{"id":"https://openalex.org/W2908479200","doi":"https://doi.org/10.1145/3293880.3294093","title":"Smooth manifolds and types to sets for linear algebra in Isabelle/HOL","display_name":"Smooth manifolds and types to sets for linear algebra in Isabelle/HOL","publication_year":2019,"publication_date":"2019-01-04","ids":{"openalex":"https://openalex.org/W2908479200","doi":"https://doi.org/10.1145/3293880.3294093","mag":"2908479200"},"language":"en","primary_location":{"id":"doi:10.1145/3293880.3294093","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3293880.3294093","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3293880.3294093","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3293880.3294093","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089633378","display_name":"Fabian Immler","orcid":"https://orcid.org/0000-0002-5468-1513"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Fabian Immler","raw_affiliation_strings":["Carnegie Mellon University, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078226330","display_name":"Bohua Zhan","orcid":"https://orcid.org/0000-0001-5377-9351"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bohua Zhan","raw_affiliation_strings":["Institute of Software at Chinese Academy of Sciences, China"],"affiliations":[{"raw_affiliation_string":"Institute of Software at Chinese Academy of Sciences, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089633378"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":1.1423,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73041242,"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":"65","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9958000183105469,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9958000183105469,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9926000237464905,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9692000150680542,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/hol","display_name":"HOL","score":0.906215488910675},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5843195915222168},{"id":"https://openalex.org/keywords/partition-of-unity","display_name":"Partition of unity","score":0.5136522650718689},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.508979082107544},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5048685669898987},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.49466702342033386},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.45694172382354736},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44779300689697266},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4411940276622772},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4214290380477905},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4029935896396637},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3986291289329529},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32086247205734253},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09850054979324341},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09804016351699829},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07017466425895691}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.906215488910675},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5843195915222168},{"id":"https://openalex.org/C102205669","wikidata":"https://www.wikidata.org/wiki/Q191690","display_name":"Partition of unity","level":3,"score":0.5136522650718689},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.508979082107544},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5048685669898987},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.49466702342033386},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.45694172382354736},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44779300689697266},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4411940276622772},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4214290380477905},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4029935896396637},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3986291289329529},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32086247205734253},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09850054979324341},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09804016351699829},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07017466425895691},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3293880.3294093","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3293880.3294093","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3293880.3294093","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3293880.3294093","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3293880.3294093","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3293880.3294093","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G164976218","display_name":null,"funder_award_id":"FA9550-18-1-0120","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3673415204","display_name":null,"funder_award_id":"FA9550-18-1-01","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4481851374","display_name":null,"funder_award_id":"Leibniz","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G653283282","display_name":null,"funder_award_id":"NI 491/16-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2908479200.pdf","grobid_xml":"https://content.openalex.org/works/W2908479200.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1521083034","https://openalex.org/W1545409775","https://openalex.org/W1557324374","https://openalex.org/W1561420154","https://openalex.org/W1572143211","https://openalex.org/W1577258119","https://openalex.org/W2068729756","https://openalex.org/W2089606669","https://openalex.org/W2106192381","https://openalex.org/W2174838357","https://openalex.org/W2404994878","https://openalex.org/W2561675875","https://openalex.org/W2751080695","https://openalex.org/W2806477068","https://openalex.org/W4214825871","https://openalex.org/W4235840289","https://openalex.org/W4247458820"],"related_works":["https://openalex.org/W2585743557","https://openalex.org/W1594958113","https://openalex.org/W3193153727","https://openalex.org/W2477568018","https://openalex.org/W43811100","https://openalex.org/W1984215587","https://openalex.org/W2381320429","https://openalex.org/W4299299922","https://openalex.org/W2593957634","https://openalex.org/W2352690124"],"abstract_inverted_index":{"We":[0,29,67],"formalize":[1],"the":[2,23,47,71,88],"definition":[3],"and":[4,19,22,38,52,74],"basic":[5],"properties":[6],"of":[7,16,46,78,93],"smooth":[8],"manifolds":[9,34],"in":[10],"Isabelle/HOL.":[11],"Concepts":[12],"covered":[13],"include":[14],"partition":[15],"unity,":[17],"tangent":[18],"cotangent":[20],"spaces,":[21],"fundamental":[24],"theorem":[25],"for":[26,50,57,64],"line":[27],"integrals.":[28],"also":[30],"construct":[31],"some":[32],"concrete":[33],"such":[35],"as":[36],"spheres":[37],"projective":[39],"spaces.":[40],"The":[41,54],"formalization":[42],"makes":[43],"extensive":[44],"use":[45],"existing":[48,55,89],"libraries":[49],"topology":[51],"analysis.":[53],"library":[56,92],"linear":[58,94],"algebra":[59,95],"is":[60],"not":[61],"flexible":[62],"enough":[63],"our":[65],"needs.":[66],"therefore":[68],"set":[69],"up":[70],"first":[72],"systematic":[73],"large":[75],"scale":[76],"application":[77],"``types":[79],"to":[80,85,96],"sets''.":[81],"It":[82],"allows":[83],"us":[84],"automatically":[86],"transform":[87],"(type":[90],"based)":[91],"one":[97],"with":[98],"explicit":[99],"carrier":[100],"sets.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-16T09:10:04.655348","created_date":"2025-10-10T00:00:00"}