{"id":"https://openalex.org/W2253568516","doi":"https://doi.org/10.1017/s0956796815000271","title":"Counting and generating terms in the binary lambda calculus","display_name":"Counting and generating terms in the binary lambda calculus","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2253568516","doi":"https://doi.org/10.1017/s0956796815000271","mag":"2253568516"},"language":"en","primary_location":{"id":"doi:10.1017/s0956796815000271","doi":"https://doi.org/10.1017/s0956796815000271","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796815000271","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/47DE83E8BD697326F0FFD43351E083E3/S0956796815000271a.pdf/div-class-title-counting-and-generating-terms-in-the-binary-lambda-calculus-a-href-afn1-ref-type-fn-a-div.pdf","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,"listed_in":["ccf-b","cwts-core","dongbi-b","jufo-2","norway-1","poland-70","russia-white-list-3"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/47DE83E8BD697326F0FFD43351E083E3/S0956796815000271a.pdf/div-class-title-counting-and-generating-terms-in-the-binary-lambda-calculus-a-href-afn1-ref-type-fn-a-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"KATARZYNA GRYGIEL","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"KATARZYNA GRYGIEL","raw_affiliation_strings":["Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Prof. \u0141ojasiewicza 6, 30-348 Krak\u00f3w, Poland (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Prof. \u0141ojasiewicza 6, 30-348 Krak\u00f3w, Poland (e-mail:","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042417161","display_name":"Pierre Lescanne","orcid":"https://orcid.org/0000-0001-9512-5276","observed_orcids":["https://orcid.org/0000-0001-9512-5276"]},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"PIERRE LESCANNE","raw_affiliation_strings":["\u00c9cole normale sup\u00e9rieure de Lyon, LIP (UMR 5668 CNRS ENS Lyon UCBL INRIA), University of Lyon, 46 all\u00e9e d'Italie, 69364 Lyon, France (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole normale sup\u00e9rieure de Lyon, LIP (UMR 5668 CNRS ENS Lyon UCBL INRIA), University of Lyon, 46 all\u00e9e d'Italie, 69364 Lyon, France (e-mail:","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144566"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2660,"currency":"USD","value_usd":2660},"apc_paid":null,"fwci":10.2273,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.97849252,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"25","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.6859999895095825,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.6859999895095825,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.17649999260902405,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.0649000033736229,"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/lambda-terms","display_name":"lambda terms","score":0.6859999895095825},{"id":"https://openalex.org/keywords/binary-string-encoding","display_name":"binary string encoding","score":0.6380000114440918},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.8569999933242798},{"id":"https://openalex.org/keywords/asymptotic-growth","display_name":"asymptotic growth","score":0.7839999794960022},{"id":"https://openalex.org/keywords/combinatorial-generation","display_name":"combinatorial generation","score":0.5600000023841858}],"concepts":[{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.7652999758720398},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.663100004196167},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6435999870300293},{"id":"https://openalex.org/C61237538","wikidata":"https://www.wikidata.org/wiki/Q855192","display_name":"Simply typed lambda calculus","level":4,"score":0.6100999712944031},{"id":"https://openalex.org/C77736955","wikidata":"https://www.wikidata.org/wiki/Q1089708","display_name":"Church encoding","level":5,"score":0.5979999899864197},{"id":"https://openalex.org/C142156749","wikidata":"https://www.wikidata.org/wiki/Q2607208","display_name":"Typed lambda calculus","level":3,"score":0.5741000175476074},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5073000192642212},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.48399999737739563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4034999907016754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39559999108314514},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3174000084400177},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C55128367","wikidata":"https://www.wikidata.org/wiki/Q2552799","display_name":"System F","level":3,"score":0.3133000135421753},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2750999927520752},{"id":"https://openalex.org/C20528804","wikidata":"https://www.wikidata.org/wiki/Q997433","display_name":"Dependent