{"id":"https://openalex.org/W7119483643","doi":"https://doi.org/10.1145/3776675","title":"Tropical Mathematics and the Lambda-Calculus II: Tropical Geometry of Probabilistic Programming Languages","display_name":"Tropical Mathematics and the Lambda-Calculus II: Tropical Geometry of Probabilistic Programming Languages","publication_year":2026,"publication_date":"2026-01-08","ids":{"openalex":"https://openalex.org/W7119483643","doi":"https://doi.org/10.1145/3776675"},"language":"en","primary_location":{"id":"doi:10.1145/3776675","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3776675","pdf_url":null,"source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1145/3776675","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032188938","display_name":"Davide Barbarossa","orcid":"https://orcid.org/0000-0003-4608-8282"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Davide Barbarossa","raw_affiliation_strings":["University of Bath, Bath, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0003-4608-8282","affiliations":[{"raw_affiliation_string":"University of Bath, Bath, United Kingdom","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059212008","display_name":"Paolo Pistone","orcid":"https://orcid.org/0000-0003-4250-9051"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Paolo Pistone","raw_affiliation_strings":["Universit\u00e9 Claude Bernard Lyon 1, Lyon, France"],"raw_orcid":"https://orcid.org/0000-0003-4250-9051","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Claude Bernard Lyon 1, Lyon, France","institution_ids":["https://openalex.org/I100532134"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07284168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"POPL","first_page":"951","last_page":"980"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.6438000202178955,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.6438000202178955,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.1412000060081482,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.047200001776218414,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tropical-geometry","display_name":"Tropical geometry","score":0.6884999871253967},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6851000189781189},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5849000215530396},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.5227000117301941},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.5058000087738037},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.40049999952316284},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.39410001039505005}],"concepts":[{"id":"https://openalex.org/C202652594","wikidata":"https://www.wikidata.org/wiki/Q2982669","display_name":"Tropical geometry","level":2,"score":0.6884999871253967},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6851000189781189},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5849000215530396},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.5227000117301941},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.5058000087738037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.503600001335144},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3970000147819519},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.39410001039505005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3880000114440918},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.37119999527931213},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.37119999527931213},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.334199994802475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3084000051021576},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28349998593330383},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C34165917","wikidata":"https://www.wikidata.org/wiki/Q188267","display_name":"Programming paradigm","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3776675","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3776675","pdf_url":null,"source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3776675","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3776675","pdf_url":null,"source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.8449118137359619}],"awards":[{"id":"https://openalex.org/G4625311374","display_name":"Imperative programs from proofs","funder_award_id":"EP/W035847/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7297252005","display_name":null,"funder_award_id":"ANR-23-CPJ1-0054-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W568081588","https://openalex.org/W1975795800","https://openalex.org/W1984499246","https://openalex.org/W2026129786","https://openalex.org/W2096172373","https://openalex.org/W2097988344","https://openalex.org/W2138140494","https://openalex.org/W2159540339","https://openalex.org/W2607150727","https://openalex.org/W2760585651","https://openalex.org/W2796158284","https://openalex.org/W2808790743","https://openalex.org/W2963242323","https://openalex.org/W2963573740","https://openalex.org/W2963579331","https://openalex.org/W2964032597","https://openalex.org/W3013397595","https://openalex.org/W3015964097","https://openalex.org/W3104156703","https://openalex.org/W3128098595","https://openalex.org/W3147570207","https://openalex.org/W3148563252","https://openalex.org/W3212658597","https://openalex.org/W4205228770","https://openalex.org/W4206570602","https://openalex.org/W4251391716","https://openalex.org/W4405299848","https://openalex.org/W4413966263","https://openalex.org/W6947647588"],"related_works":[],"abstract_inverted_index":{"In":[0,72],"the":[1,28,34,38,45,54,67],"last":[2],"few":[3],"years":[4],"there":[5],"has":[6,43],"been":[7],"a":[8,111,114,142],"growing":[9],"interest":[10],"towards":[11],"methods":[12],"for":[13],"statistical":[14,93],"inference":[15,94],"and":[16,62,83,113,144],"learning":[17],"based":[18],"on":[19],"computational":[20],"geometry":[21,87],"and,":[22],"notably,":[23],"tropical":[24,57,86],"geometry,":[25],"that":[26,81,103,117,136],"is,":[27],"study":[29],"of":[30,47,56,69],"algebraic":[31,61],"varieties":[32],"over":[33,95],"min-plus":[35],"semiring.":[36],"At":[37],"same":[39],"time,":[40],"recent":[41],"work":[42,74],"demonstrated":[44],"possibility":[46],"interpreting":[48],"higher-order":[49,96],"probabilistic":[50,97],"programming":[51],"languages":[52],"in":[53,128,141],"framework":[55],"mathematics,":[58],"by":[59],"exploiting":[60],"categorical":[63],"tools":[64,82,127],"coming":[65],"from":[66,85],"semantics":[68],"linear":[70],"logic.":[71],"this":[73],"we":[75,100,124],"combine":[76],"these":[77,126],"two":[78],"worlds,":[79],"showing":[80],"ideas":[84],"can":[88,107],"be":[89,108],"used":[90],"to":[91,130],"perform":[92],"programs.":[98],"Notably,":[99],"first":[101],"show":[102],"each":[104],"such":[105],"program":[106],"associated":[109],"with":[110],"degree":[112],"n-dimensional":[115],"polyhedron":[116],"encode":[118],"its":[119],"most":[120,138],"likely":[121,139],"runs.":[122],"Then,":[123],"use":[125],"order":[129],"design":[131],"an":[132],"intersection":[133],"type":[134],"system":[135],"estimates":[137],"runs":[140],"compositional":[143],"efficient":[145],"way.":[146]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-01-09T00:00:00"}
