{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T11:11:23Z","timestamp":1779448283751,"version":"3.53.1"},"reference-count":34,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/100018694","name":"European Commission Marie Sklodowska-Curie Actions","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100018694","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008725","name":"ANII","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006049","name":"University of the Republic Sectoral Commission for Scientific Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006049","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Theoretical Computer Science"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.tcs.2026.115845","type":"journal-article","created":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T07:57:52Z","timestamp":1772870272000},"page":"115845","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["The sup connective in IMALL: A categorical semantics"],"prefix":"10.1016","volume":"1072","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5175-6882","authenticated-orcid":false,"given":"Alejandro","family":"D\u00edaz-Caro","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0624-9285","authenticated-orcid":false,"given":"Octavio","family":"Malherbe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"299","key":"10.1016\/j.tcs.2026.115845_bib0001","article-title":"A single quantum cannot be cloned","volume":"1982","author":"Wootters","year":"1982","journal-title":"Nature"},{"key":"10.1016\/j.tcs.2026.115845_bib0002","series-title":"Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science (LICS)","first-page":"249","article-title":"A functional quantum programming language","author":"Altenkirch","year":"2005"},{"issue":"3","key":"10.1016\/j.tcs.2026.115845_bib0003","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1017\/S0960129506005238","article-title":"A lambda calculus for quantum computation with classical control","volume":"16","author":"Selinger","year":"2006","journal-title":"Math. Struct. Comput. Sci."},{"issue":"5","key":"10.1016\/j.tcs.2026.115845_bib0004","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1017\/S0960129509990089","article-title":"The algebraic lambda calculus","volume":"19","author":"Vaux","year":"2009","journal-title":"Math. Struct. Comput. Sci."},{"key":"10.1016\/j.tcs.2026.115845_bib0005","article-title":"Call-by-value, call-by-name and the vectorial behaviour of the algebraic \u03bb-calculus","volume":"10(4:8)","author":"Assaf","year":"2014","journal-title":"Log. Methods Comput. Sci."},{"key":"10.1016\/j.tcs.2026.115845_bib0006","article-title":"A system F accounting for scalars","volume":"8(1:11)","author":"Arrighi","year":"2012","journal-title":"Log. Methods Comput. Sci."},{"issue":"7","key":"10.1016\/j.tcs.2026.115845_bib0007","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1017\/S0960129514000425","article-title":"On quantum lambda calculi: a foundational perspective","volume":"26","author":"Zorzi","year":"2016","journal-title":"Math. Struct. Comput. Sci."},{"issue":"1","key":"10.1016\/j.tcs.2026.115845_bib0008","article-title":"Lineal: a linear-algebraic lambda-calculus","volume":"13","author":"Arrighi","year":"2017","journal-title":"Log. Methods Comput. Sci."},{"issue":"1","key":"10.1016\/j.tcs.2026.115845_bib0009","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.ic.2017.04.001","article-title":"The vectorial lambda-Calculus","volume":"254","author":"Arrighi","year":"2017","journal-title":"Inf. Comput."},{"key":"10.1016\/j.tcs.2026.115845_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.biosystems.2019.104012","article-title":"Two linearities for quantum computing in the lambda calculus","volume":"186","author":"D\u00edaz-Caro","year":"2019","journal-title":"BioSystems"},{"key":"10.1016\/j.tcs.2026.115845_bib0011","series-title":"Proceedings of the 34th Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS 2019)","first-page":"1","article-title":"Realizability in the unitary sphere","author":"D\u00edaz-Caro","year":"2019"},{"key":"10.1016\/j.tcs.2026.115845_bib0012","series-title":"Proceedings of the 13th Workshop on Logical and Semantic Frameworks with Applications (LSFA 2018)","first-page":"83","article-title":"A concrete categorical semantics for lambda-S","volume":"344","author":"D\u00edaz-Caro","year":"2019"},{"issue":"5","key":"10.1016\/j.tcs.2026.115845_bib0013","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1007\/s10485-020-09598-7","article-title":"A categorical construction for the computational definition of vector spaces","volume":"28","author":"D\u00edaz-Caro","year":"2020","journal-title":"Appl. Categor. Struct."},{"issue":"3","key":"10.1016\/j.tcs.2026.115845_bib0014","first-page":"32:1","article-title":"Quantum control in the unitary sphere: lambda-S1 and its categorical model","volume":"18","author":"D\u00edaz-Caro","year":"2022","journal-title":"Log. Methods Comput. Sci."},{"key":"10.1016\/j.tcs.2026.115845_bib0015","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1017\/S0960129524000197","article-title":"A linear linear lambda-calculus","volume":"34","author":"D\u00edaz-Caro","year":"2024","journal-title":"Math. Struct. Comput. Sci."