{"id":"https://openalex.org/W4416026976","doi":"https://doi.org/10.4230/lipics.itp.2025.21","title":"Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation","display_name":"Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4416026976","doi":"https://doi.org/10.4230/lipics.itp.2025.21"},"language":"en","primary_location":{"id":"pmh:oai:pure.atira.dk:openaire/a6844348-3cec-4fe0-a055-3489c63221de","is_oa":true,"landing_page_url":"https://pure.itu.dk/portal/da/publications/a6844348-3cec-4fe0-a055-3489c63221de","pdf_url":null,"source":{"id":"https://openalex.org/S4377196680","display_name":"IT University Of Copenhagen (IT University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83467386","host_organization_name":"IT University of Copenhagen","host_organization_lineage":["https://openalex.org/I83467386"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Affeldt, R, Bruni, A, Cohen, C, Saikawa, T & Roux, P 2025, Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation. in Leibniz International Proceedings in Informatics, LIPIcs. vol. 16, Leibniz International Proceedings in Informatics (LIPIcs), pp. 1-20. https://doi.org/10.4230/LIPIcs.ITP.2025.21","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure.itu.dk/portal/da/publications/a6844348-3cec-4fe0-a055-3489c63221de","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004449937","display_name":"Reynald Affeldt","orcid":"https://orcid.org/0000-0002-2327-953X"},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Affeldt, Reynald","raw_affiliation_strings":["National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan","AIST - National Institute of Advanced Industrial Science and Technology (Higashi, Tsukuba, Ibaraki 305-8561 - Japan)"],"raw_orcid":"https://orcid.org/0000-0002-2327-953X","affiliations":[{"raw_affiliation_string":"National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan","institution_ids":["https://openalex.org/I73613424"]},{"raw_affiliation_string":"AIST - National Institute of Advanced Industrial Science and Technology (Higashi, Tsukuba, Ibaraki 305-8561 - Japan)","institution_ids":["https://openalex.org/I73613424"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Bruni, Alessandro","orcid":"https://orcid.org/0000-0003-2946-9462"},"institutions":[{"id":"https://openalex.org/I83467386","display_name":"IT University of Copenhagen","ror":"https://ror.org/02309jg23","country_code":"DK","type":"education","lineage":["https://openalex.org/I83467386"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Bruni, Alessandro","raw_affiliation_strings":["IT University of Copenhagen, Denmark","ITU - IT University of Copenhagen (Rued Langgaards Vej 7, 2300 K\u00f8benhavn, Danemark - Denmark)"],"raw_orcid":"https://orcid.org/0000-0003-2946-9462","affiliations":[{"raw_affiliation_string":"IT University of Copenhagen, Denmark","institution_ids":["https://openalex.org/I83467386"]},{"raw_affiliation_string":"ITU - IT University of Copenhagen (Rued Langgaards Vej 7, 2300 K\u00f8benhavn, Danemark - Denmark)","institution_ids":["https://openalex.org/I83467386"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107271231","display_name":"Cyril Cohen","orcid":"https://orcid.org/0000-0003-3540-1050"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"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/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"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":"Cohen, Cyril","raw_affiliation_strings":["Inria, CNRS, ENS de Lyon, Universit\u00e9 Claude Bernard Lyon 1, LIP, UMR 5668, Lyon, France","LIP - Laboratoire de l'Informatique du Parall\u00e9lisme (46 All\u00e9e d'Italie 69364 LYON CEDEX 07 - France)","CASH - Compilation et Analyse, Logiciel et Mat\u00e9riel (France)"],"raw_orcid":"https://orcid.org/0000-0003-3540-1050","affiliations":[{"raw_affiliation_string":"Inria, CNRS, ENS de Lyon, Universit\u00e9 Claude Bernard Lyon 1, LIP, UMR 5668, Lyon, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIP - Laboratoire de l'Informatique du Parall\u00e9lisme (46 All\u00e9e d'Italie 69364 LYON CEDEX 07 - France)","institution_ids":["https://openalex.org/I4210144566","https://openalex.org/I113428412"]},{"raw_affiliation_string":"CASH - Compilation et Analyse, Logiciel et Mat\u00e9riel (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Roux, Pierre","orcid":"https://orcid.org/0000-0003-2910-4738"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I2801658355","display_name":"Office National d'\u00c9tudes et de Recherches A\u00e9rospatiales","ror":"https://ror.org/005y2ap84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2801658355"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Roux, Pierre","raw_affiliation_strings":["ONERA/DTIS, Universit\u00e9 de Toulouse, France","DTIS, ONERA, Universit\u00e9 Paris Saclay [Palaiseau] (91120 Palaiseau - France)"],"raw_orcid":"https://orcid.org/0000-0003-2910-4738","affiliations":[{"raw_affiliation_string":"ONERA/DTIS, Universit\u00e9 de Toulouse, France","institution_ids":["https://openalex.org/I17866349","https://openalex.org/I2801658355"]},{"raw_affiliation_string":"DTIS, ONERA, Universit\u00e9 Paris Saclay [Palaiseau] (91120 Palaiseau - France)","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I2801658355"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054151973","display_name":"Takafumi Saikawa","orcid":"https://orcid.org/0000-0003-4492-745X"},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Saikawa, Takafumi","raw_affiliation_strings":["Nagoya University, Japan","Nagoya University (Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan - Japan)"],"raw_orcid":"https://orcid.org/0000-0003-4492-745X","affiliations":[{"raw_affiliation_string":"Nagoya University, Japan","institution_ids":["https://openalex.org/I60134161"]},{"raw_affiliation_string":"Nagoya University (Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan - Japan)","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004449937"],"corresponding_institution_ids":["https://openalex.org/I73613424"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.33134481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.13009999692440033,"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/T10142","display_name":"Formal Methods in Verification","score":0.13009999692440033,"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/T10126","display_name":"Logic, programming, and type