Incremental View Maintenance For Collection Programming

In the context of incremental view maintenance (IVM), delta query derivation is an essential technique for speeding up the processing of large, dynamic datasets. The goal is to generate delta queries that, given a small change in the input, can update the materialized view more efficiently than via recomputation. In this work we propose the first solution for the efficient incrementalization of positive nested relational calculus (NRC+) on bags (with integer multiplicities). More precisely, we model the cost of NRC+ operators and classify queries as efficiently incrementalizable if their delta has a strictly lower cost than full re-evaluation. Then, we identify IncNRC+; a large fragment of NRC+ that is efficiently incrementalizable and we provide a semantics-preserving translation that takes any NRC+ query to a collection of IncNRC+ queries. Furthermore, we prove that incremental maintenance for NRC+ is within the complexity class NC0 and we showcase how recursive IVM, a technique that has provided significant speedups over traditional IVM in the case of flat queries [25], can also be applied to IncNRC+.Comment: 24 pages (12 pages plus appendix

On the Extensibility of Formal Methods Tools

Modern software systems often have long lifespans over which they must continually evolve to meet new, and sometimes unforeseen, requirements. One way to effectively deal with this is by developing the system as a series of extensions. As requirements change, the system evolves through the addition of new extensions and, potentially, the removal of existing extensions. In order for this kind of development process to thrive, it is necessary that the system have a high level of extensibility. Extensibility is the capability of a system to support the gradual addition of new, unplanned functionalities. This dissertation investigates extensibility of software systems and focuses on a particular class of software: formal methods tools. The approach is broad in scope. Extensibility of systems is addressed in terms of design, analysis and improvement, which are carried out in terms of source code and software architecture. For additional perspective, extensibility is also considered in the context of formal modelling. The work carried out in this dissertation led to the development of various extensions to the Overture tool supporting the Vienna Development Method, including a new proof obligation generator and integration with theorem provers. Additionally, the extensibility of Overture itself was also improved and it now better supports the development and integration of various kinds of extensions. Finally, extensibility techniques have been applied to formal modelling, leading to an extensible architectural style for formal models

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

Linear Time Logics - A Coalgebraic Perspective

We describe a general approach to deriving linear time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching behaviour and linear behaviour. Concretely, we define logics whose syntax is determined by the choice of linear behaviour and whose domain of truth values is determined by the choice of branching, and we provide two equivalent semantics for them: a step-wise semantics amenable to automata-based verification, and a path-based semantics akin to those of standard linear time logics. We also provide a semantic characterisation of the associated notion of logical equivalence, and relate it to previously-defined maximal trace semantics for such systems. Instances of our logics support reasoning about the possibility, likelihood or minimal cost of exhibiting a given linear time property. We conclude with a generalisation of the logics, dual in spirit to logics with discounting, which increases their practical appeal in the context of resource-aware computation by incorporating a notion of offsetting.Comment: Major revision of previous version: Sections 4 and 5 generalise the results in the previous version, with new proofs; Section 6 contains new result

Unifying Theories of Logics with Undefinedness

A relational approach to the question of how different logics relate formally is described. We consider three three-valued logics, as well as classical and semi-classical logic. A fundamental representation of three-valued predicates is developed in the Unifying Theories of Programming (UTP) framework of Hoare and He. On this foundation, the five logics are encoded semantically as UTP theories. Several fundamental relationships are revealed using theory linking mechanisms, which corroborate results found in the literature, and which have direct applicability to the sound mixing of logics in order to prove facts. The initial development of the fundamental three-valued predicate model, on which the theories are based, is then applied to the novel systems-of-systems specification language CML, in order to reveal proof obligations which bridge a gap that exists between the semantics of CML and the existing semantics of one of its sub-languages, VDM. Finally, a detailed account is given of an envisioned model theory for our proposed structuring, which aims to lift the sentences of the five logics encoded to the second order, allowing them to range over elements of existing UTP theories of computation, such as designs and CSP processes. We explain how this would form a complete treatment of logic interplay that is expressed entirely inside UTP

