{"id":"https://openalex.org/W2914814133","doi":"https://doi.org/10.23638/lmcs-16(1:10)2020","title":"Signatures and Induction Principles for Higher Inductive-Inductive Types","display_name":"Signatures and Induction Principles for Higher Inductive-Inductive Types","publication_year":2020,"publication_date":"2020-02-13","ids":{"openalex":"https://openalex.org/W2914814133","doi":"https://doi.org/10.23638/lmcs-16(1:10)2020","mag":"2914814133"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-16(1:10)2020","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-16(1:10)2020","pdf_url":"https://lmcs.episciences.org/6100/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/6100/pdf","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ambrus Kaposi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045224632","display_name":"Andr\u00e1s Kov\u00e1cs","orcid":"https://orcid.org/0000-0002-6375-9781"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andr\u00e1s Kov\u00e1cs","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047340010"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5438,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72249875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"Volume 16, Issue 1","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":0.9987999796867371,"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":0.9987999796867371,"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":0.9860000014305115,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.98089998960495,"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/type-theory","display_name":"Type theory","score":0.8950923681259155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5939292311668396},{"id":"https://openalex.org/keywords/haskell","display_name":"Haskell","score":0.5123192071914673},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.4903838634490967},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.47106000781059265},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.4588085412979126},{"id":"https://openalex.org/keywords/abstract-syntax","display_name":"Abstract syntax","score":0.4465211033821106},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4354346990585327},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.43449410796165466},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.4338510036468506},{"id":"https://openalex.org/keywords/functional-programming","display_name":"Functional programming","score":0.41162052750587463},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38958466053009033},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.3094150424003601},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25685039162635803},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22373631596565247}],"concepts":[{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.8950923681259155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5939292311668396},{"id":"https://openalex.org/C2780624054","wikidata":"https://www.wikidata.org/wiki/Q34010","display_name":"Haskell","level":3,"score":0.5123192071914673},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.4903838634490967},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.47106000781059265},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.4588085412979126},{"id":"https://openalex.org/C114408938","wikidata":"https://www.wikidata.org/wiki/Q333373","display_name":"Abstract syntax","level":3,"score":0.4465211033821106},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4354346990585327},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.43449410796165466},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.4338510036468506},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.41162052750587463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38958466053009033},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.3094150424003601},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25685039162635803},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22373631596565247},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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:10.23638/lmcs-16(1:10)2020","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-16(1:10)2020","pdf_url":"https://lmcs.episciences.org/6100/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:1902.00297","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.00297","pdf_url":"https://arxiv.org/pdf/1902.00297","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"doi:10.48550/arxiv.1902.00297","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1902.00297","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.23638/lmcs-16(1:10)2020","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-16(1:10)2020","pdf_url":"https://lmcs.episciences.org/6100/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/G1595354820","display_name":null,"funder_award_id":"ED 18-1-2019-0030","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1875477190","display_name":null,"funder_award_id":"ED_18-1-2019-0030","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"id":"https://openalex.org/G2939026455","display_name":null,"funder_award_id":"ED 18-1-2019-0030","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"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/G8712575783","display_name":null,"funder_award_id":"EFOP-3.6.3-VEKOP-16-2017-00002","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"id":"https://openalex.org/G972092959","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"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335908","display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2914814133.pdf","grobid_xml":"https://content.openalex.org/works/W2914814133.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W2145199","https://openalex.org/W1494555245","https://openalex.org/W1517671027","https://openalex.org/W1539303361","https://openalex.org/W1664326696","https://openalex.org/W1773829243","https://openalex.org/W1949275316","https://openalex.org/W2006850413","https://openalex.org/W2006941708","https://openalex.org/W2019626268","https://openalex.org/W2036487200","https://openalex.org/W2042204873","https://openalex.org/W2052183597","https://openalex.org/W2054195362","https://openalex.org/W2058174669","https://openalex.org/W2079640625","https://openalex.org/W2102861499","https://openalex.org/W2170599098","https://openalex.org/W2194904877","https://openalex.org/W2274485505","https://openalex.org/W2296612922","https://openalex.org/W2467476450","https://openalex.org/W2550513301","https://openalex.org/W2563196418","https://openalex.org/W2565502105","https://openalex.org/W2604829466","https://openalex.org/W2615373383","https://openalex.org/W2779668776","https://openalex.org/W2802510100","https://openalex.org/W2883252932","https://openalex.org/W2885792094","https://openalex.org/W2900009437","https://openalex.org/W2964029175","https://openalex.org/W2964125890","https://openalex.org/W3032285962","https://openalex.org/W3099982020"],"related_works":["https://openalex.org/W2112263414","https://openalex.org/W3004782279","https://openalex.org/W1602185604","https://openalex.org/W2028779182","https://openalex.org/W4242678340","https://openalex.org/W2140654465","https://openalex.org/W2129253059","https://openalex.org/W1488646450","https://openalex.org/W4296274916","https://openalex.org/W3006157134"],"abstract_inverted_index":{"Higher":[0],"inductive-inductive":[1],"types":[2,6,45],"(HIITs)":[3],"generalize":[4],"inductive":[5,44],"of":[7,23,46,54,66,85,95,113,122,142],"dependent":[8],"type":[9,48,67,90],"theories":[10],"in":[11,99,147],"two":[12],"ways.":[13],"On":[14,33],"the":[15,20,34,58,63,93,107,151],"one":[16],"hand":[17,36],"they":[18,37],"allow":[19],"simultaneous":[21],"definition":[22,84],"multiple":[24],"sorts":[25],"that":[26,51],"can":[27],"be":[28],"indexed":[29],"over":[30],"each":[31],"other.":[32],"other":[35],"support":[38],"equality":[39,75],"constructors,":[40],"thus":[41],"generalizing":[42],"higher":[43],"homotopy":[47],"theory.":[49],"Examples":[50],"make":[52],"use":[53],"both":[55],"features":[56],"are":[57,72],"Cauchy":[59],"real":[60],"numbers":[61],"and":[62,115,131,165],"well-typed":[64],"syntax":[65],"theory":[68,94,101,141],"where":[69],"conversion":[70],"rules":[71],"given":[73],"as":[74,163,169],"constructors.":[76,108],"In":[77],"this":[78,100],"paper":[79],"we":[80],"propose":[81],"a":[82,88,103,157],"general":[83],"HIITs":[86],"using":[87,120],"small":[89],"theory,":[91],"named":[92],"signatures.":[96],"A":[97],"context":[98],"encodes":[102],"HIIT":[104,143],"by":[105,119],"listing":[106],"We":[109,154],"also":[110,155],"compute":[111],"notions":[112],"induction":[114],"recursion":[116],"for":[117,137],"HIITs,":[118],"variants":[121],"syntactic":[123,152],"logical":[124],"relation":[125],"translations.":[126,153],"Building":[127],"full":[128],"categorical":[129],"semantics":[130],"constructing":[132],"initial":[133],"algebras":[134],"is":[135],"left":[136],"future":[138],"work.":[139],"The":[140],"signatures":[144,162],"was":[145],"formalised":[146],"Agda":[148,171],"together":[149],"with":[150],"provide":[156],"Haskell":[158],"implementation,":[159],"which":[160],"takes":[161],"input":[164],"outputs":[166],"translation":[167],"results":[168],"valid":[170],"code.":[172]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}