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. Informally, a function is computable if there is an algorithm that computes...

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

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

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

if it is not computable. A subset S {\displaystyle S} of the natural numbers is computable if there exists a total computable function f {\displaystyle...

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

implementation strategies. Systems in this family follow the LCF (Logic for Computable Functions) approach as they are implemented as a library which defines...

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...

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...

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...

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

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...

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

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...

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

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...

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

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

for methods that avoid accumulating large amounts of "garbage" history. RTMs compute precisely the set of injective (one-to-one) computable functions...

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...

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

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...

together. As a result, he went on to develop the meta language for his Logic for Computable Functions, a language that would only allow the writer to construct...

Classical logic Computability logic Deontic logic Dependence logic Description logic Deviant logic Doxastic logic Epistemic logic First-order logic Formal...

problem. The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have...

In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers...