Protocols between programs and proofs

In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting “correct” programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors, but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.

A type system for access control in an object-oriented language

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

Multi-region routing

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

Generalized Extraction of Real-Time Parameters for Homogeneous Synchronous Dataflow Graphs

23rd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP 2015). 4 to 6, Mar, 2015. Turku, Finland.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. © 2010 Elsevier B.V. All rights reserved.

Theoretical and implementation aspects in the mechanization of the metatheory of programming languages

Interactive theorem provers are tools designed for the certification of formal proofs developed by means of man-machine collaboration. Formal proofs obtained in this way cover a large variety of logical theories, ranging from the branches of mainstream mathematics, to the field of software verification. The border between these two worlds is marked by results in theoretical computer science and proofs related to the metatheory of programming languages. This last field, which is an obvious application of interactive theorem proving, poses nonetheless a serious challenge to the users of such tools, due both to the particularly structured way in which these proofs are constructed, and to difficulties related to the management of notions typical of programming languages like variable binding. This thesis is composed of two parts, discussing our experience in the development of the Matita interactive theorem prover and its use in the mechanization of the metatheory of programming languages. More specifically, part I covers: - the results of our effort in providing a better framework for the development of tactics for Matita, in order to make their implementation and debugging easier, also resulting in a much clearer code; - a discussion of the implementation of two tactics, providing infrastructure for the unification of constructor forms and the inversion of inductive predicates; we point out interactions between induction and inversion and provide an advancement over the state of the art. In the second part of the thesis, we focus on aspects related to the formalization of programming languages. We describe two works of ours: - a discussion of basic issues we encountered in our formalizations of part 1A of the Poplmark challenge, where we apply the extended inversion principles we implemented for Matita; - a formalization of an algebraic logical framework, posing more complex challenges, including multiple binding and a form of hereditary substitution; this work adopts, for the encoding of binding, an extension of Masahiko Sato's canonical locally named representation we designed during our visit to the Laboratory for Foundations of Computer Science at the University of Edinburgh, under the supervision of Randy Pollack.

Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

Query Rewriting Optimisation Techniques for Ontology-Based Data Access

Ontology-Based Data Access (OBDA) permite el acceso a diferentes tipos de fuentes de datos (tradicionalmente bases de datos) usando un modelo más abstracto proporcionado por una ontología. La reescritura de consultas (query rewriting) usa una ontología para reescribir una consulta en una consulta reescrita que puede ser evaluada en la fuente de datos. Las consultas reescritas recuperan las respuestas que están implicadas por la combinación de los datos explicitamente almacenados en la fuente de datos, la consulta original y la ontología. Al trabajar sólo sobre las queries, la reescritura de consultas permite OBDA sobre cualquier fuente de datos que puede ser consultada, independientemente de las posibilidades para modificarla. Sin embargo, producir y evaluar las consultas reescritas son procesos costosos que suelen volverse más complejos conforme la expresividad y tamaño de la ontología y las consultas aumentan. En esta tesis exploramos distintas optimizaciones que peuden ser realizadas tanto en el proceso de reescritura como en las consultas reescritas para mejorar la aplicabilidad de OBDA en contextos realistas. Nuestra contribución técnica principal es un sistema de reescritura de consultas que implementa las optimizaciones presentadas en esta tesis. Estas optimizaciones son las contribuciones principales de la tesis y se pueden agrupar en tres grupos diferentes: -optimizaciones que se pueden aplicar al considerar los predicados en la ontología que no están realmente mapeados con las fuentes de datos. -optimizaciones en ingeniería que se pueden aplicar al manejar el proceso de reescritura de consultas en una forma que permite reducir la carga computacional del proceso de generación de consultas reescritas. -optimizaciones que se pueden aplicar al considerar metainformación adicional acerca de las características de la ABox. En esta tesis proporcionamos demostraciones formales acerca de la corrección y completitud de las optimizaciones propuestas, y una evaluación empírica acerca del impacto de estas optimizaciones. Como contribución adicional, parte de este enfoque empírico, proponemos un banco de pruebas (benchmark) para la evaluación de los sistemas de reescritura de consultas. Adicionalmente, proporcionamos algunas directrices para la creación y expansión de esta clase de bancos de pruebas. ABSTRACT Ontology-Based Data Access (OBDA) allows accessing different kinds of data sources (traditionally databases) using a more abstract model provided by an ontology. Query rewriting uses such ontology to rewrite a query into a rewritten query that can be evaluated on the data source. The rewritten queries retrieve the answers that are entailed by the combination of the data explicitly stored in the data source, the original query and the ontology. However, producing and evaluating the rewritten queries are both costly processes that become generally more complex as the expressiveness and size of the ontology and queries increase. In this thesis we explore several optimisations that can be performed both in the rewriting process and in the rewritten queries to improve the applicability of OBDA in real contexts. Our main technical contribution is a query rewriting system that implements the optimisations presented in this thesis. These optimisations are the core contributions of the thesis and can be grouped into three different groups: -optimisations that can be applied when considering the predicates in the ontology that are actually mapped to the data sources. -engineering optimisations that can be applied by handling the process of query rewriting in a way that permits to reduce the computational load of the query generation process. -optimisations that can be applied when considering additional metainformation about the characteristics of the ABox. In this thesis we provide formal proofs for the correctness of the proposed optimisations, and an empirical evaluation about the impact of the optimisations. As an additional contribution, part of this empirical approach, we propose a benchmark for the evaluation of query rewriting systems. We also provide some guidelines for the creation and expansion of this kind of benchmarks.

