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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
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
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)
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)
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
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)
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
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
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 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 language
data types, pattern matching, parametric polymorphism, currying, higher-order functions, extensible records, channel and process-based concurrency, and
Flix_(programming_language)
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
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
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
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
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
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
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
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
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
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
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)
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)
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
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
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
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
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 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)
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
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
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)
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
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
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
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
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
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
Measure of the shape of a function
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)
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
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
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
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
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)
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
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
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
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)
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
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
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
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
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
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
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)
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
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)
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
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
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)
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
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
Programming construct
is a synonym for function symbol. Callback (computer programming) Closure (computer programming) Function pointer Higher-order function Command pattern
Function_object
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
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
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
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
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
Combinatorial optimization method for a family of functions of discrete variables
variables. When representing higher-order functions, the graph contains auxiliary nodes that allow to model higher-order interactions. A unary term w
Graph_cut_optimization
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
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
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)
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
Dialect of the Lisp programming language on the Java platform
Transducers enable higher-order functions such as map and fold to generalize over any source of input data. While traditionally these functions operate on sequences
Clojure
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
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
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
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
Algorithmic process of solving equations
first-order unification, T {\displaystyle T} is usually the set of first-order terms (terms built from variable and function symbols). For higher-order unification
Unification (computer science)
Unification_(computer_science)
Type of cryptanalytic attack
In cryptography, higher-order differential cryptanalysis is a generalization of differential cryptanalysis, an attack used against block ciphers. While
Higher-order differential cryptanalysis
Higher-order_differential_cryptanalysis
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
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
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
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)
(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
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
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
"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
Assignment of meaning to the symbols of a formal language
as in first-order logic. Other variables correspond to objects of higher type: subsets of the domain, functions from the domain, functions that take a
Interpretation_(logic)
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Programming syntax
usage of method chaining, involving higher-order functions. In object-oriented programming, higher-order functions and manipulation of collections can
Method_chaining
Dialect of Lisp
development of functional programming techniques involving the use of higher-order functions in Lisp. But early Lisps were not suitable expressions of the lambda
Scheme_(programming_language)
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)
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)
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computable_function
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
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
Girl/Female
Indian
Higher, Highest
Boy/Male
Australian, French, German, Greek
Order
Biblical
a digger
Girl/Female
German, Greek
Order
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’.
Girl/Female
Indian, Marathi, Sindhi
Order
Girl/Female
Indian, Traditional
Order
Boy/Male
Hindu, Indian, Punjabi, Sikh
Order
Surname or Lastname
English
English : variant of Highley.
Male
Swedish
Swedish form of Old Norse Dagr, DAGHER means "day."
Boy/Male
Greek
Order.
Boy/Male
Biblical
A digger.
Surname or Lastname
English
English : variant of Haggard.English : variant of Hager.
Girl/Female
Greek
Order.
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’.
Male
Swedish
Old Swedish form of Old Norse Oddr, ODDER means "point of a weapon."
Girl/Female
Muslim
Higher, Highest
Boy/Male
Greek
Order.
Girl/Female
Indian, Telugu
Order
Boy/Male
Greek
Order.
HIGHER ORDER-FUNCTION
HIGHER ORDER-FUNCTION
Boy/Male
Tamil
Lord of bulls
Boy/Male
Arabic, Muslim
Abu-zamzam was the Name of Al-madini; A Man of an Early Islam; About Him Amusing Anecdotes were Told
Surname or Lastname
English
English : variant spelling Arrowsmith.
Boy/Male
Hindu
Honorable, Someone honored and respected
Male
Spanish
Spanish form of Latin Jacobus, JACOBO means "supplanter."
Girl/Female
Indian, Marathi
An Old King
Female
Danish
, might, power.
Boy/Male
Arabic, Muslim
Protector; King; Defender
Surname or Lastname
English (of Norman origin) and French
English (of Norman origin) and French : from Anglo-Norman French lo(u)vet, a nickname meaning ‘wolf cub’, ‘young wolf’ (see Love, Low).Scottish : variant of Lovat, a habitational name for a sept of the Frasers from Lovat near Beauly in Inverness-shire, so named from Gaelic lobh ‘rot’, ‘putrefy’ + the locative suffix -aid.
Female
Spanish
Spanish form of English Agnes, IÑES means "chaste; holy."
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.
a.
Applied to time: On the hither side of, younger than; of fewer years than.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
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.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
conj. Either
precedes two, or more, coordinate words or phrases, and is introductory to an alternative. It is correlative to or.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
v. i.
To give orders; to issue commands.
adv.
To that place; -- opposed to hither.
adv.
In a high manner, or to a high degree; very much; as, highly esteemed.
a.
Being on the farther side from the person speaking; farther; -- a correlative of hither; as, on the thither side of the water.
a.
Applied to time: On the thither side of, older than; of more years than. See Hither, a.
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.
v. t.
To make a border for; to furnish with a border, as for ornament; as, to border a garment or a garden.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
n.
Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet; as, to preserve order in a community or an assembly.
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.
n.
To give an order to; to command; as, to order troops to advance.
n.
Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation.
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.