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Journals and Conferences
We present C-CoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) applications of such a library.
A complete and decidable Hoare-style calculus for iteration-free probabilistic sequential programs is presented using a state logic with truthfunctional propositional (not arithmetical) connectives.
This paper describes a computer-assisted non-existence proof of 9-input sorting networks consisting of 24 comparators, hence showing that the 25-comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that the 29-comparator network found by Waksman in 1969 is optimal when sorting 10 inputs. This closes the two smallest open… (More)
We have finished a constructive formalization in the theorem prover Coq of the Fundamental Theorem of Calculus, which states that differentiation and integration are inverse processes. In this formalization, we have closely followed Bishop’s work (). In this paper, we describe the formalization in some detail, focusing on how some of Bishop’s original… (More)
Previous work identifying depth-optimal n-channel sorting networks for 9 ≤ n ≤ 16 is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper revisits the problem of generating two-layer prefixes modulo symmetries. An improved notion of symmetry is… (More)
The technique of reflection is a way to automate proof construction in type theoretical proof assistants. Reflection is based on the definition of a type of syntactic expressions that gets interpreted in the domain of discourse. By allowing the interpretation function to be partial or even a relation one gets a more general method known as “partial… (More)
We give a formal account of stream-based, service-centered calculus (SSCC), a calculus for modelling service-based systems, suitable to describe both service composition (orchestration) and the protocols that services follow when invoked (conversation). The calculus includes primitives for defining and invoking services, for isolating conversations (called… (More)
It is well known that mathematical proofs often contain (abstract) algorithms, but although these algorithms can be understood by a human, it still takes a lot of time and effort to implement this algorithm on a computer; moreover, one runs the risk of making mistakes in
It is a well-known fact that algorithms are often hidden inside mathematical proofs. If these proofs are formalized inside a proof assistant, then a mechanism called extraction can generate the corresponding programs automatically. Previous work has focused on the dificulties in obtaining a program from a formalization of the Fundamental Theorem of Algebra… (More)
Active integrity constraints (AICs) are a form of integrity constraints for databases that not only identify inconsistencies, but also suggest how these can be overcome. The semantics for AICs defines different types of repairs, but deciding whether an inconsistent database can be repaired is a NPor Σ p-complete problem, depending on the type of repairs one… (More)