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Use of functions that call themselves
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same
Recursion_(computer_science)
Two functions defined from each other
In mathematics and computer science, mutual recursion is a form of recursion where two or more mathematical or computational objects, such as functions
Mutual_recursion
Process of repeating items in a self-similar way
linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its
Recursion
Topics referred to by the same term
repeating items in a self-similar way. Recursion may also refer to Recursion (computer science), a method where the solution to a problem depends on solutions
Recursion_(disambiguation)
Study of computable functions and Turing degrees
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated
Computability_theory
Pattern defining an infinite sequence of numbers
algorithms) Mathematical induction Orthogonal polynomials Recursion Recursion (computer science) Time scale calculus Jacobson, Nathan, Basic Algebra 2 (2nd
Recurrence_relation
Subroutine call performed as final action of a procedure
tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize
Tail_call
In programming languages, the object or class the currently running code belongs to
recursion, and means that these methods can be overridden by derived classes or objects. By contrast, direct named recursion or anonymous recursion of
This_(computer_programming)
Sequence of program instructions invokable by other software
initially support recursion because only one set of variables and return address were allocated for each callable. Early computer instruction sets made
Function (computer programming)
Function_(computer_programming)
This glossary of computer science is a list of definitions of terms and concepts used in computer science, its sub-disciplines, and related fields, including
Glossary_of_computer_science
Computer science textbook
hacker culture. It teaches fundamental principles of computer programming, including recursion, abstraction, modularity, and programming language design
Structure and Interpretation of Computer Programs
Structure_and_Interpretation_of_Computer_Programs
One of several equivalent definitions of a computable function
U_{2}^{3})\right)} Fibonacci number McCarthy 91 function Recursion theory Recursion Recursion (computer science) "Recursive Functions". The Stanford Encyclopedia
General_recursive_function
Mathematical puzzle game
pattern Backup rotation scheme, a TOH application Baguenaudier Recursion (computer science) "The Nine Billion Names of God", 1953 Arthur C. Clarke short
Tower_of_Hanoi
Repetition of a process
the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms.
Iteration
Finite or infinite ordered list of elements
(topology) (a generalization of sequences) Ordinal-indexed sequence Recursion (computer science) Set (mathematics) Tuple Permutation If the inequalities are
Sequence
Interdisciplinary study of systems
Multidimensional systems Open and closed systems in social science Pattern language Recursion (computer science) Reductionism Redundancy (engineering) Reversal theory
Systems_theory
In computer science, polymorphic recursion (also referred to as Milner–Mycroft typability or the Milner–Mycroft calculus) refers to a recursive parametrically
Polymorphic_recursion
Instructions a computer can execute
A computer program is a sequence or set of instructions in a programming language for a computer to execute. It is one component of software, which also
Computer_program
Academic discipline
Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three
Logic_in_computer_science
Recursive function
In computer science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the composition of an anamorphism
Hylomorphism (computer science)
Hylomorphism_(computer_science)
Limited form of tree data structure
Optimal binary search tree Random binary tree Recursion (computer science) Red–black tree Rope (computer science) Self-balancing binary search tree Splay tree
Binary_tree
Quickly growing function
Computability theory Double recursion Fast-growing hierarchy Goodstein function Primitive recursive function Recursion (computer science) with parameter order
Ackermann_function
Algorithms which recursively solve subproblems
In computer science, divide and conquer, originally a political maxim, designates an algorithm design paradigm. A divide-and-conquer algorithm recursively
Divide-and-conquer_algorithm
Function computable with bounded loops
recursive functions. Grzegorczyk hierarchy Recursion (computer science) Primitive recursive functional Double recursion Primitive recursive set function Primitive
Primitive_recursive_function
Endless sequence of integers
previous elements in a straightforward way, they are often defined using recursion. Recamán's sequence was named after its inventor, Colombian mathematician
Recamán's_sequence
Books about algorithms by Donald Knuth
The Art of Computer Programming (TAOCP) is a comprehensive multi-volume monograph (Volumes 1–7) written by the computer scientist Donald Knuth presenting
The Art of Computer Programming
The_Art_of_Computer_Programming
Programming paradigm based on applying and composing functions
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative
Functional_programming
Programming language family
in computer science, including tree data structures, automatic storage management, dynamic typing, conditionals, higher-order functions, recursion, the
