{"id":"https://openalex.org/W1578080614","doi":"https://doi.org/10.1007/1-4020-8141-3_48","title":"The Simply-Typed Pure Pattern Type System Ensures Strong Normalization","display_name":"The Simply-Typed Pure Pattern Type System Ensures Strong Normalization","publication_year":2006,"publication_date":"2006-02-21","ids":{"openalex":"https://openalex.org/W1578080614","doi":"https://doi.org/10.1007/1-4020-8141-3_48","mag":"1578080614"},"language":"en","primary_location":{"id":"doi:10.1007/1-4020-8141-3_48","is_oa":true,"landing_page_url":"https://doi.org/10.1007/1-4020-8141-3_48","pdf_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_48.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_48.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039334755","display_name":"Benjamin Wack","orcid":null},"institutions":[{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"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":true,"raw_author_name":"Benjamin Wack","raw_affiliation_strings":["LORIA & Universit\u00e9 Henri Poincar\u00e9, Nancy, France"],"affiliations":[{"raw_affiliation_string":"LORIA & Universit\u00e9 Henri Poincar\u00e9, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039334755"],"corresponding_institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I90183372"],"apc_list":null,"apc_paid":null,"fwci":0.9041,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.74314689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"633","last_page":"646"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9843000173568726,"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":0.978600025177002,"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/rewriting","display_name":"Rewriting","score":0.7685254216194153},{"id":"https://openalex.org/keywords/typed-lambda-calculus","display_name":"Typed lambda calculus","score":0.7190870046615601},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.7134653329849243},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.6973340511322021},{"id":"https://openalex.org/keywords/simply-typed-lambda-calculus","display_name":"Simply typed lambda calculus","score":0.5780941843986511},{"id":"https://openalex.org/keywords/dependent-type","display_name":"Dependent type","score":0.5540459156036377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5458865165710449},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.5306191444396973},{"id":"https://openalex.org/keywords/normalization-property","display_name":"Normalization property","score":0.5249961614608765},{"id":"https://openalex.org/keywords/system-f","display_name":"System F","score":0.5187423825263977},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4681926667690277},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4534466862678528},{"id":"https://openalex.org/keywords/expressive-power","display_name":"Expressive power","score":0.43489086627960205},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.42852669954299927},{"id":"https://openalex.org/keywords/logical-framework","display_name":"Logical framework","score":0.42714211344718933},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.41105523705482483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37289828062057495},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.36513209342956543}],"concepts":[{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.7685254216194153},{"id":"https://openalex.org/C142156749","wikidata":"https://www.wikidata.org/wiki/Q2607208","display_name":"Typed lambda calculus","level":3,"score":0.7190870046615601},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.7134653329849243},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.6973340511322021},{"id":"https://openalex.org/C61237538","wikidata":"https://www.wikidata.org/wiki/Q855192","display_name":"Simply typed lambda calculus","level":4,"score":0.5780941843986511},{"id":"https://openalex.org/C20528804","wikidata":"https://www.wikidata.org/wiki/Q997433","display_name":"Dependent type","level":3,"score":0.5540459156036377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5458865165710449},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.5306191444396973},{"id":"https://openalex.org/C159333733","wikidata":"https://www.wikidata.org/wiki/Q7051809","display_name":"Normalization property","level":2,"score":0.5249961614608765},{"id":"https://openalex.org/C55128367","wikidata":"https://www.wikidata.org/wiki/Q2552799","display_name":"System