Random Testing For Language Design

Property-based random testing can facilitate formal verification, exposing errors early on in the proving process and guiding users towards correct specifications and implementations. However, effective random testing often requires users to write custom generators for well-distributed random data satisfying complex logical predicates, a task which can be tedious and error prone. In this work, I aim to reduce the cost of property-based testing by making such generators easier to write, read and maintain. I present a domain-specific language, called Luck, in which generators are conveniently expressed by decorating predicates with lightweight annotations to control both the distribution of generated values and the amount of constraint solving that happens before each variable is instantiated. I also aim to increase the applicability of testing to formal verification by bringing advanced random testing techniques to the Coq proof assistant. I describe QuickChick, a QuickCheck clone for Coq, and improve it by incorporating ideas explored in the context of Luck to automatically derive provably correct generators for data constrained by inductive relations. Finally, I evaluate both QuickChick and Luck in a variety of complex case studies from programming languages literature, such as information-flow abstract machines and type systems for lambda calculi

Mécanismes Orientés-Objets pour l'Interopérabilité entre Systèmes de Preuve

Dedukti is a Logical Framework resulting from the combination ofdependent typing and rewriting. It can be used to encode many logicalsystems using shallow embeddings preserving their notion of reduction.These translations of logical systems in a common format are anecessary first step for exchanging proofs between systems. Thisobjective of interoperability of proof systems is the main motivationof this thesis.To achieve it, we take inspiration from the world of programminglanguages and more specifically from object-oriented languages becausethey feature advanced mechanisms for encapsulation, modularity, anddefault definitions. For this reason we start by a shallowtranslation of an object calculus to Dedukti. The most interestingpoint in this translation is the treatment of subtyping.Unfortunately, it seems very hard to incorporate logic in this objectcalculus. To proceed, object-oriented mechanisms should be restrictedto static ones which seem enough for interoperability. Such acombination of static object-oriented mechanisms and logic is alreadypresent in the FoCaLiZe environment so we propose a shallow embeddingof FoCaLiZe in Dedukti. The main difficulties arise from theintegration of FoCaLiZe automatic theorem prover Zenon and from thetranslation of FoCaLiZe functional implementation language featuringtwo constructs which have no simple counterparts in Dedukti: localpattern matching and recursion.We then demonstrate how this embedding of FoCaLiZe to Dedukti can beused in practice for achieving interoperability of proof systemsthrough FoCaLiZe, Zenon, and Dedukti. In order to avoid strengtheningto much the theory in which the final proof is expressed, we useDedukti as a meta-language for eliminating unnecessary axioms.Dedukti est un cadre logique résultant de la combinaison du typagedépendant et de la réécriture. Il permet d'encoder de nombreuxsystèmes logiques au moyen de plongements superficiels qui préserventla notion de réduction.Ces traductions de systèmes logiques dans un format commun sont unepremière étape nécessaire à l'échange de preuves entre cessystèmes. Cet objectif d'interopérabilité des systèmes de preuve estla motivation principale de cette thèse.Pour y parvenir, nous nous inspirons du monde des langages deprogrammation et plus particulièrement des langages orientés-objetparce qu'ils mettent en œuvre des mécanismes avancés d'encapsulation,de modularité et de définitions par défaut. Pour cette raison, nouscommençons par une traduction superficielle d'un calcul orienté-objeten Dedukti. L'aspect le plus intéressant de cette traduction est letraitement du sous-typage.Malheureusement, ce calcul orienté-objet ne semble pas adapté àl'incorporation de traits logiques. Afin de continuer, nous devonsrestreindre les mécanismes orientés-objet à des mécanismes statiques,plus faciles à combiner avec la logique et apparemment suffisant pournotre objectif d'interopérabilité. Une telle combinaison de mécanismesorientés-objet et de logique est présente dans l'environnementFoCaLiZe donc nous proposons un encodage superficiel de FoCaLiZe dansDedukti. Les difficultés principales proviennent de l'intégration deZenon, le prouveur automatique de théorèmes sur lequel FoCaLiZerepose, et de la traduction du langage d'implantation fonctionnel deFoCaLiZe qui présente deux constructions qui n'ont pas decorrespondance simple en Dedukti : le filtrage de motif local et larécursivité.Nous démontrons finalement comment notre encodage de FoCaLiZe dansDedukti peut servir en pratique à l'interopérabilité entre dessystèmes de preuve à l'aide de FoCaLiZe, Zenon et Dedukti. Pour éviterde trop renforcer la théorie dans laquelle la preuve finale estobtenue, nous proposons d'utiliser Dedukti en tant que méta-langagepour éliminer des axiomes superflus

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems