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
