Advanced Proof Viewing in ProofTool

Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen's original notation, some of the problems persist. In this paper, we introduce a number of criteria for proof visualization which we have found out to be crucial for analyzing proofs. We then evaluate recent developments in tree visualization with regard to these criteria and propose the Sunburst Tree layout as a complement to the traditional tree structure. This layout constructs inferences as concentric circle arcs around the root inference, allowing the user to focus on the proof's structural content. Finally, we describe its integration into ProofTool and explain how it interacts with the Gentzen layout.Comment: In Proceedings UITP 2014, arXiv:1410.785

Verification conditions for source-level imperative programs

This paper is a systematic study of verification conditions and their use in the context of program verification. We take Hoare logic as a starting point and study in detail how a verification conditions generator can be obtained from it. The notion of program annotation is essential in this process. Weakest preconditions and the use of updates are also studied as alternative approaches to verification conditions. Our study is carried on in the context of a While language. Important extensions to this language are considered toward the end of the paper. We also briefly survey modern program verification tools and their approaches to the generation of verification conditions.Fundação para a Ciência e a Tecnologia (FCT

Surreal Numbers

The purpose of this thesis is to explore the Surreal Numbers from an elementary, con- structivist point of view, with the intention of introducing the numbers in a palatable way for a broad audience with minimal background in any specific mathematical field. Created from two recursive definitions, the Surreal Numbers form a class that contains a copy of the real numbers, transfinite ordinals, and infinitesimals, combinations of these, and in- finitely many numbers uniquely Surreal. Together with two binary operations, the surreal numbers form a field. The existence of the Surreal Numbers is proven, and the class is constructed from nothing, starting with the integers and dyadic rationals, continuing into the transfinite ordinals and the remaining real numbers, and culminating with the infinitesimals and uniquely surreal numbers. Several key concepts are proven regarding the ordering and containment properties of the numbers. The concept of a surreal continuum is introduced and demonstrated. The binary operations are explored and demonstrated, and field properties are proven, using many methods, including transfinite induction

Lessons from Formally Verified Deployed Software Systems (Extended version)

The technology of formal software verification has made spectacular advances, but how much does it actually benefit the development of practical software? Considerable disagreement remains about the practicality of building systems with mechanically-checked proofs of correctness. Is this prospect confined to a few expensive, life-critical projects, or can the idea be applied to a wide segment of the software industry? To help answer this question, the present survey examines a range of projects, in various application areas, that have produced formally verified systems and deployed them for actual use. It considers the technologies used, the form of verification applied, the results obtained, and the lessons that can be drawn for the software industry at large and its ability to benefit from formal verification techniques and tools. Note: a short version of this paper is also available, covering in detail only a subset of the considered systems. The present version is intended for full reference.Comment: arXiv admin note: text overlap with arXiv:1211.6186 by other author

Title VI Compliance Report and Implementation Plan FY 2021-2022

https://digitalcommons.memphis.edu/govpubs-tn-department-commerce-insurance-tital-vi-implementation-report/1004/thumbnail.jp

Title VI Compliance Report and Implementation Plan FY2020-2021

https://digitalcommons.memphis.edu/govpubs-tn-department-commerce-insurance-tital-vi-implementation-report/1000/thumbnail.jp

Ingénierie de modèle pour la sécurité des systèmes critiques ferroviaires

Development and application of formal languages are a long-standing challenge within the computer science domain. One particular challenge is the acceptance of industry. This thesis presents some model-based methodologies for modelling and verification of the French railway interlocking systems (RIS). The first issue is the modellization of interlocking system by coloured Petri nets (CPNs). A generic and compact modelling framework is introduced, in which the interlocking rules are modelled in a hierarchical structure while the railway layout is modelled in a geographical perspective. Then, a modelling pattern is presented, which is a parameterized model respecting the French national rules. It is a reusable solution that can be applied in different stations. Then, an event-based concept is brought into the modelling process of low-level part of RIS to better describe internal interactions of relay-based logic. The second issue is the transformation of coloured Petri nets into B machines, which can help designers on the way from analysis to implementation. Firstly, a detailed mapping methodology from non-hierarchical CPNs to abstract B machine notations is presented. Then the hierarchy and the transition priority of CPNs are successively integrated into the mapping process, in order to enrich the adaptability of the transformation. This transformation is compatible with various types of colour sets and the transformed B machines can be automatically proved by Atelier B. All these works at different levels contribute towards a global safe analysis frameworkLe développement et l’application des langages formels sont un défi à long terme pour la science informatique. Un enjeu particulier est l’acceptation par l’industrie. Cette thèse présente une approche pour la modélisation et la vérification des postes d’aiguillage français. La première question est la modélisation du système d’enclenchement par les réseaux de Petri colorés (RdPC). Un cadre de modélisation générique et compact est introduit, dans lequel les règles d’enclenchement sont modélisées dans une structure hiérarchique, tandis que les installations sont modélisées dans une perspective géographique. Ensuite, un patron de modèle est présenté. C’est un modèle paramétré qui intègre les règles nationales françaises qui peut être appliquée pour différentes gares. Puis, un concept basé sur l’événement est présenté dans le processus de modélisation des parties basses des postes d’aiguillage. La deuxième question est la transformation des RdPCs en machines B, qui va aider les concepteurs sur la route de l’analyse à application. Tout d’abord, une méthodologie détaillée, s’appuyant sur une table de correspondance, du RdPCs non-hiérarchiques vers les notations B est présentée. Ensuite, la hiérarchie et la priorité des transitions du RdPC sont successivement intégrées dans le processus de mapping, afin d’enrichir les possibilités de types de modèles en entrées de la transformation. Les machines B produites par la transformation permettent la preuve automatique intégrale par l’Atelier B. L’ensemble de ces travaux, chacun à leur niveau, contribuent à renforcer l’efficacité d’un cadre global d’analyse sécuritair