Find link

language: af: Afrikaans als: Alemannisch [Alemannic] am: አማርኛ [Amharic] an: aragonés [Aragonese] ar: العربية [Arabic] arz: مصرى [Egyptian Arabic] as: অসমীয়া [Assamese] ast: asturianu [Asturian] az: azərbaycanca [Azerbaijani] azb: تۆرکجه [Southern Azerbaijani] ba: башҡортса [Bashkir] bar: Boarisch [Bavarian] bat-smg: žemaitėška [Samogitian] be: беларуская [Belarusian] be-tarask: беларуская (тарашкевіца) [Belarusian (Taraškievica)] bg: български [Bulgarian] bn: বাংলা [Bengali] bpy: বিষ্ণুপ্রিয়া মণিপুরী [Bishnupriya Manipuri] br: brezhoneg [Breton] bs: bosanski [Bosnian] bug: ᨅᨔ ᨕᨘᨁᨗ [Buginese] ca: català [Catalan] ce: нохчийн [Chechen] ceb: Cebuano ckb: کوردیی ناوەندی [Kurdish (Sorani)] cs: čeština [Czech] cv: Чӑвашла [Chuvash] cy: Cymraeg [Welsh] da: dansk [Danish] de: Deutsch [German] el: Ελληνικά [Greek] en: English eo: Esperanto es: español [Spanish] et: eesti [Estonian] eu: euskara [Basque] fa: فارسی [Persian] fi: suomi [Finnish] fo: føroyskt [Faroese] fr: français [French] fy: Frysk [West Frisian] ga: Gaeilge [Irish] gd: Gàidhlig [Scottish Gaelic] gl: galego [Galician] gu: ગુજરાતી [Gujarati] he: עברית [Hebrew] hi: हिन्दी [Hindi] hr: hrvatski [Croatian] hsb: hornjoserbsce [Upper Sorbian] ht: Kreyòl ayisyen [Haitian] hu: magyar [Hungarian] hy: Հայերեն [Armenian] ia: interlingua [Interlingua] id: Bahasa Indonesia [Indonesian] io: Ido is: íslenska [Icelandic] it: italiano [Italian] ja: 日本語 [Japanese] jv: Basa Jawa [Javanese] ka: ქართული [Georgian] kk: қазақша [Kazakh] kn: ಕನ್ನಡ [Kannada] ko: 한국어 [Korean] ku: Kurdî [Kurdish (Kurmanji)] ky: Кыргызча [Kirghiz] la: Latina [Latin] lb: Lëtzebuergesch [Luxembourgish] li: Limburgs [Limburgish] lmo: lumbaart [Lombard] lt: lietuvių [Lithuanian] lv: latviešu [Latvian] map-bms: Basa Banyumasan [Banyumasan] mg: Malagasy min: Baso Minangkabau [Minangkabau] mk: македонски [Macedonian] ml: മലയാളം [Malayalam] mn: монгол [Mongolian] mr: मराठी [Marathi] mrj: кырык мары [Hill Mari] ms: Bahasa Melayu [Malay] my: မြန်မာဘာသာ [Burmese] mzn: مازِرونی [Mazandarani] nah: Nāhuatl [Nahuatl] nap: Napulitano [Neapolitan] nds: Plattdüütsch [Low Saxon] ne: नेपाली [Nepali] new: नेपाल भाषा [Newar] nl: Nederlands [Dutch] nn: norsk nynorsk [Norwegian (Nynorsk)] no: norsk bokmål [Norwegian (Bokmål)] oc: occitan [Occitan] or: ଓଡ଼ିଆ [Oriya] os: Ирон [Ossetian] pa: ਪੰਜਾਬੀ [Eastern Punjabi] pl: polski [Polish] pms: Piemontèis [Piedmontese] pnb: پنجابی [Western Punjabi] pt: português [Portuguese] qu: Runa Simi [Quechua] ro: română [Romanian] ru: русский [Russian] sa: संस्कृतम् [Sanskrit] sah: саха тыла [Sakha] scn: sicilianu [Sicilian] sco: Scots sh: srpskohrvatski / српскохрватски [Serbo-Croatian] si: සිංහල [Sinhalese] simple: Simple English sk: slovenčina [Slovak] sl: slovenščina [Slovenian] sq: shqip [Albanian] sr: српски / srpski [Serbian] su: Basa Sunda [Sundanese] sv: svenska [Swedish] sw: Kiswahili [Swahili] ta: தமிழ் [Tamil] te: తెలుగు [Telugu] tg: тоҷикӣ [Tajik] th: ไทย [Thai] tl: Tagalog tr: Türkçe [Turkish] tt: татарча/tatarça [Tatar] uk: українська [Ukrainian] ur: اردو [Urdu] uz: oʻzbekcha/ўзбекча [Uzbek] vec: vèneto [Venetian] vi: Tiếng Việt [Vietnamese] vo: Volapük wa: walon [Walloon] war: Winaray [Waray] yi: ייִדיש [Yiddish] yo: Yorùbá [Yoruba] zh: 中文 [Chinese] zh-min-nan: Bân-lâm-gú [Min Nan] zh-yue: 粵語 [Cantonese]

