{"id":"https://openalex.org/W1554598184","doi":"https://doi.org/10.23638/lmcs-13(1:8)2017","title":"Lineal: A linear-algebraic Lambda-calculus","display_name":"Lineal: A linear-algebraic Lambda-calculus","publication_year":2017,"publication_date":"2017-03-17","ids":{"openalex":"https://openalex.org/W1554598184","doi":"https://doi.org/10.23638/lmcs-13(1:8)2017","mag":"1554598184"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-13(1:8)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(1:8)2017","pdf_url":"https://lmcs.episciences.org/3203/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/3203/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035883865","display_name":"Pablo Arrighi","orcid":"https://orcid.org/0000-0002-3535-1009"},"institutions":[{"id":"https://openalex.org/I4210104430","display_name":"Laboratoire d'Informatique de Grenoble","ror":"https://ror.org/01c8rcg82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pablo Arrighi","raw_affiliation_strings":["Laboratoire d'Informatique de Grenoble"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique de Grenoble","institution_ids":["https://openalex.org/I4210104430"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073164575","display_name":"Gilles Dowek","orcid":"https://orcid.org/0000-0001-6253-935X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gilles Dowek","raw_affiliation_strings":["Deduction modulo, interop\u00e9rabilit\u00e9 et d\u00e9monstration automatique"],"affiliations":[{"raw_affiliation_string":"Deduction modulo, interop\u00e9rabilit\u00e9 et d\u00e9monstration automatique","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035883865"],"corresponding_institution_ids":["https://openalex.org/I4210104430"],"apc_list":null,"apc_paid":null,"fwci":3.7376,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.94422879,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"Volume 13, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9991999864578247,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9991999864578247,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9925000071525574,"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":0.9850999712944031,"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/calculus","display_name":"Calculus (dental)","score":0.7341952323913574},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6431988477706909},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5899955034255981},{"id":"https://openalex.org/keywords/typed-lambda-calculus","display_name":"Typed lambda calculus","score":0.560333251953125},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.557672381401062},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4371790289878845},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.4361081123352051},{"id":"https://openalex.org/keywords/church-encoding","display_name":"Church encoding","score":0.43288615345954895},{"id":"https://openalex.org/keywords/simply-typed-lambda-calculus","display_name":"Simply typed lambda calculus","score":0.4268742501735687},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3479284346103668},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23990610241889954},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2301044464111328},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1337551474571228},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.05727925896644592}],"concepts":[{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.7341952323913574},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6431988477706909},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5899955034255981},{"id":"https://openalex.org/C142156749","wikidata":"https://www.wikidata.org/wiki/Q2607208","display_name":"Typed lambda calculus","level":3,"score":0.560333251953125},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.557672381401062},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4371790289878845},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.4361081123352051},{"id":"https://openalex.org/C77736955","wikidata":"https://www.wikidata.org/wiki/Q1089708","display_name":"Church encoding","level":5,"score":0.43288615345954895},{"id":"https://openalex.org/C61237538","wikidata":"https://www.wikidata.org/wiki/Q855192","display_name":"Simply typed lambda calculus","level":4,"score":0.4268742501735687},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3479284346103668},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23990610241889954},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2301044464111328},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1337551474571228},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.05727925896644592},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.23638/lmcs-13(1:8)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(1:8)2017","pdf_url":"https://lmcs.episciences.org/3203/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:quant-ph/0612199","is_oa":true,"landing_page_url":"http://arxiv.org/abs/quant-ph/0612199","pdf_url":"https://arxiv.org/pdf/quant-ph/0612199","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:26816753f7984b1b9c40cfbf5e10df64","is_oa":true,"landing_page_url":"https://doaj.org/article/26816753f7984b1b9c40cfbf5e10df64","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 