409 research outputs found
Extension to UML-B Notation and Toolset
The UML-B notation has been created as an attempt to combine the success and ease of use of UML, with the verification and rigorous development capabilities of formal methods. However, the notation currently only supports a basic diagram set. To address this we have, in this project, designed and implemented a set of extensions to the UML-B notation that provide a much fuller software engineering experience, critically making UML-B more appealing to industry partners. These extensions comprise five new diagram types, which are aimed at supplying a broader range of design capabilities, such as conceptual Use-Case design and future integration with the ProB animator tool
Extended Model driven Architecture to B Method
International audienceModel Driven Architecture (MDA) design approach proposes to separate design into two stages: implementation independent stage then an implementation-dependent one. This improves the reusability, the reusability, the standability, the maintainability, etc. Here we show how MDA can be augmented using a formal refinement approach: B method. Doing so enables to gradually refine the development from the abstract specification to the executing implementation; furthermore it permits to prove the coherence between components in low levels even if they are implemented in different technologies
Invariant discovery and refinement plans for formal modelling in Event-B
The continuous growth of complex systems makes the development of correct software
increasingly challenging. In order to address this challenge, formal methods o er rigorous
mathematical techniques to model and verify the correctness of systems. Refinement
is one of these techniques. By allowing a developer to incrementally introduce design
details, refinement provides a powerful mechanism for mastering the complexities that
arise when formally modelling systems. Here the focus is on a posit-and-prove style of
refinement, where a design is developed as a series of abstract models introduced via
refinement steps. Each refinement step generates proof obligations which must be discharged
in order to verify its correctness â typically requiring a user to understand the
relationship between modelling and reasoning.
This thesis focuses on techniques to aid refinement-based formal modelling, specifically,
when a user requires guidance in order to overcome a failed refinement step. An integrated
approach has been followed: combining the complementary strengths of bottomup
theory formation, in which theories about domains are built based on basic background
information; and top-down planning, in which meta-level reasoning is used to guide the
search for correct models.
On the theory formation perspective, we developed a technique for the automatic discovery
of invariants. Refinement requires the definition of properties, called invariants,
which relate to the design. Formulating correct and meaningful invariants can be tedious
and a challenging task. A heuristic approach to the automatic discovery of invariants has
been developed building upon simulation, proof-failure analysis and automated theory
formation. This approach exploits the close interplay between modelling and reasoning
in order to provide systematic guidance in tailoring the search for invariants for a given
model.
On the planning perspective, we propose a new technique called refinement plans.
Refinement plans provide a basis for automatically generating modelling guidance when
a step fails but is close to a known pattern of refinement. This technique combines both
modelling and reasoning knowledge, and, contrary to traditional pattern techniques, allow
the analysis of failure and partial matching. Moreover, when the guidance is only partially
instantiated, and it is suitable, refinement plans provide specialised knowledge to further
tailor the theory formation process in an attempt to fully instantiate the guidance.
We also report on a series of experiments undertaken in order to evaluate the approaches
and on the implementation of both techniques into prototype tools. We believe
the techniques presented here allow the developer to focus on design decisions rather than
on analysing low-level proof failures
Event-B in the Institutional Framework: Defining a Semantics, Modularisation Constructs and Interoperability for a Specification Language
Event-B is an industrial-strength specification language for verifying
the properties of a given systemâs specification. It is supported by its
Eclipse-based IDE, Rodin, and uses the process of refinement to model
systems at different levels of abstraction. Although a mature formalism,
Event-B has a number of limitations. In this thesis, we demonstrate that
Event-B lacks formally defined modularisation constructs. Additionally,
interoperability between Event-B and other formalisms has been
achieved in an ad hoc manner. Moreover, although a formal language,
Event-B does not have a formal semantics. We address each of these
limitations in this thesis using the theory of institutions.
The theory of institutions provides a category-theoretic way of representing
a formalism. Formalisms that have been represented as institutions
gain access to an array of generic specification-building operators
that can be used to modularise specifications in a formalismindependent
manner. In the theory of institutions, there are constructs
(known as institution (co)morphisms) that provide us with the facility to
create interoperability between formalisms in a mathematically sound
way.
The main contribution of this thesis is the definition of an institution
for Event-B, EVT, which allows us to address its identified limitations.