type","level":3,"score":0.26170000433921814}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1017/s0956796815000271","doi":"https://doi.org/10.1017/s0956796815000271","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796815000271","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/47DE83E8BD697326F0FFD43351E083E3/S0956796815000271a.pdf/div-class-title-counting-and-generating-terms-in-the-binary-lambda-calculus-a-href-afn1-ref-type-fn-a-div.pdf","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,"listed_in":["ccf-b","cwts-core","dongbi-b","jufo-2","norway-1","poland-70","russia-white-list-3"],"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"},{"id":"pmh:oai:arXiv.org:1401.0379","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.0379","pdf_url":"https://arxiv.org/pdf/1401.0379","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:arXiv.org:1511.05334","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.05334","pdf_url":"https://arxiv.org/pdf/1511.05334","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:ruj.uj.edu.pl:item/30957","doi":null,"is_oa":true,"landing_page_url":"http://ruj.uj.edu.pl/xmlui/handle/item/30957","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:ensl-01892453v1","doi":null,"is_oa":false,"landing_page_url":"https://hal-ens-lyon.archives-ouvertes.fr/ensl-01892453","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"\\nISSN: \\n0956-7968","raw_type":"\\ninfo:eu-repo/semantics/article\\n"},{"id":"pmh:oai:HAL:ensl-01892455v1","doi":null,"is_oa":false,"landing_page_url":"https://ens-lyon.hal.science/ensl-01892455","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Functional Programming, 2015, 25, ⟨10.1017/S0956796815000271⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1401.0379","doi":"https://doi.org/10.48550/arxiv.1401.0379","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1401.0379","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1017/s0956796815000271","doi":"https://doi.org/10.1017/s0956796815000271","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796815000271","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/47DE83E8BD697326F0FFD43351E083E3/S0956796815000271a.pdf/div-class-title-counting-and-generating-terms-in-the-binary-lambda-calculus-a-href-afn1-ref-type-fn-a-div.pdf","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,"listed_in":["ccf-b","cwts-core","dongbi-b","jufo-2","norway-1","poland-70","russia-white-list-3"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2253568516.pdf","grobid_xml":"https://content.openalex.org/works/W2253568516.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W43882553","https://openalex.org/W123238105","https://openalex.org/W129748510","https://openalex.org/W186403072","https://openalex.org/W300201706","https://openalex.org/W1494407580","https://openalex.org/W1524037972","https://openalex.org/W1528269269","https://openalex.org/W1556536463","https://openalex.org/W1638203394","https://openalex.org/W1982202832","https://openalex.org/W2023605482","https://openalex.org/W2056068307","https://openalex.org/W2071267598","https://openalex.org/W2102379027","https://openalex.org/W2115418771","https://openalex.org/W2117955223","https://openalex.org/W2119717320","https://openalex.org/W2180762724","https://openalex.org/W2280812408","https://openalex.org/W2294305355","https://openalex.org/W2296468158","https://openalex.org/W2296657109","https://openalex.org/W2340541605","https://openalex.org/W2568721247","https://openalex.org/W2582697902","https://openalex.org/W2964257550","https://openalex.org/W3098021658","https://openalex.org/W3158027121"],"related_works":["https://openalex.org/W6967151035","https://openalex.org/W1960062128","https://openalex.org/W7100005296","https://openalex.org/W4299705306","https://openalex.org/W2727395273","https://openalex.org/W2117955223","https://openalex.org/W2248235110","https://openalex.org/W2296468158","https://openalex.org/W2395639985","https://openalex.org/W7095544235"],"abstract_inverted_index":{"Abstract":[0],"In":[1,26,68],"a":[2,15,37,69],"paper,":[3],"entitled":[4],"Binary":[5],"lambda":[6,20,42,79],"calculus":[7,21],"and":[8,44],"combinatory":[9],"logic":[10],",":[11],"John":[12],"Tromp":[13],"presents":[14],"simple":[16],"way":[17],"of":[18,33,36,55,57],"encoding":[19],"terms":[22,43,56,80],"as":[23],"binary":[24,34],"sequences.":[25],"what":[27],"follows,":[28],"we":[29,72],"study":[30],"the":[31,53],"numbers":[32],"strings":[35],"given":[38],"size":[39,58],"that":[40,52],"represent":[41],"derive":[45],"results":[46],"from":[47],"their":[48],"generating":[49],"functions,":[50],"especially":[51],"number":[54],"n":[59,66],"grows":[60],"roughly":[61],"like":[62],"1.963447954.":[63],".":[64,65,67],"second":[70],"part":[71],"use":[73],"this":[74],"approach":[75],"to":[76],"generate":[77],"random":[78],"using":[81],"Boltzmann":[82],"samplers.":[83]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}