A new dialect of SOFL-Syntax formal semantics and tool support

Structured Object Orientated Formal Language (SOFL) is a formal method design methodology that combines data flows diagrams and predicates in order to describe processes that can be refined. This methodology creates a very versatile method of describing a system, which system properties can be proven rigorously. Data flows are grouped by ports that define from which data flows data can be consumed or on which flows data can be generated. For predicates, Logic of Partial Functions (LFP) are used; and an undefined element that is also used to indicate if a data flows do not contain any data. Over time SOFL “evolved organically” and a number of features were added: usability was the main consideration for a feature being added. For a formal language to be useful there must be no uncertainty of a specific design’s meaning. With SOFL, there is a possible contradiction between the requirement that a process's precondition must be true when the process fire, and the fire rules. This contradiction is due to the use of LPF. Semantics (the meaning) of SOFL was not always updated to keep track of the changes made to SOFL which resulted in an outdated and incomplete semantic. The incompleteness of the semantics is a significant factor motivating the work done in this dissertation. In this dissertation, a dialect of SOFL is created to define a semantic. Not all the elements of SOFL are added in order that a simpler semantic can be defined. Elements that were removed include: LPF, Classes, and Non-deterministic broadcast nodes. Semantics of the dialect is created by a two-step process: firstly, an intuitive understanding of the dialect is created, and secondly, both static and dynamic semantics are defined by means of translations. A translation is a mapping from the dialect to a formal language that describes a certain aspect of the dialect. Static semantics defines the meaning of the elements that are “fixed” in their state: SMT-LIB is used as the target language to describe the static semantics of the dialect. Dynamic semantics describes how an element in a design changes over time: the process algebra mCRL2 is used as the formal language which describes the dynamic behaviour of the dialect. The SMT-Solver Z3 and tools included in mCLR2 are used to analyse the translation of the dialect. Use of these tools allows properties that are necessary for a design to have a well defined meaning, to be proven. Properties that can be proven include: a process can fire, a process can fire an infinite number of times, and a predicate that described a property. An Eclipse plug-in is created so that translation is not required to be done manually. After a design is translated the tools Z3 and mCRL2 are run using script files and the results of the analysis are displayed on the screen. The desired properties could be proven but for a moderate size design, but as the size of the design increased the analysis of the translation could not be completed due to computational problem. Usability of the tool can be improved by not only using a textual representation of a design, but also visual representations as in SOFL. As a result, properties that are necessary for a design to have a well-defined meaning, can be proven using these tools.Dissertation (MSc)--University of Pretoria, 2018.Computer ScienceMScUnrestricte

Fixpoint Games on Continuous Lattices

Many analysis and verifications tasks, such as static program analyses and model-checking for temporal logics reduce to the solution of systems of equations over suitable lattices. Inspired by recent work on lattice-theoretic progress measures, we develop a game-theoretical approach to the solution of systems of monotone equations over lattices, where for each single equation either the least or greatest solution is taken. A simple parity game, referred to as fixpoint game, is defined that provides a correct and complete characterisation of the solution of equation systems over continuous lattices, a quite general class of lattices widely used in semantics. For powerset lattices the fixpoint game is intimately connected with classical parity games for $\mu$-calculus model-checking, whose solution can exploit as a key tool Jurdzi\'nski's small progress measures. We show how the notion of progress measure can be naturally generalised to fixpoint games over continuous lattices and we prove the existence of small progress measures. Our results lead to a constructive formulation of progress measures as (least) fixpoints. We refine this characterisation by introducing the notion of selection that allows one to constrain the plays in the parity game, enabling an effective (and possibly efficient) solution of the game, and thus of the associated verification problem. We also propose a logic for specifying the moves of the existential player that can be used to systematically derive simplified equations for efficiently computing progress measures. We discuss potential applications to the model-checking of latticed $\mu$-calculi and to the solution of fixpoint equations systems over the reals

A Sound and Complete Projection for Global Types

Multiparty session types is a typing discipline used to write specifications, known as global types, for branching and recursive message-passing systems. A necessary operation on global types is projection to abstractions of local behaviour, called local types. Typically, this is a computable partial function that given a global type and a role erases all details irrelevant to this role. Computable projection functions in the literature are either unsound or too restrictive when dealing with recursion and branching. Recent work has taken a more general approach to projection defining it as a coinductive, but not computable, relation. Our work defines a new computable projection function that is sound and complete with respect to its coinductive counterpart and, hence, equally expressive. All results have been mechanised in the Coq proof assistant

