The growing complexity and diversity of models used for engineering dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration requires 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 semantics. 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, algebraic and axiomatic semantics, proof tools for Hoare logic and refinement calculus, and UTP theories to encode computational paradigms.

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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.

Specifying budgets and deadlines using a process algebra like CSP requires an explicit notion of time. The tock-CSP encoding embeds a rich and flexible approach for modelling discrete-time behaviours with powerful tool support. It uses an event tock, interpreted to mark passage of time. Analysis, however, has traditionally used the standard semantics of CSP, which is inadequate for reasoning about timed refinement. The most recent version of the model checker FDR provides tailored support for tock-CSP, including specific operators, but the standard semantics remains inadequate. In this paper, we characterise tock-CSP as a language in its own right, rich enough to model budgets and deadlines, and reason about Zeno behaviour. We present the first sound tailored semantic model for tock-CSP that captures timewise refinement. It is fully mechanised in Isabelle/HOL and, to enable use of FDR4 to check refinement in this novel model, we use model shifting, which is a technique that explicitly encodes refusals in traces.

Lenses are a useful algebraic structure for giving a unifying semantics to program variables in a variety of store models. They support efficient automated proof in the Isabelle/UTP verification framework. In this paper, we expand our lens library with (1) dynamic lenses, that support mutable indexed collections, such as arrays, and (2) symmetric lenses, which allow partitioning of a state space into disjoint local and global regions to support variable scopes. From this basis, we provide an enriched program model in Isabelle/UTP for collection variables and variable blocks. For the latter, we adopt an approach first used by Back and von Wright, and derive weakest precondition and Hoare calculi. We demonstrate several examples, including verification of insertion sort.