Sheaves, Objects, and Distributed Systems

Abstract

We review and extend some recent work that uses sheaf theory to provide a semantic foundation for distributed concurrent systems. A sheaf can be thought of as a system of observations on a topological space, with the key property that consistent local observations can be uniquely pasted together to provide a global observation. We suggest that sheaf theory can provide a framework for the semantics of distributed concurrent systems by exploring the relationships between sheaves and basic models of concurrent processes, particularly labelled transition systems and algebraic specifications of classes and objects.