is a real number, in which case the function value is also real. In some older texts, the error function is defined
Error_function
Application that uses a web browser as a client
A web application (or web app) is application software that is created with web technologies and runs via a web browser. Web applications emerged during
Web_application
Association of one output to each input
increased the possible applications of the concept. A function is often denoted by a letter such as f, g or h. The value of a function f at an element x of
Function_(mathematics)
Interface to software defined in terms of in-process, machine code access
An application binary interface (ABI) is an interface exposed by software that is defined for in-process machine code access. Often, the exposing software
Application_binary_interface
Type of computer application
A decentralised application (DApp, dApp, Dapp, or dapp) is an application that can operate autonomously, typically through the use of smart contracts
Decentralized_application
Act of placing two elements side by side
juxtaposition f x {\displaystyle fx} denotes function application (not to be confused with the function notation f ( x ) {\displaystyle f(x)} which does
Juxtaposition
Intermediate structure between functors and monads
demonstrates how applicatives allow a sort of generalized function application. Functor Monad McBride, Conor; Paterson, Ross (2008-01-01). "Applicative programming
Applicative_functor
Function that takes one or more functions as an input or that outputs a function
computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a procedural
Higher-order_function
Software application designed to run on mobile devices
A mobile app or application is a computer program or software application designed to run on a mobile device such as a smartphone, tablet, or smartwatch
Mobile_app
Extension of the factorial function
quotients of the gamma function, called Mellin–Barnes integrals. An application of the gamma function is the study of the Riemann zeta function. A fundamental
Gamma_function
Program function without side effects
In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments
Pure_function
Control flow operator in functional programming
continuation object is a first-class value and is represented as a function, with function application as its only operation. When a continuation object is applied
Call-with-current-continuation
Call-with-current-continuation
Function whose job is only to call another subroutine
used in the native application. In case the third party functions change or are updated, only the wrappers in the native application need to be modified
Wrapper_function
Key on a computer or terminal keyboard
A function key is a key on a computer or terminal keyboard that can be programmed to cause the operating system or an application program to perform certain
Function_key
Spreadsheet editor by Microsoft
original on November 5, 2018. Retrieved November 4, 2018. "Functions (Visual Basic for Applications)". Office VBA Reference. Microsoft. September 13, 2021
Microsoft_Excel
Function that takes two inputs
to indicate both function application and the formation of an ordered pair.) Division of whole numbers can be thought of as a function. If ℤ is the set
Binary_function
Construct related to weighted sums and averages
the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics
Weight_function
One of several equivalent definitions of a computable function
computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers
General_recursive_function
Type of interpreter in computing
language. For example, interpreting a lambda application may be implemented using function application. Meta-circular evaluation is most prominent in
Meta-circular_evaluator
Correlation of a signal with a time-shifted copy of itself, as a function of shift
note on the sum of the sample autocorrelation function". Physica A: Statistical Mechanics and Its Applications. 389 (8): 1601–1606. Bibcode:2010PhyA..389
Autocorrelation
that views the formation of phrase structure by analogy to function application in an applicative programming language. Among the innovations in this approach
Applicative_universal_grammar
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
Highest layer in network protocol models
the foundation of the modern Internet, integrates these functions into a broader application layer that handles process-to-process communication. This
Application_layer
Serial communications protocol
other parties. MODBUS TCP/IP ADU = MODBUS Application Protocol Header + Function code + Data MODBUS Application Protocol header - is the dedicated header
