arXiv subjects

Simon Foster

Publications and source records attributed to Simon Foster.

31 records · Page 2Linked to original sources

arXiv2020

Unifying Semantic Foundations for Automated Verification Tools in Isabelle/UTP

The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration relies on unified semantic foundations for the various notations, and co-ordination of a variety of automated verification tools. The contribution of this paper is Isabelle/UTP, an implementation of Hoare and He's Unifying Theories of Programming, a framework for unification of formal semantics. Isabelle/UTP permits the mechanisation of computational theories for diverse paradigms, and their use in constructing formalised semantic models. These can be further applied in the development of verification tools, harnessing Isabelle's proof automation facilities. Several layers of mathematical foundations are developed, including lenses to model variables and state spaces as algebraic objects, alphabetised predicates and relations to model programs, including algebraic and axiomatic semantics, proof tools for Hoare logic and refinement calculus, and UTP theories to encode computational paradigms.

cs.LO↗

arXiv2020

Towards Deductive Verification of Control Algorithms for Autonomous Marine Vehicles

The use of autonomous vehicles in real-world applications is often precluded by the difficulty of providing safety guarantees for their complex controllers. The simulation-based testing of these controllers cannot deliver sufficient safety guarantees, and the use of formal verification is very challenging due to the hybrid nature of the autonomous vehicles. Our work-in-progress paper introduces a formal verification approach that addresses this challenge by integrating the numerical computation of such a system (in GNU/Octave) with its hybrid system verification by means of a proof assistant (Isabelle). To show the effectiveness of our approach, we use it to verify differential invariants of an Autonomous Marine Vehicle with a controller switching between multiple modes.

cs.SE↗

arXiv2019

New Opportunities for Integrated Formal Methods

Formal methods have provided approaches for investigating software engineering fundamentals and also have high potential to improve current practices in dependability assurance. In this article, we summarise known strengths and weaknesses of formal methods. From the perspective of the assurance of robots and autonomous systems (RAS), we highlight new opportunities for integrated formal methods and identify threats to the adoption of such methods. Based on these opportunities and threats, we develop an agenda for fundamental and empirical research on integrated formal methods and for successful transfer of validated research to RAS assurance. Furthermore, we outline our expectations on useful outcomes of such an agenda.

cs.SE↗

arXiv2019

Differential Hoare Logics and Refinement Calculi for Hybrid Systems with Isabelle/HOL

We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification conditions at this level. Lenses capture hybrid program stores in a generic algebraic way. The approach has been formalised with the Isabelle/HOL proof assistant. A number of examples explains the workflow with the resulting verification components.

cs.LO↗

arXiv2019

Unifying Theories of Reactive Design Contracts

Design-by-contract is an important technique for model-based design in which a composite system is specified by a collection of contracts that specify the behavioural assumptions and guarantees of each component. In this paper, we describe a unifying theory for reactive design contracts that provides the basis for modelling and verification of reactive systems. We provide a language for expression and composition of contracts that is supported by a rich calculational theory. In contrast with other semantic models in the literature, our theory of contracts allow us to specify both the evolution of state variables and the permissible interactions with the environment. Moreover, our model of interaction is abstract, and supports, for instance, discrete time, continuous time, and hybrid computational models. Being based in Unifying Theories of Programming (UTP), our theory can be composed with further computational theories to support semantics for multi-paradigm languages. Practical reasoning support is provided via our proof framework, Isabelle/UTP, including a proof tactic that reduces a conjecture about a reactive program to three predicates, symbolically characterising its assumptions and guarantees about intermediate and final observations. This allows us to verify programs with a large or infinite state space. Our work advances the state-of-the-art in semantics for reactive languages, description of their contractual specifications, and compositional verification.

cs.LO↗

arXiv2019

Mechanised Assurance Cases with Integrated Formal Methods in Isabelle

Assurance cases are often required as a means to certify a critical system. Use of formal methods in assurance can improve automation, and overcome problems with ambiguity, faulty reasoning, and inadequate evidentiary support. However, assurance cases can rarely be fully formalised, as the use of formal methods is contingent on models validated by informal processes. Consequently, we need assurance techniques that support both formal and informal artifacts, with explicated inferential links and assumptions that can be checked by evaluation. Our contribution is a mechanical framework for developing assurance cases with integrated formal methods based in the Isabelle system. We demonstrate an embedding of the Structured Assurance Case Meta-model (SACM) using Isabelle/DOF, and show how this can be linked to formal analysis techniques originating from our verification framework, Isabelle/UTP. We validate our approach by mechanising a fragment of the Tokeneer security case, with evidence supplied by formal verification.

