{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T20:46:40Z","timestamp":1790542000535,"version":"4.1.0"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030638818","type":"print"},{"value":"9783030638825","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-63882-5_6","type":"book-chapter","created":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T14:08:03Z","timestamp":1605794883000},"page":"83-100","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Calculational Proofs in Relational Graphical Linear Algebra"],"prefix":"10.1007","author":[{"given":"Jo\u00e3o","family":"Paix\u00e3o","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pawe\u0142","family":"Soboci\u0144ski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,11,19]]},"reference":[{"issue":"1","key":"6_CR1","doi-asserted-by":"publisher","first-page":"9","DOI":"10.2140\/pjm.1961.11.9","volume":"11","author":"R Arens","year":"1961","unstructured":"Arens, R., et al.: Operational calculus of linear relations. Pac. J. Math. 11(1), 9\u201323 (1961)","journal-title":"Pac. J. Math."},{"key":"6_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/3-540-47797-7_4","volume-title":"Algebraic and Coalgebraic Methods in the Mathematics of Program Construction","author":"R Backhouse","year":"2002","unstructured":"Backhouse, R.: Galois connections and fixed point calculus. In: Backhouse, R., Crole, R., Gibbons, J. (eds.) Algebraic and Coalgebraic Methods in the Mathematics of Program Construction. LNCS, vol. 2297, pp. 89\u2013150. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-47797-7_4"},{"key":"6_CR3","first-page":"836","volume":"30","author":"J Baez","year":"2015","unstructured":"Baez, J., Erbele, J.: Categories in control. Theory Appl. Categ. 30, 836\u2013881 (2015)","journal-title":"Theory Appl. Categ."},{"key":"6_CR4","unstructured":"Bonchi, F., Holland, J., Pavlovic, D., Sobocinski, P.: Refinement for signal flow graphs. In: 28th International Conference on Concurrency Theory (CONCUR 2017). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2017)"},{"key":"6_CR5","doi-asserted-by":"crossref","unstructured":"Bonchi, F., Holland, J., Piedeleu, R., Soboci\u0144ski, P., Zanasi, F.: Diagrammatic algebra: from linear to concurrent systems. Proc. ACM Program. Lang. 3(POPL), 1\u201328 (2019)","DOI":"10.1145\/3290338"},{"key":"6_CR6","unstructured":"Bonchi, F., Pavlovic, D., Sobocinski, P.: Functorial semantics for relational theories. arXiv preprint arXiv:1711.08699 (2017)"},{"key":"6_CR7","doi-asserted-by":"crossref","unstructured":"Bonchi, F., Piedeleu, R., Fabio Zanasi, P.S.: Graphical affine algebra. In: ACM\/IEEE Symposium on Logic and Computer Science (LiCS 2019) (2019)","DOI":"10.1109\/LICS.2019.8785877"},{"key":"6_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/978-3-662-44584-6_30","volume-title":"CONCUR 2014 \u2013 Concurrency Theory","author":"F Bonchi","year":"2014","unstructured":"Bonchi, F., Soboci\u0144ski, P., Zanasi, F.: A categorical semantics of signal flow graphs. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 435\u2013450. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-44584-6_30"},{"key":"6_CR9","doi-asserted-by":"crossref","unstructured":"Bonchi, F., Sobocinski, P., Zanasi, F.: Full abstraction for signal flow graphs. In: POPL 2015, pp. 515\u2013526. ACM (2015)","DOI":"10.1145\/2775051.2676993"},{"issue":"1","key":"6_CR10","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.jpaa.2016.06.002","volume":"221","author":"F Bonchi","year":"2017","unstructured":"Bonchi, F., Soboci\u0144ski, P., Zanasi, F.: Interacting Hopf algebras. J. Pure Appl. Algebra 221(1), 144\u2013184 (2017)","journal-title":"J. Pure Appl. Algebra"},{"issue":"1\u20132","key":"6_CR11","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/0022-4049(87)90121-6","volume":"49","author":"A Carboni","year":"1987","unstructured":"Carboni, A., Walters, R.F.: Cartesian bicategories I. J. Pure Appl. Algebra 49(1\u20132), 11\u201332 (1987)","journal-title":"J. Pure Appl. Algebra"},{"key":"6_CR12","doi-asserted-by":"crossref","unstructured":"Coddington, E.A.: Extension Theory of Formally Normal and Symmetric Subspaces, vol. 134. American Mathematical Soc. (1973)","DOI":"10.1090\/memo\/0134"},{"key":"6_CR13","volume-title":"Multivalued Linear Operators","author":"R Cross","year":"1998","unstructured":"Cross, R.: Multivalued Linear Operators, vol. 213. CRC Press, Boca Raton (1998)"},{"key":"6_CR14","unstructured":"Erbele, J.: Redundancy and zebra snakes. https:\/\/graphicallinearalgebra.net\/2017\/10\/23\/episode-r1-redundancy-and-zebra-snakes\/"},{"key":"6_CR15","volume-title":"Categories, Allegories","author":"PJ Freyd","year":"1990","unstructured":"Freyd, P.J., Scedrov, A.: Categories, Allegories, vol. 39. Elsevier, Amsterdam (1990)"},{"issue":"9","key":"6_CR16","first-page":"147","volume":"13","author":"S Lack","year":"2004","unstructured":"Lack, S.: Composing props. Theory Appl. Categ. 