An Algebraic Theory for Shared-State Concurrency

We present a monadic denotational semantics for higher-order programming language with shared-state concurrency, i.e. global-state in the presence of interleaving concurrency. Central to our approach is use Plotkin and Power’s algebraic effect methodology: designing an equational theory that captures intended semantics, proving representation theorem it. Hyland et al.’s resumptions extends non-deterministic operator yielding environment. The based on Brookes-style traces. Based this we define directionally adequate respect standard operational semantics. justify compiler transformations interest: redundant access eliminations, each following from mundane calculation; while structural follow reasoning over monad’s interface.