{"id":"https://openalex.org/W28925417","doi":"https://doi.org/10.1017/s0956796800020062","title":"Theoretical Pearls: <i>Self-interpretation in lambda calculus</i>","display_name":"Theoretical Pearls: <i>Self-interpretation in lambda calculus</i>","publication_year":1991,"publication_date":"1991-04-01","ids":{"openalex":"https://openalex.org/W28925417","doi":"https://doi.org/10.1017/s0956796800020062","mag":"28925417"},"language":"en","primary_location":{"id":"doi:10.1017/s0956796800020062","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0956796800020062","pdf_url":null,"source":{"id":"https://openalex.org/S12266929","display_name":"Journal of Functional Programming","issn_l":"0956-7968","issn":["0956-7968","1469-7653"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Functional Programming","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/A5016150987","display_name":"Henk Barendregt","orcid":"https://orcid.org/0000-0002-3735-4078"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Henk Barendregt","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Catholic University of Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Catholic University of Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016150987"],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":null,"apc_paid":null,"fwci":4.8551,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.94692563,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"1","issue":"2","first_page":"229","last_page":"233"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9968000054359436,"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":0.9968000054359436,"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":0.9861999750137329,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9424999952316284,"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":0.7237316370010376},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.65772545337677},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.5804256796836853},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.514153778553009},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.470674604177475},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.46600088477134705},{"id":"https://openalex.org/keywords/typed-lambda-calculus","display_name":"Typed lambda calculus","score":0.43005502223968506},{"id":"https://openalex.org/keywords/functional-programming","display_name":"Functional programming","score":0.4160575866699219},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3615860044956207},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17897439002990723}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7237316370010376},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.65772545337677},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.5804256796836853},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.514153778553009},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.470674604177475},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.46600088477134705},{"id":"https://openalex.org/C142156749","wikidata":"https://www.wikidata.org/wiki/Q2607208","display_name":"Typed lambda calculus","level":3,"score":0.43005502223968506},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.4160575866699219},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3615860044956207},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17897439002990723},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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":1,"locations":[{"id":"doi:10.1017/s0956796800020062","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0956796800020062","pdf_url":null,"source":{"id":"https://openalex.org/S12266929","display_name":"Journal of Functional Programming","issn_l":"0956-7968","issn":["0956-7968","1469-7653"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Functional Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W1964062928"],"related_works":["https://openalex.org/W4246531319","https://openalex.org/W1562483556","https://openalex.org/W2752311799","https://openalex.org/W2038167131","https://openalex.org/W2466581924","https://openalex.org/W1545794938","https://openalex.org/W2475825068","https://openalex.org/W2612681346","https://openalex.org/W351893248","https://openalex.org/W2151540855"],"abstract_inverted_index":{"Programming":[0],"languages":[1],"which":[2],"are":[3,108,174,185],"capable":[4],"of":[5,25,37,40,60,64,67,83,103,125,132,200],"interpreting":[6,61],"themselves":[7],"have":[8],"been":[9],"fascinating":[10],"computer":[11],"scientists.":[12],"Indeed,":[13,43],"if":[14,44],"this":[15,196],"is":[16,28,33,88,96,121,197],"possible":[17,77],"then":[18,54,195],"a":[19,34,52,65,122,189],"\u2018strange":[20],"loop\u2019":[21],"(in":[22],"the":[23,31,38,57,62,91,97,126,130,198,201,205],"sense":[24],"Hofstadter,":[26],"1979)":[27],"involved.":[29],"Nevertheless,":[30],"phenomenon":[32],"direct":[35],"consequence":[36],"existence":[39],"universal":[41],"languages.":[42],"all":[45],"computable":[46],"functions":[47],"can":[48,56,145,192],"be":[49,72,76,146,193],"captured":[50],"by":[51,90,111,117,163,177],"language,":[53],"so":[55],"particular":[58],"job":[59],"code":[63],"program":[66,206],"that":[68,128,148,171],"language.":[69],"Self-interpretation":[70],"will":[71],"shown":[73],"here":[74],"to":[75,165,168],"in":[78,141],"lambda":[79],"calculus.":[80],"The":[81],"set":[82,98],"\u03bb-terms":[84],",":[85],"notation":[86],"\u039b,":[87],"defined":[89],"following":[92],"abstract":[93],"syntax":[94],"where":[95],"{v,":[99],"v\u2032,":[100],"v\u2033,":[101],"v\u2032\u2033,\u2026}":[102],"variables":[104,107],".":[105],"Arbitrary":[106],"usually":[109],"denoted":[110],"x,":[112],"y,z,\u2026":[113],"and":[114],"\u03bb":[115,123,149],"-terms":[116,150],"M,N,L,\u2026.":[118],"A":[119,157],"redex":[120],"-term":[124],"form":[127,191],"is,":[129,172],"result":[131],"substituting":[133],"N":[134],"for":[135],"(the":[136],"free":[137],"occurrences":[138],"of)":[139],"x":[140],"M.":[142],"Stylistically,":[143],"it":[144],"said":[147],"represent":[151],"functional":[152,202],"programs":[153],"including":[154],"their":[155,178],"input.":[156],"reduction":[158],"machine":[159],"executes":[160],"such":[161,188],"terms":[162],"trying":[164],"reduce":[166],"them":[167],"normal":[169,190],"form;":[170],"redexes":[173,184],"continuously":[175],"replaced":[176],"contracta":[179],"until":[180],"hopefully":[181],"no":[182],"more":[183],"present.":[186],"If":[187],"reached,":[194],"output":[199],"program;":[203],"otherwise,":[204],"diverges.":[207]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2025-10-10T00:00:00"}