jump to random article

Longer titles found: General recursive function (view), Primitive recursive function (view), Elementary recursive function (view), Primitive recursive functional (view)

searching for Recursive function 119 found (485 total)

alternate case: recursive function

Word problem for groups (4,932 words) [view diff] exact match in snippet view article find links to article

in }}X{\text{ and }}u=v{\text{ in }}G\ \}} then there is a partial recursive function f P {\displaystyle f_{P}} such that: f P ( ⟨ u , v ⟩ ) = { 0 if  

Mathematicians in Oslo. These papers helped to found the modern field of recursive function theory as a separate area of mathematical research. In 1937, she was

In recursive function theory, double recursion is an extension of primitive recursion which allows the definition of non-primitive recursive functions

science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the composition of an anamorphism (which first builds

In computer science, the Tak function is a recursive function, named after Ikuo Takeuchi [ja]. It is defined as follows: τ ( x , y , z ) = { τ ( τ ( x

rule for subsequences, but in 1940 Alonzo Church defined it as any recursive function which having read the first N elements of the sequence decides if

mathematician, making contributions to constructive mathematics and recursive function theory. Andrey Markov was born on 14 June 1856 in Ryazan, Russia.

which has anonymous unary functions, but is able to compute any recursive function. This anonymous recursion can be produced generically via fixed-point

The McCarthy 91 function is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer

objects; recursive function calls; and more. At the end, the reader is left with an "interpreter" that uses nothing but tail-recursive function calls and

development of the theory is quite different. The same definition of recursive function can be given, in computability theory, by applying Kleene's recursion

Active rules conforming to the event condition action (ECA) paradigm Recursive function definitions Metamodeling with arbitrarily many abstraction levels

closure. A set of axioms is primitive recursive if there is a primitive recursive function that decides membership in the set. To obtain a primitive recursive

The mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational)

recurrence relation means obtaining a closed-form solution: a non-recursive function of n {\displaystyle n} . The concept of a recurrence relation can

introduction to intuitionistic logic and mathematical intuitionism. [...] recursive function theory is of central importance in computer science. Kleene is responsible

the notation of the programming language bondi, it is given by the recursive function let rec size = | x y -> (size x) + (size y) | x -> 1 The second, or

mathematics). μ-recursive functions A computation consists of a μ-recursive function, i.e. its defining sequence, any input value(s) and a sequence of

to use jumps instead of calls. This could be reduced to a single recursive function is_even. In that case, is_odd, which could be inlined, would call

{\displaystyle \ln n=o(n)} . For every recursive function f {\displaystyle f} , there is a recursive function g {\displaystyle g} which is time constructible

\gamma (x,y)} is a function obtained from an arbitrary primitive recursive function ϱ {\displaystyle \varrho } such that ∃ p ∀ s ( ϱ ( p , s , y ) = 0

encapsulate an action and its parameters "Externalize the stack" Turn a recursive function into an iterative function that uses a stack Interpreter pattern Implement

and the SECD machine. The Krivine machine explains how to compute a recursive function. More specifically it aims to define rigorously head normal form reduction

machine is undecidable. A universal Turing machine can calculate any recursive function, decide any recursive language, and accept any recursively enumerable

