A type-sound calculus of computational fields

• We introduce a core calculus for the notion of computational fields.
• We illustrate applications to self-organising spatial structures.
• We introduce a type inference system a la ML for the proposed calculus, capturing key requirements on “domain alignment”.
• We prove type soundness.

A number of recent works have investigated the notion of “computational fields” as a means of coordinating systems in distributed, dense and dynamic 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. We formalise a notion of type soundness for the calculus that encompasses the concept of domain alignment, and present a sound static type inference system. This calculus and its type inference system can act as a core for actual implementation of coordination languages and models, as well as to 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.