Cette thèse s’intéresse à la sémantique dénotationnelle (en théorie desmodèles et en théorie des jeux) de quatre langages de programmation logique: - LP, le plus restrictif de tous, - DLP, une extension de LP aux disjonctions, - LPN, une extension de LP aux négations, et - DLPN, qui inclut les deux.Ce manuscrit apporte trois contributions principales:(1) Un cadre abstrait pour la sémantique de la programmation logique yest défini, et toutes les approches sémantiques que nous étudions par lasuite prennent place dans ce cadre.Nous définissons la notion générale d'espace de valeurs de vérité commeune structure algébrique spécifique, satisfaisant un certain ensembled'axiomes. Les booléens forment l'exemple canonique d'un tel espace,mais nous devons étudier des cas plus généraux si nous voulonsconsidérer la "négation par l'échec". Pour cela, nous définissons etétudions une famille infinie d'espaces, paramétrée par un ordinal.(2) Une sémantique des jeux pour LP a été définie en 1986, et son étudea été approfondie en 1998. Elle a ensuite été étendue au cas desprogrammes LPN en 2005.Ici nous développons en détails une sémantique pour les programmes DLP.Nous prouvons qu'elle est correcte et complète par rapport aux modèlesminimaux de Minker.(3) Nous définissons un opérateur sémantique qui, étant donnée une sémantique abstraite d'un langage non disjonctif, la transforme en une sémantique disjonctive associée.La correction de cette transformation découle du fait qu'elle conserveles équivalences de sémantiques.Nous en présentons ensuite quelques applications qui permettent, entre autres, d'obtenir la première sémantique des jeux pour DLPN. / In this thesis, we study denotational semantics (model-theoretic andgame-theoretic) of four logic programming languages:- LP which is the most restrictive one;- DLP which extends LP by allowing disjunctions;- LPN which extends LP by allowing negations; and- DLPN which allows both.The three main contributions of this dissertation can be summarized as follows:(1) An abstract framework for logic programming semantics is definedand all semantic approaches that we study are placed within this framework.We define the general notion of a truth value space as an appropriate algebraicstructure that satisfies a set of axioms.The booleans form the canonical example of such a space, but we need toconsider much more general ones when dealing with negation-as-failure. Forthis we define and study an infinite family of spaces, parametrized over anordinal number.(2) A game semantics for LP was defined in 1986 and further studied in 1998.Then in 2005 it was extended for the case of LPN programs.Here a game semantics for DLP programs is developed in full detail; we provethat it is sound and complete with respect to the standard, minimal modelssemantics of Minker.(3) We define a semantic operator which transforms any given abstractsemantics of a non-disjunctive language to a semantics of the"corresponding" disjunctive one. We exhibit the correctness of thistransformation by proving that it preserves equivalences of semantics,and we present some applications of it, obtaining new game semantics forDLPN, among others.

