Algebra, Logic, Locality, Concurrency

This talk reports on ongoing work – with Tony Hoare, Akbar Hussain, Bernhard Möller, Rasmus Petersen, Georg Struth, Ian Wehrman, and others – on models and logics for concurrent processes [10,6,5]. The approach we are taking abstracts from syntax or particular models. Message passing and shared memory process interaction, and strong (interleaving) and weak (partial order) approaches to sequencing, are accomodated as different models of the same core axioms. Rules of program logic, related to Hoare and Separation logics, flow at once from the algebraic axioms. So, one gets a generic program logic from the algebra, which holds for a range of concrete models. The most notable amongst the algebra laws is an ordered cousin of the exchange law of 2-categories or bicategories, which here links primitives for sequential and parallel composition (p ‖ r); (q ‖ s) (p; q) ‖ (r; s).