Unifying Theories of Logics with Undefinedness

A relational approach to the question of how different logics relate formally is described. We consider three three-valued logics, as well as classical and semi-classical logic. A fundamental representation of three-valued predicates is developed in the Unifying Theories of Programming (UTP) framework of Hoare and He. On this foundation, the five logics are encoded semantically as UTP theories. Several fundamental relationships are revealed using theory linking mechanisms, which corroborate results found in the literature, and which have direct applicability to the sound mixing of logics in order to prove facts. The initial development of the fundamental three-valued predicate model, on which the theories are based, is then applied to the novel systems-of-systems specification language CML, in order to reveal proof obligations which bridge a gap that exists between the semantics of CML and the existing semantics of one of its sub-languages, VDM. Finally, a detailed account is given of an envisioned model theory for our proposed structuring, which aims to lift the sentences of the five logics encoded to the second order, allowing them to range over elements of existing UTP theories of computation, such as designs and CSP processes. We explain how this would form a complete treatment of logic interplay that is expressed entirely inside UTP

Heterogeneous Semantics and Unifying Theories

Model-driven development is being used increasingly in the development of modern computer-based systems. In the case of cyber-physical systems (including robotics and autonomous systems) no single modelling solution is adequate to cover all aspects of a system, such as discrete control, continuous dynamics, and communication networking. Instead, a heterogeneous modelling solution must be adopted. We propose a theory engineering technique involving Isabelle/HOL and Hoare & He’s Unifying Theories of Programming. We illustrate this approach with mechanised theories for building a contractual theory of sequential programming, a theory of pointer-based programs, and the reactive theory underpinning CSP’s process algebra. Galois connections provide the mechanism for linking these theories

On the Extensibility of Formal Methods Tools

Modern software systems often have long lifespans over which they must continually evolve to meet new, and sometimes unforeseen, requirements. One way to effectively deal with this is by developing the system as a series of extensions. As requirements change, the system evolves through the addition of new extensions and, potentially, the removal of existing extensions. In order for this kind of development process to thrive, it is necessary that the system have a high level of extensibility. Extensibility is the capability of a system to support the gradual addition of new, unplanned functionalities. This dissertation investigates extensibility of software systems and focuses on a particular class of software: formal methods tools. The approach is broad in scope. Extensibility of systems is addressed in terms of design, analysis and improvement, which are carried out in terms of source code and software architecture. For additional perspective, extensibility is also considered in the context of formal modelling. The work carried out in this dissertation led to the development of various extensions to the Overture tool supporting the Vienna Development Method, including a new proof obligation generator and integration with theorem provers. Additionally, the extensibility of Overture itself was also improved and it now better supports the development and integration of various kinds of extensions. Finally, extensibility techniques have been applied to formal modelling, leading to an extensible architectural style for formal models

Unifying heterogeneous state-spaces with lenses

Most verification approaches embed a model of program state into their semantic treatment. Though a variety of heterogeneous state-space models exists,they all possess common theoretical properties one would like to capture abstractly,such as the common algebraic laws of programming. In this paper,we propose lenses as a universal state-space modelling solution. Lenses provide an abstract interface for manipulating data types through spatially-separated views. We define a lens algebra that enables their composition and comparison,and apply it to formally model variables and alphabets in Hoare and He’s Unifying Theories of Programming (UTP). The combination of lenses and relational algebra gives rise to a model for UTP in which its fundamental laws can be verified. Moreover,we illustrate how lenses can be used to model more complex state notions such as memory stores and parallel states. We provide a mechanisation in Isabelle/HOL that validates our theory,and facilitates its use in program verification

A discrete geometric model of concurrent program execution

A trace of the execution of a concurrent object-oriented program can be displayed in two-dimensions as a diagram of a non-metric finite geometry. The actions of a programs are represented by points, its objects and threads by vertical lines, its transactions by horizontal lines, its communications and resource sharing by sloping arrows, and its partial traces by rectangular figures. We prove informally that the geometry satisfies the laws of Concurrent Kleene Algebra (CKA); these describe and justify the interleaved implementation of multithreaded programs on computer systems with a lesser number of concurrent processors. More familiar forms of semantics (e.g., verification-oriented and operational) can be derived from CKA. Programs are represented as sets of all their possible traces of execution, and non-determinism is introduced as union of these sets. The geometry is extended to multiple levels of abstraction and granularity; a method call at a higher level can be modelled by a specification of the method body, which is implemented at a lower level. The final section describes how the axioms and definitions of the geometry have been encoded in the interactive proof tool Isabelle, and reports on progress towards automatic checking of the proofs in the paper