{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T15:07:49Z","timestamp":1787065669401,"version":"build-2736575974"},"reference-count":106,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T00:00:00Z","timestamp":1617148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["2007582"],"award-info":[{"award-number":["2007582"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Program. Lang. Syst."],"published-print":{"date-parts":[[2021,3,31]]},"abstract":"<jats:p>Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of effects is irrelevant. Understanding such systems in terms of a semilattice of effects grounds understanding of the essential issues and provides guidance when designing new effect systems. By contrast, sequential effect systems\u2014where the order of effects is important\u2014lack an established algebraic structure on effects.<\/jats:p>\n                  <jats:p>We present an abstract polymorphic effect system parameterized by an effect quantale\u2014an algebraic structure with well-defined properties that can model the effects of a range of existing sequential effect systems. We define effect quantales, derive useful properties, and show how they cleanly model a variety of known sequential effect systems.<\/jats:p>\n                  <jats:p>We show that for most effect quantales, there is an induced notion of iterating a sequential effect; that for systems we consider the derived iteration agrees with the manually designed iteration operators in prior work; and that this induced notion of iteration is as precise as possible when defined. We also position effect quantales with respect to work on categorical semantics for sequential effect systems, clarifying the distinctions between these systems and our own in the course of giving a thorough survey of these frameworks. Our derived iteration construct should generalize to these semantic structures, addressing limitations of that work. Finally, we consider the relationship between sequential effects and Kleene Algebras, where the latter may be used as instances of the former.<\/jats:p>","DOI":"10.1145\/3450272","type":"journal-article","created":{"date-parts":[[2021,4,17]],"date-time":"2021-04-17T06:14:20Z","timestamp":1618640060000},"page":"1-79","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":19,"title":["Polymorphic Iterable Sequential Effect Systems"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9012-4490","authenticated-orcid":false,"given":"Colin S.","family":"Gordon","sequence":"first","affiliation":[{"name":"Drexel University, Philadelphia, PA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2021,4,17]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1119479.1119480"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"Andreas Abel. 2010. MiniAgda: Integrating sized and dependent types. In Partiality and Recursion in Theorem Proving. EPTCS. http:\/\/eptcs.web.cse.unsw.edu.au\/content.cgi?PAR2010.","DOI":"10.4204\/EPTCS.43.2"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500000189"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-08-04712-0"},{"key":"e_1_2_1_5_1","volume-title":"Proceedings of the 19th International Workshop on Foundations of Object-oriented Languages (FOOL\u201912)","author":"Amin Nada","year":"2012","unstructured":"Nada Amin, Adriaan Moors, and Martin Odersky. 2012. Dependent object types. In Proceedings of the 19th International Workshop on Foundations of Object-oriented Languages (FOOL\u201912)."},{"key":"e_1_2_1_6_1","volume-title":"Type and Effect Systems: Behaviours for Concurrency","author":"Amtoft Torben","unstructured":"Torben Amtoft, Flemming Nielson, and Hanne Riis Nielson. 1999. Type and Effect Systems: Behaviours for Concurrency. Imperial College Press, London, UK."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1561\/2500000031"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the International Workshop on Computer Science Logic. Springer, 1--15","author":"Aspinall David","year":"1994","unstructured":"David Aspinall. 1994. Subtyping with singleton types. In Proceedings of the International Workshop on Computer Science Logic. Springer, 1--15."},{"key":"e_1_2_1_9_1","volume-title":"Parameterised notions of computation. J. Funct. Program. 19 (July","author":"Atkey Robert","year":"2009","unstructured":"Robert Atkey. 2009. Parameterised notions of computation. J. Funct. Program. 19 (July 2009), 335--376."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2500365.2500597"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2628136.2628149"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-87531-4_35"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1190315.1190320"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2013.27"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00025-6"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/237721.237771"},{"key":"e_1_2_1_17_1","volume-title":"Lattice Theory","author":"Birkhoff Garrett","unstructured":"Garrett Birkhoff. 1940. Lattice Theory (3rd ed.). Colloquium Publications, Vol. 25. American Mathematical Society.","edition":"3"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/b139095"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1640089.1640097"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/582419.582440"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/504282.504287"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2049697.2049700"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2007.30"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2983990.2984017"},{"key":"e_1_2_1_25_1","volume-title":"The Algebraic Theory of Semigroups","author":"Clifford Alfred Hoblitzelle","unstructured":"Alfred Hoblitzelle Clifford and Gordon Bamford Preston. 