Configuration Theories

A new framework for describing concurrent systems is presented. Rules for composing configurations of concurrent programs are represented by sequents Γ ⊢ρ Δ, where Γ and Δ are sequences of partially ordered sets (of events) and ρ is a matrix of monotone maps from the components of Γ to the components of Δ. Such a sequent expresses that whenever a configuration has certain specified subposets of events (Γ), then it extends to a configuration containing one of several specified subposets (Δ). The structural rules of Gentzen’s sequent calculus are decorated by suitable operations on matrices, where cut corresponds to product. The calculus thus obtained is shown to be sound with respect to interpretation in configuration structures [GG90]. Completeness is proven for a restriction of the calculus to finite sequents. As a case study we axiomatise the Java memory model, and formally derive a non-trivial property of thread-memory interaction.