F","level":3,"score":0.5187423825263977},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4681926667690277},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4534466862678528},{"id":"https://openalex.org/C195818886","wikidata":"https://www.wikidata.org/wiki/Q5421724","display_name":"Expressive power","level":2,"score":0.43489086627960205},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.42852669954299927},{"id":"https://openalex.org/C20693621","wikidata":"https://www.wikidata.org/wiki/Q6667502","display_name":"Logical framework","level":2,"score":0.42714211344718933},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.41105523705482483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37289828062057495},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.36513209342956543},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/1-4020-8141-3_48","is_oa":true,"landing_page_url":"https://doi.org/10.1007/1-4020-8141-3_48","pdf_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_48.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.2878","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.2878","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://rho.loria.fr/data/rhoSN.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00100109v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00100109","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":"3rd IFIP International Conference on Theoretical Computer Science - TCS'2004, Jean-Jacques L\u00e9vy, 2004, Toulouse, France, pp.633-646","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1007/1-4020-8141-3_48","is_oa":true,"landing_page_url":"https://doi.org/10.1007/1-4020-8141-3_48","pdf_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_48.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1578080614.pdf","grobid_xml":"https://content.openalex.org/works/W1578080614.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1504030085","https://openalex.org/W1601124623","https://openalex.org/W1679853627","https://openalex.org/W1986402635","https://openalex.org/W2018854027","https://openalex.org/W2028630528","https://openalex.org/W2044758536","https://openalex.org/W2056977394","https://openalex.org/W2145044561","https://openalex.org/W2248166198","https://openalex.org/W2618516565","https://openalex.org/W4212868911","https://openalex.org/W4285719527","https://openalex.org/W4388310127","https://openalex.org/W6664752800","https://openalex.org/W6691389151"],"related_works":["https://openalex.org/W3123171335","https://openalex.org/W21537352","https://openalex.org/W4205386752","https://openalex.org/W2027907817","https://openalex.org/W1983748102","https://openalex.org/W32986836","https://openalex.org/W2153353244","https://openalex.org/W2189323991","https://openalex.org/W1594451895","https://openalex.org/W2112776683"],"abstract_inverted_index":{"Pure":[0],"Pattern":[1],"Type":[2],"Systems":[3],"(P":[4,71,106,137,162],"2":[5,72,107,138,163],"TS)":[6,73,108,139,164],"combine":[7],"in":[8,47,89,127],"a":[9,29,52,64],"unified":[10],"setting":[11],"the":[12,56,75,90,101,110,119,132,143,157],"capabilities":[13],"of":[14,32,66,100,105,122,136,160],"rewriting":[15],"and":[16,68,151,153],"\u03bb-calculus.":[17,76,91,111],"Their":[18],"type":[19],"systems,":[20],"adapted":[21],"from":[22,28,70],"Barendregt\u2019s":[23],"\u03bb-cube":[24],"are":[25,86],"especially":[26],"interesting":[27],"logical":[30,39],"point":[31],"view.Strong":[33],"normalization,":[34],"an":[35,97],"essential":[36],"property":[37],"for":[38,55],"soundness,":[40],"had":[41],"only":[42],"been":[43],"conjectured":[44],"so":[45],"far:":[46],"this":[48],"paper,":[49],"we":[50,78,94,113,154],"give":[51],"positive":[53],"answer":[54],"simply-typed":[57,161],"system.":[58],"The":[59],"proof":[60],"is":[61,125,145],"based":[62],"on":[63,96],"translation":[65],"terms":[67],"types":[69],"into":[74,109],"First,":[77],"deal":[79],"with":[80,147,156],"untyped":[81],"terms,":[82],"ensuring":[83],"that":[84,142],"reductions":[85,150],"faithfully":[87],"mimicked":[88],"For":[92],"this,":[93],"rely":[95],"original":[98,133],"encoding":[99,144],"pattern":[102],"matching":[103],"capability":[104],"Then":[112],"show":[114],"how":[115],"to":[116,129,149],"translate":[117],"types:":[118],"expressive":[120],"power":[121],"System":[123],"F\u03c9":[124],"needed":[126],"order":[128],"fully":[130],"reproduce":[131],"typing":[134],"judgments":[135],"We":[140],"prove":[141],"correct":[146],"respect":[148],"typing,":[152],"conclude":[155],"strong":[158],"normalization":[159],"terms.":[165]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}