Final Report Summary - ECSYM (Events, Causality and Symmetry-the next-generation semantics)
The goal of ECSYM (Events, Causality and Symmetry) is to build the next-generation semantics - a new mathematical foundation with which to understand and analyse computation of the complexity we see today. The proposal arose in answer to anomalies found in today's theories of computation and to the commonality and need for shared techniques becoming apparent across a range of seemingly disparate areas, through security protocols, systems biology, model checking, computational games, types and proof. At the time of the proposal the evidence pointed to a new intensional semantics, one in which the current distinctions between operational and denotational semantics disappear, one based on a marriage of the vision of Scott and Strachey, who sought a comprehensive semantics of computation, with Petri's analysis of computation, as emergent from local causal structure between basic events. A guiding insight was the increased expressivity a treatment of behavioural symmetry brings to causal models, to the types, processes, operations and applications they can support. In the project these ideas have been refined into a theory of distributed games. This has brought considerable life to the original mathematical intuitions. What was originally a hope, that we could subsume and enhance existing work on games in computation, became a central plank of the project. The work leads not only to a new foundation for computation, in the form of distributed games and strategies, but also, as a byproduct, to a new semantics of classical proof in terms of distributed strategies and to a structural view of game theory, in which games and optimal strategies can be built up in a compositional fashion.