On a Higher-Order Calculus of Computational Fields

none5siheld as part of the 14th International Federated Conference on Distributed Computing Techniques, DisCoTec 2019Computational fields have been proposed as an effective abstraction to fill the gap between the macro-level of distributed systems (specifying a system’s collective behaviour) and the micro-level (individual devices’ actions of computation and interaction to implement that collective specification), thereby providing a basis to better facilitate the engineering of collective APIs and complex systems at higher levels of abstraction. This approach is particularly suited to complex large-scale distributed systems, like the Internet-of-Things and Cyber-Physical Systems, where new mechanisms are needed to address composability and reusability of collective adaptive behaviour. This work introduces a full formal foundation for field computations, in terms of a core calculus equipped with typing, denotational, and operational semantics. Critically, we apply techniques for formal programming languages to collective adaptive systems: we provide formal establishment of a link between the micro- and macro-levels of collective adaptive systems, via a result of computational adequacy and abstraction for the (aggregate) denotational semantics with respect to the (per-device) operational semantics.mixedGiorgio Audrito, Mirko Viroli, Ferruccio Damiani, Danilo Pianini, Jacob BealGiorgio Audrito, Mirko Viroli, Ferruccio Damiani, Danilo Pianini, Jacob Bea