Computation Against a Neighbour: Addressing Large-Scale Distribution and Adaptivity with Functional Programming and Scala

Abstract

Recent works in contexts like the Internet of Things (IoT) and large-scale Cyber-Physical Systems (CPS) propose the idea of programming distributed systems by focussing on their global behaviour across space and time. In this view, a potentially vast and heterogeneous set of devices is considered as an "aggregate" to be programmed as a whole, while abstracting away the details of individual behaviour and exchange of messages, which are expressed declaratively. One such a paradigm, known as aggregate programming, builds on computational models inspired by field-based coordination. Existing models such as the field calculus capture interaction with neighbours by a so-called "neighbouring field" (a map from neighbours to values). This requires ad-hoc mechanisms to smoothly compose with standard values, thus complicating programming and introducing clutter in aggregate programs, libraries and domain-specific languages (DSLs). To address this key issue we introduce the novel notion of "computation against a neighbour", whereby the evaluation of certain subexpressions of the aggregate program are affected by recent corresponding evaluations in neighbours. We capture this notion in the neighbours calculus (NC), a new field calculus variant which is shown to smoothly support declarative specification of interaction with neighbours, and correspondingly facilitate the embedding of field computations as internal DSLs in common general-purpose programming languages -- as exemplified by a Scala implementation, called ScaFi. This paper formalises NC, thoroughly compares it with respect to the classic field calculus, and shows its expressiveness by means of a case study in edge computing, developed in ScaFi.

The Exchange Calculus (Xc): A Functional Programming Language Design for Distributed Collective Systems

“…𝖷𝖢 can be framed in the context of a long-term research thread on programming languages and tools for programming collective adaptive systems, known under the umbrella terms of field-based coordination (Mamei and Zambonelli, 2006;Viroli et al, 2019) and aggregate computing (Beal et al, 2015;Viroli et al, 2019). This research area is characterised by works on formal calculi (Audrito et al, 2019(Audrito et al, , 2023a, new constructs (Audrito et al, 2020;Casadei et al, 2019), formal properties of programs and computations (Viroli et al, 2018;Beal et al, 2017;Audrito et al, 2018a), programming language implementations of formal calculi as DSLs (Casadei et al, 2022b(Casadei et al, , 2021Audrito, 2020), simulators (Pianini et al, 2013;Audrito et al, 2022e), algorithms and patterns (Beal, 2009;Audrito et al, 2017b,a;Pianini et al, 2021b;Audrito et al, 2021a;Pianini et al, 2022), execution models (Pianini et al, 2021a), distributed platforms and deployments (Casadei et al, 2020(Casadei et al, , 2022a, and libraries for application domains such as swarm robotics (Aguzzi et al, 2023) and distributed monitoring (Audrito et al, 2021b). In a nutshell, this work proposes a new calculus, 𝖷𝖢, inspired by previous calculi, that subsumes them and is strictly more expressive in its ability to model messages differentiated on a neighbour basis (see Section 8.3 for a more detailed comparison).…”

“…The neighbours calculus (Audrito et al, 2023a) is a variant of FC that aims to simplify embeddability of DSLs inside general-purpose host languages by not requiring to deal with fields at the type level. This is achieved by considering a primitive folding operator inside which 𝚗𝚋𝚛 expressions can be evaluated.…”

“…This manuscript is an extended version of the conference paper (Audrito et al, 2022a), where the additional contributions, mainly related to the formalisation, include the parts on typing (Section 4.2), network semantics (Section 4.3), and formal proofs regarding types (Section 5.1), expressiveness (Section 5.2), and self-stabilisation (Section 5.3). The paper is structured as follows.…”