eprintid: 10081075 rev_number: 21 eprint_status: archive userid: 608 dir: disk0/10/08/10/75 datestamp: 2019-09-09 09:08:02 lastmod: 2021-09-20 22:19:23 status_changed: 2019-09-09 09:08:02 type: proceedings_section metadata_visibility: show creators_name: Bonchi, F creators_name: Piedeleu, R creators_name: Sobocinski, P creators_name: Zanasi, F title: Graphical affine algebra ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: Graphical linear algebra is a diagrammatic language allowing to reason compositionally about different types of linear computing devices. In this paper, we extend this formalism with a connector for affine behaviour. The extension, which we call graphical affine algebra, is simple but remarkably powerful: it can model systems with richer patterns of behaviour such as mutual exclusion—with modules over the natural numbers as semantic domain—or non-passive electrical components—when considering modules over a certain field. Our main technical contribution is a complete axiomatisation for graphical affine algebra over these two interpretations. We also show, as case studies, how graphical affine algebra captures electrical circuits and the calculus of stateless connectors—a coordination language for distributed systems date: 2019-08-05 date_type: published publisher: IEEE official_url: https://doi.org/10.1109/LICS.2019.8785877 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1685381 doi: 10.1109/LICS.2019.8785877 isbn_13: 9781728136080 lyricists_name: Piedeleu, Robin lyricists_name: Zanasi, Fabio lyricists_id: RPIED00 lyricists_id: FZANA74 actors_name: Zanasi, Fabio actors_id: FZANA74 actors_role: owner full_text_status: public publication: Proceedings - Symposium on Logic in Computer Science place_of_pub: Vancouver, BC, Canada event_title: The 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) event_location: Vancouver, BC, Canada event_dates: 24-27 June 2019 issn: 1043-6871 book_title: Proceedings of the 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) citation: Bonchi, F; Piedeleu, R; Sobocinski, P; Zanasi, F; (2019) Graphical affine algebra. In: Proceedings of the 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE: Vancouver, BC, Canada. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10081075/1/paperLICS19.pdf