Automated Algebraic Reasoning for Collections and Local Variables with Lenses

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, that 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 sor

Hybrid Systems Verification with Isabelle/HOL: Simpler Syntax, Better Models, Faster Proofs

We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and domain-specific deductive and calculational support. The new store model yields clean separations and dynamic local views of variables, e.g. discrete/continuous, mutable/immutable, program/logical, and enhanced ways of manipulating them using combinators, projections and framing. This leads to more local inference rules, procedures and tactics for reasoning with invariant sets, certifying solutions of hybrid specifications or calculating derivatives with increased proof automation and scalability. The new expression model provides more user-friendly syntax, better control of name spaces and interfaces connecting the framework with real-world modelling languages.Comment: 18 pages, submitted to FM 202

Integration of Formal Proof into Unified Assurance Cases with Isabelle/SACM

Assurance cases are often required to certify critical systems. The use of formal methods in assurance can improve automation, increase confidence, and overcome errant reasoning. However, assurance cases can never be fully formalised, as the use of formal methods is contingent on models that are validated by informal processes. Consequently, assurance techniques should support both formal and informal artifacts, with explicated inferential links between them. In this paper, we contribute a formal machine-checked interactive language, called Isabelle/SACM, supporting the computer-assisted construction of assurance cases compliant with the OMG Structured Assurance Case Meta-Model. The use of Isabelle/SACM guarantees well-formedness, consistency, and traceability of assurance cases, and allows a tight integration of formal and informal evidence of various provenance. In particular, Isabelle brings a diverse range of automated verification techniques that can provide evidence. To validate our approach, we present a substantial case study based on the Tokeneer secure entry system benchmark. We embed its functional specification into Isabelle, verify its security requirements, and form a modular security case in Isabelle/SACM that combines the heterogeneous artifacts. We thus show that Isabelle is a suitable platform for critical systems assurance

Unifying Semantic Foundations for Automated Verification Tools in Isabelle/UTP

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