Unifying Theories of Parallel Programming

We are developing a shared-variable refinement calculus in the style of the sequential calculi of Back, Morgan, and Morris. As part of this work, we’re studying different theories of shared-variable programming. Using the concepts and notations of Hoare & He’s unifying theories of programming (UTP), we give a formal semantics to a programming language that contains sequential composition, conditional statements, while loops, nested parallel composition, and shared variables. We first give a UTP semantics to labelled action systems, and then use this to give the semantics of our programs. Labelled action systems have a unique normal form that allows a simple formalisation and validation of different logics for reasoning about shared-variable programs. In this paper, we demonstrate how this is done for Lamport’s Concurrent Hoare Logic.