A Calculus of Computational Fields

A number of recent works have investigated the notion of “computational fields” as a means of coordinating systems in distributed, dense and mobile environments such as pervasive computing, sensor networks, and robot swarms. We introduce a minimal core calculus meant to capture the key ingredients of languages that make use of computational fields: functional composition of fields, functions over fields, evolution of fields over time, construction of fields of values from neighbours, and restriction of a field computation to a sub-region of the network. This calculus can act as a core for actual implementation of coordination languages and models, as well as pave the way towards formal analysis of properties concerning expressiveness, self-stabilisation, topology independence, and relationships with the continuous space-time semantics of spatial computations