course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a function f by course-of-values recursion...

Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines...

and recursion on S gives primitive recursion. If we consider the order relation (N, <), we obtain complete induction, and course-of-values recursion. The...

mutual recursion is a form of recursion where two or more mathematical or computational objects, such as functions or datatypes, are defined in terms of each...

natural for reading or writing. Course-of-values recursion defines primitive recursive functions. Some forms of mutual recursion also define primitive recursive...

Look up tail recursion in Wiktionary, the free dictionary. Course-of-values recursion Recursion (computer science) Primitive recursive function Inline expansion...

course-of-values recursion are in fact primitive recursive functions. Once a Gödel numbering for a formal theory is established, each inference rule of the...

{\displaystyle f(0)\cdot f(1)\cdot \ldots \cdot f(n-1)=0} ; with course-of-values recursion each of these can be defined by a single primitive recursive function...

combinator to some general programming task may see it only as a means of implementing recursion. Many functions do not have any fixed points, for instance f :...

because the recursion eventually reaches the base case of 0. The definition may also be thought of as giving a procedure for computing the value of the function n...

branch of metamathematics that studies formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

semantics of modal logic, suggesting that objects in possible worlds have counterparts in other possible worlds. course of values recursion A principle...

functions, recursion, the self-hosting compiler, and the read–eval–print loop. The name LISP derives from "LISt Processor". Linked lists are one of Lisp's...

tail recursion" refers to the property of all Scheme implementations, that they perform tail-call optimization so as to support an indefinite number of active...

this value were to contain itself by value, it would have to be of infinite size, which is impossible. Other notations, which support recursion natively...

sense is closely related to recursion. Mathematical induction is an inference rule used in formal proofs, and is the foundation of most correctness proofs...

recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable...

start) / 2; cilk_spawn recursion(a, start, midpoint); recursion(a, midpoint, end); cilk_sync; } } void loop(int *a, int n) { recursion(a, 0, n); } The reasons...

Kleene's definition of "general recursion" (known now as mu-recursion) was used by Church in his 1935 paper An Unsolvable Problem of Elementary Number Theory...

ready derivation of it. This binomial type identity, for α = β = ⁠1/2⁠, has already been encountered in the above section on #Recursion relations.) Since...

numbers of bits in the corresponding products decrease by a constant factor at each level of recursion, so the total time for these steps at all levels of recursion...

Hensel's lemma, which uses the recursion from Newton's method on the p-adic numbers. Because of the more stable behavior of addition and multiplication in...

-> a -- Using recursion (with the "ifthenelse" expression) factorial n = if n < 2 then 1 else n * factorial (n - 1) -- Using recursion (with pattern matching)...

some large integer m. Use that as an approximation for the value of Hm+x. Then use the recursion relation Hn = Hn−1 + 1/n backwards m times, to unwind it...

these series from elementary recursion relations derived from the differential equation. Being defined as fractions of entire functions, the other trigonometric...

there is a simple recursion relating the cases n + 2 and n allowing to compute, e.g., the three-dimensional Fourier transform of a radial function from...

transfinite recursion. The Cantor normal form provides a standardized way of writing ordinals. It uniquely represents each ordinal as a finite sum of ordinal...

stack space is severely constrained (e.g. Microcontrollers). Moving the recursion into a data structure (either a stack or a queue) prevents a stack overflow...

It also is not capable of expressing recursion. The addition of new registers for this sort of duty was a key design goal of EDSAC 2. This example demonstrates...

(described in detail below). The result of each iteration is used as the starting values for the next. The values are checked during each iteration to see...