{"id":6826,"date":"2023-06-05T07:26:40","date_gmt":"2023-06-05T05:26:40","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=6826"},"modified":"2023-06-14T16:26:30","modified_gmt":"2023-06-14T14:26:30","slug":"a-journey-through-the-semantics-of-higher-order-probabilistic-languagesdomain-theory-and-topology","status":"publish","type":"page","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=6826","title":{"rendered":"A journey through the semantics of higher-order probabilistic languages,domain theory, and topology"},"content":{"rendered":"\n

This is a talk I gave at the yearly seminar of LMF<\/a> in \u00c9tiolles, France, on June 13th, 2023.<\/p>\n\n\n\n

Abstract<\/h2>\n\n\n\n

I have been asked to give an introduction to topology in computer science “for dummies”. I understand this as an introduction to my own view of topology, as seen through computer science, and I have decided to concentrate on the semantics of programming languages; more precisely, of pure, higher-order, probabilistic programming languages, with a focus on denotational semantics based on directed-complete partial orders<\/em> (dcpos).<\/p>\n\n\n\n

This will give me the opportunity to introduce some of the notions of domain theory, with a glimpse of topology, or of that bit of topology we need for the task. In the end, there will not really be much of topology in this talk, but I hope you can still get something out of it in terms of semantics of programming languages.<\/p>\n\n\n\n

Slides<\/h2>\n\n\n\n

The full slides<\/a>, with all animation steps (229 pages); the shorter<\/a> presentation, without animation steps (72 pages).<\/p>\n\n\n\n

Videos<\/h2>\n\n\n\n

In six parts:<\/p>\n\n\n\n

    \n
  1. Introduction, topology, domain theory, Plotkin’s classic study of the language PCF<\/a> (17:32)<\/li>\n\n\n\n
  2. Probabilistic PCF, and continuous valuations<\/a> (23:17)<\/li>\n\n\n\n
  3. Continuous dcpos, a.k.a. domains<\/a> (7:02)<\/li>\n\n\n\n
  4. Statistical programming languages, and ISPCF<\/a> (20:57)<\/li>\n\n\n\n
  5. Commutativity, and Fubini-Tonelli theorems<\/a> (15:07)<\/li>\n\n\n\n
  6. Concluding remarks<\/a> (7:06)<\/li>\n<\/ol>\n\n\n
    \n
    \"jgl-2011\"<\/figure>\n<\/div>\n\n\n

    \u2014 Jean Goubault-Larrecq<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    This is a talk I gave at the yearly seminar of LMF in \u00c9tiolles, France, on June 13th, 2023. Abstract I have been asked to give an introduction to topology in computer science “for dummies”. I understand this as an … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_crdt_document":"","footnotes":""},"class_list":["post-6826","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/pages\/6826","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6826"}],"version-history":[{"count":13,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/pages\/6826\/revisions"}],"predecessor-version":[{"id":6851,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/pages\/6826\/revisions\/6851"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}