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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
Higher-order_function
Computer programming function
In many programming languages, map is a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning
Map_(higher-order_function)
Family of higher-order functions
In functional programming, a fold is a higher-order function that analyzes a recursive data structure and, through use of a given combining operation
Fold_(higher-order_function)
Computer programming function
functional programming, filter is a higher-order function that processes a data structure (usually a list) in some order to produce a new data structure containing
Filter (higher-order function)
Filter_(higher-order_function)
Design pattern in functional programming to build generic types
additional natural transformations. So to begin, a structure requires a higher-order function (or "functional") named map to qualify as a functor: map : (a →
Monad (functional programming)
Monad_(functional_programming)
Programming language feature
mid-1960s. First-class functions are a necessity for the functional programming style, in which the use of higher-order functions is a standard practice
First-class_function
Function definition that is not bound to an identifier
passed to higher-order functions or used for constructing the result of a higher-order function that needs to return a function. If the function is only
Anonymous_function
Instantaneous rate of change (mathematics)
interval. Higher-order derivatives are the result of differentiating a function repeatedly. Given that f {\displaystyle f} is a differentiable function, the
Derivative
Programming paradigm based on applying and composing functions
Higher-order functions are closely related to first-class functions in that higher-order functions and first-class functions both allow functions as arguments
Functional_programming
Programming paradigm
Higher-order programming is a style of computer programming that uses software components, like functions, modules or objects, as values. It is usually
Higher-order_programming
Calculus for deriving computer programs
using the Larch Prover. Map is a well-known second-order function that applies a given function to every element of a list; in BMF, it is written ∗ {\displaystyle
Bird–Meertens_formalism
Programming language
(succ) and addition (add). A Church numeral n is a higher-order function that accepts a function f and a value x and applies f to x exactly n times.
OCaml
Operation on mathematical functions
square root Functional equation Higher-order function Infinite compositions of analytic functions Iterated function Lambda calculus The strict sense
Function_composition
Mathematical-logic system based on functions
uncurried arguments to a function: 0 := λfx.x 1 := λfx.f x 2 := λfx.f (f x) 3 := λfx.f (f (f x)) A Church numeral is a higher-order function—it takes a single-argument
Lambda_calculus
Higher-order function Y for which Y f = f (Y f)
fixed-point combinator (or fixpoint combinator) is a higher-order function (i.e., a function that takes a function as argument) that returns some fixed point (a
Fixed-point_combinator
Higher-order function that combines several parsers
is a higher-order function that accepts several parsers as input and returns a new parser as its output. In this context, a parser is a function accepting
Parser_combinator
Programming function applied recursively to its previous result
function that generates a sequence by repeated application of the function to its previous result. You begin with some value A and apply a function f
Anamorphism
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
Programming language
f'(x)=3x^{2}-1\rightarrow f'(3)=27-1=26} . The function d is called a "higher-order function" because it accepts another function (f) as an argument. Going further
Caml
Programming language
data types, pattern matching, parametric polymorphism, currying, higher-order functions, extensible records, channel and process-based concurrency, and
Flix_(programming_language)
Using existing code in new software
families of applications[citation needed]. In functional programming higher-order functions can be used in many cases where design patterns or frameworks were
Code_reuse
Function which maps a tuple of sequences into a sequence of tuples
programming portal Map (higher-order function) map from ClojureDocs map(function, iterable, ...) from section Built-in Functions from Python v2.7.2 documentation
Zipping_(computer_science)
Alternate way to define a function in APL
A direct function (dfn, pronounced "dee fun") is an alternative way to define a function and operator (a higher-order function) in the programming language
Direct_function
Set of functions between two fixed sets
calculus, function types are used to express the idea of higher-order functions In programming more generally, many higher-order function concepts occur
Function_space
Association of one output to each input
function Higher-order function Homomorphism Morphism Microfunction Distribution Functor Associative array Closed-form expression Elementary function Functional
Function_(mathematics)
respectively. These are functions that operate on functions or produce other functions; see Higher order function. Examples are: Function composition. Integral
