Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in...

Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion...

1993. It inspired: Logic for Computable Functions (LCF), theorem proving logic by Robin Milner. Programming Computable Functions (PCF), small theoretical...

science, Programming Computable Functions (PCF), or Programming with Computable Functions, or Programming language for Computable Functions, is a programming...

with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability...

notation, for cubic Hamiltonian graphs Logic of Computable Functions, a deductive system for computable functions, 1969 formalism by Dana Scott Logic for Computable...

answer) for numbers not in the set. A subset S {\displaystyle S} of the natural numbers is called computable if there exists a total computable function f {\displaystyle...

prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As a Logic for Computable Functions (LCF) style theorem prover...

above, and so, all computable functions are representable in Q. The conclusion of Gödel's second incompleteness theorem also holds for Q: no consistent...

classical logic, the validity of an argument depends only on its form, not on its meaning. In CoL, validity means being always computable. More generally...

of computable functions. It states that a function on the natural numbers can be calculated by an effective method if and only if it is computable by...

Standard ML is a modern dialect of ML, the language used in the Logic for Computable Functions (LCF) theorem-proving project. It is distinctive among widely...

recursive functions that are also total functions. The importance of primitive recursive functions lies in the fact that most computable functions that are...

recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines...

computable functions, the set { ⟨ x , y , z ⟩ ∣ ϕ x ( y ) = z } {\displaystyle \{\left\langle x,y,z\right\rangle \mid \phi _{x}(y)=z\}} is computably...

required function h. As in the sketch of the concept, given any total computable binary function f, the following partial function g is also computable by some...

the recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel...

usual for such a proof, computable means computable by any model of computation that is Turing complete. In fact computability can itself be defined via...

also called computability theory, studies the properties of computable functions and the Turing degrees, which divide the uncomputable functions into sets...

fact, both the functions Σ(n) and S(n) eventually become larger than any computable function. This has implications in computability theory, the halting...

In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can...

level text; most of Chapter XIII Computable functions is on Turing machine proofs of computability of recursive functions, etc. Knuth, Donald E. (1973)....

could compute the same class of computable functions. Church's thesis holds that this class of functions exhausts all the number-theoretic functions that...

consequence Truth value Computability theory – branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees...

In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional...

a Turing machine. Hypercomputers compute functions that a Turing machine cannot and which are, hence, not computable in the Church–Turing sense. Technically...

up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application...

membership functions. Execute all applicable rules in the rulebase to compute the fuzzy output functions. De-fuzzify the fuzzy output functions to get "crisp"...

intuitive notion of "effectively calculable" is captured by the functions computable by a Turing machine (or equivalently, by those expressible in the...

In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit...