{"id":"https://openalex.org/W2533751554","doi":"https://doi.org/10.1145/3018610.3018614","title":"Formalising real numbers in homotopy type theory","display_name":"Formalising real numbers in homotopy type theory","publication_year":2016,"publication_date":"2016-12-22","ids":{"openalex":"https://openalex.org/W2533751554","doi":"https://doi.org/10.1145/3018610.3018614","mag":"2533751554"},"language":"en","primary_location":{"id":"doi:10.1145/3018610.3018614","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3018610.3018614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.05072","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ga\u00ebtan Gilbert","orcid":null},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ga\u00ebtan Gilbert","raw_affiliation_strings":["ENS Lyon, France"],"affiliations":[{"raw_affiliation_string":"ENS Lyon, France","institution_ids":["https://openalex.org/I113428412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I113428412"],"apc_list":null,"apc_paid":null,"fwci":1.3331,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.87670413,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"112","last_page":"124"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9975000023841858,"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":0.9975000023841858,"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":0.9926999807357788,"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"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/cauchy-sequence","display_name":"Cauchy sequence","score":0.8172000050544739},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.6572999954223633},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.602400004863739},{"id":"https://openalex.org/keywords/cauchys-convergence-test","display_name":"Cauchy's convergence test","score":0.5968999862670898},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5827999711036682},{"id":"https://openalex.org/keywords/cauchys-integral-formula","display_name":"Cauchy's integral formula","score":0.5422000288963318},{"id":"https://openalex.org/keywords/residue-theorem","display_name":"Residue theorem","score":0.532800018787384},{"id":"https://openalex.org/keywords/cauchys-integral-theorem","display_name":"Cauchy's integral theorem","score":0.5169000029563904}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8414000272750854},{"id":"https://openalex.org/C203192437","wikidata":"https://www.wikidata.org/wiki/Q217847","display_name":"Cauchy sequence","level":2,"score":0.8172000050544739},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6572999954223633},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.602400004863739},{"id":"https://openalex.org/C76835800","wikidata":"https://www.wikidata.org/wiki/Q859102","display_name":"Cauchy's convergence test","level":5,"score":0.5968999862670898},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5827999711036682},{"id":"https://openalex.org/C82006148","wikidata":"https://www.wikidata.org/wiki/Q913764","display_name":"Cauchy's integral formula","level":4,"score":0.5422000288963318},{"id":"https://openalex.org/C88246228","wikidata":"https://www.wikidata.org/wiki/Q830513","display_name":"Residue theorem","level":4,"score":0.532800018787384},{"id":"https://openalex.org/C189658257","wikidata":"https://www.wikidata.org/wiki/Q834025","display_name":"Cauchy's integral theorem","level":5,"score":0.5169000029563904},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5113999843597412},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.46950000524520874},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.41029998660087585},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.40779998898506165},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.361299991607666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35910001397132874},{"id":"https://openalex.org/C71287196","wikidata":"https://www.wikidata.org/wiki/Q847204","display_name":"Limit of a sequence","level":3,"score":0.33489999175071716},{"id":"https://openalex.org/C10682574","wikidata":"https://www.wikidata.org/wiki/Q769374","display_name":"Cauchy principal value","level":5,"score":0.3278999924659729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2777000069618225},{"id":"https://openalex.org/C93361540","wikidata":"https://www.wikidata.org/wiki/Q848569","display_name":"Complete metric space","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.26420000195503235}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3018610.3018614","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3018610.3018614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1610.05072","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.05072","pdf_url":"https://arxiv.org/pdf/1610.05072","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":"pmh:oai:HAL:hal-01449326v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01449326","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"6th ACM SIGPLAN Conference on Certified Programs and Proofs , Jan 2017, Paris, France. pp.112 - 124, &#x27E8;10.1145/3018610.3018614&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.05072","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.05072","pdf_url":"https://arxiv.org/pdf/1610.05072","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2144335283"],"related_works":[],"abstract_inverted_index":{"Cauchy":[0,9,20,23,34],"reals":[1,24],"can":[2],"be":[3],"defined":[4,26],"as":[5],"a":[6,19,31],"quotient":[7],"of":[8,11,18,22,33,36],"sequences":[10,35],"rationals.":[12,37],"In":[13],"this":[14],"case,":[15],"the":[16],"limit":[17],"sequence":[21,32],"is":[25],"through":[27],"lifting":[28],"it":[29],"to":[30]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-10-28T00:00:00"}
