Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were...

after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented...

Recursion theorem can refer to: The recursion theorem in set theory Kleene's recursion theorem, also called the fixed point theorem, in computability...

first incompleteness theorem Tarski's undefinability theorem Halting problem Kleene's recursion theorem Diagonalization (disambiguation) This disambiguation...

Q_{e}(x)=\varphi _{a}(x)} when e ∉ P {\displaystyle e\notin P} . By Kleene's recursion theorem, there exists e {\displaystyle e} such that φ e = Q e {\displaystyle...

Turing-complete programming language, as a direct consequence of Kleene's recursion theorem. For amusement, programmers sometimes attempt to develop the shortest...

results about undecidable sets in recursion theory. Kleene (1943) presented a proof of Gödel's incompleteness theorem using basic results of computability...

calculus Church-Rosser theorem Calculus of constructions Combinatory logic Post correspondence problem Kleene's recursion theorem Recursively enumerable...

(g42) ((lambda (x y) (+ x y)) 3 g42)). Currying Kleene's recursion theorem Partial evaluation Kleene, S. C. (1936). "General recursive functions of natural...

Kanamori–McAloon theorem (mathematical logic) Kirby–Paris theorem (proof theory) Kleene's recursion theorem (recursion theory) König's theorem (set theory...

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated...

computability theory, by applying Kleene's recursion theorem. These results are not equivalent theorems; the Knaster–Tarski theorem is a much stronger result...

yet developed in 1934. The diagonal lemma is closely related to Kleene's recursion theorem in computability theory, and their respective proofs are similar...

Gödel's incompleteness theorem marks not only a milestone in recursion theory and proof theory, but has also led to Löb's theorem in modal logic. The method...

1965, p. 115 Lucas 2021. Kleene 1952, p. 382. Rosser, "Informal Exposition of Proofs of Gödel's Theorem and Church's Theorem", reprinted in Davis 1965...

of primitive recursion as those do not provide a mechanism for "infinite loops" (undefined values). A normal form theorem due to Kleene says that for...

recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves...

machine, or λ-function, or carefully invoke recursion axioms, or at best, cleverly invoke various theorems of computability theory. But because the computability...

studied because several important results like the Kleene's recursion theorem and Rice's theorem, which were originally proven for the Gödel-numbered...

variables of a lambda expression, M, is denoted as FV(M) and is defined by recursion on the structure of the terms, as follows: FV(x) = {x}, where x is a variable...

Reprinted in The Undecidable, p. 237ff. Kleene's definition of "general recursion" (known now as mu-recursion) was used by Church in his 1935 paper An...

p {\displaystyle p} can get access to its own source code by Kleene's recursion theorem). If this eventually returns true, then this first task continues...

Darlington developed the functional language NPL. NPL was based on Kleene Recursion Equations and was first introduced in their work on program transformation...

of creating a malformed program. In computational theory, Kleene's second recursion theorem provides a form of code-is-data, by proving that a program...

sequences, and structures. recursion theorem 1.  Master theorem (analysis of algorithms) 2.  Kleene's recursion theorem recursive definition A definition...

and projection functions, and is closed under composition, primitive recursion, and the μ operator. Equivalently, computable functions can be formalized...

impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of first-order logic, a statement is universally valid if and only if it...

not converge with the least fixed point. Unfortunately, whereas Kleene's recursion theorem shows that the least fixed point is effectively computable, the...

Church and his two students Stephen Kleene and J. B. Rosser by use of Church's lambda-calculus and Gödel's recursion theory (1934). Church's paper (published...

the index of such a machine. Build a Turing machine M, using Kleene's recursion theorem, which on input 0 simulates the machine with index e running on...