{"id":"https://openalex.org/W1995574761","doi":"https://doi.org/10.1145/1141277.1141584","title":"Assisted verification of elementary functions using Gappa","display_name":"Assisted verification of elementary functions using Gappa","publication_year":2006,"publication_date":"2006-04-23","ids":{"openalex":"https://openalex.org/W1995574761","doi":"https://doi.org/10.1145/1141277.1141584","mag":"1995574761"},"language":"en","primary_location":{"id":"doi:10.1145/1141277.1141584","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1141277.1141584","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 ACM symposium on Applied computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035966925","display_name":"Florent de Dinechin","orcid":"https://orcid.org/0000-0003-4927-3301"},"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"]},{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Florent de Dinechin","raw_affiliation_strings":["LIP, projet Ar\u00e9naire, \u00c9NS-Lyon all\u00e9e d'Italie, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP, projet Ar\u00e9naire, \u00c9NS-Lyon all\u00e9e d'Italie, France","institution_ids":["https://openalex.org/I4210144566","https://openalex.org/I113428412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000711113","display_name":"Christoph Lauter","orcid":"https://orcid.org/0000-0001-7335-8220"},"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"]},{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christoph Quirin Lauter","raw_affiliation_strings":["LIP, projet Ar\u00e9naire, \u00c9NS-Lyon all\u00e9e d'Italie, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP, projet Ar\u00e9naire, \u00c9NS-Lyon all\u00e9e d'Italie, France","institution_ids":["https://openalex.org/I4210144566","https://openalex.org/I113428412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073473823","display_name":"Guillaume Melquiond","orcid":"https://orcid.org/0000-0002-6697-1809"},"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":false,"raw_author_name":"Guillaume Melquiond","raw_affiliation_strings":["LIP, projet Ar\u00e9naire, \u00c9NS-Lyon, all\u00e9e d'Italie, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP, projet Ar\u00e9naire, \u00c9NS-Lyon, all\u00e9e d'Italie, France","institution_ids":["https://openalex.org/I113428412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3729,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.91932847,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1318","last_page":"1322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9732999801635742,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7527147531509399},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6563423275947571},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.6408213376998901},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6193655729293823},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.5650435090065002},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5451012849807739},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.5148831605911255},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5028886198997498},{"id":"https://openalex.org/keywords/formal-proof","display_name":"Formal proof","score":0.4900442361831665},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4597944915294647},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44302427768707275},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3893778324127197},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.199905127286911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19821372628211975},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.16815117001533508}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7527147531509399},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6563423275947571},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.6408213376998901},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6193655729293823},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5650435090065002},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5451012849807739},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.5148831605911255},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5028886198997498},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.4900442361831665},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4597944915294647},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44302427768707275},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3893778324127197},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.199905127286911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19821372628211975},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.16815117001533508},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1141277.1141584","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1141277.1141584","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 ACM symposium on Applied computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.108.4476","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.4476","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.msr-inria.inria.fr/~gmelquio/doc/06-mcms-article.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1607943221","https://openalex.org/W1672719503","https://openalex.org/W1980965137","https://openalex.org/W1986396242","https://openalex.org/W2012407419","https://openalex.org/W2137458298","https://openalex.org/W2149796605","https://openalex.org/W2167811272","https://openalex.org/W2437213251","https://openalex.org/W2615208225","https://openalex.org/W2743922485","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W3023573452","https://openalex.org/W4232621341","https://openalex.org/W6998509810"],"related_works":["https://openalex.org/W3026697850","https://openalex.org/W1524804222","https://openalex.org/W3173194202","https://openalex.org/W2153177892","https://openalex.org/W2951182230","https://openalex.org/W4297608983","https://openalex.org/W3100311625","https://openalex.org/W26319539","https://openalex.org/W1825610764","https://openalex.org/W4386746735"],"abstract_inverted_index":{"The":[0,20],"implementation":[1,32],"of":[2,30,46,48,87,169,193],"a":[3,23,159,166,178],"correctly":[4],"rounded":[5],"or":[6,68],"interval":[7,124],"elementary":[8],"function":[9,42],"needs":[10],"to":[11,35,62,109,114,131,138,158],"be":[12,56,129,174],"proven":[13],"carefully":[14],"in":[15,92,190],"the":[16,27,31,36,59,63,85,88,110,139,170,191,194],"very":[17,74,107],"last":[18],"details.":[19],"proof":[21,90,168,180],"requires":[22],"tight":[24],"bound":[25],"on":[26],"overall":[28],"error":[29,119],"with":[33],"respect":[34],"mathematical":[37,135],"function.":[38],"Such":[39],"work":[40],"is":[41,73,106,156],"specific,":[43],"concerns":[44],"tens":[45],"lines":[47],"code":[49,64,113],"for":[50,66],"each":[51],"function,":[52],"and":[53,76,116,121,154],"will":[54],"usually":[55],"broken":[57],"by":[58,80,177],"smallest":[60],"change":[61],"(e.g.":[65],"maintenance":[67],"optimization":[69],"purpose).":[70],"Therefore,":[71],"it":[72,117,127,143],"tedious":[75],"error-prone":[77],"if":[78],"done":[79],"hand.":[81],"This":[82],"article":[83],"discusses":[84],"use":[86],"Gappa":[89,95,163],"assistant":[91,181],"this":[93],"context.":[94],"has":[96],"two":[97],"main":[98],"advantages":[99],"over":[100],"previous":[101],"approaches:":[102],"Its":[103],"input":[104],"format":[105],"close":[108],"actual":[111],"C":[112,140],"validate,":[115],"automates":[118],"evaluation":[120],"propagation":[122],"using":[123],"arithmetic.":[125],"Besides,":[126],"can":[128,173],"used":[130],"incrementally":[132],"prove":[133],"complex":[134],"properties":[136],"pertaining":[137],"code.":[141,196],"Yet":[142],"does":[144],"not":[145],"require":[146],"any":[147],"specific":[148],"knowledge":[149],"about":[150],"automatic":[151],"theorem":[152],"proving,":[153],"thus":[155],"accessible":[157],"wider":[160],"community.":[161],"Moreover,":[162],"may":[164],"generate":[165],"formal":[167],"results":[171],"that":[172],"checked":[175],"independently":[176],"lower-level":[179],"like":[182],"Coq,":[183],"hence":[184],"providing":[185],"an":[186],"even":[187],"higher":[188],"confidence":[189],"certification":[192],"numerical":[195]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}