{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/314814"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/314814","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Probabilistic concurrent game semantics","abstract":"This thesis presents a variety of models for probabilistic programming languages in the framework of concurrent games. Our starting point is the model of concurrent games with symmetry of Castellan, Clairambault and Winskel. We show that they form a symmetric monoidal closed bicategory, and that this can be turned into a cartesian closed bicategory using a linear exponential pseudo-comonad inspired by linear logic. Then, we enrich this with probability, relying heavily on Winskel's model of probabilistic concurrent strategies. We see that the bicategorical structure is not perturbed by the addition of probability. We apply this model to two probabilistic languages: a probabilistic untyped λ-calculus, and Probabilistic PCF. For the former, we relate the semantics to the probabilistic Nakajima trees of Leventis, thus obtaining a characterisation of observational equivalence for programs in terms of strategies. For the latter, we show a definability result in the spirit of the game semantics tradition. This solves an open problem, as it is notoriously difficult to model Probabilistic PCF with sequential game semantics. Finally, we introduce a model for measurable game semantics, in which games and strategies come equipped with measure-theoretic structure allowing for an accurate description of computation with continuous data types. The objective of this model is to support computation with arbitrary probability measures on the reals. In the last part of this thesis we see how this can be done by equipping strategies with parametrised families of probability measures (also known as stochastic kernels), and we construct a bicategory of measurable concurrent games and probabilistic measurable strategies.","abstract_html":"This thesis presents a variety of models for probabilistic programming languages in the framework of concurrent games. Our starting point is the model of concurrent games with symmetry of Castellan, Clairambault and Winskel. We show that they form a symmetric monoidal closed bicategory, and that this can be turned into a cartesian closed bicategory using a linear exponential pseudo-comonad inspired by linear logic. Then, we enrich this with probability, relying heavily on Winskel's model of probabilistic concurrent strategies. We see that the bicategorical structure is not perturbed by the addition of probability. We apply this model to two probabilistic languages: a probabilistic untyped λ-calculus, and Probabilistic PCF. For the former, we relate the semantics to the probabilistic Nakajima trees of Leventis, thus obtaining a characterisation of observational equivalence for programs in terms of strategies. For the latter, we show a definability result in the spirit of the game semantics tradition. This solves an open problem, as it is notoriously difficult to model Probabilistic PCF with sequential game semantics. Finally, we introduce a model for measurable game semantics, in which games and strategies come equipped with measure-theoretic structure allowing for an accurate description of computation with continuous data types. The objective of this model is to support computation with arbitrary probability measures on the reals. In the last part of this thesis we see how this can be done by equipping strategies with parametrised families of probability measures (also known as stochastic kernels), and we construct a bicategory of measurable concurrent games and probabilistic measurable strategies.","abstract_has_math":false,"creators":["Paquet, Hugo"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Winskel, Glynn"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-01-17","date_published":"2020-01-17","updated_at":"2026-07-22T22:24:14Z","subjects":["Denotational Semantics","Game semantics","Probabilistic programming","Event structures"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e6b2d932-f9ab-4fa7-8688-8918b1e328df/download","http://purl.org/NET/rdflicense/allrightsreserved"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.61919","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Winskel, Glynn"]},{"key":"dc:creator","label":"Author","values":["Paquet, Hugo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2020-01-17"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/314814"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Denotational Semantics","Game semantics","Probabilistic programming","Event structures"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e6b2d932-f9ab-4fa7-8688-8918b1e328df/download","http://purl.org/NET/rdflicense/allrightsreserved"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.61919"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/b39e1a0d-fa92-4f17-814c-c6ac9bd4b13f/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis presents a variety of models for probabilistic programming languages in the framework of concurrent games. Our starting point is the model of concurrent games with symmetry of Castellan, Clairambault and Winskel. We show that they form a symmetric monoidal closed bicategory, and that this can be turned into a cartesian closed bicategory using a linear exponential pseudo-comonad inspired by linear logic. Then, we enrich this with probability, relying heavily on Winskel's model of probabilistic concurrent strategies. We see that the bicategorical structure is not perturbed by the addition of probability. We apply this model to two probabilistic languages: a probabilistic untyped λ-calculus, and Probabilistic PCF. For the former, we relate the semantics to the probabilistic Nakajima trees of Leventis, thus obtaining a characterisation of observational equivalence for programs in terms of strategies. For the latter, we show a definability result in the spirit of the game semantics tradition. This solves an open problem, as it is notoriously difficult to model Probabilistic PCF with sequential game semantics. Finally, we introduce a model for measurable game semantics, in which games and strategies come equipped with measure-theoretic structure allowing for an accurate description of computation with continuous data types. The objective of this model is to support computation with arbitrary probability measures on the reals. In the last part of this thesis we see how this can be done by equipping strategies with parametrised families of probability measures (also known as stochastic kernels), and we construct a bicategory of measurable concurrent games and probabilistic measurable strategies."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["a5eec7b1265c55e0ccde787a6de5ac62","353adac0d1ebdfd65ab16480263c3c87"]},{"key":"dc:title","label":"Title","values":["Probabilistic concurrent game semantics"]}]}],"canonical_facts":{"dc:contributor.advisor":["Winskel, Glynn"],"dc:creator":["Paquet, Hugo"],"dc:date.issued":["2020-01-17"],"dc:description.abstract":["This thesis presents a variety of models for probabilistic programming languages in the framework of concurrent games. Our starting point is the model of concurrent games with symmetry of Castellan, Clairambault and Winskel. We show that they form a symmetric monoidal closed bicategory, and that this can be turned into a cartesian closed bicategory using a linear exponential pseudo-comonad inspired by linear logic. Then, we enrich this with probability, relying heavily on Winskel's model of probabilistic concurrent strategies. We see that the bicategorical structure is not perturbed by the addition of probability. We apply this model to two probabilistic languages: a probabilistic untyped λ-calculus, and Probabilistic PCF. For the former, we relate the semantics to the probabilistic Nakajima trees of Leventis, thus obtaining a characterisation of observational equivalence for programs in terms of strategies. For the latter, we show a definability result in the spirit of the game semantics tradition. This solves an open problem, as it is notoriously difficult to model Probabilistic PCF with sequential game semantics. Finally, we introduce a model for measurable game semantics, in which games and strategies come equipped with measure-theoretic structure allowing for an accurate description of computation with continuous data types. The objective of this model is to support computation with arbitrary probability measures on the reals. In the last part of this thesis we see how this can be done by equipping strategies with parametrised families of probability measures (also known as stochastic kernels), and we construct a bicategory of measurable concurrent games and probabilistic measurable strategies."],"dc:format.checksum.md5":["a5eec7b1265c55e0ccde787a6de5ac62","353adac0d1ebdfd65ab16480263c3c87"],"dc:identifier.doi":["10.17863/CAM.61919"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/b39e1a0d-fa92-4f17-814c-c6ac9bd4b13f/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/314814"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e6b2d932-f9ab-4fa7-8688-8918b1e328df/download","http://purl.org/NET/rdflicense/allrightsreserved"],"dc:subject":["Denotational Semantics","Game semantics","Probabilistic programming","Event structures"],"dc:title":["Probabilistic concurrent game semantics"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:14Z"}