{"id":"https://openalex.org/W3119184403","doi":"https://doi.org/10.46298/lmcs-18(2:15)2022","title":"Quotients, inductive types, and quotient inductive types","display_name":"Quotients, inductive types, and quotient inductive types","publication_year":2022,"publication_date":"2022-06-07","ids":{"openalex":"https://openalex.org/W3119184403","doi":"https://doi.org/10.46298/lmcs-18(2:15)2022","mag":"3119184403"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-18(2:15)2022","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-18(2:15)2022","pdf_url":"https://lmcs.episciences.org/9655/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/9655/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080675787","display_name":"Marcelo Fiore","orcid":"https://orcid.org/0000-0001-8558-3492"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Marcelo P. Fiore","raw_affiliation_strings":["Department of Computer Science and Technology, University of Cambridge, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, University of Cambridge, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035484728","display_name":"Andrew M. Pitts","orcid":"https://orcid.org/0000-0001-7775-3471"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andrew M. Pitts","raw_affiliation_strings":["Department of Computer Science and Technology, University of Cambridge, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, University of Cambridge, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058369615","display_name":"S. C. Steenkamp","orcid":"https://orcid.org/0000-0003-3105-4098"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. C. Steenkamp","raw_affiliation_strings":["Department of Computer Science and Technology, University of Cambridge, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0003-3105-4098","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, University of Cambridge, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":1.3943,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.82919251,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"Volume 18, Issue 2","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9919999837875366,"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":0.940500020980835,"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":0.7785750031471252},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6975241899490356},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.621161937713623},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5465625524520874},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4975323975086212},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.4973612129688263},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4761790633201599},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.46717697381973267},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45209556818008423},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44711560010910034},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43049126863479614},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40989673137664795},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34588032960891724},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2813132405281067},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.163350909948349},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12985754013061523}],"concepts":[{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.7785750031471252},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6975241899490356},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.621161937713623},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5465625524520874},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4975323975086212},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.4973612129688263},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4761790633201599},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.46717697381973267},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45209556818008423},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44711560010910034},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43049126863479614},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40989673137664795},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34588032960891724},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2813132405281067},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.163350909948349},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12985754013061523},{"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},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.46298/lmcs-18(2:15)2022","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-18(2:15)2022","pdf_url":"https://lmcs.episciences.org/9655/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2101.02994","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.02994","pdf_url":"https://arxiv.org/pdf/2101.02994","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:d6c0156202344fa4a0b0117038b5ac8a","is_oa":true,"landing_page_url":"https://doaj.org/article/d6c0156202344fa4a0b0117038b5ac8a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 18, Issue 2 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/lmcs-18(2:15)2022","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-18(2:15)2022","pdf_url":"https://lmcs.episciences.org/9655/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2723597063","display_name":null,"funder_award_id":"EP/V002309/1","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3119184403.pdf","grobid_xml":"https://content.openalex.org/works/W3119184403.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W156546173","https://openalex.org/W814004361","https://openalex.org/W1549977012","https://openalex.org/W1580323916","https://openalex.org/W1594900487","https://openalex.org/W1773829243","https://openalex.org/W1836508668","https://openalex.org/W1983905931","https://openalex.org/W1998865204","https://openalex.org/W2010076922","https://openalex.org/W2052183597","https://openalex.org/W2079355284","https://openalex.org/W2079640625","https://openalex.org/W2079655821","https://openalex.org/W2081325813","https://openalex.org/W2098691999","https://openalex.org/W2102036964","https://openalex.org/W2117477507","https://openalex.org/W2121213425","https://openalex.org/W2124798629","https://openalex.org/W2136604612","https://openalex.org/W2274485505","https://openalex.org/W2485511814","https://openalex.org/W2490492614","https://openalex.org/W2499105636","https://openalex.org/W2563196418","https://openalex.org/W2773625575","https://openalex.org/W2788394322","https://openalex.org/W2802510100","https://openalex.org/W2885792094","https://openalex.org/W2900009437","https://openalex.org/W2964305797","https://openalex.org/W2964835846","https://openalex.org/W3021779990","https://openalex.org/W3028596397","https://openalex.org/W3101976357","https://openalex.org/W3120995647","https://openalex.org/W3148505520","https://openalex.org/W4206667141","https://openalex.org/W4240072532","https://openalex.org/W4240300612"],"related_works":["https://openalex.org/W4246327958","https://openalex.org/W2579704584","https://openalex.org/W4388322088","https://openalex.org/W2556917400","https://openalex.org/W2949083576","https://openalex.org/W2905232526","https://openalex.org/W4226410745","https://openalex.org/W1882235344","https://openalex.org/W2786712325","https://openalex.org/W2125274893"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"an":[3],"expressive":[4],"class":[5],"of":[6,16,27,54,70,83,86,98],"indexed":[7,25],"quotient-inductive":[8],"types,":[9,12],"called":[10],"QWI":[11,39,79],"within":[13],"the":[14,51,66,103,108,114],"framework":[15],"constructive":[17],"type":[18,52],"theory.":[19],"They":[20],"are":[21],"initial":[22],"algebras":[23],"for":[24],"families":[26],"equational":[28],"theories":[29],"with":[30,56],"possibly":[31],"infinitary":[32],"operators":[33],"and":[34,47,60,110],"equations.":[35],"We":[36,74,106],"prove":[37],"that":[38],"types":[40,46,49,80],"can":[41],"be":[42],"derived":[43],"from":[44],"quotient":[45],"inductive":[48],"in":[50],"theory":[53],"toposes":[55],"natural":[57],"number":[58],"object":[59],"universes,":[61],"provided":[62],"those":[63],"universes":[64],"satisfy":[65],"Weakly":[67],"Initial":[68],"Set":[69],"Covers":[71],"(WISC)":[72],"axiom.":[73,105],"do":[75],"so":[76],"by":[77,91],"constructing":[78],"as":[81],"colimits":[82],"a":[84,95],"family":[85],"approximations":[87],"to":[88],"them":[89],"defined":[90],"well-founded":[92],"recursion":[93],"over":[94],"suitable":[96],"notion":[97],"size,":[99],"whose":[100],"definition":[101],"involves":[102],"WISC":[104],"developed":[107],"proof":[109],"checked":[111],"it":[112],"using":[113],"Agda":[115],"theorem":[116],"prover.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}