{"id":"https://openalex.org/W4394002269","doi":"https://doi.org/10.1007/978-3-031-57231-9_8","title":"Clones, closed categories, and combinatory logic","display_name":"Clones, closed categories, and combinatory logic","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4394002269","doi":"https://doi.org/10.1007/978-3-031-57231-9_8"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-57231-9_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-57231-9_8","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57231-9_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57231-9_8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038782398","display_name":"Philip Saville","orcid":"https://orcid.org/0000-0002-8320-0280"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Philip Saville","raw_affiliation_strings":["Department of Computer Science, University of Oxford, Oxford, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038782398"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10686536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"160","last_page":"181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9987000226974487,"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":0.998199999332428,"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":0.8165156841278076},{"id":"https://openalex.org/keywords/combinatory-logic","display_name":"Combinatory logic","score":0.43538007140159607},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.4070461094379425}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8165156841278076},{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.43538007140159607},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.4070461094379425}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-031-57231-9_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-57231-9_8","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57231-9_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:2405.01675","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.01675","pdf_url":"https://arxiv.org/pdf/2405.01675","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-57231-9_8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-57231-9_8","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57231-9_8.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4394002269.pdf","grobid_xml":"https://content.openalex.org/works/W4394002269.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W136934826","https://openalex.org/W586500741","https://openalex.org/W1488638832","https://openalex.org/W1522025572","https://openalex.org/W1549977012","https://openalex.org/W1594900487","https://openalex.org/W1677393765","https://openalex.org/W1761411969","https://openalex.org/W1954279992","https://openalex.org/W1996404651","https://openalex.org/W2005173090","https://openalex.org/W2012968289","https://openalex.org/W2028227938","https://openalex.org/W2112970627","https://openalex.org/W2125224752","https://openalex.org/W2130762722","https://openalex.org/W2388408070","https://openalex.org/W2798754626","https://openalex.org/W2963010814","https://openalex.org/W2989833183","https://openalex.org/W3039816335","https://openalex.org/W3093908277","https://openalex.org/W3094358738","https://openalex.org/W3100695210","https://openalex.org/W3118915851","https://openalex.org/W3175598350","https://openalex.org/W4210839962","https://openalex.org/W4212902885","https://openalex.org/W4230069580","https://openalex.org/W4233993919","https://openalex.org/W4242125186","https://openalex.org/W4243544101","https://openalex.org/W4244525635","https://openalex.org/W4249736722","https://openalex.org/W4288080212","https://openalex.org/W6630804320"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2026765907","https://openalex.org/W4307413753","https://openalex.org/W1975604118","https://openalex.org/W119766800","https://openalex.org/W2162268423","https://openalex.org/W2135888537","https://openalex.org/W2183434207","https://openalex.org/W2147822230"],"abstract_inverted_index":{"Abstract":[0],"We":[1,27,64,89,120],"explain":[2],"how":[3,48],"to":[4,36,49,69,127],"recast":[5],"the":[6,9,52,61,71,78,109,137,149],"semantics":[7],"of":[8,74,130,152],"simply-typed":[10,79,110,138],"$$\\uplambda":[11,80,111,139],"$$":[12,81,112,140],"<mml:math":[13,82,113,141],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[14,83,114,142],"<mml:mi>\u03bb</mml:mi>":[15,84,115,143],"</mml:math>":[16,85,116,144],"-calculus,":[17],"and":[18,21,33,43,56,77,93,98,108],"its":[19,57],"linear":[20],"ordered":[22],"variants,":[23],"using":[24],"multi-ary":[25,62],"structures.":[26],"define":[28],"universal":[29],"properties":[30],"for":[31,40,100],"multicategories,":[32],"use":[34,66],"these":[35,67,95],"derive":[37],"familiar":[38],"rules":[39],"products,":[41],"tensors,":[42],"exponentials.":[44],"Finally":[45],"we":[46],"outline":[47],"recover":[50],"both":[51,101],"category-theoretic":[53],"syntactic":[54],"model":[55],"semantic":[58,72],"interpretation":[59,73],"from":[60],"framework.":[63],"then":[65,121],"ideas":[68],"study":[70],"combinatory":[75,102],"logic":[76,103],"-calculus":[86,117,145],"without":[87,118,146],"products.":[88,119],"introduce":[90],"extensional":[91,105],"SK-clones":[92,124],"show":[94,122],"are":[96,125],"sound":[97],"complete":[99],"with":[104],"weak":[106],"equality":[107],"such":[123],"equivalent":[126],"a":[128],"variant":[129],"closed":[131],"categories":[132],"called":[133],"SK-categories":[134],",":[135],"so":[136],"products":[147],"is":[148],"internal":[150],"language":[151],"SK-categories.":[153]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}