Coalgebras and Their Logics

Transition systems pervade much of computer science. This article outlines the beginnings of a general theory of specification languages for transition systems. More specifically, transition systems are generalised to coalgebras. Specification languages together with their proof systems, in the following called (logical or modal) calculi, are presented by the associated classes of algebras (e.g., classical propositional logic by Boolean algebras). Stone duality will be used to relate the logics and their coalgebraic semantics

A BDD-representation for the logic of equality and uninterpreted functions (a full version with proofs).

The logic of equality and uninterpreted functions (EUF) has been proposed for processor verification. This paper presents a new data structure called Binary Decision Diagrams for representing EUF formulas (EUF-BDDs). We define EUF-BDDs similar to BDDs, but we allow equalities between terms as labels instead of Boolean variables. We provide an approach to build a reduced ordered EUF-BDD (EUF-ROBDD) and prove that every path to a leaf is satisfiable by construction. Moreover, EUF-ROBDDs are logically equivalent representations of EUF-formulae, so they can also be used to represent state spaces in symbolic model checking with dat

Logic-based techniques for program analysis and specification synthesis

La Tesis investiga técnicas ágiles dentro del paradigma declarativo para dar solución a dos problemas: el análisis de programas y la inferencia de especificaciones a partir de programas escritos en lenguajes multiparadigma y en lenguajes imperativos con tipos, objetos, estructuras y punteros. Respecto al estado actual de la tesis, la parte de análisis de programas ya está consolidada, mientras que la parte de inferencia de especificaciones sigue en fase de desarrollo activo. La primera parte da soluciones para la ejecución de análisis de punteros especificados en Datalog. En esta parte se han desarrollado dos técnicas de ejecución de especificaciones en dicho lenguaje Datalog: una de ellas utiliza resolutores de sistemas de ecuaciones booleanas, y la otra utiliza la lógica de reescritura implementada eficientemente en el lenguaje Maude. La segunda parte desarrolla técnicas de inferencia de especificaciones a partir de programas. En esta parte se han desarrollado dos métodos de inferencia de especificaciones. El primer método se desarrolló para el lenguaje lógico-funcional Curry y permite inferir especificaciones ecuacionales mediante interpretación abstracta de los programas. El segundo método está siendo desarrollado para lenguajes imperativos realistas, y se ha aplicado a un subconjunto del lenguaje de programación C. Este método permite inferir especificaciones en forma de reglas que representan las distintas relaciones entre las propiedades que el estado de un programa satisface antes y después de su ejecución. Además, estas propiedades son expresables en términos de las abstracciones funcionales del propio programa, resultando en una especificación de muy alto nivel y, por lo tanto, de más fácil comprensión.Feliú Gabaldón, MA. (2013). Logic-based techniques for program analysis and specification synthesis [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33747TESI

Evaluation of Datalog queries and its application to the static analysis of Java code

Two approaches for evaluating Datalog programs are presented: one based on boolean equation systems, and the other based on rewriting logic. The work is presented in the context of the static analysis of Java programs specified in Datalog.Feliú Gabaldón, MA. (2010). Evaluation of Datalog queries and its application to the static analysis of Java code. http://hdl.handle.net/10251/14016Archivo delegad

Mechanising an algebraic rely-guarantee refinement calculus

PhD ThesisDespite rely-guarantee (RG) being a well-studied program logic established in the 1980s, it was not until recently that researchers realised that rely and guarantee conditions could be treated as independent programming constructs. This recent reformulation of RG paved the way to algebraic characterisations which have helped to better understand the difficulties that arise in the practical application of this development approach. The primary focus of this thesis is to provide automated tool support for a rely-guarantee refinement calculus proposed by Hayes et. al., where rely and guarantee are defined as independent commands. Our motivation is to investigate the application of an algebraic approach to derive concrete examples using this calculus. In the course of this thesis, we locate and fix a few issues involving the refinement language, its operational semantics and preexisting proofs. Moreover, we extend the refinement calculus of Hayes et. al. to cover indexed parallel composition, non-atomic evaluation of expressions within specifications, and assignment to indexed arrays. These extensions are illustrated via concrete examples. Special attention is given to design decisions that simplify the application of the mechanised theory. For example, we leave part of the design of the expression language on the hands of the user, at the cost of the requiring the user to define the notion of undefinedness for unary and binary operators; and we also formalise a notion of indexed parallelism that is parametric on the type of the indexes, this is done deliberately to simplify the formalisation of algorithms. Additionally, we use stratification to reduce the number of cases in in simulation proofs involving the operational semantics. Finally, we also use the algebra to discuss the role of types in program derivation