List_of_types_of_functions
a higher-order function taking or returning a function. A function type depends on the type of the parameters and the result type of the function (it
Function_type
Extensible Access Control Markup Language
functions Arithmetic functions String functions Logical functions (and, or, not) Set and bag functions Aggregate functions Higher order functions Regular expression
XACML
Programming language family
structures, automatic storage management, dynamic typing, conditionals, higher-order functions, recursion, the self-hosting compiler, and the read–eval–print loop
Lisp_(programming_language)
passed to higher-order functions or used for constructing the result of a higher-order function that needs to return a function. If the function is only
Examples of anonymous functions
Examples_of_anonymous_functions
Sequence in computer science
algorithms such as counting sort, and they form the basis of the scan higher-order function in functional programming languages. Prefix sums have also been
Prefix_sum
Typically linear operator defined in terms of differentiation of functions
an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science). This article considers
Differential_operator
Programming mechanism
in function composition using the symbol ∘. This higher-order function extends function composition to dyadic application of the left side function such
Function composition (computer science)
Function_composition_(computer_science)
General-purpose functional programming language
List.map from the basis library is one of the most commonly used higher-order functions in Standard ML: fun map _ [] = [] | map f (x :: xs) = f x :: map
Standard_ML
Transforming a function in such a way that it only takes a single argument
"currying" is not used, while Curry is mentioned later in the context of higher-order functions. John C. Reynolds defined "currying" in a 1972 paper, but did not
Currying
Concept in quantum optics
interfere – of electromagnetic radiation, like optical light. Higher order coherence or n-th order coherence (for any positive integer n>1) extends the concept
Higher_order_coherence
Microsoft .NET Framework component
other two operators. This implements the Bind higher-order function. These operators optionally take a function that retrieves a certain numeric value from
Language_Integrated_Query
In mathematics, a quantitative measure of the shape of a set of points
Moments of a function in mathematics are certain quantitative measures related to the shape of the function's graph. For example, if the function represents
Moment_(mathematics)
Topics referred to by the same term
physics Reduce (higher-order function), in functional programming, a family of higher-order functions that process a data structure in some order and build
Reduction
Logical formalism using combinators instead of variables
functions — and to remove any mention of variables — particularly in predicate logic. A combinator is a higher-order function that uses only function
Combinatory_logic
Compile-time transformation
compile-time transformation which eliminates higher-order functions, replacing them by a single first-order apply function. The technique was first described by
Defunctionalization
Topics referred to by the same term
Filter, filtering, filters or filtration may also refer to: Filter (higher-order function), in functional programming Filter (software), a computer program
Filter
Behavioral design pattern
first-class functions and higher-order functions in functional programming languages. Specifically, the invoker object is a higher-order function of which
Command_pattern
Process of repeating items in a self-similar way
combinator – Higher-order function Y for which Y f = f (Y f)Pages displaying short descriptions of redirect targets Infinite compositions of analytic functions –
Recursion
Command-line utility for text search
language, grep is a built-in function that finds elements in a list that satisfy a certain property. This higher-order function is typically named filter
Grep
Number of arguments required by a function
type such as a tuple, or in languages with higher-order functions, by currying. In computer science, a function that accepts a variable number of arguments
Arity
Types of mappings in mathematics
computer science, it is synonymous with a higher-order function, which is a function that takes one or more functions as arguments or returns them.[citation
Functional_(mathematics)
Formal system of logic
In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers
Higher-order_logic
Vector operation
adverb f/; in R, as the function outer(A, B, f) or the special %o%; in Mathematica, as Outer[f, A, B]. In MATLAB, the function kron(A, B) is used for this
Outer_product
Topics referred to by the same term
context of functional analysis Higher-order function, also called a functional, a function that takes other functions as arguments "Functional" (noun)
Functional
Basic programming language construct
possible to define as a user-defined function (e.g. sizeof in C) or has syntax different from that of a function (e.g. infix addition as in a+b). Like
Operator (computer programming)
Operator_(computer_programming)
Software programming optimization technique
implementation of the algorithm in PADL’08[citation needed] as a set of higher-order functions (called parser combinators) in Haskell, which enables the construction
Memoization
Named function defined within a function
Closure (computer science) Function composition (computer science) Inner class Nesting (computing) Bright 2004. Higher-Order Functions and Lambdas - Kotlin
Nested_function
Typed lambda calculus
n is a function that takes a function f as argument and returns the nth power of f. That is to say, a Church numeral is a higher-order function – it takes
System_F
Microsoft programming language
Immutable variables and objects Lazy evaluation support Higher-order functions Nested functions Currying Pattern matching Algebraic data types Tuples List
F Sharp (programming language)
F_Sharp_(programming_language)
Table that summarizes data from another table
Data visualization Data warehouse Extract, transform, load Fold (higher-order function) OLAP cube Relational algebra Wide and narrow data "United States
Pivot_table
In statistics, the term higher-order statistics (HOS) refers to functions which use the third or higher power of a sample, as opposed to more conventional
Higher-order_statistics
Software design pattern
applyBrake(); // This will invoke class "Brake" } } Dependency injection Higher-order function List of object-oriented programming terms Mixin Policy-based design
Strategy_pattern
Topics referred to by the same term
(Berkeley Internet Name Daemon), Domain Name System software Bind (higher-order function), an operation in a monad Bind, a client to a server in client–server
Bind
Type of function in database management
Fold (higher-order function) Group by (SQL), SQL clause OLAP cube Online analytical processing Pivot table Relational algebra Utility functions on indivisible
Aggregate_function
first class functions and higher order functions, including function types and anonymous functions // A top-level higher-order function using block syntax
Ceylon_(programming_language)
Software that provides access that hides details
related to functions, such as lambda abstractions (making a term into a function of some variable) and higher-order functions (parameters are functions). Modern
Abstraction (computer science)
Abstraction_(computer_science)
Type of logical system
over even higher types than second-order logic permits. These higher types include relations between relations, functions from relations to relations between
First-order_logic
Approach to natural language semantics
constituent expressions, either by forming a new higher-order function, or by applying a higher-order function for one expression to the meaning of another
Montague_grammar
Top-down parser utilizing recursion
the recursive-descent parsing algorithm. Parser combinator – a higher-order function used in combinatory parsing, a method of factoring recursive descent
Recursive_descent_parser
Sentence, idea or formula that refers to itself
(mathematics) – Element mapped to itself by a mathematical function Fixed-point combinator – Higher-order function Y for which Y f = f (Y f) Fourth wall – Separation
Self-reference
Subset of lambda calculus
system for defining first-order functions. Unlike lambda calculus, kappa calculus has no higher-order functions; its functions are not first class objects
Kappa_calculus
Programming construct
is a synonym for function symbol. Callback (computer programming) Closure (computer programming) Function pointer Higher-order function Command pattern
Function_object
Cognitive processes necessary for control of behavior
and cognitive flexibility. Higher-order executive functions require the simultaneous use of multiple basic executive functions and include planning and
Executive_functions
Combinatorial optimization method for a family of functions of discrete variables
submodular. For higher-order functions, regularity is a necessary condition for representability. Graph construction for a representable function is simplified
Graph_cut_optimization
The higher-order sinusoidal input describing functions (HOSIDF) were first introduced by dr. ir. P.W.J.M. Nuij. The HOSIDFs are an extension of the sinusoidal
Higher-order sinusoidal input describing function
Higher-order_sinusoidal_input_describing_function
Object-oriented programming language
abstracted into higher-order functions. For example, the message select: on a Collection is equivalent to the higher-order function filter on an appropriate
Smalltalk
In functional programming
assuming". docs.perl6.org. Retrieved 2018-09-12. "10.2. functools — Higher-order functions and operations on callable objects — Python 3.7.0 documentation"
Partial_application
Programming language implementation
with inheritance and interfaces, and functional constructs like higher-order functions, closures, map(), and reduce(). Lucee was created by the Lucee Association
Lucee
Topics referred to by the same term
accumulation, the gathering of objects of value Accumulate (higher-order function), a family of functions to analyze a recursive data structure in computer science
Accumulation
Topics referred to by the same term
Code folding, a techique used by full screen and GUI editors Fold (higher-order function), a type of programming operation on data structures fold (Unix)
Folding
