{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:12:31Z","timestamp":1760202751677,"version":"3.41.0"},"reference-count":36,"publisher":"Association for Computing Machinery (ACM)","issue":"POPL","license":[{"start":{"date-parts":[[2017,12,27]],"date-time":"2017-12-27T00:00:00Z","timestamp":1514332800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"ANR","award":["ANR-14-CE25-0005"],"award-info":[{"award-number":["ANR-14-CE25-0005"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Proc. ACM Program. Lang."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the main primitives of probabilistic functional programming, like continuous and discrete probabilistic distributions, sampling, conditioning and full recursion. We prove the soundness and adequacy of this model with respect to a call-by-name operational semantics and give some examples of its denotations.<\/jats:p>","DOI":"10.1145\/3158147","type":"journal-article","created":{"date-parts":[[2017,12,29]],"date-time":"2017-12-29T14:21:49Z","timestamp":1514557309000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":30,"title":["Measurable cones and stable, measurable functions: a model for probabilistic higher-order programming"],"prefix":"10.1145","volume":"2","author":[{"given":"Thomas","family":"Ehrhard","sequence":"first","affiliation":[{"name":"University of Paris Diderot, France \/ CNRS, France"}]},{"given":"Michele","family":"Pagani","sequence":"additional","affiliation":[{"name":"University of Paris Diderot, France \/ CNRS, France"}]},{"given":"Christine","family":"Tasson","sequence":"additional","affiliation":[{"name":"University of Paris Diderot, France \/ CNRS, France"}]}],"member":"320","published-online":{"date-parts":[[2017,12,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1962.12.1163"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1215\/ijm\/1255631584"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-08860-1_7"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2951913.2951942"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2011.02.001"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/507382.507385"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2011.29"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2535838.2535865"},{"key":"e_1_2_2_10_1","volume-title":"The cartesian closed category of measurable cones and stable, measurable functions A model for probabilistic higher-order programming. (Oct","author":"Ehrhard Thomas","year":"2017","unstructured":"Thomas Ehrhard , Michele Pagani , and Christine Tasson . 2017. The cartesian closed category of measurable cones and stable, measurable functions A model for probabilistic higher-order programming. (Oct . 2017 ). https:\/\/hal.archives- ouvertes.fr\/ hal- 01622046 working paper or preprint. Thomas Ehrhard, Michele Pagani, and Christine Tasson. 2017. The cartesian closed category of measurable cones and stable, measurable functions A model for probabilistic higher-order programming. (Oct. 2017). https:\/\/hal.archives- ouvertes.fr\/ hal- 01622046 working paper or preprint."},{"key":"e_1_2_2_11_1","unstructured":"Thomas Ehrhard and Christine Tasson. 2016. Probabilistic call by push value. (2016). Submitted preprint available at http:\/\/arxiv.org\/abs\/1607.04690.  Thomas Ehrhard and Christine Tasson. 2016. Probabilistic call by push value. (2016). Submitted preprint available at http:\/\/arxiv.org\/abs\/1607.04690."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129504004360"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00250-2"},{"key":"e_1_2_2_14_1","unstructured":"Florian Faissole and Bas Spitters. 2017. Synthetic topology in Homotopy Type Theory for probabilistic programming. (2017). available at: https:\/\/pps2017.soic.indiana.edu\/files\/2016\/12\/ProbProg.pdf .  Florian Faissole and Bas Spitters. 2017. Synthetic topology in Homotopy Type Theory for probabilistic programming. (2017). available at: https:\/\/pps2017.soic.indiana.edu\/files\/2016\/12\/ProbProg.pdf ."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0092872"},{"key":"e_1_2_2_16_1","volume-title":"Tenenbaum","author":"Goodman Noah D.","year":"2014","unstructured":"Noah D. Goodman and Joshua B . Tenenbaum . 2014 . Probabilistic models of cognition. (2014). http:\/\/probmods.org. Noah D. Goodman and Joshua B. Tenenbaum. 2014. Probabilistic models of cognition. (2014). http:\/\/probmods.org."},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2011.23"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2017.8005137"},{"key":"e_1_2_2_19_1","unstructured":"Daniel Huang and Greg Morrisett. 2017. An application of computable distributions to the semantics of probabilistic programs: part 2. (2017). available at: https:\/\/pps2017.soic.indiana.edu\/files\/2016\/12\/comp- dist- sem.pdf .  Daniel Huang and Greg Morrisett. 2017. An application of computable distributions to the semantics of probabilistic programs: part 2. (2017). available at: https:\/\/pps2017.soic.indiana.edu\/files\/2016\/12\/comp- dist- sem.pdf ."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.1989.39173"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0661(05)80216-6"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.23638\/LMCS-13(1:2)2017"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(81)90036-2"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2013.36"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.2307\/1969847"},{"key":"e_1_2_2_26_1","volume-title":"Domains and Random Variables. CoRR abs\/1607.07698","author":"Mislove Michael W.","year":"2016","unstructured":"Michael W. Mislove . 2016. Domains and Random Variables. CoRR abs\/1607.07698 ( 2016 ). http:\/\/arxiv.org\/abs\/1607.07698 Michael W. Mislove. 2016. Domains and Random Variables. CoRR abs\/1607.07698 (2016). http:\/\/arxiv.org\/abs\/1607.07698"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0661(05)80602-4"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/1452044.1452048"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(77)90044-5"},{"key":"e_1_2_2_30_1","volume-title":"Convexity and Order in Probabilistic Call-by-Name FPC. CoRR abs\/1607.04332","author":"Rennela Mathys","year":"2016","unstructured":"Mathys Rennela . 2016. Convexity and Order in Probabilistic Call-by-Name FPC. CoRR abs\/1607.04332 ( 2016 ). http: \/\/arxiv.org\/abs\/1607.04332 Mathys Rennela. 2016. Convexity and Order in Probabilistic Call-by-Name FPC. CoRR abs\/1607.04332 (2016). http: \/\/arxiv.org\/abs\/1607.04332"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(80)90003-1"},{"key":"e_1_2_2_32_1","volume-title":"Proceedings of the 2nd International Workshop on Quantum Programming Languages, Peter Selinger (Ed.)","volume":"33","author":"Selinger Peter","year":"2004","unstructured":"Peter Selinger . 2004 . Toward a semantics for higher-order quantum computation . In Proceedings of the 2nd International Workshop on Quantum Programming Languages, Peter Selinger (Ed.) , Vol. 33 . TUCS General Publication, 127\u2013143. Peter Selinger. 2004. Toward a semantics for higher-order quantum computation. In Proceedings of the 2nd International Workshop on Quantum Programming Languages, Peter Selinger (Ed.), Vol. 33. TUCS General Publication, 127\u2013143."},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-54434-1_32"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2933575.2935313"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2009.01.002"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/62678.62681"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-06880-0_25"}],"container-title":["Proceedings of the ACM on Programming Languages"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3158147","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3158147","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T02:11:30Z","timestamp":1750212690000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3158147"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,27]]},"references-count":36,"journal-issue":{"issue":"POPL","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1145\/3158147"],"URL":"https:\/\/doi.org\/10.1145\/3158147","relation":{},"ISSN":["2475-1421"],"issn-type":[{"type":"electronic","value":"2475-1421"}],"subject":[],"published":{"date-parts":[[2017,12,27]]},"assertion":[{"value":"2017-12-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}