cs.LO↗

arXiv2018

Automating Verification of State Machines with Reactive Designs and Isabelle/UTP

State-machine based notations are ubiquitous in the description of component systems, particularly in the robotic domain. To ensure these systems are safe and predictable, formal verification techniques are important, and can be cost-effective if they are both automated and scalable. In this paper, we present a verification approach for a diagrammatic state machine language that utilises theorem proving and a denotational semantics based on Unifying Theories of Programming (UTP). We provide the necessary theory to underpin state machines (including induction theorems for iterative processes), mechanise an action language for states and transitions, and use these to formalise the semantics. We then describe the verification approach, which supports infinite state systems, and exemplify it with a fully automated deadlock-freedom check. The work has been mechanised in our proof tool, Isabelle/UTP, and so also illustrates the use of UTP to build practical verification tools.

cs.LO↗

arXiv2018

Calculational Verification of Reactive Programs with Reactive Relations and Kleene Algebra

Reactive programs are ubiquitous in modern applications, and so verification is highly desirable. We present a verification strategy for reactive programs with a large or infinite state space utilising algebraic laws for reactive relations. We define novel operators to characterise interactions and state updates, and an associated equational theory. With this we can calculate a reactive program's denotational semantics, and thereby facilitate automated proof. Of note is our reasoning support for iterative programs with reactive invariants, which is supported by Kleene algebra. We illustrate our strategy by verifying a reactive buffer. Our laws and strategy are mechanised in Isabelle/UTP, which provides soundness guarantees, and practical verification support.

cs.LO↗

arXiv2018

Unifying Theories of Time with Generalised Reactive Processes

Hoare and He's theory of reactive processes provides a unifying foundation for the formal semantics of concurrent and reactive languages. Though highly applicable, their theory is limited to models that can express event histories as discrete sequences. In this paper, we show how their theory can be generalised by using an abstract trace algebra. We show how the algebra, notably, allows us to also consider continuous-time traces and thereby facilitate models of hybrid systems. We then use this algebra to reconstruct the theory of reactive processes in our generic setting, and prove characteristic laws for sequential and parallel processes, all of which have been mechanically verified in the Isabelle/HOL proof assistant.

cs.LO↗

arXiv2016

An automated image analysis framework for segmentation and division plane detection of single live Staphylococcus aureus cells which can operate at millisecond sampling time scales using bespoke Slimfield microscopy

Staphylococcus aureus is an important pathogen, giving rise to antimicrobial resistance in cell strains such as Methicillin Resistant S. aureus (MRSA). Here we report an image analysis framework for automated detection and image segmentation of cells in S. aureus cell clusters, and explicit identification of their cell division planes. We use a new combination of several existing analytical tools of image analysis to detect cellular and subcellular morphological features relevant to cell division from millisecond time scale sampled images of live pathogens at a detection precision of single molecules. We demonstrate this approach using a fluorescent reporter GFP fused to the protein EzrA that localises to a mid-cell plane during division and is involved in regulation of cell size and division. This image analysis framework presents a valuable platform from which to study candidate new antimicrobials which target the cell division machinery, but may also have more general application in detecting morphologically complex structures of fluorescently labelled proteins present in clusters of other types of cells.

physics.bio-ph↗

arXiv2016

Automated image segmentation and division plane detection in single live Staphylococcus aureus cells

Staphylococcus aureus is a coccal bacterium, which divides by binary fission. After division the cells remain attached giving rise to small clusters, with a characteristic 'bunch of grapes' morphology. S. aureus is an important human pathogen and this, combined with the increasing prevalence of antibiotic-resistant strains, such as Methicillin Resistant S. aureus (MRSA), make it an excellent subject for studies of new methods of antimicrobial action. Many antibiotics, such as penicillin, prevent S. aureus cell division and so an understanding of this fundamental process may pave the way to the identification of novel drugs. We present here a novel image analysis framework for automated detection and segmentation of cells in S. aureus clusters, and identification of their cell division planes. We demonstrate the technique on GFP labelled EzrA, a protein that localises to a mid-cell plane during division and is involved in regulation of cell size and division. The algorithms may have wider applicability in detecting morphologically complex structures of fluorescently-labelled proteins within cells in other cell clusters.

q-bio.SC↗

arXiv2014

Towards Verification of Constituent Systems through Automated Proof

This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state invariants and operation preconditions, which can be used to specify contractual obligations on the constituent systems of a SoS. To support verification of these obligations we have developed a proof obligation generator and theorem prover plugin for Symphony. The latter uses the Isabelle/HOL theorem prover to automatically discharge the proof obligations arising from a CML model. Our hope is that the resulting proofs can then be used to formally verify the conformance of each constituent system, which is turn would result in a dependable SoS.

cs.SE↗

arXiv2011

Dependently Typed Programming based on Automated Theorem Proving

Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting. Such integrations are essential for supporting program development in dependently typed languages. We integrate the equational theorem prover Waldmeister and test it on more than 800 proof goals from the TPTP library. In contrast to previous approaches, the reconstruction of Waldmeister proofs within Mella is quite robust and does not generate a significant overhead to proof search. Mella thus yields a template for integrating more expressive theorem provers in more sophisticated languages.

cs.PL↗