{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T20:15:16Z","timestamp":1770408916474,"version":"3.49.0"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783031169113","type":"print"},{"value":"9783031169120","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-16912-0_4","type":"book-chapter","created":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T07:04:02Z","timestamp":1663743842000},"page":"102-128","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Flexibly Graded Monads and\u00a0Graded Algebras"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6705-1449","authenticated-orcid":false,"given":"Dylan","family":"McDermott","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1297-0579","authenticated-orcid":false,"given":"Tarmo","family":"Uustalu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"key":"4_CR1","doi-asserted-by":"publisher","unstructured":"Altenkirch, T., Chapman, J., Uustalu, T.: Monads need not be endofunctors. Log. Methods Comput. Sci 11(1), 3:1\u20133:40 (2015). https:\/\/doi.org\/10.2168\/lmcs-11(1:3)2015","DOI":"10.2168\/lmcs-11(1:3)2015"},{"key":"4_CR2","doi-asserted-by":"publisher","unstructured":"Dorsch, U., Milius, S., Schr\u00f6der, L.: Graded monads and graded logics for the linear time - branching time spectrum. In: Fokkink, W., van Glabbeek, R. (eds.) Proc. of 30th Int. Conf. on Concurrency Theory, CONCUR 2019, Leibniz Int. Proc. in Informatics, vol. 140, pp. 36:1\u201336:16. Dagstuhl Publishing, Saarbr\u00fccken\/Wadern (2019). https:\/\/doi.org\/10.4230\/lipics.concur.2019.36","DOI":"10.4230\/lipics.concur.2019.36"},{"key":"4_CR3","unstructured":"Fritz, T., Perrone, P.: A probability monad as the colimit of spaces of finite samples. Theor. Appl. Categ. 34(7), 170\u2013220 (2019). http:\/\/www.tac.mta.ca\/tac\/volumes\/34\/7\/34-07abs.html"},{"key":"4_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/978-3-662-49630-5_30","volume-title":"Foundations of Software Science and Computation Structures","author":"S Fujii","year":"2016","unstructured":"Fujii, S., Katsumata, S., Melli\u00e8s, P.-A.: Towards a formal theory of graded monads. In: Jacobs, B., L\u00f6ding, C. (eds.) FoSSaCS 2016. LNCS, vol. 9634, pp. 513\u2013530. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49630-5_30"},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/978-3-030-72019-3_9","volume-title":"Programming Languages and Systems","author":"M Gaboardi","year":"2021","unstructured":"Gaboardi, M., Katsumata, S., Orchard, D., Sato, T.: Graded hoare logic and its categorical semantics. In: ESOP 2021. LNCS, vol. 12648, pp. 234\u2013263. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-72019-3_9"},{"key":"4_CR6","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1016\/j.aim.2017.10.039","volume":"323","author":"R Garner","year":"2018","unstructured":"Garner, R.: An embedding theorem for tangent categories. Adv. Math. 323, 668\u2013687 (2018). https:\/\/doi.org\/10.1016\/j.aim.2017.10.039","journal-title":"Adv. Math."},{"key":"4_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1007\/978-3-642-40206-7_13","volume-title":"Algebra and Coalgebra in Computer Science","author":"S Goncharov","year":"2013","unstructured":"Goncharov, S.: Trace semantics via generic observations. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 158\u2013174. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40206-7_13"},{"issue":"2","key":"4_CR8","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/s0022-4049(97)00094-7","volume":"130","author":"R Gordon","year":"1998","unstructured":"Gordon, R., Power, A.: Algebraic structure for bicategory enriched categories. J. Pure Appl. Algebra 130(2), 119\u2013132 (1998). https:\/\/doi.org\/10.1016\/s0022-4049(97)00094-7","journal-title":"J. Pure Appl. Algebra"},{"key":"4_CR9","doi-asserted-by":"publisher","unstructured":"Katsumata, S.: Parametric effect monads and semantics of effect systems. In: Proceedings of 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2014, pp. 633\u2013645. ACM Press, New York (2014). https:\/\/doi.org\/10.1145\/2535838.2535846","DOI":"10.1145\/2535838.2535846"},{"key":"4_CR10","doi-asserted-by":"publisher","unstructured":"Katsumata, S., McDermott, D., Uustalu, T., Wu, N.: Flexible presentations of graded monads. Proc. ACM Program. Lang. 6(ICFP), 123:1\u2013123:29 (2022). https:\/\/doi.org\/10.1145\/3547654","DOI":"10.1145\/3547654"},{"key":"4_CR11","unstructured":"Kelly, G.M.: Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Note Series, vol. 64. Cambridge University Press, Cambridge (1982), reprinted as: Reprints Theor. Appl. Categ. 10 (2005). http:\/\/www.tac.mta.ca\/tac\/reprints\/articles\/10\/tr10abs.html"},{"key":"4_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/978-3-030-45231-5_21","volume-title":"Foundations of Software Science and Computation Structures","author":"S Kura","year":"2020","unstructured":"Kura, S.: Graded algebraic theories. In: FoSSaCS 2020. LNCS, vol. 12077, pp. 401\u2013421. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45231-5_21"},{"key":"4_CR13","unstructured":"Levy, P.B.: Locally graded categories. Slides (2019). https:\/\/www.cs.bham.ac.uk\/~pbl\/papers\/locgrade.pdf"},{"key":"4_CR14","unstructured":"Lobbia, G.: Distributive laws for relative monads. arXiv preprint arXiv:2007.12982 [math.CT] (2020). https:\/\/arxiv.org\/abs\/2007.12982"},{"key":"4_CR15","unstructured":"Marmolejo, F., Wood, R.J.: Monads as extension systems: No iteration is necessary. Theor. Appl. Categ. 