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A type-sound calculus of computational fields

Ferruccio Damiani, Mirko Viroli, Jacob Beal
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.
Keywords: Computational field
Science of Computer Programming 117, pages 17-44, 28 pages, 2016, Elsevier Science B.V.
@article{compfields-scp117,
	Author = {Damiani, Ferruccio and Viroli, Mirko and Beal, Jacob},
	Doi = {10.1016/j.scico.2015.11.005},
	Issn = {0167-6423},
	Journal = {Science of Computer Programming},
	Keywords = {Computational field, Core calculus, Operational semantics, Spatial computing, Type soundness},
	Pages = {17--44},
	Title = {A type-sound calculus of computational fields},
	Url = {http://www.sciencedirect.com/science/article/pii/S0167642315003573},
	Volume = 117,
	Year = 2016}