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

Heterogeneous verification of model transformations

Esta tesis trata sobre la verificación formal en el contexto de la Ingeniería Dirigida por Modelos (MDE por sus siglas en inglés). El paradigma propone un ciclo de vida de la ingeniería de software basado en una abstracción de su complejidad a través de la definición de modelos y en un proceso de construcción (semi)automático guiado por transformaciones de estos modelos. Nuestro propósito es abordar la verificación de transformaciones de modelos la cual incluye, por extensión, la verificación de sus modelos. Comenzamos analizando la literatura relacionada con la verificación de transformaciones de modelos para concluir que la heterogeneidad de las propiedades que interesa verificar y de los enfoques para hacerlo, sugiere la necesidad de utilizar diversos dominios lógicos, lo cual es la base de nuestra propuesta. En algunos casos puede ser necesario realizar una verificación heterogénea, es decir, utilizar diferentes formalismos para la verificación de cada una de las partes del problema completo. Además, es beneficioso permitir a los expertos formales elegir el dominio en el que se encuentran más capacitados para llevar a cabo una prueba formal. El principal problema reside en que el mantenimiento de múltiples representaciones formales de los elementos de MDE en diferentes dominios lógicos, puede ser costoso si no existe soporte automático o una relación formal clara entre estas representaciones. Motivados por esto, definimos un entorno unificado que permite la verificación formal transformaciones de modelos mediante el uso de métodos de verificación heterogéneos, de forma tal que es posible automatizar la traducción formal de los elementos de MDE entre dominios logicos. Nos basamos formalmente en la Teoría de Instituciones, la cual proporciona una base sólida para la representación de los elementos de MDE (a través de instituciones) sin depender de ningúningún dominio lógico específico. También proporciona una forma de especificar traducciones (a través de comorfismos) que preservan la semántica entre estos elementos y otros dominios lógicos. Nos basamos en estándares para la especificación de los elementos de MDE. De hecho, definimos una institución para la buena formación de los modelos especificada con una versión simplificada del MetaObject Facility y otra institución para transformaciones utilizando Query/View/Transformation Relations. No obstante, la idea puede ser generalizada a otros enfoques de transformación y lenguajes.Por último, demostramos la viabilidad del entorno mediante el desarrollo de un prototipo funcional soportado por el Heterogeneous Tool Set (HETS). HETS permite realizar una especificación heterogénea y provee facilidades para el monitoreo de su corrección global. Los elementos de MDE se conectan con otras lógicas ya soportadas en HETS (por ejemplo: lógica de primer orden, lógica modal, entre otras) a través del Common Algebraic Specification Language (CASL). Esta conexión se expresa teóricamente mediante comorfismos desde las instituciones de MDE a la institución subyacente en CASL. Finalmente, discutimos las principales contribuciones de la tesis. Esto deriva en futuras líneas de investigación que contribuyen a la adopción de métodos formales para la verificación en el contexto de MDE.This thesis is about formal verification in the context of the Model-Driven Engineering (MDE) paradigm. The paradigm proposes a software engineering life-cycle based on an abstraction from its complexity by defining models, and on a (semi)automatic construction process driven by model transformations. Our purpose is to address the verification of model transformations which includes, by extension, the verification of their models. We first review the literature on the verification of model transformations to conclude that the heterogeneity we find in the properties of interest to verify, and in the verification approaches, suggests the need of using different logical domains, which is the base of our proposal. In some cases it can be necessary to perform a heterogeneous verification, i.e. using different formalisms for the verification of each part of the whole problem. Moreover, it is useful to allow formal experts to choose the domain in which they are more skilled to address a formal proof. The main problem is that the maintenance of multiple formal representations of the MDE elements in different logical domains, can be expensive if there is no automated assistance or a clear formal relation between these representations. Motivated by this, we define a unified environment that allows formal verification of model transformations using heterogeneous verification approaches, in such a way that the formal translations of the MDE elements between logical domains can be automated. We formally base the environment on the Theory of Institutions, which provides a sound basis for representing MDE elements (as so called institutions) without depending on any specific logical domain. It also provides a way for specifying semantic-preserving translations (as so called comorphisms) from these elements to other logical domains. We use standards for the specification of the MDE elements. In fact, we define an institution for the well-formedness of models specified with a simplified version of the MetaObject Facility, and another institution for Query/View/Transformation Relations transformations. However, the idea can be generalized to other transformation approaches and languages. Finally, we evidence the feasibility of the environment by the development of a functional prototype supported by the Heterogeneous Tool Set (HETS). HETS supports heterogeneous specifications and provides capabilities for monitoring their overall correctness. The MDE elements are connected to the other logics already supported in HETS (e.g. first-order logic, modal logic, among others) through the Common Algebraic Specification Language (CASL). This connection is defined by means of comorphisms from the MDE institutions to the underlying institution of CASL. We carry out a final discussion of the main contributions of this thesis. This results in future research directions which contribute with the adoption of formal tools for the verification in the context of MDE