Lisp_(programming_language)
Overview of and topical guide to logic
function Recursion (computer science) Recursive language Recursive set Recursively enumerable language Recursively enumerable set Reduction (recursion theory)
Outline_of_logic
Type of algorithm in computer science
In computer science, corecursion is a type of operation that is dual to (structural) recursion. Whereas recursion consumes a data structure by first handling
Corecursion
Concept in mathematical logic
type theory (ITT), a discipline within mathematical logic, induction-recursion is a feature for simultaneously declaring a type and function on that
Induction-recursion
Defining elements of a set in terms of other elements in the set
programming Mathematical induction Recursive data types Recursion Recursion (computer science) Structural induction Henkin, Leon (1960). "On Mathematical
Recursive_definition
American computer scientist
compiling the language. He invented the continuation to solve a double recursion problem for one of the users of his Lisp implementation. In 1962, Russell
Steve Russell (computer scientist)
Steve_Russell_(computer_scientist)
Theory of computer sciences
In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by
Left_recursion
Sequence of operations for a task
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve
Algorithm
Synchronization mechanism for enforcing limits on access to a resource
In computer science, a lock or mutex (from mutual exclusion) is a synchronization primitive that prevents state from being modified or accessed by multiple
Lock_(computer_science)
Recursively defined sequence of continuous closed plane fractal curves
polygon Peano curve List of fractals by Hausdorff dimension Recursion (computer science) Sierpiński triangle Weisstein, Eric W. "Sierpiński Curve". MathWorld
Sierpiński_curve
metarules, transformations and recursions. The Antikythera mechanism is believed to be an early mechanical analog computer. It was designed to calculate
History_of_computer_science
Programming paradigm restricted to provably terminating programs
restricted form of recursion, which operates only upon 'reduced' forms of its arguments, such as Walther recursion, substructural recursion, or "strongly normalizing"
Total_functional_programming
use of recursion to extend the expressibility of the logic, and is commonly referred to as 'Hennessy-Milner Logic with recursion'. Recursion is enabled
Hennessy–Milner_logic
American scientist (1927–2011)
committee that designed ALGOL 60. In August 1959 he proposed the use of recursion and conditional expressions, which became part of ALGOL. He then became
John McCarthy (computer scientist)
John_McCarthy_(computer_scientist)
computer science awards List of computer science journals List of computer scientists List of Internet pioneers List of pioneers in computer science List
List of pioneers in computer science
List_of_pioneers_in_computer_science
Computer science and recursion theory
In computer science and recursion theory the McCarthy formalism (1963) of computer scientist John McCarthy clarifies the notion of recursive functions
McCarthy_Formalism
Algorithm to compare text strings using wildcard syntax
In computer science, an algorithm for matching wildcards (also known as globbing) is useful in comparing text strings that may contain wildcard syntax
Matching_wildcards
Algorithmic process of solving equations
In logic and computer science, specifically automated reasoning, unification is an algorithmic process of solving equations between symbolic expressions
Unification (computer science)
Unification_(computer_science)
Self-replicating program
standard terms for these programs in the computability theory and computer science literature are "self-replicating programs", "self-reproducing programs"
Quine_(computing)
Computer programming textbook by Matthias Felleisen and colleagues
knowledge than that of SICP. The paper distinguishes between structural recursion, where the related data definition happens to be self-referential, requiring
How_to_Design_Programs
parser – Recursion (computer science) – Recursive set – Recursively enumerable language – Recursively enumerable set – Reference (computer science) – Referential
Index_of_computing_articles
American mathematician (1909–1994)
mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the
Stephen_Cole_Kleene
programming formalisms — such as restricted formal languages, type systems, or recursion schemes — whose expressive power coincides exactly with a given complexity
Implicit computational complexity
Implicit_computational_complexity
Section of code that details a specific command
metalanguage. Pascal used both syntax diagrams and equivalent BNF. BNF uses recursion to express repetition, so various extensions have been proposed to allow
Statement_(computer_science)
British mathematician
on category theory applied to logic (proof theory, recursion theory), theoretical computer science (lambda-calculus and semantics) and higher-dimensional
Martin_Hyland
Academic subfield of computer science
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation
Theory_of_computation
Research computer scientist
Phil.) from the University of Oxford in 1984 with a dissertation titled "Recursion theories on the continuous functionals". Thompson's doctoral adviser was
Simon_Thompson_(professor)
Computing problem
In computer science, the range query problem consists of efficiently answering several queries regarding a given interval of elements within an array.
Range query (computer science)
Range_query_(computer_science)
English programmer, venture capitalist, and writer (born 1964)
1986. He then received a Master of Science in 1988, and a Doctor of Philosophy in 1990, both in computer science from Harvard University. Graham also
Paul_Graham_(programmer)
Computer science and logic conference
Symposium on Logic in Computer Science (LICS) is an annual academic conference on the theory and practice of computer science in relation to mathematical
Symposium on Logic in Computer Science
Symposium_on_Logic_in_Computer_Science
Italian mathematician
connections between concepts utilized in computer science and mathematical structures derived from generalized recursion, demonstration theory, and category
Giuseppe_Longo
supervised by computer scientist Nell B. Dale, was titled, "Conceptual models and individual cognitive learning styles in teaching recursion to novices"
Cheng-Chih_Wu
Canadian computer scientist (born 1964)
received his Bachelor of Engineering degree (Computer engineering), MSc (computer science) and PhD (computer science) from McGill University. Bengio is the
Yoshua_Bengio
Recursion without calling a function by name
In computer science, anonymous recursion is recursion which does not explicitly call a function by name. This can be done either explicitly, by using a
Anonymous_recursion
Top-down parser utilizing recursion
left recursion. Any context-free grammar can be transformed into an equivalent grammar that has no left recursion, but removal of left recursion does
Recursive_descent_parser
Computer programming language
and recursion in scripts, and can be used to teach all computer science concepts, as UC Berkeley lecturer Brian Harvey did in his Computer Science Logo
Logo_(programming_language)
Type of computing function
In computer science, a computational problem is memory-bound when the time it takes for it to complete is decided primarily by the amount of free memory
Memory-bound_function
Study of circular causal processes
transdisciplinary study of circular causal processes such as feedback and recursion, where the outcomes of actions return as inputs for subsequent actions
Cybernetics
Overview of and topical guide to computer programming
automate performing a given task or solving a given problem. History of computer science History of computing hardware History of computing hardware (1960s–present)
Outline of computer programming
Outline_of_computer_programming
Subfield of mathematics
problem, a result with far-ranging implications in both recursion theory and computer science. There are many known examples of undecidable problems from
Mathematical_logic
American computer scientist (born 1947)
IIT Kanpur, India in 1969 and a Ph.D. in electrical engineering and computer science from the Johns Hopkins University, Baltimore, Maryland in 1972. After
Jayadev_Misra
Higher-order function Y for which Y f = f (Y f)
In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) is a higher-order function (i.e., a function that takes a
Fixed-point_combinator
American computer scientist
received his doctorate in computer science from Harvard in 1985, advised by Harry R. Lewis. His thesis was titled Recursion-Theoretic Techniques in Complexity
William_Gasarch
Spline function
internal knots. B-splines can be constructed by means of the Cox–de Boor recursion formula. We start with the B-splines of degree p = 0 {\displaystyle p=0}
B-spline
Generalization of addition, multiplication, exponentiation, tetration, etc.
