Related papers: Inductive types in the Calculus of Algebraic Const…
We report on an original formalization of measure and integration theory in the Coq proof assistant. We build the Lebesgue measure following a standard construction that had not yet been formalized in proof assistants based on dependent…
Fixed points are a recurring theme in computer science and are often constructed as limits of suitably seeded fixed point iterations. We present the algebra of iterative constructions (AIC) -- a purely algebraic approach to reasoning about…
It is discussed a practical possibility of a provable programming of mathematics basing on intuitionism and the dependent types feature of a programming language.The principles of constructive mathematics and provable programming are…
After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations.
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
The capture calculus is an extension of System F<: that tracks free variables of terms in their type, allowing one to represent capabilities while limiting their scope. While previous calculi had mechanized soundness proofs -- notably…
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…
Higher inductive types are inductive types that include nontrivial higher-dimensional structure, represented as identifications that are not reflexivity. While work proceeds on type theories with a computational interpretation of univalence…
Formal transformations somehow resembling the usual derivative are surprisingly common in computer science, with two notable examples being derivatives of regular expressions and derivatives of types. A newcomer to this list is the…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
We use the notion of multi-Reedy category to prove that, if $\mathcal C$ is a Reedy category, then $\Theta \mathcal C$ is also a Reedy category. This result gives a new proof that the categories $\Theta_n$ are Reedy categories. We then…
In this project, a rather complete proof-theoretical formalization of Lambek Calculus (non-associative with arbitrary extensions) has been ported from Coq proof assistent to HOL4 theorem prover, with some improvements and new theorems.…
Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their…
Proofs of Concept (PoCs) are widely adopted practices in software engineering. Despite their relevance, PoCs remain conceptually underdefined and methodologically ad hoc in both research and industry, with definitions and implementation…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…