Mechanising an algebraic rely-guarantee refinement calculus

PhD ThesisDespite rely-guarantee (RG) being a well-studied program logic established in the 1980s, it was not until recently that researchers realised that rely and guarantee conditions could be treated as independent programming constructs. This recent reformulation of RG paved the way to algebraic characterisations which have helped to better understand the difficulties that arise in the practical application of this development approach. The primary focus of this thesis is to provide automated tool support for a rely-guarantee refinement calculus proposed by Hayes et. al., where rely and guarantee are defined as independent commands. Our motivation is to investigate the application of an algebraic approach to derive concrete examples using this calculus. In the course of this thesis, we locate and fix a few issues involving the refinement language, its operational semantics and preexisting proofs. Moreover, we extend the refinement calculus of Hayes et. al. to cover indexed parallel composition, non-atomic evaluation of expressions within specifications, and assignment to indexed arrays. These extensions are illustrated via concrete examples. Special attention is given to design decisions that simplify the application of the mechanised theory. For example, we leave part of the design of the expression language on the hands of the user, at the cost of the requiring the user to define the notion of undefinedness for unary and binary operators; and we also formalise a notion of indexed parallelism that is parametric on the type of the indexes, this is done deliberately to simplify the formalisation of algorithms. Additionally, we use stratification to reduce the number of cases in in simulation proofs involving the operational semantics. Finally, we also use the algebra to discuss the role of types in program derivation

Enhancing Total Correctness Proofs in Program Verification

Ph.DDOCTOR OF PHILOSOPH

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Certified Reasoning for Automated Verification

Ph.DDOCTOR OF PHILOSOPH

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.