copies of }}a},\quad n\geq 2} It may also be defined according to the recursion rule part of the definition, as in Knuth's up-arrow version of the Ackermann
Hyperoperation
Programming language
functions Linked lists Macros M-expressions (deprecated) Read–eval–print loop Recursion S-expressions Self-hosting compiler Tree data structures Object systems
Flavors (programming language)
Flavors_(programming_language)
Models of computation
the correct answer.)" L. K. Schubert's 1974 paper "Iterated Limiting Recursion and the Program Minimization Problem" studied the effects of iterating
Hypercomputation
Proof method in mathematical logic
induction. Structural recursion is a recursion method bearing the same relationship to structural induction as ordinary recursion bears to ordinary mathematical
Structural_induction
Computation model defining an abstract machine
Chapter IX "Turing Machines" includes some recursion theory. Davis, Martin (2000). The Universal Computer: The Road from Leibniz to Turing. W. W. Norton
Turing_machine
Mathematical-logic system
EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). pp. 1–10. arXiv:1601
Lambda_calculus
Principle of interchangeability of data and code
In computer science, the expression code as data refers to the idea that source code written in a programming language can be manipulated as data, such
Code_as_data
Algorithm that arranges lists in order
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order
Sorting_algorithm
Integration of programming as part of running program
and recursion solutions, but timing had been a major issue. While the general form of a temporal recursion, being any asynchronous function recursion through
Live_coding
Rewriting system and type of formal grammar
above to the earlier recursion, one gets: Axiom First recursion Second recursion Third recursion Fourth recursion Seventh recursion, scaled down ten times
L-system
Type of grammar for describing formal languages
In computer science, a parsing expression grammar (PEG) is a type of analytic formal grammar, i.e. it describes a formal language in terms of a set of
Parsing_expression_grammar
Indian-American mathematician
Indian-American mathematician, logician, computer scientist and philosopher known for his contributions to mathematical logic, recursion theory, proof theory, epistemic
Rohit_Jivanlal_Parikh
Topics referred to by the same term
an aircraft Comet tail, a visible part of a comet Tail recursion, a type of recursion in computer programming Tail rotor, a small vertical propeller mounted
Tail_(disambiguation)
General-purpose programming language
language, supporting structured programming, lexical variable scope, and recursion, with a static type system. It was designed to be compiled to provide
C_(programming_language)
Topics referred to by the same term
operator ("μ operator"), the add-on to primitive recursion to obtain μ-recursive functions in computer science Optimization (mathematics) Minimal (disambiguation)
Minimisation
Value that is not changed during execution
languages since they favour programming styles with no side-effect (e.g., recursion) or make most declarations immutable by default, such as ML. Purely functional
Constant (computer programming)
Constant_(computer_programming)
2012 studio album by Finite Automata
written between 2007 and 2010. Its name is a reference to the computer science concept of recursion, and alludes to conflict that feeds back into itself. Mod
Recurse_(album)
American scientist and entrepreneur
was later acquired by Recursion in 2020. Betts-LaCroix is also a biotech angel investor in such companies as StemCentrx, Recursion Pharma and Spring Discovery
Joe_Betts-LaCroix
Mathematical proof at least partially generated by computer
A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been
Computer-assisted_proof
Thesis on the nature of computability
regarding both physical and biological computers, are also discussed in Odifreddi's 1989 textbook on recursion theory. One can formally define functions
Church–Turing_thesis
Programming paradigm based on objects
differ from how OOP is commonly understood, and has implied that the computer science establishment did not adopt his notion. A 1976 MIT memo co-authored
Object-oriented_programming
Divide and conquer sorting algorithm
analysis, in The Computer Journal Volume 5, Issue 1, 1962, Pages 10–16. Later, Hoare learned about ALGOL and its ability to do recursion, which enabled
Quicksort
Non-comparative lexicographical sorting algorithm
In computer science, radix sort is a non-comparative sorting algorithm. It avoids comparison by creating and distributing elements into buckets according
Radix_sort
American computer scientist; creator of Morris Worm; associate professor at MIT
joined the faculty in the department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology (MIT), where he received
Robert_Tappan_Morris
Type of Knowledge Graph Management System
knowledge graphs also makes the presence of recursion in these rules a particularly important aspect. Recursion means that the same rules might be called
Vadalog
Class of algorithms
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting
Tree_traversal
Symbolics operating system based on Lisp
Genera was also sold by Symbolics as Open Genera, which runs Genera on computers based on a Digital Equipment Corporation (DEC) Alpha processor using Tru64
Genera_(software)
Bulgarian mathematician
of Mathematical Logic and Applications, Faculty of Mathematics and Computer Science at the University of Sofia. Chairman of the department in 1972-2000
Dimiter_Skordev
In computer science, a loop variant is a mathematical function defined on the state space of a computer program whose value is monotonically decreased
Loop_variant
RECURSION COMPUTER-SCIENCE
RECURSION COMPUTER-SCIENCE
Boy/Male
Arabic, Muslim
Compiler of Hadith
Girl/Female
Muslim
Pleasure trip, Excursion spot
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Male
German
Middle High German byname HEIDEN means "heathen." The composer Josef Haydn's surname was a respelling of this name.
Boy/Male
Latin
He who loves God. Famous Bearer: late composer Wolfgang Amadeus Mozart.
Girl/Female
Muslim/Islamic
Excursion spot
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Boy/Male
Latin
He who loves God. Famous Bearer: late composer Wolfgang Amadeus Mozart.