1961. The Algebraic Theory of Semigroups, Volume I. American Mathematical Society."},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/10722010_4"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/292540.292564"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/582153.582176"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/2429069.2429094"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2500365.2500587"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-00590-9_26"},{"key":"e_1_2_1_32_1","volume-title":"Proceedings of the International Conference on Developments in Language Theory. Springer, 240--251","author":"\u00c9sik Zolt\u00e1n","year":"2015","unstructured":"Zolt\u00e1n \u00c9sik, Uli Fahrenberg, and Axel Legay. 2015. *-Continuous Kleene -Algebras. In Proceedings of the International Conference on Developments in Language Theory. Springer, 240--251."},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/1217935.1217953"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/292540.292557"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/1706299.1706354"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48320-9_21"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-49099-X_7"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/349299.349328"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/781131.781169"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/604174.604176"},{"key":"e_1_2_1_41_1","series-title":"International Series of Monographs on Pure and Applied Mathematics","volume-title":"Partially Ordered Algebraic Systems","author":"Fuchs Laszlo","unstructured":"Laszlo Fuchs. 2011. Partially Ordered Algebraic Systems. International Series of Monographs on Pure and Applied Mathematics, Vol. 28. Dover Publications."},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-49630-5_30"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/3022670.2951939"},{"key":"e_1_2_1_44_1","volume-title":"Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Studies in Logic and the Foundations of Mathematics","author":"Galatos Nikolaos","year":"2007","unstructured":"Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski, and Hiroakira Ono. 2007. Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Studies in Logic and the Foundations of Mathematics, Vol. 151. Elsevier."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/2629609"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/319838.319848"},{"key":"e_1_2_1_47_1","volume-title":"Proceedings of the European Conference on Object-oriented Programming (ECOOP\u201917)","author":"Gordon Colin S.","year":"2017","unstructured":"Colin S. Gordon. 2017. A generic approach to flow-sensitive polymorphic effects. In Proceedings of the European Conference on Object-oriented Programming (ECOOP\u201917)."},{"key":"e_1_2_1_48_1","volume-title":"Proceedings of the 34th European Conference on Object-oriented Programming (ECOOP\u201920)","author":"Gordon Colin S.","year":"2020","unstructured":"Colin S. Gordon. 2020. Lifting sequential effects to control operators. In Proceedings of the 34th European Conference on Object-oriented Programming (ECOOP\u201920). Berlin, Germany."},{"key":"e_1_2_1_49_1","volume-title":"Proceedings of the European Conference on Object-oriented Programming (ECOOP\u201913)","author":"Gordon Colin S.","year":"2013","unstructured":"Colin S. Gordon, Werner Dietl, Michael D. Ernst, and Dan Grossman. 2013. JavaUI: Effects for controlling UI object access. In Proceedings of the European Conference on Object-oriented Programming (ECOOP\u201913)."},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/2103786.2103796"},{"key":"e_1_2_1_51_1","unstructured":"James Gosling Bill Joy Guy L. Steele Gilad Bracha and Alex Buckley. 2014. The Java Language Specification: Java SE 8 Edition. Pearson Education."},{"key":"e_1_2_1_52_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45306-7_14"},{"key":"e_1_2_1_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/512529.512563"},{"key":"e_1_2_1_54_1","doi-asserted-by":"publisher","DOI":"10.1145\/155090.155099"},{"key":"e_1_2_1_55_1","volume-title":"Advanced Topics in Types and Programming Languages, Benjamin C","author":"Henglein Fritz","unstructured":"Fritz Henglein, Henning Makholm, and Henning Niss. 2005. Effect types and region-based memory management. In Advanced Topics in Types and Programming Languages, Benjamin C. Pierce (Ed.). The MIT Press, 87--136."},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/1328438.1328472"},{"key":"e_1_2_1_57_1","doi-asserted-by":"publisher","DOI":"10.1145\/1272996.1273032"},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/1243418.1243424"},{"key":"e_1_2_1_59_1","doi-asserted-by":"publisher","DOI":"10.1145\/503272.503303"},{"key":"e_1_2_1_60_1","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.FSCD.2020.15"},{"key":"e_1_2_1_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/3371108"},{"key":"e_1_2_1_62_1","doi-asserted-by":"publisher","DOI":"10.1145\/2535838.2535846"},{"key":"e_1_2_1_63_1","doi-asserted-by":"publisher","DOI":"10.1145\/2254064.2254071"},{"key":"e_1_2_1_64_1","doi-asserted-by":"publisher","DOI":"10.1145\/2603088.2603138"},{"key":"e_1_2_1_65_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1994.1037"},{"key":"e_1_2_1_66_1","doi-asserted-by":"publisher","DOI":"10.1145\/256167.256195"},{"key":"e_1_2_1_67_1","volume-title":"Laurence and Georg Struth","author":"Michael","year":"2011","unstructured":"Michael R. Laurence and Georg Struth. 