24(4), 84\u2013113 (2010). http:\/\/www.tac.mta.ca\/tac\/volumes\/24\/4\/24-04abs.html"},{"key":"4_CR16","unstructured":"Melli\u00e8s, P.A.: Parametric monads and enriched adjunctions. Manuscript (2012). https:\/\/www.irif.fr\/~mellies\/tensorial-logic\/8-parametric-monads-and-enriched-adjunctions.pdf"},{"key":"4_CR17","doi-asserted-by":"publisher","unstructured":"Milius, S., Pattinson, D., Schr\u00f6der, L.: Generic trace semantics and graded monads. In: Moss, L.S., Soboci\u0144ski, P. (eds.) Proceedings of 6th Conference on Algebra and Coalgebra in Computer Science, CALCO 2015, Leibniz Int. Proceedings in Informatics, vol. 35, pp. 253\u2013269. Dagstuhl Publishing, Saarbr\u00fccken\/Wadern (2015). https:\/\/doi.org\/10.4230\/lipics.calco.2015.253","DOI":"10.4230\/lipics.calco.2015.253"},{"key":"4_CR18","doi-asserted-by":"publisher","unstructured":"Moggi, E.: Computational lambda-calculus and monads. In: Proceedings of 4th Annual Symposium on Logic in Computer Science, LICS 1989, pp. 14\u201323. IEEE Press, Los Alamitos, CA (1989). https:\/\/doi.org\/10.1109\/lics.1989.39155","DOI":"10.1109\/lics.1989.39155"},{"issue":"1","key":"4_CR19","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/0890-5401(91)90052-4","volume":"93","author":"E Moggi","year":"1991","unstructured":"Moggi, E.: Notions of computation and monads. Inf. Comput. 93(1), 55\u201392 (1991). https:\/\/doi.org\/10.1016\/0890-5401(91)90052-4","journal-title":"Inf. Comput."},{"key":"4_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-319-27810-0_1","volume-title":"Semantics, Logics, and Calculi","author":"A Mycroft","year":"2016","unstructured":"Mycroft, A., Orchard, D., Petricek, T.: Effect systems revisited\u2014control-flow algebra and semantics. In: Probst, C.W., Hankin, C., Hansen, R.R. (eds.) Semantics, Logics, and Calculi. LNCS, vol. 9560, pp. 1\u201332. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-27810-0_1"},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1023\/a:1023064908962","volume":"11","author":"G Plotkin","year":"2003","unstructured":"Plotkin, G., Power, J.: Algebraic operations and generic effects. Appl. Categ. Struct. 11, 69\u201394 (2003). https:\/\/doi.org\/10.1023\/a:1023064908962","journal-title":"Appl. Categ. Struct."},{"issue":"3","key":"4_CR22","doi-asserted-by":"publisher","first-page":"3032","DOI":"10.1007\/s10958-008-9013-7","volume":"151","author":"A Smirnov","year":"2008","unstructured":"Smirnov, A.: Graded monads and rings of polynomials. J. Math. Sci. 151(3), 3032\u20133051 (2008). https:\/\/doi.org\/10.1007\/s10958-008-9013-7","journal-title":"J. Math. Sci."},{"key":"4_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/978-3-642-37075-5_26","volume-title":"Foundations of Software Science and Computation Structures","author":"S Staton","year":"2013","unstructured":"Staton, S.: An algebraic presentation of predicate logic. In: Pfenning, F. (ed.) FoSSaCS 2013. LNCS, vol. 7794, pp. 401\u2013417. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-37075-5_26"},{"key":"4_CR24","doi-asserted-by":"crossref","unstructured":"Street, R.: Two constructions on lax functors. Cah. Topol. G\u00e9om. Diff. Cat\u00e9g. 13(3), 217\u2013264 (1972). http:\/\/www.numdam.org\/item\/CTGDC_1972__13_3_217_0","DOI":"10.1016\/0009-2614(72)85045-0"},{"issue":"1","key":"4_CR25","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/0021-8693(68)90036-7","volume":"8","author":"F Ulmer","year":"1968","unstructured":"Ulmer, F.: Properties of dense and relative adjoint functors. J. Algebra 8(1), 77\u201395 (1968). https:\/\/doi.org\/10.1016\/0021-8693(68)90036-7","journal-title":"J. Algebra"},{"key":"4_CR26","unstructured":"Wood, R.J.: Indicial Methods for Relative Categories. Ph.D. thesis, Dalhousie University (1976). http:\/\/hdl.handle.net\/10222\/55465"}],"container-title":["Lecture Notes in Computer Science","Mathematics of Program Construction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-16912-0_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T23:36:18Z","timestamp":1663803378000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-16912-0_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031169113","9783031169120"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-16912-0_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"22 September 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"MPC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Mathematics of Program Construction","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Tblilisi","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Georgia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 September 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 September 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"mpc2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.macs.hw.ac.uk\/mpc22\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-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":"14","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":"9","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":"64% - 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":"4","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 (given as abstracts in preface)","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)"}}]}}