JSTOR 1996261 Carl Groos Jockusch Jr. (June 1966). Reducibilities in recursive function theory (PDF) (Thesis). Massachusetts Institute of Technology. Archived

mathematics from the Massachusetts Institute of Technology for a thesis in recursive function theory supervised by Hartley Rogers. Kreider spent a postdoctoral

extraordinarily large, sometimes even greater than any primitive recursive function; see the Paris–Harrington theorem for an example. Graham's number

+ to these n arguments, for n = 0, 1, 2, 3, and 4. The following recursive function is accumulator-based and eventually reverses the accumulator before

1980:78). Nigel Cutland (1980), Computability: An Introduction to Recursive Function Theory, Cambridge University Press. ISBN 9780521294652. Richard M

Mahlo if it is admissible and for any α {\displaystyle \alpha } -recursive function f : α → α {\displaystyle f:\alpha \rightarrow \alpha } there is an

Mahlo if it is admissible and for any α {\displaystyle \alpha } -recursive function f : α → α {\displaystyle f:\alpha \rightarrow \alpha } there is an

Balinsky-Young quota method. Every house-monotone method can be defined as a recursive function of the house size h. Formally, an apportionment method M ( t , h )

and in a declarative language it would apply to the argument of a recursive function. For example, f x = ... (3 ** x) ... (f (x + 1)) ... becomes f x =

variables stored on the call stack directly. This means that when a recursive function calls itself, local variables in each instance of the function are

Quantum computer Universal quantum computer Church–Turing thesis Recursive function Entscheidungsproblem Halting problem Correctness Post correspondence

an extremely simple E program: println("Hello, world!") Here is a recursive function for computing the factorial of a number, written in E. Functions are

does two stacks S and P (in addition to the normal call stack for a recursive function). Stack S contains all the vertices that have not yet been assigned

: int) : int = n * fac (n - 1) This describes the factorial as a recursive function, with a single terminating base case. It is similar to the descriptions

effectively immune if I {\displaystyle I} is infinite, but there exists a recursive function f {\displaystyle f} such that for every index e {\displaystyle e}

Congress of Mathematicians in Oslo, helping to found the modern field of recursive function theory. Inge Lehmann argues that the Earth's molten interior has a

min(binEdgeLengths) < value || binDepth > value if exitConditionsMet return; % Exit recursive function end % Otherwise, split this bin into 8 new sub-bins with a new division

1⁄91 can be obtained by using powers of 9. McCarthy 91 function, a recursive function in discrete mathematics Sloane, N. J. A. (ed.). "Sequence A001358"

Dame Journal of Formal Logic. Bronze Star Medal Research Problem 8: Recursive function theory (A modern look at a Euclidean idea), Bull. Amer. Math. Soc

Rózsa Péter (b. 1905), Hungarian mathematician, "founding mother of recursive function theory". June 3 – Archibald Hill (b. 1886), English physiologist,

Rózsa Péter (died 1977), Hungarian mathematician, "founding mother of recursive function theory" February 23 – Derrick Henry Lehmer (died 1991), American mathematician

"Explorer's Demise" "NBPD Theme" "Trenchant Preliator" "Music For A Recursive Function" "Isolation" ugress (2010-06-21). "Collectronics". Ugress. Retrieved

in current intuitionistic mathematics". In F. D. E. Dekker (ed.). Recursive Function Theory: Proc. Symposia in Pure Mathematics. Vol. 5. American Mathematical

Analysis. Cutland, Nigel (1980). Computability: An Introduction to Recursive Function Theory. Cambridge University Press. ISBN 9780521294652. Capinski,

series of papers. Rózsa Péter presents the results of her paper on recursive function theory, "Rekursive Funktionen," to the International Congress of Mathematicians

However, another advantage of the call stack method is that it allows recursive function calls, since each nested call to the same procedure gets a separate

{\displaystyle \forall a\in Y,X\vdash a.} The return value of a partial recursive function, which either returns a natural number or goes into an infinite recursion

trampolining. Programmers can use trampolined functions to implement tail-recursive function calls in stack-oriented programming languages. In Java, trampoline

research was in the area of intuitionistic logic and its connection with recursive function theory. He investigated the relationship, in intuitionistic formal

language supporting basic logic operations that also allows a self-recursive function to be constructed as an expression. Two mechanisms that support the

anywhere. Here is a complete program defining and using the traditional recursive function to calculate a factorial. % Accepts a number and calculates its factorial

