{"id":"https://openalex.org/W2052212743","doi":"https://doi.org/10.1142/s012905419200019x","title":"A UNIFICATION ALGORITHM FOR THE \u03bb\u03a0-CALCULUS","display_name":"A UNIFICATION ALGORITHM FOR THE \u03bb\u03a0-CALCULUS","publication_year":1992,"publication_date":"1992-09-01","ids":{"openalex":"https://openalex.org/W2052212743","doi":"https://doi.org/10.1142/s012905419200019x","mag":"2052212743"},"language":"en","primary_location":{"id":"doi:10.1142/s012905419200019x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905419200019x","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5013218535","display_name":"David Pym","orcid":"https://orcid.org/0000-0002-6504-5838"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"DAVID PYM","raw_affiliation_strings":["University of Edinburgh, Laboratory for Foundations of Computer Science, Department of Computer Science, The King\u2019s Buildings, Edinburgh EH9 3JZ, Scotland, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Edinburgh, Laboratory for Foundations of Computer Science, Department of Computer Science, The King\u2019s Buildings, Edinburgh EH9 3JZ, Scotland, U.K","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013218535"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":1.6741,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.86092024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"03","issue":"03","first_page":"333","last_page":"378"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9901999831199646,"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":0.9901999831199646,"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":0.9485999941825867,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9466000199317932,"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/unification","display_name":"Unification","score":0.7224161028862},{"id":"https://openalex.org/keywords/simply-typed-lambda-calculus","display_name":"Simply typed lambda calculus","score":0.6176263689994812},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.5931755304336548},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5808083415031433},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.5708556771278381},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5530638098716736},{"id":"https://openalex.org/keywords/typed-lambda-calculus","display_name":"Typed lambda calculus","score":0.543408989906311},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5073599219322205},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5042203664779663},{"id":"https://openalex.org/keywords/dependent-type","display_name":"Dependent type","score":0.5002334117889404},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.4662880599498749},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44002413749694824},{"id":"https://openalex.org/keywords/church-encoding","display_name":"Church encoding","score":0.42999985814094543},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4179782271385193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36726075410842896},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36315470933914185},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2595621943473816},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.18662869930267334},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16724041104316711}],"concepts":[{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.7224161028862},{"id":"https://openalex.org/C61237538","wikidata":"https://www.wikidata.org/wiki/Q855192","display_name":"Simply typed lambda calculus","level":4,"score":0.6176263689994812},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.5931755304336548},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5808083415031433},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.5708556771278381},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5530638098716736},{"id":"https://openalex.org/C142156749","wikidata":"https://www.wikidata.org/wiki/Q2607208","display_name":"Typed lambda calculus","level":3,"score":0.543408989906311},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5073599219322205},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5042203664779663},{"id":"https://openalex.org/C20528804","wikidata":"https://www.wikidata.org/wiki/Q997433","display_name":"Dependent type","level":3,"score":0.5002334117889404},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.4662880599498749},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44002413749694824},{"id":"https://openalex.org/C77736955","wikidata":"https://www.wikidata.org/wiki/Q1089708","display_name":"Church encoding","level":5,"score":0.42999985814094543},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4179782271385193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36726075410842896},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36315470933914185},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2595621943473816},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.18662869930267334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16724041104316711},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s012905419200019x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905419200019x","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3123171335","https://openalex.org/W2146437601","https://openalex.org/W21537352","https://openalex.org/W2189323991","https://openalex.org/W2153353244","https://openalex.org/W1458664253","https://openalex.org/W2804798465","https://openalex.org/W3091937109","https://openalex.org/W2112776683","https://openalex.org/W1592479913"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,43,74,86,115],"unification":[3,136],"algorithm":[4,17,23,106,189],"for":[5,24,135],"the":[6,8,25,35,48,52,94,112,120,156,163,166],"\u03bb\u03a0-calculus,":[7],"lambda":[9,27,37],"calculus":[10,28,38],"with":[11,193],"first-order":[12,30],"dependent":[13,31,56],"function":[14,32],"types.":[15,33],"Our":[16,170],"is":[18,138,174],"an":[19,175],"extension":[20],"of":[21,45,47,77,79,88,90,111,114,118,122,126,133,155,165,172,181,209],"Huet\u2019s":[22,105],"simply-typed":[26,36],"to":[29,41,84,152,161,186],"In":[34],"one":[39,60],"attempts":[40],"unify":[42,62,85,144],"pair":[44,87,117],"terms":[46,58,89,145,208],"same":[49],"type;":[50],"in":[51,184,202],"\u03bb\u03a0-calculus":[53],"types":[54,68,95,127,148],"are":[55,96,101,159,179,205],"on":[57],"so":[59],"must":[61,143,191],"not":[63,97,102,108,139,211],"only":[64,82],"terms,":[65,119],"but":[66],"their":[67,147],"as":[69],"well.":[70],"Accordingly,":[71,141],"we":[72,142,190],"identify":[73],"suitable":[75,131],"notion":[76,171],"similarity":[78],"types,":[80],"and":[81,146,195,199],"attempt":[83],"similar":[91,98],"type:":[92],"if":[93],"then":[99],"they":[100],"unifiable.":[103],"Since":[104],"does":[107],"enumerate":[109],"all":[110,154],"unifiers":[113],"given":[116],"strategy":[121],"first":[123],"unifying":[124],"pairs":[125,132],"\u2014":[128,137,197],"by":[129,207],"identifying":[130],"subterms":[134],"complete.":[140],"simultaneously,":[149],"taking":[150],"care":[151],"maintain":[153],"conditions":[157],"that":[158],"necessary":[160],"ensure":[162],"well-formedness":[164],"resulting":[167],"calculated":[168],"substitution.":[169],"substitution":[173],"algebraic":[176],"one:":[177],"substitutions":[178,198],"morphisms":[180],"\u03bb\u03a0-contexts.":[182],"However,":[183],"order":[185],"define":[187],"our":[188],"work":[192],"psubstitutions":[194],"pcontexts":[196],"contexts,":[200],"respectively,":[201],"which":[203],"variables":[204],"replaced":[206],"similar,":[210],"\u03b2(\u03b7)-equal,":[212],"type.":[213]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