Surname or Lastname
English
English : occupational name for a mower or reaper of grass or hay, Old English mǣðere. Compare Mead, Mower. Hay was formerly of great importance, not only as feed for animals in winter but also for bedding.English : in southern Lancashire, where it has long been a common surname, it is probably a relatively late development of Madder (see Mader).English : The prominent Mather family of New England were established in America by Richard Mather (1596–1669) in 1635. He was a Puritan clergyman from a well-established family of Lowton, Lancashire, England. After he emigrated, he was in great demand as a preacher, finally settling in Dorchester, MA. His son Increase Mather (1639–1723) was a diplomat and president of Harvard. He married his step-sister Maria Cotton, herself the daughter of an eminent Puritan divine, John Cotton. Their son Cotton Mather (1663–1728) bore both family names. The latter was a minister who is remembered for his part in witchcraft trials, but he was also a man of science and a fellow of the Royal Society in London.
Girl/Female
Arabic, Muslim
To Compete with Pride
Boy/Male
Hindu
Computer
Girl/Female
Muslim
To compete with pride
Boy/Male
Tamil
Computer
Boy/Male
Arabic, Muslim
Abu Isa Muhammad Al-tirmidhi; Compiler of the One Collection of Prophet Muhammad
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Boy/Male
Muslim
Compiler of Hadith
Boy/Male
Hindu, Indian, Sanskrit
Compiler of the Vedas
Girl/Female
Arabic, Hindu, Indian, Kannada, Marathi, Muslim, Sindhi
Pleasure Trip; Excursion Spot
Girl/Female
Arabic, Muslim
Pleasure Trip; Excursion Spot
Boy/Male
Indian, Sanskrit
Unattained; Cannot be Competed with
RECURSION COMPUTER-SCIENCE
RECURSION COMPUTER-SCIENCE
Girl/Female
German, Polish, Teutonic
Home Ruler; Ruler of the Estate; Female Version of Henry
Girl/Female
Tamil
Love
Female
Scottish
Feminine form of Scottish Murdoch, MURDANN means "sea warrior."
Male
Hebrew
(×‘Ö¼Ö¸× Ö´×™) Hebrew name derived from the word banah, BANIY means "built." In the bible, this is the name of several characters, including one of David's warriors.
Boy/Male
Arabic, Indian, Muslim, Parsi
Name of Mazdak's Father; Early Morning
Boy/Male
Tamil
Goddess Lakshmi
Girl/Female
Muslim
Aromatic
Boy/Male
American, Australian, British, Chinese, Christian, English, Irish, Scottish
From Scotland; Form of Scott; A Scotsman; Wanderer
Boy/Male
Anglo Saxon
Name of a king.
Girl/Female
Hindu, Indian, Japanese, Sindhi
Red Colour; Lakshmi
RECURSION COMPUTER-SCIENCE
RECURSION COMPUTER-SCIENCE
RECURSION COMPUTER-SCIENCE
RECURSION COMPUTER-SCIENCE
RECURSION COMPUTER-SCIENCE
n.
The act of ceding back; restoration; repeated cession; as, the recession of conquered territory to its former sovereign.
imp. & p. p.
of Compute
p. pr. & vb. n.
of Compute
n.
A computer.
v. i.
To calculate; to compute.
n.
One who commutes; especially, one who commutes in traveling.
n.
One who composes or writes a book; a composer, as distinguished from an editor, translator, or compiler.
v. i.
To contend emulously; to seek or strive for the same thing, position, or reward for which another is striving; to contend in rivalry, as for a prize or in business; as, tradesmen compete with one another.
n.
The power, either inherent or due to some physical action, by which bodies, or the particles of bodies, are made to recede from each other, or to resist each other's nearer approach; as, molecular repulsion; electrical repulsion.
v. i.
To pay, or arrange to pay, in gross instead of part by part; as, to commute for a year's travel over a route.
n.
A composer or compiler of hymns; one versed in hymnology.
imp. & p. p.
of Commute
n.
One who computes.
imp. & p. p.
of Compete
n.
Compiler.
v. t.
To exchange; to put or substitute something else in place of, as a smaller penalty, obligation, or payment, for a greater, or a single thing for an aggregate; hence, to lessen; to diminish; as, to commute a sentence of death to one of imprisonment for life; to commute tithes; to commute charges for fares.
n.
A flowing; also, a hostile incursion.
n.
A preparation of fruit in sirup in such a manner as to preserve its form, either whole, halved, or quartered; as, a compote of pears.
v. t.
To compute erroneously.