Branch of game theory and computer science
software tools. A higher-order simultaneous game is a generalization of a Simultaneous game in which players are defined by selection functions rather than
Compositional_game_theory
Branch of mathematical logic
corresponding results in computable analysis. In higher-order reverse mathematics, the focus is on subsystems of higher-order arithmetic, and the associated richer
Reverse_mathematics
General-purpose programming language
influenced by ideas from functional programming, including immutability, higher-order functions, algebraic data types, and pattern matching. It also supports object-oriented
Rust_(programming_language)
Homomorphism from an initial algebra into another algebra
000. The cata map is closely related to the right fold (see Fold (higher-order function)) of lists foldrList. The morphism lift defined by lift :: (a ->
Catamorphism
Block-based programming language
anonymous functions, represented by a block inside a gray ring, having one or more empty slot(s)/argument(s) that are filled by a "higher order function" (the
Snap!_(programming_language)
Compiler technique
For example, in a programming language with higher-order functions like Scheme, the target of a function call may not be explicit: in the isolated expression
Control-flow_analysis
Functional programming and query language for XML
added support for JSON and introduced maps, arrays, and additional higher-order functions, significantly expanding the language's capabilities for modern
XQuery
Programming style in which control is passed explicitly
(b -> c) and a -> b -> c are equivalent, so CPS function -- may be viewed as a higher order function sqrt' :: Float -> ((Float -> a) -> a) sqrt' x = \cont
Continuation-passing_style
(that is being bound) and a meta-level function exp → exp (the body of the let). This function is the higher-order part: an expression with a free variable
Higher-order_abstract_syntax
Element mapped to itself by a mathematical function
fixed-point combinator is a higher-order function f i x {\displaystyle {\mathsf {fix}}} that returns a fixed point of its argument function, if one exists. Formally
Fixed_point_(mathematics)
Representation of natural numbers and other data types in lambda calculus
numbers under Church encoding. The higher-order function that represents natural number n is a function that maps any function f {\displaystyle f} to its n-fold
Church_encoding
"Codewalk: First-Class Functions in Go". Go supports first class functions, higher-order functions, user-defined function types, function literals, closures
Comparison of programming languages
Comparison_of_programming_languages
Family of solutions to related differential equations
determines the shape of the solution. This number is called the order of the Bessel function and can be any complex number. Although the same equation arises
Bessel_function
Multi-paradigm system programming language
as function literals, closures, recursively-immutable objects and the use of higher-order functions. There are two syntaxes for anonymous functions, including
D_(programming_language)
Topics referred to by the same term
a former prison in Holmestrand municipality in Vestfold county Higher-order function, in mathematics and computer science Horton overland flow, in soil
Hof
General-purpose programming language
"stranger" println("Hello $name") } Kotlin supports higher-order functions and anonymous functions, or lambdas. Lambdas are declared using braces, { }
Kotlin
Property of an intermediate representation in a compiler
Using CPS as the intermediate representation is more natural for higher-order functions and interprocedural analysis. CPS also easily encodes call/cc, whereas
Static_single-assignment_form
Programming language running on the Erlang virtual machine
an emphasis, like other functional languages, on recursion and higher-order functions instead of side-effect-based looping Shared nothing concurrent programming
Elixir_(programming_language)
Computer programming paradigm
atoms functions, which take atoms to atoms Higher-order functions (which he calls "functional forms"), which take one or two functions to functions ...and
Function-level_programming
A higher order message (HOM) in a computer programming language is a form of higher-order programming that allows messages that have other messages as
Higher_order_message
Joining of strings in a programming language
Wikifunctions has a concat function. In formal language theory and computer programming, concatenation is the operation of joining sequential objects,
Concatenation
Programming language for statistics
0, functions can be written in a short notation (inspired by the lambda calculus), which is useful for passing anonymous functions to higher-order functions:
R_(programming_language)
Computer programming paradigm
programming languages tend to rely on tail call optimization and higher-order functions instead of imperative looping constructs. Many functional languages
Procedural_programming
Topics referred to by the same term
type composed of a collection of key/value pairs Map (higher-order function), used to apply a function to a list of values and return another list with the
Map_(disambiguation)
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
Boy/Male
Greek
Order.
