Writing bug-free code is fraught with difficulty, and existing tools for the formal verification of programs do not scale well to large, complicated codebases such as that of systems software. This thesis presents USIMPL, a component of the Orca project for formal verification that builds on Foster’s Isabelle/UTP with features of Schirmer’s Simpl in order to achieve a modular, scalable framework for deductive proofs of program correctness utilizing Hoare logic and Hoare-style algebraic laws of programming. / Master of Science / Writing bug-free code is fraught with difficulty, and existing tools for the formal verification of programs do not scale well to large, complicated codebases such as that of systems software (OSes, compilers, and similar programs that have a high level of complexity but work on a lower level than typical user applications such as text editors, image viewers, and the like). This thesis presents USIMPL, a component of the Orca project for formal verification that builds on an existing framework for computer-aided, deductive mathematical proofs (Foster’s Isabelle/UTP) with features inspired by a simple but featureful language used for verification (Schirmer’s Simpl) in order to achieve a modular, scalable framework for proofs of program correctness utilizing the rule-based mathematical representation of program behavior known as Hoare logic and Hoare-style algebraic laws of programming, which provide a formal methodology for transforming programs to equivalent formulations.

Hoare and He's Unifying Theories of Programming (UTP) provides a rich model of programs as relational predicates. This theory is intended to provide a single framework in which any programming paradigms, languages, and features, can be modelled, compared and contrasted. The UTP already has models for several programming formalisms, such as imperative programming, higher-order programming (e.g. programing with procedures), several styles of concurrent programming (or reactive systems), class-based object-orientation, and transaction processing. We believe that the UTP ought to be able to represent all significant computer programming language formalisms, in order for it to be considered a unifying theory. One gap in the UTP work is that of object-based object-orientation, such as that presented in Abadi and Cardelli's untyped object calculi (sigma-calculi). These sigma-calculi provide a prominent formalism of object-based object-oriented (OO) programs, which models programs as objects. We address this gap within this dissertation by presenting an embedding of an Abadi--Cardelli-style object calculus in the UTP. More formally, the thesis that his dissertation argues is that it is possible to provide an object-based object rientation to the UTP, with value- and reference-based objects, and a fully abstract model of references. We have made three contributions to our area of study: first, to extend the UTP with a notion of object-based object orientation, in contrast with the existing class-based models; second, to provide an alternative model of pointers (references) for the UTP that supports both value-based compound values (e.g. objects) and references (pointers), in contrast to existing UTP models with pointers that have reference-based compound values; and third, to model an Abadi-Cardelli notion of an object in the UTP, and thus demonstrate that it can unify this style of object formalism.