Die Integration von Verifikation und Test in Übersetzungssysteme

In dieser Arbeit wird die Architektur für einen Compiler vorgestellt, der die Korrektheit der übersetzten Quellen als Teil des Übersetzungsvorgangs überprüfen kann. Dabei soll es möglich sein, verschiedene Methoden, wie etwa formaler Test und formaler Beweis, einzusetzen, um die Korrektheit nachzuweisen. Ein vollautomatischer Nachweis ist sehr aufwendig und häufig auch gar nicht möglich. Es ist also nicht praktikabel, aus Spezifikation und Programm die Korrektheit automatisch abzuleiten. Wir erweitern daher die Sprache um Korrektheitsnachweise (justifications), die der Benutzer in den Quelltext einfügen muß ("literate justification"). Je nach gewählter Methode muß der Benutzer den Korrektheitsnachweis mehr oder weniger genau ausführen. Durch die Einführung der Korrektheitsnachweise muß der Übersetzer Beweise nur noch überprüfen anstatt sie automatisch abzuleiten. Die Überprüfung der Korrektheitsnachweise kann in den Übersetzer integriert werden oder an ein externes Werkzeug delegiert werden. Ein externes Werkzeug erlaubt die Einbindung bereits existierender Werkzeuge, aber auch eine Neuentwicklung eigener Werkzeuge ist möglich. Wir zeigen am Beispiel eines taktischen Theorembeweisers, daß eine Eigenentwicklung nicht unbedingt aufwendiger ist als die Anpassung eines vorhandenen Werkzeugs. Um Tests während der Übersetzung durchführen zu können, muß ein Interpreter zur Verfügung stehen. Die Ausführung ungetesteten Codes birgt allerdings auch Sicherheitsprobleme. Wir diskutieren verschiedene Möglichkeiten, mit diesem Problem umzugehen. Der Korrektheit einer Übersetzungseinheit entspricht in der Semantik die Konsistenz einer algebraischen Spezifikation. Wir betrachten zwei Beweismethoden: zum einen durch Konstruktion eines Modells und zum andern durch Nachweis einer korrektheitserhaltenden Relation. Die Beweisverpflichtungen ergeben sich zunächst aus der Beweismethode, außerdem werden Beweisverpflichtungen eingeführt, um die Korrektheit von zusammengesetzten (modularen) Programmen zuzusichern. Die in dieser Arbeit beschriebene Architektur ist prototypisch implementiert worden. Dazu wurde das Opal-System um Elemente zur Spezifikation und zur Beschreibung von Korektheitsnachweisen erweitert. In der Arbeit werden einige kurze Beispiele vorgeführt. Der Opal/J-Prototyp ist seit Version 2.3e Teil der Opal-Distribution.In this thesis we present a compiler architecture that enables the compiler to check the correctness of the source code as part of the compilation process. It allows to perform these correctness checks with different methods, in particular formal testing and formal proof. A fully automated check is very expensive and often impossible. Hence, it is not feasible to check correctness automatically with the help of specification and implementation. We extend the programming language by (correctness) justifications that the user must insert into the source code ("literate justification"). Depending on the chosen justification method the user must work out the justification in more or less detail. The introduction of justifications changes the compiler's task from deriving a correctness proof by itself to checking a correctness proof provided by the user. The correctness check for justifications can be integrated into the compiler or delegated to an external tool. An external tool allows the integration of existing tools but the development of specialized tools is also possible. The example development of a specialized tactical theorem-prover shows that the development of a specialized tool is not necessarily more expensive than the adaptation of an existing tool. For test execution during the compilation an interpreter must be available. The execution of untested code causes security risks. We discuss different possibilities to deal with this problem. The correctnessof a compilation unit corresponds to the consistency of an algebraic specification. We study two proof methods: either by construction of a model or by establishing a correctness-preserving relation. The proofo bligations result from the proof method, in addition proof obligations arei ntroduced to ensure the correctness of modular programs. The compiler architecture described in this thesis has been prototypically implemented. The Opal system has been extended with language elements to denote specifications and (correctness) justifications. The thesis presents some short examples. The Opal/J prototype is part of the Opal distribution since version 2.3e