2011. Omega algebras and regular equations. In Proceedings of the International Conference on Relational and Algebraic Methods in Computer Science. Springer, 248--263."},{"key":"e_1_2_1_68_1","doi-asserted-by":"publisher","DOI":"10.1145\/361227.361234"},{"key":"e_1_2_1_69_1","doi-asserted-by":"publisher","DOI":"10.1145\/73560.73564"},{"key":"e_1_2_1_70_1","volume-title":"Proceedings of the 39th IEEE\/ACM International Symposium on Microarchitecture (MICRO\u201906)","author":"Maher Bertrand A.","unstructured":"Bertrand A. Maher, Aaron Smith, Doug Burger, and Kathryn S. McKinley. 2006. Merging head and tail duplication for convergent hyperblock formation. In Proceedings of the 39th IEEE\/ACM International Symposium on Microarchitecture (MICRO\u201906). IEEE, 65--76."},{"key":"e_1_2_1_71_1","doi-asserted-by":"publisher","DOI":"10.1145\/1481861.1481868"},{"key":"e_1_2_1_72_1","doi-asserted-by":"publisher","DOI":"10.1145\/2603088.2603132"},{"key":"e_1_2_1_73_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1902-1500616-8"},{"key":"e_1_2_1_74_1","first-page":"99","volume":"12","author":"Mulvey Christopher J.","year":"1986","unstructured":"Christopher J. Mulvey. 1986. Suppl. Rend. Circ. Mat. Palermo (2) 12 (1986), 99--104.","journal-title":"Suppl. Rend. Circ. Mat. Palermo (2)"},{"key":"e_1_2_1_75_1","volume-title":"Proceedings of the Canadian Mathematical Society Conference. 345--360","author":"Christopher","unstructured":"Christopher J. Mulvey and Joan W. Pelletier. 1992. A quantisation of the calculus of relations. In Proceedings of the Canadian Mathematical Society Conference. 345--360."},{"key":"e_1_2_1_76_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-27810-0_1"},{"key":"e_1_2_1_77_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-57208-2_34"},{"key":"e_1_2_1_78_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1096-9942(199901\/03)5:1<35::AID-TAPO4>3.0.CO;2-4"},{"key":"e_1_2_1_79_1","doi-asserted-by":"publisher","DOI":"10.1145\/2837614.2837634"},{"key":"e_1_2_1_80_1","volume-title":"Proc. ACM Program. Lang. 4, POPL","author":"P\u00e9drot Pierre-Marie","year":"2019","unstructured":"Pierre-Marie P\u00e9drot and Nicolas Tabareau. 2019. The fire triangle: How to mix substitution, dependent elimination, and effects. Proc. ACM Program. Lang. 4, POPL (2019), 58."},{"key":"e_1_2_1_81_1","doi-asserted-by":"publisher","DOI":"10.1145\/291251.289448"},{"key":"e_1_2_1_82_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0018436"},{"key":"e_1_2_1_83_1","doi-asserted-by":"publisher","DOI":"10.1145\/199448.199462"},{"key":"e_1_2_1_84_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-27866-5_42"},{"key":"e_1_2_1_85_1","doi-asserted-by":"publisher","DOI":"10.1145\/2983990.2984008"},{"key":"e_1_2_1_87_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31057-7_13"},{"key":"e_1_2_1_88_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(96)00072-2"},{"key":"e_1_2_1_89_1","doi-asserted-by":"publisher","DOI":"10.1145\/99583.99627"},{"key":"e_1_2_1_90_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10990-008-9032-6"},{"key":"e_1_2_1_91_1","doi-asserted-by":"publisher","DOI":"10.1109\/CSF49147.2020.00018"},{"key":"e_1_2_1_92_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0956796807006466"},{"key":"e_1_2_1_93_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-008-9013-7"},{"key":"e_1_2_1_94_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89330-1_12"},{"key":"e_1_2_1_95_1","doi-asserted-by":"publisher","DOI":"10.1145\/2048066.2048122"},{"key":"e_1_2_1_96_1","doi-asserted-by":"publisher","DOI":"10.1145\/2034773.2034811"},{"key":"e_1_2_1_97_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0956796800000393"},{"key":"e_1_2_1_98_1","doi-asserted-by":"publisher","DOI":"10.1145\/2429069.2429074"},{"key":"e_1_2_1_99_1","doi-asserted-by":"publisher","DOI":"10.1145\/291891.291894"},{"key":"e_1_2_1_100_1","doi-asserted-by":"publisher","DOI":"10.1145\/174675.177855"},{"key":"e_1_2_1_101_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1996.2613"},{"key":"e_1_2_1_102_1","doi-asserted-by":"publisher","DOI":"10.1145\/2814270.2814315"},{"key":"e_1_2_1_103_1","doi-asserted-by":"publisher","DOI":"10.1145\/1094811.1094847"},{"key":"e_1_2_1_104_1","doi-asserted-by":"publisher","DOI":"10.1145\/601775.601776"},{"key":"e_1_2_1_105_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22655-7_22"},{"key":"e_1_2_1_106_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1994.1093"},{"key":"e_1_2_1_107_1","doi-asserted-by":"publisher","DOI":"10.2307\/2274953s"}],"container-title":["ACM Transactions on Programming Languages and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3450272","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3450272","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3450272","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T16:46:59Z","timestamp":1750178819000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3450272"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,31]]},"references-count":106,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,3,31]]}},"alternative-id":["10.1145\/3450272"],"URL":"https:\/\/doi.org\/10.1145\/3450272","relation":{},"ISSN":["0164-0925","1558-4593"],"issn-type":[{"value":"0164-0925","type":"print"},{"value":"1558-4593","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,31]]},"assertion":[{"value":"2019-05-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}