},{"key":"10.1016\/j.tcs.2026.115845_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.tcs.2023.113840","article-title":"A new connective in natural deduction, and its application to quantum computing","volume":"957","author":"D\u00edaz-Caro","year":"2023","journal-title":"Theor. Comput. Sci."},{"key":"10.1016\/j.tcs.2026.115845_bib0017","series-title":"Proceedings of the 28rd Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS 2013)","first-page":"301","article-title":"Weighted relational models of typed lambda-calculi","author":"Laird","year":"2013"},{"key":"10.1016\/j.tcs.2026.115845_bib0018","series-title":"APLAS 2025: 23rd Asian Symposium on Programming Languages and Systems","article-title":"IMALL With a mixed-state modality: a logical approach to quantum computation","author":"Dave","year":"2025"},{"key":"10.1016\/j.tcs.2026.115845_bib0019","unstructured":"Mitchell, B., 1965. Theory of categories. Academic Press."},{"issue":"1","key":"10.1016\/j.tcs.2026.115845_bib0020","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0890-5401(91)90052-4","article-title":"Notions of computation and monads","volume":"93","author":"Moggi","year":"1991","journal-title":"Inf. Comput."},{"key":"10.1016\/j.tcs.2026.115845_bib0021","series-title":"Quantum Computation and Quantum Information","author":"Nielsen","year":"2010"},{"key":"10.1016\/j.tcs.2026.115845_bib0022","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0022-4049(80)90101-2","article-title":"Coherence for compact closed categories","volume":"19","author":"Kelly","year":"1980","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/j.tcs.2026.115845_bib0023","series-title":"Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.","first-page":"415","article-title":"A categorical semantics of quantum protocols","author":"Abramsky","year":"2004"},{"issue":"6","key":"10.1016\/j.tcs.2026.115845_bib0024","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1016\/j.ic.2011.02.001","article-title":"Probabilistic coherence spaces as a model of higher-order probabilistic computation","volume":"209","author":"Danos","year":"2011","journal-title":"Inf. Comput."},{"key":"10.1016\/j.tcs.2026.115845_bib0025","series-title":"Between Logic and Quantic: a Tract","first-page":"346","author":"Girard","year":"2004"},{"key":"10.1016\/j.tcs.2026.115845_bib0026","series-title":"2nd International Workshop on Quantum Programming Languages (QPL 2004)","first-page":"127","article-title":"Toward a semantics for higher-order quantum computation","volume":"33","author":"Selinger","year":"2004"},{"key":"10.1016\/j.tcs.2026.115845_bib0027","series-title":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2017)","first-page":"1","article-title":"Measurable cones and stable, measurable functions: a model for probabilistic higher-order programming","volume":"2","author":"Ehrhard","year":"2017"},{"key":"10.1016\/j.tcs.2026.115845_bib0028","series-title":"Proceedings of the 35th Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS 2020)","first-page":"370","article-title":"Cones as a model of intuitionistic linear logic","author":"Ehrnard","year":"2020"},{"key":"10.1016\/j.tcs.2026.115845_bib0029","series-title":"Proceedings of the 33rd Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS 2018)","first-page":"275","article-title":"Probabilistic stable functions on discrete cones are power series","author":"Crubill\u00e9","year":"2018"},{"key":"10.1016\/j.tcs.2026.115845_bib0030","series-title":"Proceedings of the 31st Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS 2016)","first-page":"347","article-title":"Fixed points in quantitative semantics","author":"Laird","year":"2016"},{"key":"10.1016\/j.tcs.2026.115845_bib0031","unstructured":"A. D\u00edaz-Caro, O. Malherbe, Semimodules and the (syntactically-)linear lambda calculus, 2022, (arXiv: 2205.02142v2)."},{"issue":"4","key":"10.1016\/j.tcs.2026.115845_bib0032","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1017\/S0960129504004256","article-title":"Towards a quantum programming language","volume":"14","author":"Selinger","year":"2004","journal-title":"Math. Struct. Comput. Sci."},{"key":"10.1016\/j.tcs.2026.115845_bib0033","series-title":"Proceedings of the 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2014)","first-page":"647","article-title":"Applying quantitative semantics to higher-order quantum computing","author":"Pagani","year":"2014"},{"key":"10.1016\/j.tcs.2026.115845_bib0034","first-page":"371","article-title":"Linear logic, *-autonomous categories and cofree coalgebras","author":"Seely","year":"1989","journal-title":"Categor. Comput. Sci. Logic"}],"container-title":["Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397526001040?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397526001040?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T11:02:32Z","timestamp":1779447752000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0304397526001040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":34,"alternative-id":["S0304397526001040"],"URL":"https:\/\/doi.org\/10.1016\/j.tcs.2026.115845","relation":{},"ISSN":["0304-3975"],"issn-type":[{"value":"0304-3975","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"The sup connective in IMALL: A categorical semantics","name":"articletitle","label":"Article Title"},{"value":"Theoretical Computer Science","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.tcs.2026.115845","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115845"}}