13, Issue 1 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.23638/lmcs-13(1:8)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(1:8)2017","pdf_url":"https://lmcs.episciences.org/3203/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1554598184.pdf","grobid_xml":"https://content.openalex.org/works/W1554598184.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W93314864","https://openalex.org/W944083597","https://openalex.org/W1485061101","https://openalex.org/W1514385409","https://openalex.org/W1541150383","https://openalex.org/W1542860149","https://openalex.org/W1544810690","https://openalex.org/W1567354447","https://openalex.org/W1570171385","https://openalex.org/W1785637000","https://openalex.org/W1991856459","https://openalex.org/W1993688167","https://openalex.org/W1997143185","https://openalex.org/W1999626800","https://openalex.org/W2002372750","https://openalex.org/W2011180881","https://openalex.org/W2012968289","https://openalex.org/W2018674325","https://openalex.org/W2027907817","https://openalex.org/W2042924775","https://openalex.org/W2044212944","https://openalex.org/W2049352524","https://openalex.org/W2049471987","https://openalex.org/W2050334794","https://openalex.org/W2056016391","https://openalex.org/W2070230244","https://openalex.org/W2088376608","https://openalex.org/W2091036953","https://openalex.org/W2101894951","https://openalex.org/W2102549858","https://openalex.org/W2110240249","https://openalex.org/W2113152322","https://openalex.org/W2114421037","https://openalex.org/W2115048135","https://openalex.org/W2121382061","https://openalex.org/W2131283815","https://openalex.org/W2132938661","https://openalex.org/W2133177432","https://openalex.org/W2137722266","https://openalex.org/W2145862486","https://openalex.org/W2154536801","https://openalex.org/W2159566537","https://openalex.org/W2323378191","https://openalex.org/W2736955251","https://openalex.org/W2911865844","https://openalex.org/W2911874855","https://openalex.org/W2912818154","https://openalex.org/W2913788899","https://openalex.org/W2952947094","https://openalex.org/W2952988636","https://openalex.org/W2962969097","https://openalex.org/W3007889862","https://openalex.org/W3099155063","https://openalex.org/W3111297213"],"related_works":["https://openalex.org/W2761902706","https://openalex.org/W3123171335","https://openalex.org/W2114151019","https://openalex.org/W1595139175","https://openalex.org/W2088376608","https://openalex.org/W2110435210","https://openalex.org/W2189323991","https://openalex.org/W236003875","https://openalex.org/W2153353244","https://openalex.org/W1583714326"],"abstract_inverted_index":{"We":[0,14,47,83],"provide":[1],"a":[2,20,57,73,125],"computational":[3],"definition":[4],"of":[5,8,42,56,75,87,93,112,124,147],"the":[6,32,35,65,70,85,91,105,110,113,121,134],"notions":[7],"vector":[9,129],"space":[10],"and":[11,26,61,78,144],"bilinear":[12],"functions.":[13],"use":[15],"this":[16,52,88],"result":[17],"to":[18,37,50],"introduce":[19],"minimal":[21],"language":[22,30,53,71,74],"combining":[23],"higher-order":[24,143],"computation":[25],"linear":[27,40,76],"algebra.":[28],"This":[29],"extends":[31],"Lambda-calculus":[33,141],"with":[34],"possibility":[36],"make":[38],"arbitrary":[39],"combinations":[41],"terms":[43,55],"alpha.t":[44],"+":[45],"beta.u.":[46],"describe":[48],"how":[49],""execute"":[51],"in":[54,90,104,133],"few":[58],"rewrite":[59,126],"rules,":[60],"justify":[62],"them":[63],"through":[64],"two":[66],"fundamental":[67],"requirements":[68],"that":[69,79],"be":[72,81,101],"operators,":[77],"it":[80],"higher-order.":[82],"mention":[84],"perspectives":[86],"work":[89],"field":[92],"quantum":[94],"computation,":[95],"whose":[96],"circuits":[97],"we":[98,108],"show":[99],"can":[100],"easily":[102],"encoded":[103],"calculus.":[106,115],"Finally,":[107],"prove":[109],"confluence":[111],"entire":[114],"Comment:":[116],"The":[117],"complementary":[118],"note":[119],""On":[120],"critical":[122],"pairs":[123],"system":[127],"for":[128],"spaces"":[130],"is":[131],"provided":[132],"source":[135],"files.":[136],"Short":[137],"version":[138,158],":":[139,142,159],""Linear-algebraic":[140],"confluence",":[145],"Proceedings":[146],"RTA":[148],"08,":[149],"Hagenberg,":[150],"July":[151],"2008.":[152],"LNCS":[153],"5117,":[154],"17,":[155],"(2008).":[156],"Long":[157],"LMCS":[160]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}