Developments in Concurrent Kleene Algebra

This report summarises recent progress in the research of its co-authors towards the construction of links between algebraic presentations of the principles of programming and the exploitation of concurrency in modern programming practice. The research concentrates on the construction of a realistic family of partial order models for Concurrent Kleene Algebra (aka, the Laws of Programming). The main elements of the model are objects and the events in which they engage. Further primitive concepts are traces, errors and failures, and transferrable ownership. In terms of these we can define other concepts which have proved useful in reasoning about concurrent programs, for example causal dependency and independence, sequentiality and concurrency, allocation and disposal, synchrony and asynchrony, sharing and locality, input and output.