Manufacturing, a Japanese heavy equipment manufacturer Tak, mathematical recursive function named after Ikuo Takeuchi (竹内郁雄) The Takeuchi Documents, texts in

n\;f(n)=0\rightarrow \exists n\;f(n)=0} for f {\displaystyle f} a total recursive function on the natural numbers. In the presence of the Church's thesis principle

is a weight-balanced tree t that represents A ∪ B. The following recursive function computes this union: function union(t1, t2): if t1 = nil: return t2

whose body was a recursive type. The revised version specifies a recursive function on types. (The type variable ϕ {\displaystyle \phi } is used to suggest

discrete time by a mapping on vector sequences. These mappings are a recursive function of two competing terms: an individual non-linear reaction, and a spatial

just a singleton, since there are several indices computing the same recursive function. So here the second entry of the objects represent the realizing data

A_{1}\otimes _{K}1_{2^{n-1}}} . The sum of these two terms gives a recursive function for the adjacency matrix of a hypercube: A n = { 1 2 ⊗ K A n − 1 +

designer of the Programma 101 programmable calculator Rózsa Péter – recursive function theory Simon Peyton Jones – functional programming, Glasgow Haskell

not to include all primes. Euclid number Mullin, Albert A. (1963), "Recursive function theory (A modern look at a Euclidean idea)", Research problems, Bulletin

fact an e {\displaystyle e} that is the Gödel number of a partial recursive function that will, for every x {\displaystyle x} , produce such a y {\displaystyle

Retrieved 2025-01-06. Weihrauch 2000, p. 6. Myhill, J. (1971). "A recursive function, defined on a compact interval and having a continuous derivative

321170. Cutland, Nigel (1980). Computability: An Introduction to Recursive Function Theory (PDF). Cambridge University Press. p. 12. ISBN 9780521223843

oracle was available, which could compute a single arbitrary (non-recursive) function from naturals to naturals. He used this device to prove that even

being solved are automatically stored in the procedure call stack. A recursive function is a function that calls itself within its definition. Divide-and-conquer

Retrieved 2025-01-06. Weihrauch 2000, p. 6. Myhill, J. (1971). "A recursive function, defined on a compact interval and having a continuous derivative

Induction-recursion – for simultaneously declaring some inductive type and some recursive function on this type . Dybjer, Peter (June 2000). "A general formulation of

support for multi-core programming, and removed any fixed limit on recursive function calls. It also supported the creation of user-space concurrency facilities

result is then the left factor. This may be implemented as a tail-recursive function: Function exp_by_squaring(x, n) return exp_by_squaring2(1, x, n) Function

crashes. Instead, use a Boolean data type tag array to operate the recursive function to release the memory. The extra memory space required is close to

ISBN 1-58488-237-9. Cutland, Nigel J. (1980). Computability, an introduction to recursive function theory. Cambridge-New York: Cambridge University Press. p. 251. ISBN 0-521-22384-9

found. (For example, in the case of failed μ operator in a partial recursive function.) Functions which terminate the computation, such as the exit system

variables. A nested function typically acts as a helper function or a recursive function. Nested functions can be used for unstructured control flow, by using

ordered set partially persistent data structure partial order partial recursive function partition (set theory) passive data structure patience sorting path

Some Results on t {\displaystyle t} -Regressive Isols, concerned recursive function theory and was supervised by Matt Hassett. After holding a faculty

fundamental datatypes in OCaml. The following code example defines a recursive function sum that accepts one argument, integers, which is supposed to be a

compiled as fixed addresses. Similarly, an identifier bound to a recursive function is also technically a free variable within its own body but is treated

