and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to...

Primitive recursive functions form a strict subset of those general recursive functions that are also total functions. The importance of primitive recursive functions...

Recursive function may refer to: Recursive function (programming), a function which references itself General recursive function, a computable partial...

acceptable definition of a computable function defines also the same functions. General recursive functions are partial functions from integers to integers that...

function is generally simply called a function. In computability theory, a general recursive function is a partial function from the integers to the integers;...

and general recursive functions. Although these four are of a very different nature, they provide exactly the same class of computable functions, and...

Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions. Suppose that R(y, x1, ..., xk) is a fixed...

The special case of tail-recursive calls, when a function calls itself, may be more amenable to call elimination than general tail calls. When the language...

smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach...

and recursive rule, one can generate the set of all natural numbers. Other recursively defined mathematical objects include factorials, functions (e.g...

recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions...

Herbrand, formalized the definition of the class of general recursive functions: the smallest class of functions (with arbitrarily many arguments) that is closed...

the general recursive definition will be given below. Let A be a set and let a0 be an element of A. If ρ is a function which assigns to each function f...

probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process...

higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing...

while according to Robert I. Soare it is a total recursive (equivalently, general recursive) function. This article follows the second of these conventions...

operator (M operator), a function-building operator for General recursive function Möbius function, a multiplicative function in number theory and combinatorics...

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

tail call optimization in general (when the function called is not the same as the original function, as in tail-recursive calls) may be more difficult...

M; this means a recursive function definition cannot be written with let. The letrec construction would allow writing recursive function definitions, where...

There may also be systems for certain general recursive functions, for example a system for the Ackermann function may contain the rule A(a+, b+) → A(a...

Primitive recursive function General recursive function LOOP (programming language) – a programming language with the property that the functions it can...

statements end Do while loop Foreach While loop Primitive recursive function General recursive function Wirth, Niklaus (1973). "Preface". Systematic Programming:...

effective calculability led to a variety of proposed definitions (general recursive functions, Turing machines, λ-calculus) that later were shown to be equivalent...

computable if and only if the indicator function 1 S {\displaystyle \mathbb {1} _{S}} is computable. Every recursive language is a computable. Every finite...

and a discussion of, his proof. Kleene, Stephen C. (1936). "General Recursive Functions of Natural Numbers". Mathematische Annalen. 112 (5): 727–742...

computer science, a recursive descent parser is a kind of top-down parser built from a set of mutually recursive procedures (or a non-recursive equivalent) where...

Recursive self-improvement (RSI) is a process in which an early or weak artificial general intelligence (AGI) system enhances its own capabilities and...

arithmetic propositions involving natural numbers and any primitive recursive function, including the operations of addition, multiplication, and exponentiation...

incompleteness theorem. This work, along with Gödel's work on general recursive functions, established that there are sets of simple instructions, which...