{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:26Z","timestamp":1753894406459,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,1,3]]},"abstract":"<jats:p>Measurable cones, with linear and measurable functions as morphisms, are a model of intuitionistic linear logic and of call-by-name probabilistic PCF which accommodates &amp;quot;continuous data types&amp;quot; such as the real line. So far however, they lacked a major feature to make them a model of more general probabilistic programming languages (notably call-by-value and call-by-push-value languages): a theory of integration for functions whose codomain is a cone, which is the key ingredient for interpreting the sampling programming primitives. The goal of this paper is to develop such a theory: our definition of integrals is an adaptation to cones of Pettis integrals in topological vector spaces. We prove that such integrable cones, with integral-preserving linear maps as morphisms, form a model of Linear Logic for which we develop two exponential comonads: the first based on a notion of stable and measurable functions introduced in earlier work and the second based on a new notion of integrable analytic function on cones.<\/jats:p>","DOI":"10.46298\/lmcs-21(1:1)2025","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T19:25:09Z","timestamp":1735932309000},"source":"Crossref","is-referenced-by-count":0,"title":["Integration in Cones"],"prefix":"10.46298","volume":"Volume 21, Issue 1","author":[{"given":"Thomas","family":"Ehrhard","sequence":"first","affiliation":[]},{"given":"Guillaume","family":"Geoffroy","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,1,3]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/15021\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/15021\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T19:25:09Z","timestamp":1735932309000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10815"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,3]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(1:1)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2212.02371v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2212.02371v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2212.02371v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2212.02371","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2212.02371","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,1,3]]},"article-number":"10815"}}