13(9), 147\u2013163 (2004)","journal-title":"Theory Appl. Categ."},{"issue":"5","key":"6_CR17","doi-asserted-by":"publisher","first-page":"869","DOI":"10.1073\/pnas.50.5.869","volume":"50","author":"FW Lawvere","year":"1963","unstructured":"Lawvere, F.W.: Functorial semantics of algebraic theories. Proc. Natl. Acad. Sci. 50(5), 869\u2013872 (1963)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"7","key":"6_CR18","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1073\/pnas.47.7.1043","volume":"47","author":"S Mac Lane","year":"1961","unstructured":"Mac Lane, S.: An algebra of additive relations. Proc. Natl. Acad. Sci. U. S. A. 47(7), 1043 (1961)","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"issue":"7","key":"6_CR19","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1073\/pnas.47.7.1043","volume":"47","author":"S Mac Lane","year":"1961","unstructured":"Mac Lane, S.: An algebra of additive relations. Proc. Natl. Acad. Sci. U. S. A. 47(7), 1043\u20131051 (1961)","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"issue":"11","key":"6_CR20","doi-asserted-by":"publisher","first-page":"2160","DOI":"10.1016\/j.scico.2012.07.012","volume":"78","author":"HD Macedo","year":"2013","unstructured":"Macedo, H.D., Oliveira, J.N.: Typing linear algebra: a biproduct-oriented approach. Sci. Comput. Program. 78(11), 2160\u20132191 (2013)","journal-title":"Sci. Comput. Program."},{"issue":"6","key":"6_CR21","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1016\/j.jlap.2012.05.003","volume":"81","author":"SC Mu","year":"2012","unstructured":"Mu, S.C., Oliveira, J.N.: Programming from Galois connections. J. Log. Algebraic Program. 81(6), 680\u2013704 (2012)","journal-title":"J. Log. Algebraic Program."},{"key":"6_CR22","doi-asserted-by":"publisher","unstructured":"Santos, A., Oliveira, J.N.: Type your matrices for great good: a haskell library of typed matrices and applications (functional pearl). In: Proceedings of the 13th ACM SIGPLAN International Symposium on Haskell, p. 54\u201366. Haskell 2020, Association for Computing Machinery, New York (2020). https:\/\/doi.org\/10.1145\/3406088.3409019","DOI":"10.1145\/3406088.3409019"},{"key":"6_CR23","series-title":"Lecture Notes in Physics","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/978-3-642-12821-9_4","volume-title":"New Structures for Physics","author":"P Selinger","year":"2010","unstructured":"Selinger, P.: A survey of graphical languages for monoidal categories. In: Coecke, B. (ed.) New Structures for Physics. LNP, vol. 813, pp. 289\u2013355. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-12821-9_4"},{"key":"6_CR24","unstructured":"Soboci\u0144ski, P.: Graphical linear algebra. Mathematical blog. https:\/\/graphicallinearalgebra.net"},{"key":"6_CR25","unstructured":"Zanasi, F.: Interacting Hopf Algebras: the theory of linear systems. Ph.D. thesis, Ecole Normale Sup\u00e9rieure de Lyon (2015)"}],"container-title":["Lecture Notes in Computer Science","Formal Methods: Foundations and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-63882-5_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,24]],"date-time":"2021-04-24T12:30:40Z","timestamp":1619267440000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-63882-5_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030638818","9783030638825"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-63882-5_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"19 November 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SBMF","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Brazilian Symposium on Formal Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ouro Preto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Brazil","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25 November 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 November 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sbmf2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/sbmf2020.ufop.br\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"17","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"10","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"59% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3 invited talks are also included. The symposium was held virtually due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}