{"id":"https://openalex.org/W2900009437","doi":"https://doi.org/10.1145/3290315","title":"Constructing quotient inductive-inductive types","display_name":"Constructing quotient inductive-inductive types","publication_year":2019,"publication_date":"2019-01-02","ids":{"openalex":"https://openalex.org/W2900009437","doi":"https://doi.org/10.1145/3290315","mag":"2900009437"},"language":"en","primary_location":{"id":"doi:10.1145/3290315","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3290315","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3290315","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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://dl.acm.org/doi/pdf/10.1145/3290315","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047340010","display_name":"Ambrus Kaposi","orcid":"https://orcid.org/0000-0001-9897-8936"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Ambrus Kaposi","raw_affiliation_strings":["E\u00f6tv\u00f6s Lor\u00e1nd University, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"E\u00f6tv\u00f6s Lor\u00e1nd University, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045224632","display_name":"Andr\u00e1s Kov\u00e1cs","orcid":"https://orcid.org/0000-0002-6375-9781"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Andr\u00e1s Kov\u00e1cs","raw_affiliation_strings":["E\u00f6tv\u00f6s Lor\u00e1nd University, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"E\u00f6tv\u00f6s Lor\u00e1nd University, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"last","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":false,"raw_author_name":"Thorsten Altenkirch","raw_affiliation_strings":["University of Nottingham, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Nottingham, UK","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2644,"has_fulltext":true,"cited_by_count":44,"citation_normalized_percentile":{"value":0.95023266,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"3","issue":"POPL","first_page":"1","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994000196456909,"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":0.9994000196456909,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9846000075340271,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9456999897956848,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.8216435313224792},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.631016731262207},{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.6229164004325867},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5856166481971741},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5840654373168945},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5460515022277832},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5251685976982117},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5181923508644104},{"id":"https://openalex.org/keywords/domain-theory","display_name":"Domain theory","score":0.5079014897346497},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.47477054595947266},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4586179256439209},{"id":"https://openalex.org/keywords/inductive-method","display_name":"Inductive method","score":0.44079363346099854},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.43952909111976624},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3838747441768646},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3732585310935974},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3198174238204956},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18077966570854187},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07069522142410278}],"concepts":[{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.8216435313224792},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.631016731262207},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.6229164004325867},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5856166481971741},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5840654373168945},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5460515022277832},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5251685976982117},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5181923508644104},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.5079014897346497},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.47477054595947266},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4586179256439209},{"id":"https://openalex.org/C2993131915","wikidata":"https://www.wikidata.org/wiki/Q484511","display_name":"Inductive method","level":3,"score":0.44079363346099854},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.43952909111976624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3838747441768646},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3732585310935974},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3198174238204956},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18077966570854187},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07069522142410278},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C88610354","wikidata":"https://www.wikidata.org/wiki/Q1813494","display_name":"Teaching method","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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":2,"locations":[{"id":"doi:10.1145/3290315","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3290315","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3290315","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:1314154","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/1314154","pdf_url":null,"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":"Journal Article"}],"best_oa_location":{"id":"doi:10.1145/3290315","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3290315","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3290315","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":[],"awards":[{"id":"https://openalex.org/G2196163011","display_name":null,"funder_award_id":"EFOP 3.6.3-VEKOP-16- 2017-00002","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G467271090","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16-2017-00002.","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4693063966","display_name":null,"funder_award_id":"EFOP-3","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G6551428496","display_name":null,"funder_award_id":"00002","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G7101391507","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"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"},{"id":"https://openalex.org/G8725523790","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2900009437.pdf","grobid_xml":"https://content.openalex.org/works/W2900009437.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W326743114","https://openalex.org/W1487998695","https://openalex.org/W1517671027","https://openalex.org/W1664326696","https://openalex.org/W1773829243","https://openalex.org/W1821509023","https://openalex.org/W1949275316","https://openalex.org/W2006941708","https://openalex.org/W2012619465","https://openalex.org/W2042204873","https://openalex.org/W2052183597","https://openalex.org/W2058174669","https://openalex.org/W2079640625","https://openalex.org/W2158830522","https://openalex.org/W2175195909","https://openalex.org/W2274485505","https://openalex.org/W2296612922","https://openalex.org/W2384122606","https://openalex.org/W2550513301","https://openalex.org/W2561675875","https://openalex.org/W2563196418","https://openalex.org/W2604829466","https://openalex.org/W2605094208","https://openalex.org/W2615373383","https://openalex.org/W2795378980","https://openalex.org/W2802510100","https://openalex.org/W2885792094","https://openalex.org/W2963511234","https://openalex.org/W2964029175","https://openalex.org/W2964125890","https://openalex.org/W3003433637","https://openalex.org/W3099982020","https://openalex.org/W3101976357","https://openalex.org/W3103592512","https://openalex.org/W3104964042","https://openalex.org/W4213279211","https://openalex.org/W6736166930"],"related_works":["https://openalex.org/W2036375467","https://openalex.org/W4308234048","https://openalex.org/W4225619403","https://openalex.org/W3216376486","https://openalex.org/W1563447122","https://openalex.org/W2802510100","https://openalex.org/W2932790846","https://openalex.org/W2785208452","https://openalex.org/W4297685946","https://openalex.org/W4200558465"],"abstract_inverted_index":{"Quotient":[0],"inductive-inductive":[1,55],"types":[2,6],"(QIITs)":[3],"generalise":[4],"inductive":[5],"in":[7,38],"two":[8],"ways:":[9],"a":[10,39,60,82,103,121,131,134],"QIIT":[11,51,61,104],"can":[12,22],"have":[13,120],"more":[14],"than":[15],"one":[16],"sort":[17],"and":[18,118,139],"the":[19,26,49,63,89,96,141],"later":[20],"sorts":[21],"be":[23],"indexed":[24],"over":[25],"previous":[27],"ones.":[28],"In":[29,73],"addition,":[30],"equality":[31],"constructors":[32],"are":[33],"also":[34,126],"allowed.":[35],"We":[36,125],"work":[37],"setting":[40],"with":[41,136],"uniqueness":[42],"of":[43,53,59,67,91,95,98,130,144],"identity":[44],"proofs,":[45],"hence":[46],"we":[47,77,87,111],"use":[48,140],"term":[50],"instead":[52],"higher":[54],"type.":[56],"An":[57],"example":[58],"is":[62,100,152],"well-typed":[64],"(intrinsic)":[65],"syntax":[66,94,110],"type":[68,84],"theory":[69,85,90,97],"quotiented":[70],"by":[71,102],"conversion.":[72],"this":[74,109,145],"paper":[75],"first":[76],"specify":[78],"finitary":[79],"QIITs":[80,116],"using":[81,108],"domain-specific":[83],"which":[86],"call":[88],"signatures.":[92],"The":[93],"signatures":[99],"given":[101],"as":[105],"well.":[106],"Then,":[107],"show":[112,127,148],"that":[113,128,149],"all":[114],"specified":[115],"exist":[117],"they":[119],"dependent":[122,150],"elimination":[123,151],"principle.":[124],"algebras":[129],"signature":[132],"form":[133],"category":[135],"families":[137],"(CwF)":[138],"internal":[142],"language":[143],"CwF":[146],"to":[147,154],"equivalent":[153],"initiality.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":7}],"updated_date":"2026-08-13T07:04:57.449891","created_date":"2025-10-10T00:00:00"}
