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

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

Preface

Overview of the contents of "Foundations of Software Science and Computational Structures: Selected papers from FOSSACS 2005

A Unary Semigroup Trace Algebra

The Unifying Theories of Programming (UTP) of Hoare and He promote the unification of semantics catering for different concerns, such as, termination, data modelling, concurrency and time. Process calculi like Circus and CSP can be given semantics in the UTP using reactive designs whose traces can be abstractly specified using a monoid trace algebra. The prefix order over traces is defined in terms of the monoid operator. This order, however, is inadequate to characterise a broader family of timed process algebras whose traces are preordered instead. To accommodate these, we propose a unary semigroup trace algebra that is weaker than the monoid algebra. This structure satisfies some of the axioms of restriction semigroups and is a right P-Ehresmann semigroup. Reactive designs specified using it satisfy core laws that have been mechanised so far in Isabelle/UTP. More importantly, our results improve the support for unifying trace models in the UTP

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.Comment: 18 pages, 16th Intl. Conf. on Formal Aspects of Component Software (FACS 2018), October 2018, Pohang, South Kore

Coordination approaches and systems - part I : a strategic perspective

This is the first part of a two-part paper presenting a fundamental review and summary of research of design coordination and cooperation technologies. The theme of this review is aimed at the research conducted within the decision management aspect of design coordination. The focus is therefore on the strategies involved in making decisions and how these strategies are used to satisfy design requirements. The paper reviews research within collaborative and coordinated design, project and workflow management, and, task and organization models. The research reviewed has attempted to identify fundamental coordination mechanisms from different domains, however it is concluded that domain independent mechanisms need to be augmented with domain specific mechanisms to facilitate coordination. Part II is a review of design coordination from an operational perspective

Towards Verification of Cyber-Physical Systems with UTP and Isabelle/HOL

In this paper, we outline our vision for building verification tools for Cyber-Physical Systems based on Hoare and He’s Unifying Theories of Programming (UTP) and interactive proof technology in Isabelle/HOL. We describe our mechanisation and explain some of the design decisions that we have taken to get a convenient and smooth implementation. In particular, we describe our use of lenses to encode state. We illustrate our work with an example UTP theory and describe the implementation of three foundational theories: designs, reactive processes, and the hybrid relational calculus. We conclude by reflecting on how tools are linked by unifying theories

Hybrid Relations in Isabelle/UTP

We describe our UTP theory of hybrid relations, which extends the relational calculus with continuous variables and differential equations. This enables the use of UTP in modelling and verification of hybrid systems, supported by our mechanisation in Isabelle/UTP. The hybrid relational calculus is built upon the same foundation as the UTP’s theory of reactive processes, which is accomplished through a generalised trace algebra and a model of piecewise-continuous functions. From this foundation, we give semantics to hybrid programs, including ordinary differential equations and preemption, and show how the theory can be used to reason about sequential hybrid systems