Modbus
Calling conventions used in x86 architecture programming
"Vector Function Application Binary Interface version 0.9.8". April 6, 2016. "libmvec". sourceware.org. (see VectorABI.txt) "x86 Function Attributes
X86_calling_conventions
Root-finding algorithm
, x 2 , … {\displaystyle x_{0},x_{1},x_{2},\dots } of iterated function applications x 0 , f ( x 0 ) , f ( f ( x 0 ) ) , … {\displaystyle x_{0},f(x_{0})
Fixed-point_iteration
S-shaped curve
the sigmoid function. It is also sometimes called the expit, being the inverse function of the logit. The logistic function finds applications in a range
Logistic_function
Type of activation function
ReLU is one of the most popular activation functions for artificial neural networks, and finds application in computer vision and speech recognition using
Rectified_linear_unit
Mathematical transform that expresses a function of time as a function of frequency
many applications requiring a more sophisticated integration theory. For example, many relatively simple applications use the Dirac delta function, which
Fourier_transform
Unit of measurement
method version 2.3 – Definitions and counting guidelines for the application of Function Point Analysis COSMIC: ISO/IEC 19761:2011 Software engineering
Function_point
Software targeted towards corporations/organisations
processes with that data." Enterprise application software is application software that performs business functions such as order processing, procurement
Enterprise_software
Computer programming paradigm
calls correspond to function application. Functions and their modules separated from each other in the same manner, by the use of function arguments, return
Procedural_programming
Logarithm to the base of the mathematical constant e
to a multi-valued function: see complex logarithm for more. The natural logarithm function, if considered as a real-valued function of a positive real
Natural_logarithm
Intermediate representation in a functional compiler
serve as operands of function applications, and requiring that the result of a non-trivial expression (such as a function application) be immediately captured
A-normal_form
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
Generalized function whose value is zero everywhere except at zero
zero. (However, even in some applications, highly oscillatory functions are used as approximations to the delta function, see below.) The Dirac delta
Dirac_delta_function
Analytic function in mathematics
continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied
Riemann_zeta_function
Architectural framework of telecommunications
services IP Multimedia Service Switching Function (IM-SSF): Interfaces SIP to CAP to communicate with CAMEL Application Servers OSA service capability server
IP_Multimedia_Subsystem
Integral expressing the amount of overlap of one function as it is shifted over another
For complex-valued functions, the cross-correlation operator is the adjoint of the convolution operator. Convolution has applications that include probability
Convolution
Element of a basis for a function space
particularly in applications such as interpolation. In this application, a mixture of the basis functions provides an interpolating function, with the coefficients
Basis_function
Monetary symbol used in many national currencies
refers to the same thing as SomeName. In Haskell, $ is used as a function application operator. In an AutoHotkey script, a hotkey declared with $ is not
Dollar_sign
Higher-order function which returns some fixed point of the input function
denotes x applied to itself. Juxtaposition of expressions denotes function application, is left-associative, and has higher precedence than the period.)
Fixed-point_combinator
Interface to call functions from other programming languages
runtime environments and application binary interfaces of both. This can be done in several ways: Requiring that guest-language functions which are to be host-language
Foreign_function_interface
Complex exponential in terms of sine and cosine
fundamental relationship between the trigonometric functions and the complex exponential function. It is named after Leonhard Euler, who mentioned the
Euler's_formula
Mathematical function resembling a boxcar
which are usually best chosen depending on the individual application. When a boxcar function is selected as the impulse response of a filter, the result
Boxcar_function
Fundamental trigonometric functions
trigonometric polynomial's ample applications may be acquired in its interpolation, and its extension of a periodic function known as the Fourier series.
