{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T17:33:22Z","timestamp":1781976802651,"version":"3.54.5"},"reference-count":57,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2019,1,4]],"date-time":"2019-01-04T00:00:00Z","timestamp":1546560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"European Union's Horizon 2020 research and innovation programme","award":["644298"],"award-info":[{"award-number":["644298"]}]},{"name":"Ateneo\/CSP project RunVar"},{"name":"HyVar"},{"name":"ICT COST Action IC1402 ARVI"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2019,1,31]]},"abstract":"<jats:p>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\u2019s collective behaviour) and the micro-level (individual devices\u2019 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.<\/jats:p>","DOI":"10.1145\/3285956","type":"journal-article","created":{"date-parts":[[2019,1,7]],"date-time":"2019-01-07T13:42:28Z","timestamp":1546868548000},"page":"1-55","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":78,"title":["A Higher-Order Calculus of Computational Fields"],"prefix":"10.1145","volume":"20","author":[{"given":"Giorgio","family":"Audrito","sequence":"first","affiliation":[{"name":"Dipartimento di Informatica, University of Turin, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mirko","family":"Viroli","sequence":"additional","affiliation":[{"name":"Dipartimeno di Informatica - Scienza e Ingegneria, Universit\u00e0 di Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8109-1706","authenticated-orcid":false,"given":"Ferruccio","family":"Damiani","sequence":"additional","affiliation":[{"name":"Dipartimento di Informatica, University of Turin, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Danilo","family":"Pianini","sequence":"additional","affiliation":[{"name":"Dipartimeno di Informatica - Scienza e Ingegneria, Universit\u00e0 di Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacob","family":"Beal","sequence":"additional","affiliation":[{"name":"Raytheon BBN Technologies, Cambridge, MA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2019,1,4]]},"reference":[{"key":"e_1_2_1_1_1","series-title":"Lecture Notes in Computer Science","volume-title":"Proceedings of the Coordination Models and Languages (COORDINATION\u201918)","author":"Audrito Giorgio","unstructured":"Giorgio Audrito , Jacob Beal , Ferruccio Damiani , and Mirko Viroli . 2018. Space-time universality of field calculus . In Proceedings of the Coordination Models and Languages (COORDINATION\u201918) , Lecture Notes in Computer Science , Vol. 10852 . Springer , 1--20. Giorgio Audrito, Jacob Beal, Ferruccio Damiani, and Mirko Viroli. 2018. Space-time universality of field calculus. In Proceedings of the Coordination Models and Languages (COORDINATION\u201918), Lecture Notes in Computer Science, Vol. 10852. Springer, 1--20."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/SASO.2017.18"},{"key":"e_1_2_1_3_1","series-title":"Lecture Notes in Computer Science","volume-title":"Proceedings of the Coordination Models and Languages, Proceedings (COORDINATION\u201917)","author":"Audrito Giorgio","unstructured":"Giorgio Audrito , Ferruccio Damiani , and Mirko Viroli . 2017. Optimally-self-healing distributed gradient structures through bounded information speed . 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