{"id":"https://openalex.org/W1533915816","doi":"https://doi.org/10.1007/3-540-45648-1_19","title":"\u201cHigher-Order\u201d Mathematics in B","display_name":"\u201cHigher-Order\u201d Mathematics in B","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1533915816","doi":"https://doi.org/10.1007/3-540-45648-1_19","mag":"1533915816"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45648-1_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45648-1_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5113780795","display_name":"Jean-Raymond Abrial","orcid":null},"institutions":[{"id":"https://openalex.org/I4210136988","display_name":"D\u00e9l\u00e9gation Provence et Corse","ror":"https://ror.org/049qgqg40","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210136988","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Raymond Abrial","raw_affiliation_strings":["Consultant, Marseille, France"],"affiliations":[{"raw_affiliation_string":"Consultant, Marseille, France","institution_ids":["https://openalex.org/I4210136988"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007751056","display_name":"Dominique Cansell","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominique Cansell","raw_affiliation_strings":["LORIA, Metz, France"],"affiliations":[{"raw_affiliation_string":"LORIA, Metz, France","institution_ids":["https://openalex.org/I4210121838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002772225","display_name":"Guy Laffitte","orcid":null},"institutions":[{"id":"https://openalex.org/I1339876250","display_name":"Institut National de la Statistique et des Etudes Economiques","ror":"https://ror.org/03v6yxf25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1339876250"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guy Laffitte","raw_affiliation_strings":["INSEE, Nantes, France"],"affiliations":[{"raw_affiliation_string":"INSEE, Nantes, France","institution_ids":["https://openalex.org/I1339876250"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113780795"],"corresponding_institution_ids":["https://openalex.org/I4210136988"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0798,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.76485957,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"370","last_page":"393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991999864578247,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991999864578247,"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/T11567","display_name":"semigroups and automata theory","score":0.9990000128746033,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9973000288009644,"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/computer-science","display_name":"Computer science","score":0.5973126888275146},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5787469744682312},{"id":"https://openalex.org/keywords/mathematical-structure","display_name":"Mathematical structure","score":0.5658001899719238},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5474664568901062},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.47840985655784607},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.4597172737121582},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4460071325302124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4191354513168335},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33213290572166443},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32705116271972656},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22897523641586304},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.19424974918365479},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.1738744080066681}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5973126888275146},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5787469744682312},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.5658001899719238},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5474664568901062},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.47840985655784607},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.4597172737121582},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4460071325302124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4191354513168335},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33213290572166443},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32705116271972656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22897523641586304},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.19424974918365479},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.1738744080066681},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-45648-1_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45648-1_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:inria-00100923v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00100923","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2nd International Conference of B and Z Users - ZB'2002, D. Bert, J.P. Bowen, M.C. Henson, K. Robinson, Jan 2002, Grenoble, France, pp.370-393","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1479972615","https://openalex.org/W1559870885","https://openalex.org/W1985132925","https://openalex.org/W2073127449","https://openalex.org/W2122063022","https://openalex.org/W2137343774","https://openalex.org/W4206054285","https://openalex.org/W4254354208"],"related_works":["https://openalex.org/W2468279273","https://openalex.org/W2354198838","https://openalex.org/W1989130879","https://openalex.org/W2103419012","https://openalex.org/W2988126442","https://openalex.org/W1974414866","https://openalex.org/W2063982682","https://openalex.org/W2338543196","https://openalex.org/W1544691147","https://openalex.org/W2046415586"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