Prosoft é um grupo de pesquisa do Instituto de Informática da UFRGS, desenvolvido pelo grupo de pesquisa homônimo e coordenado pelo Professor Daltro José Nunes. O objetivo do projeto é desenvolver um ambiente de desenvolvimento de software completo, o Ambiente Prosoft, que é baseado nos conceitos de Modelos, Cálculo Lambda, Tipos Abstratos de Dados e Orientação a Objetos. Um dos componentes do Ambiente Prosoft é sua linguagem de especificação algébrica: o Prosoft Algébrico. Apesar de ser base e tema de diversos trabalhos no grupo de pesquisa Prosoft, o Prosoft Algébrico não tem sua semântica devidamente definida. Os trabalhos desenvolvidos até agora foram baseados em noções operacionais, e apresentam diferentes interpretações do Prosoft Algébrico. Esta dissertação apresenta uma especificação de semântica denotacional para o Prosoft Algébrico, compreendendo, entre outras características, sua primitiva de comunicação entre tipos de dados, chamada ICS, e sua notação gráfica para representação de instanciação de tipos abstratos de dados. Essa dissertação apresenta também um estudo sobre prototipação semântica usando a linguagem de programação Haskell. O conceito de Literate Programming e a proximidade entre Cálculo Lambda e Haskell foram cruciais no rápido desenvolvimento de uma implementação protótipo do Prosoft Algébrico, baseada na sua semântica especificada. As principais contribuições dessa dissertação incluem: uma interpretação precisa e sem ambiguidades do Prosoft Algébrico, através da especificação da sua semântica; a definição de semântica para a ICS, um conceito único (até o limite do nosso conhecimento) que fornece um mecanismo de passagem de mensagens entre tipos de dados algébricos; uma implementação protótipo do Prosoft Algébrico, que pode realmente ser utilizada para experimentar e testar a definição da linguagem e a especificação da semântica do Prosoft Algébrico; resultados sobre prototipação semântica de especificações tanto de semântica denotacional quanto de semântica operacional usando a linguagem de programação Haskell para desenvolvimento rápido de protótipos de linguagens baseados na sua semântica. Como grande parte do desenvolvimento do Ambiente Prosoft é realizado através de projetos de cooperação internacional e essa dissertação irá influenciar fortemente o seu desenvolvimento futuro, o texto foi escrito em inglês para facilitar a troca de informação entre o grupo Prosoft e seus parceiros estrangeiros. / Prosoft is a research project at Instituto de Informática da UFRGS, developed by the research group with the same name and coordinated by Professor Daltro José Nunes. The project’s goal is to develop a full software development environment, the Prosoft Environment, based on the concepts of Models, Lambda Calculus, Abstract Data Types and Object orientation. One of the components of the Prosoft Environment is its algebraic specification language: Algebraic Prosoft. Although being the basis and theme of several works in the Prosoft research group, Algebraic Prosoft doesn’t have its semantics properly defined. Works done up to now were based on operational notions and presented different interpretations of Algebraic Prosoft. This thesis presents a denotational semantics specification for Algebraic Prosoft, comprising, among other features, its “inter-data type” communication primitive, called ICS, and its graphical notation for representing instantiations of abstract data types. This thesis also presents a study of semantic prototyping using the Haskell programming language. The concept of Literate Programing and the proximity between lambda calculus and Haskell were crucial to the rapid development of a prototype implementation of Algebraic Prosoft, based on its specified semantics. This thesis’ main contributions include: a precise and unambiguous interpretation of Algebraic Prosoft, through a semantics specification; the definition of semantics to the ICS, a unique (to the best of our knowledge) concept that provides a messagepassing mechanism between algebraic data types; a prototype implementation of Algebraic Prosoft, which can actually be used to experiment and test the Algebraic Prosoft language definition and semantics specification; results regarding semantics prototyping of both denotational and operational semantics specifications using the Haskell programming language for rapid development of semantics-based prototypes of languages. Since a large portion of Prosoft Environment’s development is done through international cooperation projects and this thesis will strongly influence its future development, the text was written in English in order to facilitate the information exchange between the Prosoft research group and its foreign partners.

Cette thèse est une étude de la géométrie de l'interaction dans le facteur hyperfini (GdI5), introduite par Jean-Yves Girard, et de ses liens avec les constructions plus anciennes. Nous commençons par montrer comment obtenir des adjonctions purement géométriques comme une identité entre des ensembles de cycles apparaissant entre des graphes. Il est alors possible, en choisissant une fonction qui mesure les cycles, d'obtenir une adjonction numérique. Nous montrons ensuite comment construire, sur la base d'une adjonction numérique, une géométrie de l'interaction pour la logique linéaire multiplicative additive où les preuves sont interprétées par des graphes. Nous expliquons également comment cette construction permet de définir une sémantique dénotationnelle de MALL, et une notion de vérité. Nous étudions finalement une généralisation de ce cadre afin d'interpréter les exponentielles et le second ordre. Les constructions sur les graphes étant paramétrées par une fonction de mesure des cycles, nous entreprenons ensuite l'étude de deux cas particuliers. Le premier s'avère être une version combinatoire de la GdI5, et nous obtenons donc une interprétation géométrique de l'orthogonalité basée sur le déterminant de Fuglede-Kadison. Le second cas particulier est une version combinatoire des constructions plus anciennes de la géométrie de l'interaction, où l'orthogonalité est basée sur la nilpotence. Ceci permet donc de comprendre le lien entre les différentes versions de la géométrie de l'interaction, et d'en déduire que les deux adjonctions — qui semblent à première vue si différentes — sont des conséquences d'une même identité géométrique. / This work is a study of the geometry of interaction in the hyperfinite factor introduced by Jean-Yves Girard, and of its relations with ancient constructions. We start by showing how to obtain purely geometrical adjunctions as an identity between sets of cycles appearing between graphs. It is then possible, by chosing a function that measures those cycles, to obtain a numerical adjunction. We then show how to construct, on the basis of such a numerical adjunction, a geometry of interaction for multiplicative additive linear logic where proofs are interpreted as graphs. We also explain how to define from this construction a denotational semantics for MALL, and a notion of truth. We extend this setting in order to deal with exponential connectives and show a full soundness result for a variant of elementary linear logic (ELL). Since the constructions on graphs we define are parametrized by a function that measures cycles, we then focus our study to two particular cases. The first case turns out to be a combinatorial version of GoI5, and we thus obtain a geometrical caracterisation of its orthogonality which is based on Fuglede-Kadison determinant. The second particular case we study will giveus a refined version of older constructions of geometry of interaction, where orthogonality is based on nilpotency. This allows us to show how these two versions of GoI, which seem quite different, are related and understand that the respective adjunctions are both consequences of a unique geometrical property. In the last part, we study the notion of subjective truth.

