{"id":"https://openalex.org/W2274485505","doi":"https://doi.org/10.1145/2837614.2837638","title":"Type theory in type theory using quotient inductive types","display_name":"Type theory in type theory using quotient inductive types","publication_year":2016,"publication_date":"2016-01-07","ids":{"openalex":"https://openalex.org/W2274485505","doi":"https://doi.org/10.1145/2837614.2837638","mag":"2274485505"},"language":"en","primary_location":{"id":"doi:10.1145/2837614.2837638","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2837614.2837638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://nottingham-repository.worktribe.com/preview/771870/popl16main-mainpopl16-157-p-6ba8421-25791-preprint.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056420469","display_name":"Thorsten Altenkirch","orcid":"https://orcid.org/0000-0002-6582-5025"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Thorsten Altenkirch","raw_affiliation_strings":["University of Nottingham, UK"],"affiliations":[{"raw_affiliation_string":"University of Nottingham, UK","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047340010","display_name":"Ambrus Kaposi","orcid":"https://orcid.org/0000-0001-9897-8936"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ambrus Kaposi","raw_affiliation_strings":["University of Nottingham, UK"],"affiliations":[{"raw_affiliation_string":"University of Nottingham, UK","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056420469"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":null,"apc_paid":null,"fwci":14.1354,"has_fulltext":true,"cited_by_count":86,"citation_normalized_percentile":{"value":0.9879089,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"18","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9991999864578247,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9991999864578247,"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.9307000041007996,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9186000227928162,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.9118876457214355},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6623952388763428},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.5908522605895996},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5465091466903687},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5277113318443298},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.48350122570991516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4305887520313263},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4185337424278259},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.41295135021209717},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38819554448127747},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33557790517807007},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32726800441741943},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2914988398551941},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.22208482027053833},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21302348375320435}],"concepts":[{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.9118876457214355},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6623952388763428},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.5908522605895996},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5465091466903687},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5277113318443298},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.48350122570991516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4305887520313263},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4185337424278259},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.41295135021209717},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38819554448127747},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33557790517807007},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32726800441741943},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2914988398551941},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.22208482027053833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21302348375320435},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2837614.2837638","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2837614.2837638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","raw_type":"proceedings-article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:771860","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/771860","pdf_url":"https://nottingham-repository.worktribe.com/preview/771870/popl16main-mainpopl16-157-p-6ba8421-25791-preprint.pdf","source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:eprints.nottingham.ac.uk:31169","is_oa":true,"landing_page_url":"http://eprints.nottingham.ac.uk/31169/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402013","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"}],"best_oa_location":{"id":"pmh:oai:nottingham-repository.worktribe.com:771860","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/771860","pdf_url":"https://nottingham-repository.worktribe.com/preview/771870/popl16main-mainpopl16-157-p-6ba8421-25791-preprint.pdf","source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2918151187","display_name":"Homotopy Type Theory: Programming and Verification","funder_award_id":"EP/M016951/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7305158591","display_name":null,"funder_award_id":"EP/M016951/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7487386128","display_name":null,"funder_award_id":"EP/M016994/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2274485505.pdf","grobid_xml":"https://content.openalex.org/works/W2274485505.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W326743114","https://openalex.org/W1481180394","https://openalex.org/W1494555245","https://openalex.org/W1517671027","https://openalex.org/W1532711231","https://openalex.org/W1533094521","https://openalex.org/W1548537769","https://openalex.org/W1575675278","https://openalex.org/W1664326696","https://openalex.org/W1765415708","https://openalex.org/W1773829243","https://openalex.org/W1844544548","https://openalex.org/W1975335792","https://openalex.org/W2002359740","https://openalex.org/W2006941708","https://openalex.org/W2041111005","https://openalex.org/W2079103712","https://openalex.org/W2102861499","https://openalex.org/W2116438866","https://openalex.org/W2117477507","https://openalex.org/W2133629640","https://openalex.org/W2145108549","https://openalex.org/W2147289514","https://openalex.org/W2156830909","https://openalex.org/W2186289717","https://openalex.org/W2274485505","https://openalex.org/W3070676115","https://openalex.org/W3200836119","https://openalex.org/W4205241946","https://openalex.org/W4290655614","https://openalex.org/W4293770342","https://openalex.org/W4399412362"],"related_works":["https://openalex.org/W4306816010","https://openalex.org/W2787703111","https://openalex.org/W4386614239","https://openalex.org/W19518518","https://openalex.org/W3120415410","https://openalex.org/W4306353309","https://openalex.org/W4225424606","https://openalex.org/W4283575722","https://openalex.org/W2163980057","https://openalex.org/W2117463039"],"abstract_inverted_index":{"We":[0,57],"present":[1],"an":[2,54],"internal":[3],"formalisation":[4,35],"of":[5,19,36],"a":[6,16,44],"type":[7,37],"heory":[8],"with":[9,80],"dependent":[10],"types":[11,22,32],"in":[12],"Type":[13,25],"Theory":[14,26],"using":[15,75,82],"special":[17],"case":[18],"higher":[20],"inductive":[21,31,55],"from":[23],"Homotopy":[24],"which":[27],"we":[28],"call":[29],"quotient":[30],"(QITs).":[33],"Our":[34],"theory":[38],"avoids":[39],"referring":[40],"to":[41,62],"preterms":[42],"or":[43],"typability":[45],"relation":[46],"but":[47],"defines":[48],"directly":[49],"well":[50],"typed":[51],"objects":[52],"by":[53],"definition.":[56],"use":[58],"the":[59,64,76],"elimination":[60],"principle":[61],"define":[63],"set-theoretic":[65],"and":[66],"logical":[67],"predicate":[68],"interpretation.":[69],"The":[70],"work":[71],"has":[72],"been":[73],"formalized":[74],"Agda":[77],"system":[78],"extended":[79],"QITs":[81],"postulates.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":7}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