{\displaystyle \phi _{a}} denotes the a {\displaystyle a} -th partial recursive function in a standard Gödel numbering. This pca can also be relativized to

fundamental datatypes in OCaml. The following code example defines a recursive function sum that accepts one argument, integers, which is supposed to be a

printList2 lst = List.iter (printfn "%d") lst /// Iteration using a recursive function and pattern matching let rec printList3 lst = match lst with | []

implements the Laplace expansion: def determinant(M): # Base case of recursive function: 1x1 matrix if len(M) == 1: return M[0][0] total = 0 for column, element

executing high-level language programs, especially those allowing recursive function calls. This was a forward-looking decision at the time, because it

constraint, it has a very high complexity that dominates every multiply recursive function. The Identity Correspondence Problem (ICP) asks whether a finite set

intuitionistic arithmetic into the pair of a recursive function and of a proof of a formula expressing that the recursive function "realizes", i.e. correctly instantiates

particular characteristic. Some examples include the first primitive recursive function that results in complexity, the smallest universal Turing machine

explicitly. The implementation of the traversal can be done without recursive function calls and only a stack is required to store the nodes to be visited

on the stack. Stacks are an important way of supporting nested or recursive function calls. This type of stack is used implicitly by the compiler to support

completeness implies recursive enumerability. It follows that there is no recursive function f such that: if φ has a finite model, then it has a model of size

maximum]. In general, it can be represented as a recursive function as follows: Recursive function Head/tail Breaks: Rank the input data values from

}} . While this example, an explicit sequence of sums, is a total recursive function to begin with, the encoding also means these objects are in scope

Rezaiifar, and P. S. Krishnaprasad, "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition," in Proc

JSTOR 20016214. Cutland, Nigel (1980). Computability, an introduction to recursive function theory. Cambridge University Press. p. 251. ISBN 978-0-521-29465-2

sub-graphs of size k, let Sk be this set. ESU can be implemented as a recursive function; the running of this function can be displayed as a tree-like structure

interpretation requires looping constructs to be considered in terms of recursive function calls). In some languages, such as ECMAScript, return refers to the

Rezaiifar, R.; Krishnaprasad, P. (1993). "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition". Proceedings

and B, is a red–black tree t that represents A ∪ B. The following recursive function computes this union: function union(t1, t2): if t1 = NULL return t2

support a branching "tree" of rays. In simple implementations, a recursive function is called to trace each ray. Ray tracing usually performs anti-aliasing

"I ate %d apples".format(x) or (with a return type declared for a recursive function) def factorial(x: Int): Int = if x == 0 then 1 else x * factorial(x

Krishnaprasad, P. S. (November 1993). "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition". Proceedings

word problem, then the Dehn function of G growths faster than any recursive function. For the Thompson group F the Dehn function is quadratic, that is

Simple No No Definition Simple non recursive function definition. Recursive No Yes Definition Recursive function definition (implemented using the Y

number theory and the Lucas–Lehmer primality test; Rózsa Péter's recursive function theory; Claude Shannon's information theory; signal processing; data

× (n - 1)!. To recursively compute its result on a given input, a recursive function calls (a copy of) itself with a different ("smaller" in some way)

then n * factorial (n-1) else 1 This describes the factorial as a recursive function, with one terminating base case. It is similar to the descriptions

within a block, to visually set it apart from the surrounding code. A recursive function named foo, which is passed a single parameter, x, and if the parameter

described which allows Scott's topology to be applicable to logic and recursive function theory. Scott approaches his derivation using a complete lattice,

expects the input formula f in the negation normal form. It calls recursive function expand that builds the graph by populating global variables Nodes

recursively constructs machines for any number of states and provides the recursive function that computes their score (computes σ), thus providing a lower bound

S2CID 118241294 Morris, Edie; Harkleroad, Leon (1990), "Rózsa Péter: recursive function theory's founding mother", The Mathematical Intelligencer, 12 (1):

representing sets A and B, is a tree t that represents A ∪ B. The following recursive function computes this union: function union(t1, t2) if t1 = nil return t2

factorial(x: Int) -> Int { // The public function calls the private tail recursive function factorial_loop(x, 1) } fn factorial_loop(x: Int, accumulator: Int)

multi-dimensional integration. For volume = integrate(fy, ybounds) We might have RECURSIVE FUNCTION integrate(f, bounds) ! Integrate f(x) from bounds(1) to bounds(2)

\ldots } is not constant-recursive. More generally, every constant-recursive function is asymptotically bounded by an exponential function (see #Closed-form

to further number theory and the Lucas-Lehmer test; Rózsa Péter's recursive function theory; Claude Shannon's information theory; signal processing; data

recursive set A set whose characteristic function is a primitive recursive function, indicating that membership in the set can be decided by a computable