Essential mathematics:a refresher course for business and social studies

Many students starting courses in business, accounting and similar areas want to update their mathematical skills, and are seeking a suitable text; this book addresses their needs. Written in an informal style, emphasising understanding and application of techniques rather than formal proofs, it covers all the mathematics needed by entrants to BTEC, undergraduate, MBA and related professional courses. Plentiful worked examples and exercises with solutions make the book a practical self-study aid for those wishing to revise before starting their course.

Formal methods within a totally functional approach to programming

Taking functional programming to its extremities in search of simplicity still requires integration with other development (e.g. formal) methods. Induction is the key to deriving and verifying functional programs, but can be simplified through packaging proofs with functions, particularly folds, on data (structures). Totally Functional Programming avoids the complexities of interpretation by directly representing data (structures) as platonic combinators - the functions characteristic to the data. The link between the two simplifications is that platonic combinators are a kind of partially-applied fold, which means that platonic combinators inherit fold-theoretic properties, but with some apparent simplifications due to the platonic combinator representation. However, despite observable behaviour within functional programming that suggests that TFP is widely-applicable, significant work remains before TFP as such could be widely adopted.

Formal development and quantitative verification of dependable systems

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Extraction of structured programs from specification proofs

We present a method using an extended logical system for obtaining programs from specifications written in a sublanguage of CASL. These programs are “correct” in the sense that they satisfy their specifications. The technique we use is to extract programs from proofs in formal logic by techniques due to Curry and Howard. The logical calculus, however, is novel because it adds structural rules corresponding to the standard ways of modifying specifications: translating (renaming), taking unions, and hiding signatures. Although programs extracted by the Curry-Howard process can be very cumbersome, we use a number of simplifications that ensure that the programs extracted are in a language close to a standard high-level programming language. We use this to produce an executable refinement of a given specification and we then provide a method for producing a program module that maximally respects the original structure of the specification. Throughout the paper we demonstrate the technique with a simple example.

Pedagogia do esporte : organização, sistematização, aplicação e avaliação de conteúdos esportivos na educação não formal = Sport pedagogy : organization, systematization and application of sports content in non-formal education

Universidade Estadual de Campinas . Faculdade de Educação Física

Popularização do autoexame da boca: um exemplo de educação não formal - Parte II

Um dos maiores desafios das universidades, em especial das públicas, é transpor o conhecimento científico produzido entre seus muros para a população em geral. A educação não formal é uma ferramenta importante e ainda pouco utilizada pelos pesquisadores e docentes para aproximar o cotidiano do conhecimento científico. O câncer de boca atinge mais 11.000 brasileiros por ano. A despeito da alta incidência, esta patologia é ainda pouco conhecida da população em geral e de parte da classe médica e odontológica. Baseando-se nos dados epidemiológicos, em pesquisas e artigos científicos, o câncer de boca foi o tema eleito para a ação em educação e comunicação da primeira campanha nacional, de caráter não governamental, de prevenção de câncer de boca, um ótimo exemplo de como isso pode ser feito. Este trabalho se propõe a descrever a metodologia de comunicação utilizada e os resultados obtidos nesta experiência.