La sémantique des jeux est une sémantique dénotationnelle centrée sur l’interaction : preuves et programmes y sont représentés par des stratégies modélisant, par le flot d’exécution, leur manière de réagir à leur environnement. Malgré cette présentation intensionnelle, les sémantiques de jeux ne suffisent pas à capturer certaines informations calculatoires annexes au flot d’exécution telles que, par exemple, la production de témoins en logique du premier ordre ou la consommation de ressources dans les langages de programmation. Dans cette thèse nous proposons un enrichissement du modèle des jeux concurrent à base de structures d’événements permettant de garder trace de ces informations.Nous construisons d’abord un modèle de jeux concurrent dans lequel les coups joueurs d’une stratégie sont annotés par les termes d’une théorie (in)équationnelle. Cette théorie est un paramètre de notre modèle et les annotations permettent de refléter de manière compacte des informations d’exécution n’ayant pas d’influence sur le flot d’exécution. Nous montrons que le modèle ainsi construit préserve la structure catégorique compacte fermée du modèle sans annotation.Nous explorons ensuite l’expressivité de notre modèle et présentons deux interprétations nouvelles en sémantique des preuves et des programmes : l’une interprétant les preuves de la logique classique du premier ordre par des stratégies concurrentes avec échange de témoins, donnant une version compositionnelle au théorème de Herbrand ; l’autre permettant de refléter les aspects quantitatifs liés à la consommation de ressources telles que le temps, dans l’exécution de programmes concurrents d’ordre supérieur avec mémoire partagée. / This thesis presents a general framework for enriching causal concurrent games model with annotations. These annotations can be viewed as meta-data on strategies: they are modified throughout interactions but do not affect their general flow of control. These data can be of various nature, in particular our enrichment is parametrised over any multi-sorted equational theory and can also reflect structure upon these data such as a partial order. From a semantics point of view, this construction is motivated by problems from both logic and programming languages: On the logic side, the annotated games model specialised to first-order terms enables us to give a novel interpretation of first-order classical proofs as concurrent strategies carrying first-order witnesses. In particular this answer the question of giving a compositional version to Herbrand’s theorem while avoiding the usual proof sequentialization of other denotational approaches. On the programming language side, annotations on games offer intrinsic quantitative models. We show that those can be used to provide denotational semantics for resource consumption analysis of concurrent higher order programming language with shared memory.These enrichments, strongly connected to the causal structure of concurrent games, give an argument in favor of a causal meaning of computations.

A fin de diseñar e implementar lenguajes de programación que tengan en cuenta el paradigma borroso modificaremos el lambda cálculo clásico, adjuntando a cada término un grado, y redefiniendo la beta-reducción, obteniendo que para que el nuevo cálculo verifique la propiedad de Church-Rosser la transmisión de los grados debe hacerse por medio de una función que sea una t-norma o s-conorma. Utilizando esta nueva herramienta diseñamos un lenguaje no determinista que satisface los requerimientos de la programación con datos borrosos. / With the aim of designing and implementing programming languages that take into account the fuzzy paradigm we will modify the classical lambda calculus by adding a degree to each term and by redefining the b-reduction. Thus, for the new calculus to verify the Church-Rosser property, the degree computed with can be made through a function that is a t-norm or an s-conorm. With this new tool we design a nondeterminist language that satisfies fuzzy dataprogramming requirements, and an example of its behaviour is shown.

Enforcing security policies to distributed systems is difficult, in particular, when a system contains untrusted components. We designed AspectKE*, a distributed AOP language based on a tuple space, to tackle this issue. In AspectKE*, aspects can enforce access control policies that depend on future behavior of running processes. One of the key language features is the predicates and functions that extract results of static program analysis, which are useful for defining security aspects that have to know about future behavior of a program. AspectKE* also provides a novel variable binding mechanism for pointcuts, so that pointcuts can uniformly specify join points based on both static and dynamic information about the program. Our implementation strategy performs fundamental static analysis at load-time, so as to retain runtime overheads minimal. We implemented a compiler for AspectKE*, and demonstrate usefulness of AspectKE* through a security aspect for a distributed chat system.