systems","score":0.08129999786615372,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.053300000727176666,"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/hierarchy","display_name":"Hierarchy","score":0.5534999966621399},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.49079999327659607},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.4878000020980835},{"id":"https://openalex.org/keywords/automation","display_name":"Automation","score":0.4410000145435333},{"id":"https://openalex.org/keywords/probability-theory","display_name":"Probability theory","score":0.4325999915599823},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4244000017642975},{"id":"https://openalex.org/keywords/complete-information","display_name":"Complete information","score":0.375},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.37439998984336853}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5534999966621399},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.49079999327659607},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45500001311302185},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44699999690055847},{"id":"https://openalex.org/C115901376","wikidata":"https://www.wikidata.org/wiki/Q184199","display_name":"Automation","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4244000017642975},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.375},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C130648207","wikidata":"https://www.wikidata.org/wiki/Q6007562","display_name":"Imprecise probability","level":3,"score":0.35989999771118164},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34049999713897705},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.31700000166893005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3068999946117401},{"id":"https://openalex.org/C195579931","wikidata":"https://www.wikidata.org/wiki/Q3623548","display_name":"Applied probability","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2831000089645386},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C71564387","wikidata":"https://www.wikidata.org/wiki/Q249514","display_name":"Chebyshev's inequality","level":5,"score":0.250900000333786},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.25060001015663147},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.25029999017715454}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:pure.atira.dk:openaire/a6844348-3cec-4fe0-a055-3489c63221de","is_oa":true,"landing_page_url":"https://pure.itu.dk/portal/da/publications/a6844348-3cec-4fe0-a055-3489c63221de","pdf_url":null,"source":{"id":"https://openalex.org/S4377196680","display_name":"IT University Of Copenhagen (IT University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83467386","host_organization_name":"IT University of Copenhagen","host_organization_lineage":["https://openalex.org/I83467386"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Affeldt, R, Bruni, A, Cohen, C, Saikawa, T & Roux, P 2025, Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation. in Leibniz International Proceedings in Informatics, LIPIcs. vol. 16, Leibniz International Proceedings in Informatics (LIPIcs), pp. 1-20. https://doi.org/10.4230/LIPIcs.ITP.2025.21","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:drops-oai.dagstuhl.de:24619","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.21","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol352-itp2025/LIPIcs.ITP.2025.21/LIPIcs.ITP.2025.21.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:HAL:hal-05318685v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05318685","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"16th International Conference on Interactive Theorem Proving (ITP 2025), Sep 2025, Reykjavik, Iceland. &#x27E8;10.4230/LIPIcs.ITP.2025.21&#x27E9;","raw_type":"Conference papers"},{"id":"doi:10.4230/lipics.itp.2025.21","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.itp.2025.21","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/a6844348-3cec-4fe0-a055-3489c63221de","is_oa":true,"landing_page_url":"https://pure.itu.dk/portal/da/publications/a6844348-3cec-4fe0-a055-3489c63221de","pdf_url":null,"source":{"id":"https://openalex.org/S4377196680","display_name":"IT University Of Copenhagen (IT University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83467386","host_organization_name":"IT University of Copenhagen","host_organization_lineage":["https://openalex.org/I83467386"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Affeldt, R, Bruni, A, Cohen, C, Saikawa, T & Roux, P 2025, Formalizing Concentration Inequalities in Rocq: Infrastructure and Automation. in Leibniz International Proceedings in Informatics, LIPIcs. vol. 16, Leibniz International Proceedings in Informatics (LIPIcs), pp. 1-20. https://doi.org/10.4230/LIPIcs.ITP.2025.21","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G391346137","display_name":"Formal Foundations for Verification of Physical and Probabilistic Systems","funder_award_id":"22H00520","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Concentration":[0],"inequalities":[1],"are":[2],"standard":[3],"lemmas":[4,25],"providing":[5],"upper":[6],"bounds":[7],"on":[8,53,74],"deviations":[9],"of":[10,24,43,55,82,95,102],"random":[11],"variables.":[12],"To":[13],"formalize":[14,87],"concentration":[15,104],"inequalities,":[16],"we":[17,51],"have":[18],"been":[19],"developing":[20],"a":[21,69,103],"general":[22,56],"library":[23],"for":[26,65,106],"probability":[27,96],"theory":[28,97],"in":[29],"the":[30,44,80,99],"Rocq":[31],"prover.":[32],"This":[33],"effort":[34],"led":[35],"us":[36],"to":[37,86],"revisit":[38],"already":[39],"established":[40],"technical":[41],"aspects":[42],"Mathematical":[45],"Components":[46],"libraries.":[47],"In":[48],"this":[49],"paper,":[50],"report":[52],"improvements":[54],"interest":[57],"resulting":[58],"from":[59],"our":[60,92],"formalization.":[61],"We":[62,77,90],"devise":[63],"types":[64],"numeric":[66],"values":[67],"and":[68],"lightweight":[70],"semi-decision":[71],"procedure,":[72],"based":[73],"interval":[75],"arithmetic.":[76],"also":[78],"extend":[79],"hierarchy":[81],"available":[83],"mathematical":[84],"structures":[85],"Lebesgue":[88],"spaces.":[89],"illustrate":[91],"new":[93],"formalization":[94],"with":[98],"complete":[100],"proof":[101],"inequality":[105],"Bernoulli":[107],"sampling.":[108]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
