A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints

We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Certification of nontermination proofs using strategies and nonlooping derivations

© 2014 Springer International Publishing Switzerland. The development of sophisticated termination criteria for term rewrite systems has led to powerful and complex tools that produce (non)termination proofs automatically. While many techniques to establish termination have already been formalized—thereby allowing to certify such proofs—this is not the case for nontermination. In particular, the proof checker CeTA was so far limited to (innermost) loops. In this paper we present an Isabelle/HOL formalization of an extended repertoire of nontermination techniques. First, we formalized techniques for nonlooping nontermination. Second, the available strategies include (an extended version of) forbidden patterns, which cover in particular outermost and context-sensitive rewriting. Finally, a mechanism to support partial nontermination proofs further extends the applicability of our proof checker

Automatically proving termination and memory safety for programs with pointer arithmetic

While automated verification of imperative programs has been studied intensively, proving termination of programs with explicit pointer arithmetic fully automatically was still an open problem. To close this gap, we introduce a novel abstract domain that can track allocated memory in detail. We use it to automatically construct a symbolic execution graph that over-approximates all possible runs of a program and that can be used to prove memory safety. This graph is then transformed into an integer transition system, whose termination can be proved by standard techniques. We implemented this approach in the automated termination prover AProVE and demonstrate its capability of analyzing C programs with pointer arithmetic that existing tools cannot handle

Concentration or representation : the struggle for popular sovereignty

There is a tension in the notion of popular sovereignty, and the notion of democracy associated with it, that is both older than our terms for these notions themselves and more fundamental than the apparently consensual way we tend to use them today. After a review of the competing conceptions of 'the people' that underlie two very different understandings of democracy, this article will defend what might be called a 'neo-Jacobin' commitment to popular sovereignty, understood as the formulation and imposition of a shared political will. A people's egalitarian capacity to concentrate both its collective intelligence and force, from this perspective, takes priority over concerns about how best to represent the full variety of positions and interests that differentiate and divide a community

A Type-Based Termination Criterion for Dependently-Typed Higher-Order Rewrite Systems

Full versionInternational audienceSeveral authors devised type-based termination criteria for ML-like languages allowing non-structural recursive calls. We extend these works to general rewriting and dependent types, hence providing a powerful termination criterion for the combination of rewriting and beta-reduction in the Calculus of Constructions

Contribution à l'évaluation des vulnérabilités en zone périurbaine sensible aux incendies de forêt, recours à des indicateurs socio-économiques, programme 1999

[Departement_IRSTEA]GT [TR1_IRSTEA]31 - RURAMEN / CERESThe fire as a physical risk is rather well known. The complete knowledge of the risk requires now that the vulnerability with fire is studied. Knowledge concerning this question being relatively poor, we reflected, in this report requested by the ministry for ecology, with a methodological approach of the vulnerability. Three tracks are explored: insurances, land market and socio-economy of the firms. We end to the report that the conscience of the fire hazard is very thin and that the risk generates only little consequence material. It is thus difficult to justify heavy regulations (for example Risks zonings).L'incendie en tant qu'aléa physique est assez bien connu. La connaissance complète du risque nécessite maintenant que soit étudiée la vulnérabilité au feu. Les connaissances concernant cette question étant relativement pauvre, nous avons réfléchi, dans ce rapport demandé par le ministère de l'écologie te du développement durable, à une approche méthodologique des vulnérabilité. Trois pistes sont explorées : les assurances, le marché foncier et la socio-économie des entreprises. Nous aboutissons au constat que la conscience du risque d'incendie est très ténue et que le risque ne génère que peu de conséquence matérielles. Il est donc difficile de justifier des régulations lourdes (par exemple au niveau des Plans de Prévention des Risques)

Weak βη-normalization and normalization by evaluation for System F

Abstract. A general version of the fundamental theorem for System F is presented which can be instantiated to obtain proofs of weak β- and βη-normalization and normalization by evaluation. 1 Introduction and Related Work Dependently typed lambda-calculi have been successfully used as proof languages in proof assistants like Agda [Nor07], Coq [INR07], LEGO [Pol94], and NuPrl [Ct86]. Since types may depend on values in these type theories, checking equality of types, which is crucial for type and, thus, proof checking, is non-trivial for thes

Embedding pure type systems in the lambda-Pi-calculus modulo

The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension is surprisingly expressive and, in particular, that all functional Pure Type Systems, such as the system F, or the Calculus of Constructions, can be embedded in it. And, moreover, that this embedding is conservative under termination hypothesis

Family Trees Making from Parish Records

Táto práca rozoberá obor genealógie, rôzne druhy záznamov a údaje v nich. V práci je opísaná tematika porovnávania a klasifikovania záznamov. Ďalej rozoberá návrh a implementáciu výsledného systému. Vyvinutý systém prepája osoby z matričných záznamoch do väčších rodokmeňov. Tie sú následne uložené vo forme grafovej databázy. Úspešnosť prepájania záznamov bola testovaná nad poskytnutými dátovými sadami.This work discusses the field of genealogy, different types of records and data in them. The thesis describes the topic of comparison of data and record linkage. It further it also discusses the design and implementation of the resulting system. The developed system connects people from parish records to larger pedigrees. These are then stored in the form of a graph database. The success of the interconnection of records was tested on the provided data sets.