Sine_and_cosine
Software design pattern
is that the application is responsible not just for a particular task, but can perform every step needed to complete a particular function. Some personal
Monolithic_application
Base of natural logarithms
1/2π. This function is symmetric around x = 0, where it attains its maximum value 1/2π, and has inflection points at x = ±1. Another application of e, also
E_(mathematical_constant)
involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves
List of trigonometric identities
List_of_trigonometric_identities
Category of cloud computing services
Function as a service is a "platform-level cloud capability" that enables its users "to build and manage microservices applications with low initial investment
Function_as_a_service
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
Techniques to alter a program
augment the behaviour of an operating system, applications, or other software components by intercepting function calls, messages, or events passed between
Hooking
Indicator function of positive numbers
The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside
Heaviside_step_function
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Mathematical function, denoted exp(x) or e^x
especially in applications, functions of the general form f ( x ) = a b x {\displaystyle f(x)=ab^{x}} are also called exponential functions. They grow
Exponential_function
Approach to natural language semantics
expression is obtained as a function of its components, either by function application (indicated by boldface parentheses enclosing function and argument) or by
Montague_grammar
Response of an optical system to a point source of light
The point spread function (PSF) describes the response of a focused optical imaging system to an idealized point source of light. In casual terms, for
Point_spread_function
Branch of mathematics
properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a function and a point
Calculus
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Function that is continuous everywhere but differentiable nowhere
wide acceptance until practical applications such as models of Brownian motion necessitated infinitely jagged functions (nowadays known as fractal curves)
Weierstrass function (nowhere-differentiable function)
Weierstrass_function_(nowhere-differentiable_function)
an expression tree made up from functional elements like OMA for function application or OMV for variables): <OMOBJ xmlns="http://www.openmath.org/OpenMath">
OpenMath
Quickly growing function
Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not
Ackermann_function
Programming paradigm based on applying and composing functions
1930s by Alonzo Church, is a formal system of computation built from function application. In 1937 Alan Turing proved that the lambda calculus and Turing machines
Functional_programming
Set of cryptographic hash functions
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published
SHA-2
Reference model for network communication
highest-level representation of data of a distributed application. Each layer has well-defined functions and semantics and serves a class of functionality
OSI_model
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Typographical mark (`) (Freestanding grave accent)
calls an existing term. Unlambda: The backtick character denotes function application. Verilog HDL: The backtick is used at the beginning of compiler's
Backtick
Multivalued function in mathematics
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse
Lambert_W_function
Relationship between programs and proofs
(such as languages with arbitrary recursive functions) must be interpreted with care, as naive application of the correspondence leads to an inconsistent
Curry–Howard_correspondence
Instantaneous rate of change (mathematics)
subsequent derivatives of that function are zero. One application of higher-order derivatives is in physics. For example, if the function x represents an object's
Derivative
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Instructions a computer can execute
mapped by the function times_10() to a range of values. One value happens to be 20. This occurs when x is 2. So, the application of the function is mathematically
Computer_program
Artificial neural network node function
In artificial neural networks, the activation function of a node is a function that calculates the output of the node based on its individual inputs and
Activation_function
Branch of mathematics studying functions of a complex variable
pictures of fractals produced by iterating holomorphic functions. Another important application of complex analysis is in string theory which examines
Complex_analysis
General purpose functional programming language
int Functions are defined with let. Function application is higher precedent than mathematical operators, so f 3 + 4 means (f 3) + 4. Functions defined
ML_(programming_language)
Special functions of several complex variables
systems using the tools of analysis. For this reason, theta functions have useful applications in topics such as number theory: "in how many ways can a number
Theta_function
Medium to store keys for signing cryptocurrency transactions
private keys for cryptocurrency transactions. In addition to this basic function of storing the keys, a cryptocurrency wallet more often offers the functionality
Cryptocurrency_wallet
Function that derives secret keys from a secret value
material to application- and context-specific information. Key stretching and key strengthening. Key derivation functions are also used in applications to derive
Key_derivation_function
Probability of survival beyond any specified time
while the term survival function is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative
Survival_function
that would mean combining mutually exclusive possible worlds. The application of functions to value sets creates combinations of value sets from different
Narrowing of algebraic value sets
Narrowing_of_algebraic_value_sets
Mathematical functions having established names and notations
applications. The term is defined by consensus, and thus lacks a general formal definition, but the list of mathematical functions contains functions
Special_functions
On finding a repeating loop in a sequence
algorithms trade off larger amounts of memory for fewer function evaluations. The applications of cycle detection include testing the quality of pseudorandom
Cycle_detection
travel, tourism, insurance
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