A Higher-Order Calculus of Computational Fields

• DOI: 10.1145/3285956
• Publication Date: 2019-01-07T13:42:28Z
• Authors: Giorgio Audrito; Mirko Viroli; Ferruccio Damiani; Danilo Pianini; Jacob Beal
• Keywords: FOS: Computer and information sciences; Computer Science - Logic in Computer Science; 0202 electrical engineering, electronic engineering, information engineering; Adequacy; Aggregate programming; Computational field; Core calculus; Full abstraction; Spatial computing; Type inference system; Type soundness; Theoretical Computer Science; Computer Science (all); Logic; Computational Mathematics; Adequacy, aggregate programming, computational field, core calculus, full abstraction, spatial computing, type inference system, type soundness; 02 engineering and technology; Logic in Computer Science (cs.LO)

The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as an effective abstraction to fill the gap between the macro-level of such 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 article proposes a full formal foundation for field computations, in terms of a core (higher-order) calculus of computational fields containing a few key syntactic constructs, and equipped with typing, denotational and operational semantics. Critically, this allows formal establishment of a link between the micro- and macro-levels of collective adaptive systems by a result of computational adequacy and abstraction for the (aggregate) denotational semantics with respect to the (per-device) operational semantics.