To this end, we formally define a translational semantics from Event-
B to EVT. We show how specification-building operators can provide
a unified set of modularisation constructs for Event-B. In fact, the institutional
framework that we have incorporated Event-B into is more
accommodating to modularisation than the current state-of-the-art for
Rodin. Furthermore, we present institution morphisms that facilitate interoperability between the respective institutions for Event-B and UML.
This approach is more generic than the current approach to interoperability
for Event-B and in fact, allows access to any formalism or logic
that has already been defined as an institution. Finally, by defining
EVT, we have outlined the steps required in order to include similar
formalisms into the institutional framework. Hence, this thesis acts as a
template for defining an institution for a specification language
Diagrammatic Languages and Formal Verification : A Tool-Based Approach
The importance of software correctness has been accentuated as a growing number of safety-critical systems have been developed relying on software operating these systems. One of the more prominent methods targeting the construction of a correct program is formal verification. Formal verification identifies a correct program as a program that satisfies its specification and is free of defects. While in theory formal verification guarantees a correct implementation with respect to the specification, applying formal verification techniques in practice has shown to be difficult and expensive. In response to these challenges, various support methods and tools have been suggested for all phases from program specification to proving the derived verification conditions. This thesis concerns practical verification methods applied to diagrammatic modeling languages.
While diagrammatic languages are widely used in communicating system design (e.g., UML) and behavior (e.g., state charts), most formal verification platforms require the specification to be written in a textual specification language or in the mathematical language of an underlying logical framework. One exception is invariant-based programming, in which programs together with their specifications are drawn as invariant diagrams, a type of state transition diagram annotated with intermediate assertions (preconditions, postconditions, invariants). Even though the allowed program statesâcalled situationsâare described diagrammatically, the intermediate assertions defining a situationâs meaning in the domain of the program are still written in conventional textual form. To explore the use of diagrams in expressing the intermediate assertions of invariant diagrams, we designed a pictorial language for expressing array properties. We further developed this notation into a diagrammatic domain-specific language (DSL) and implemented it as an extension to the Why3 platform. The DSL supports expression of array properties. The language is based on Reynoldsâs interval and partition diagrams and includes a construct for mapping array intervals to logic predicates.
Automated verification of a program is attained by generating the verification conditions and proving that they are true. In practice, full proof automation is not possible except for trivial programs and verifying even simple properties can require significant effort both in specification and proof stages. An animation tool which supports run-time evaluation of the program statements and intermediate assertions given any user-defined input can support this process. In particular, an execution trace leading up to a failed assertion constitutes a refutation of a verification condition that requires immediate attention. As an extension to Socos, a verificion tool for invariant diagrams built on top of the PVS proof system, we have developed an execution model where program statements and assertions can be evaluated in a given program state. A program is represented by an abstract datatype encoding the program state, together with a small-step state transition function encoding the evaluation of a single statement. This allows the programâs runtime behavior to be formally inspected during verification. We also implement animation and interactive debugging support for Socos.
The thesis also explores visualization of system development in the context of model decomposition in Event-B. Decomposing a software system becomes increasingly critical as the system grows larger, since the workload on the theorem provers must be distributed effectively. Decomposition techniques have been suggested in several verification platforms to split the models into smaller units, each having fewer verification conditions and therefore imposing a lighter load on automatic theorem provers. In this work, we have investigated a refinement-based decomposition technique that makes the development process more resilient to change in specification and allows parallel development of sub-models by a team. As part of the research, we evaluated the technique on a small case study, a simplified version of a landing gear system verification presented by Boniol and Wiels, within the Event-B specification language.Vikten av programvaras korrekthet har accentuerats dÄ ett vÀxande antal sÀkerhetskritiska system, vilka Àr beroende av programvaran som styr dessa, har utvecklas. En av de mer framtrÀdande metoderna som riktar in sig pÄ utveckling av korrekt programvara Àr formell verifiering. Inom formell verifiering avses med ett korrekt program ett program som uppfyller sina specifikationer och som Àr fritt frÄn defekter. Medan formell verifiering teoretiskt sett kan garantera ett korrekt program med avseende pÄ specifikationerna, har tillÀmpligheten av formella verifieringsmetod visat sig i praktiken vara svÄr och dyr. Till svar pÄ dessa utmaningar har ett stort antal olika stödmetoder och automatiseringsverktyg föreslagits för samtliga faser frÄn specifikationen till bevisningen av de hÀrledda korrekthetsvillkoren. Denna avhandling behandlar praktiska verifieringsmetoder applicerade pÄ diagrambaserade modelleringssprÄk.
