{"id":"https://openalex.org/W1986750872","doi":"https://doi.org/10.1007/s10472-009-9156-3","title":"Invariants for the FoCaL language","display_name":"Invariants for the FoCaL language","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W1986750872","doi":"https://doi.org/10.1007/s10472-009-9156-3","mag":"1986750872"},"language":"en","primary_location":{"id":"doi:10.1007/s10472-009-9156-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10472-009-9156-3","pdf_url":null,"source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-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/A5022157208","display_name":"Renaud Rioboo","orcid":null},"institutions":[{"id":"https://openalex.org/I124158823","display_name":"Conservatoire National des Arts et M\u00e9tiers","ror":"https://ror.org/0175hh227","country_code":"FR","type":"education","lineage":["https://openalex.org/I124158823","https://openalex.org/I4210134562"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I4210097372","display_name":"\u00c9cole Nationale Sup\u00e9rieure d\u2019Informatique pour l\u2019Industrie et l\u2019Entreprise","ror":"https://ror.org/00tx98v53","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210097372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Renaud Rioboo","raw_affiliation_strings":["\u00c9cole Nationale Sup\u00e9rieure d\u2019Informatique pour l\u2019Industrie et l\u2019Entreprise, Centre de Recherche en Informatique du CNAM, 1 place de la r\u00e9sistance, 91025, Evry, France","\u00c9cole Nationale Sup\u00e9rieure d'Informatique pour l'Industrie et l'Entreprise, Centre de Recherche en Informatique du CNAM, Evry, France 91025#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Nationale Sup\u00e9rieure d\u2019Informatique pour l\u2019Industrie et l\u2019Entreprise, Centre de Recherche en Informatique du CNAM, 1 place de la r\u00e9sistance, 91025, Evry, France","institution_ids":["https://openalex.org/I124158823","https://openalex.org/I4210097372"]},{"raw_affiliation_string":"\u00c9cole Nationale Sup\u00e9rieure d'Informatique pour l'Industrie et l'Entreprise, Centre de Recherche en Informatique du CNAM, Evry, France 91025#TAB#","institution_ids":["https://openalex.org/I124158823","https://openalex.org/I29607241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022157208"],"corresponding_institution_ids":["https://openalex.org/I124158823","https://openalex.org/I29607241","https://openalex.org/I4210097372"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.5221,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7795054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"56","issue":"3-4","first_page":"273","last_page":"296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9904000163078308,"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/T10142","display_name":"Formal Methods in Verification","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.7706927061080933},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6365863084793091},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5889348387718201},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5464280843734741},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5413780808448792},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5320554375648499},{"id":"https://openalex.org/keywords/certification","display_name":"Certification","score":0.4641870856285095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42415645718574524},{"id":"https://openalex.org/keywords/cardinal-point","display_name":"Cardinal point","score":0.41974854469299316},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4168984293937683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4072958827018738},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.36826837062835693},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.34487491846084595},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30511653423309326},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2926018238067627}],"concepts":[{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7706927061080933},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6365863084793091},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5889348387718201},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5464280843734741},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5413780808448792},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5320554375648499},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.4641870856285095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42415645718574524},{"id":"https://openalex.org/C138395690","wikidata":"https://www.wikidata.org/wiki/Q376733","display_name":"Cardinal point","level":2,"score":0.41974854469299316},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4168984293937683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4072958827018738},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.36826837062835693},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.34487491846084595},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30511653423309326},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2926018238067627},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10472-009-9156-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10472-009-9156-3","pdf_url":null,"source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.44999998807907104,"display_name":"Quality Education"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323400","display_name":"Universit\u00e9 Pierre et Marie Curie","ror":"https://ror.org/02en5vm52"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1477903","https://openalex.org/W196166933","https://openalex.org/W603208740","https://openalex.org/W1498091397","https://openalex.org/W1508641834","https://openalex.org/W1531924917","https://openalex.org/W1553511155","https://openalex.org/W1560253649","https://openalex.org/W1628745019","https://openalex.org/W1836537838","https://openalex.org/W1878755246","https://openalex.org/W1945317924","https://openalex.org/W1988136938","https://openalex.org/W2013140497","https://openalex.org/W2020559348","https://openalex.org/W2093058647","https://openalex.org/W2097327552","https://openalex.org/W2103898608","https://openalex.org/W2106192381","https://openalex.org/W2120905340","https://openalex.org/W2149969760","https://openalex.org/W2593114892","https://openalex.org/W2912472557","https://openalex.org/W3122722170","https://openalex.org/W4250846042","https://openalex.org/W4302439999"],"related_works":["https://openalex.org/W2069431043","https://openalex.org/W1493730236","https://openalex.org/W1985488429","https://openalex.org/W2062762081","https://openalex.org/W2040411183","https://openalex.org/W2074988888","https://openalex.org/W1482793357","https://openalex.org/W2063829785","https://openalex.org/W2056317466","https://openalex.org/W4230018645"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}