{"id":"https://openalex.org/W4230647180","doi":"https://doi.org/10.1145/2103656.2103721","title":"A type theory for probability density functions","display_name":"A type theory for probability density functions","publication_year":2012,"publication_date":"2012-01-24","ids":{"openalex":"https://openalex.org/W4230647180","doi":"https://doi.org/10.1145/2103656.2103721"},"language":"en","primary_location":{"id":"doi:10.1145/2103656.2103721","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2103656.2103721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087604926","display_name":"Sooraj Bhat","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sooraj Bhat","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027820479","display_name":"Ashish Agarwal","orcid":null},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ashish Agarwal","raw_affiliation_strings":["New York University, New York, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University, New York, USA","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016738770","display_name":"Richard Vuduc","orcid":"https://orcid.org/0000-0003-2178-138X"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Vuduc","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005255629","display_name":"Alexander Gray","orcid":"https://orcid.org/0000-0003-0337-7359"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Gray","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"545","last_page":"556"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9994999766349792,"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/T11106","display_name":"Data Management and Algorithms","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.8323304653167725},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6875101327896118},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.684101402759552},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.643867015838623},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5471283197402954},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5443429946899414},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.5440877676010132},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4894203245639801},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4574131667613983},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3961728811264038},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31577926874160767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2665994167327881},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09285634756088257}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.8323304653167725},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6875101327896118},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.684101402759552},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.643867015838623},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5471283197402954},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5443429946899414},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.5440877676010132},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4894203245639801},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4574131667613983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3961728811264038},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31577926874160767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2665994167327881},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09285634756088257},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2103656.2103721","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2103656.2103721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W32064870","https://openalex.org/W342302233","https://openalex.org/W628624666","https://openalex.org/W1585529040","https://openalex.org/W1814275833","https://openalex.org/W1831716037","https://openalex.org/W1969555173","https://openalex.org/W1977970897","https://openalex.org/W2000436552","https://openalex.org/W2009086942","https://openalex.org/W2009776842","https://openalex.org/W2024355065","https://openalex.org/W2032320656","https://openalex.org/W2110787810","https://openalex.org/W2129905273","https://openalex.org/W2135394066","https://openalex.org/W2140654465","https://openalex.org/W2152828142","https://openalex.org/W2174515752","https://openalex.org/W2999905431","https://openalex.org/W3005561798","https://openalex.org/W4289258965","https://openalex.org/W6605288784","https://openalex.org/W6619775460","https://openalex.org/W6629510986","https://openalex.org/W6639796194","https://openalex.org/W6727685696","https://openalex.org/W6998801685"],"related_works":["https://openalex.org/W2477720232","https://openalex.org/W2893341095","https://openalex.org/W2002739602","https://openalex.org/W2009776842","https://openalex.org/W4241043257","https://openalex.org/W2345647014","https://openalex.org/W2201192772","https://openalex.org/W1935138604","https://openalex.org/W1990418105","https://openalex.org/W3136891595"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"great":[3],"interest":[4],"in":[5],"creating":[6],"probabilistic":[7,40,63],"programming":[8],"languages":[9],"to":[10,36,80],"simplify":[11],"the":[12,34,61,78,118,121],"coding":[13],"of":[14,50,112,124],"statistical":[15,57,126],"tasks;":[16],"however,":[17],"there":[18],"still":[19],"does":[20],"not":[21],"exist":[22],"a":[23,73,109],"formal":[24],"language":[25,64],"that":[26,65],"simultaneously":[27],"provides":[28],"(1)":[29],"continuous":[30,92],"probability":[31,44],"distributions,":[32],"(2)":[33],"ability":[35],"naturally":[37],"express":[38],"custom":[39],"models,":[41],"and":[42,69,99],"(3)":[43],"density":[45],"functions":[46],"(PDFs).":[47],"This":[48],"collection":[49],"features":[51],"is":[52],"necessary":[53],"for":[54,76,90,108],"mechanizing":[55],"fundamental":[56],"techniques.":[58],"We":[59],"formalize":[60],"first":[62],"exhibits":[66],"these":[67],"features,":[68],"it":[70],"serves":[71],"as":[72],"foundational":[74],"framework":[75],"extending":[77],"ideas":[79],"more":[81],"general":[82],"languages.":[83],"Particularly":[84],"novel":[85],"are":[86],"our":[87,100],"type":[88],"system":[89],"absolutely":[91],"(AC)":[93],"distributions":[94],"(those":[95],"which":[96,104],"permit":[97],"PDFs)":[98],"PDF":[101,106],"calculation":[102],"procedure,":[103],"calculates":[105],"s":[107],"large":[110],"class":[111],"AC":[113],"distributions.":[114],"Our":[115],"formalization":[116],"paves":[117],"way":[119],"toward":[120],"rigorous":[122],"encoding":[123],"powerful":[125],"reformulations.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