Medan diagrambaserade sprĂ„k ofta anvĂ€nds för kommunikation av programvarudesign (t.ex. UML) samt beteende (t.ex. tillstĂ„ndsdiagram), krĂ€ver de flesta verifieringsplattformar att specifikationen kodas medelst ett textuellt specifikationsspĂ„k eller i sprĂ„ket hos det underliggande logiska ramverket. Ett undantag Ă€r invariantbaserad programmering, inom vilken ett program tillsammans med dess specifikation ritas upp som sk. invariantdiagram, en typ av tillstĂ„ndstransitionsdiagram annoterade med mellanliggande logiska villkor (förvillkor, eftervillkor, invarianter). Ăven om de tillĂ„tna programtillstĂ„ndenâsk. situationerâbeskrivs diagrammatiskt Ă€r de logiska predikaten som beskriver en situations betydelse i programmets domĂ€n fortfarande skriven pĂ„ konventionell textuell form. För att vidare undersöka anvĂ€ndningen av diagram vid beskrivningen av mellanliggande villkor inom invariantbaserad programming, har vi konstruerat ett bildbaserat sprĂ„k för villkor över arrayer. Vi har dĂ€refter vidareutvecklat detta sprĂ„k till ett diagrambaserat domĂ€n-specifikt sprĂ„k (domain-specific language, DSL) och implementerat stöd för det i verifieringsplattformen Why3. SprĂ„ket lĂ„ter anvĂ€ndaren uttrycka egenskaper hos arrayer, och Ă€r baserat pĂ„ Reynolds intevall- och partitionsdiagram samt inbegriper en konstruktion för mappning av array-intervall till logiska predikat.
Automatisk verifiering av ett program uppnÄs genom generering av korrekthetsvillkor och Ätföljande bevisning av dessa. I praktiken kan full automatisering av bevis inte uppnÄs utom för trivial program, och Àven bevisning av enkla egenskaper kan krÀva betydande anstrÀngningar bÄde vid specifikations- och bevisfaserna. Ett animeringsverktyg som stöder exekvering av sÄvÀl programmets satser som mellanliggande villkor för godtycklig anvÀndarinput kan vara till hjÀlp i denna process. SÀrskilt ett exekveringspÄr som leder upp till ett falskt mellanliggande villkor utgör ett direkt vederlÀggande (refutation) av ett bevisvillkor, vilket krÀver omedelbar uppmÀrksamhet frÄn programmeraren. Som ett tillÀgg till Socos, ett verifieringsverktyg för invariantdiagram baserat pÄ bevissystemet PVS, har vi utvecklat en exekveringsmodell dÀr programmets satser och villkor kan evalueras i ett givet programtillstÄnd. Ett program representeras av en abstrakt datatyp för programmets tillstÄnd tillsammans med en small-step transitionsfunktion för evalueringen av en enskild programsats. Detta möjliggör att ett programs exekvering formellt kan analyseras under verifieringen. Vi har ocksÄ implementerat animation och interaktiv felsökning i Socos.
Avhandlingen undersöker ocksÄ visualisering av systemutveckling i samband med modelluppdelning inom Event-B. Uppdelning av en systemmodell blir allt mer kritisk dÄ ett systemet vÀxer sig större, emedan belastningen pÄ underliggande teorembe visare mÄste fördelas effektivt. Uppdelningstekniker har föreslagits inom mÄnga olika verifieringsplattformar för att dela in modellerna i mindre enheter, sÄ att varje enhet har fÀrre verifieringsvillkor och dÀrmed innebÀr en mindre belastning pÄ de automatiska teorembevisarna. I detta arbete har vi undersökt en refinement-baserad uppdelningsteknik som gör utvecklingsprocessen mer kapabel att hantera förÀndringar hos specifikationen och som tillÄter parallell utveckling av delmodellerna inom ett team. Som en del av forskningen har vi utvÀrderat tekniken pÄ en liten fallstudie: en förenklad modell av automationen hos ett landningsstÀll av Boniol and Wiels, uttryckt i Event-B-specifikationsprÄket
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