Boy/Male
Greek
Order.
Girl/Female
Greek
Order.
Surname or Lastname
English
English : variant of Highley.
Boy/Male
Hindu, Indian, Punjabi, Sikh
Order
Boy/Male
Greek
Order.
Girl/Female
German, Greek
Order
Male
Swedish
Old Swedish form of Old Norse Oddr, ODDER means "point of a weapon."
Girl/Female
Muslim
Higher, Highest
Surname or Lastname
English
English : variant of Haggard.English : variant of Hager.
Surname or Lastname
English
English : topographic name for someone who lived at the edge of a village or by some other boundary, Middle English border, from Old French bordure ‘edge’.
Male
Swedish
Swedish form of Old Norse Dagr, DAGHER means "day."
Girl/Female
Indian, Traditional
Order
Girl/Female
Indian, Telugu
Order
Girl/Female
Indian, Marathi, Sindhi
Order
Girl/Female
Indian
Higher, Highest
Surname or Lastname
English
English : variant of Cordier.Catalan : occupational name for a maker of cord or string, from an agent derivative of Catalan corda ‘string’, ‘cord’.
Boy/Male
Biblical
A digger.
Boy/Male
Australian, French, German, Greek
Order
Biblical
a digger
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
Girl/Female
American, Australian, British, Chinese, Christian, English, Latin
Freedom; Independence
Boy/Male
Hindu, Indian, Kannada, Marathi, Sanskrit, Tamil, Telugu
Lord of the Earth
Boy/Male
Scandinavian Hebrew
Pledge.
Female
Hebrew
(עֵיפָה) Hebrew unisex name EYPHAH means "darkness" or "gloomy." In the bible, this is the name of several characters, including a son of Midian and one of Caleb's concubines. Also spelled Efah. The Anglicized form is Ephah.
Male
Slovene
Slovene form of English Isidoros, IZIDOR means "gift of Isis."
Girl/Female
Tamil
Pure, Innocent, Female friend
Boy/Male
Hindu, Indian
Gift of Clouds
Girl/Female
Australian, German, Spanish
Wise Guardian
Boy/Male
American, British, English
Lives in the Forest; From the Thicket of Trees
Boy/Male
Tamil
Sashreek | ஸஷà¯à®°à¯€à®•Â
Prosperous
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
n.
A body of persons having some common honorary distinction or rule of obligation; esp., a body of religious persons or aggregate of convents living under a common rule; as, the Order of the Bath; the Franciscan order.
v. t.
To make a border for; to furnish with a border, as for ornament; as, to border a garment or a garden.
v. i.
To give orders; to issue commands.
adv.
In a high manner, or to a high degree; very much; as, highly esteemed.
n.
To give an order to; to command; as, to order troops to advance.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
n.
An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; -- often used in the plural; as, to take orders, or to take holy orders, that is, to enter some grade of the ministry.
a.
Applied to time: On the thither side of, older than; of more years than. See Hither, a.
n.
Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation.
a.
Applied to time: On the hither side of, younger than; of fewer years than.
conj. Either
precedes two, or more, coordinate words or phrases, and is introductory to an alternative. It is correlative to or.
n.
Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet; as, to preserve order in a community or an assembly.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
adv.
To that place; -- opposed to hither.
adv.
To this place; -- used with verbs signifying motion, and implying motion toward the speaker; correlate of hence and thither; as, to come or bring hither.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
a.
Being on the side next or toward the person speaking; nearer; -- correlate of thither and farther; as, on the hither side of a hill.
a.
Being on the farther side from the person speaking; farther; -- a correlative of hither; as, on the thither side of the water.
n.
A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a group or division of men in the same social or other position; also, a distinct character, kind, or sort; as, the higher or lower orders of society; talent of a high order.