{"id":"https://openalex.org/W3004380331","doi":"https://doi.org/10.48550/arxiv.2001.11816","title":"Understanding Profunctor Optics: a representation theorem","display_name":"Understanding Profunctor Optics: a representation theorem","publication_year":2020,"publication_date":"2020-01-27","ids":{"openalex":"https://openalex.org/W3004380331","doi":"https://doi.org/10.48550/arxiv.2001.11816","mag":"3004380331"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2001.11816","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.11816","pdf_url":"https://arxiv.org/pdf/2001.11816","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.11816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056706196","display_name":"Guillaume Boisseau","orcid":"https://orcid.org/0000-0001-5244-893X","observed_orcids":["https://orcid.org/0000-0001-5244-893X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Boisseau, Guillaume","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5056706196"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"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":0.9980000257492065,"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":0.9980000257492065,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10533","display_name":"Teaching and Learning Programming","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1706","display_name":"Computer Science Applications"},"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/representation-theorem","display_name":"representation theorem","score":0.9179999828338623}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.618967592716217},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.5517791509628296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36493515968322754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36065196990966797},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21629592776298523},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.16342002153396606},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.05493617057800293},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2001.11816","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.11816","pdf_url":"https://arxiv.org/pdf/2001.11816","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":"doi:10.48550/arxiv.2001.11816","doi":"https://doi.org/10.48550/arxiv.2001.11816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.11816","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.11816","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.11816","pdf_url":"https://arxiv.org/pdf/2001.11816","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"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2057292961","https://openalex.org/W2096533573","https://openalex.org/W2125713144","https://openalex.org/W2963683507","https://openalex.org/W2990129438","https://openalex.org/W3122561139"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2155782347"],"abstract_inverted_index":{"Optics,":[0],"aka":[1],"functional":[2],"references,":[3],"are":[4,109],"classes":[5],"of":[6,29,55,67,80,82,148,163],"tools":[7],"that":[8,37,134,169],"allow":[9],"composable":[10],"access":[11],"into":[12],"compound":[13],"data":[14,30],"structures.":[15,45],"Usually":[16],"defined":[17],"as":[18,32],"programming":[19],"language":[20,51],"libraries,":[21],"they":[22,47],"provide":[23],"combinators":[24],"to":[25,41,52,61,111,145,153,173,177,185,198],"manipulate":[26],"different":[27,59,103],"shapes":[28],"such":[31],"sums,":[33],"products":[34],"and":[35,86,114,152,175],"collections,":[36],"can":[38],"be":[39,186],"composed":[40],"operate":[42],"on":[43,128],"larger":[44],"Together":[46],"form":[48],"a":[49,94,129,196],"powerful":[50,183],"describe":[53],"transformations":[54],"data.":[56],"Among":[57],"the":[58,83],"approaches":[60],"describing":[62],"optics,":[63,68,71,165,168],"one":[64],"particular":[65],"type":[66],"called":[69,166],"profunctor":[70,107,121,150,164,190,202],"stands":[72],"out.":[73],"It":[74],"describes":[75],"alternative":[76],"but":[77],"equivalent":[78,120,161],"representations":[79],"most":[81],"common":[84],"combinators,":[85],"enhances":[87],"them":[88],"with":[89,118,132],"elegant":[90],"composability":[91],"properties":[92,147],"via":[93],"higher-order":[95],"encoding.":[96],"Notably,":[97],"it":[98,142],"enables":[99,182],"easy":[100],"composition":[101],"across":[102],"optic":[104,206],"families.":[105,207],"Unfortunately,":[106],"optics":[108,117,151],"difficult":[110],"reason":[112,178],"about,":[113],"linking":[115],"usual":[116],"an":[119,160],"representation":[122,162],"has":[123],"so":[124],"far":[125],"been":[126],"done":[127],"case-by-case":[130],"basis,":[131],"definitions":[133],"sometimes":[135],"seem":[136],"very":[137],"ad":[138],"hoc.":[139],"This":[140,157,180],"makes":[141],"hard":[143],"both":[144,171],"analyse":[146],"existing":[149],"define":[154],"new":[155,201],"ones.":[156],"thesis":[158,194],"presents":[159],"isomorphism":[167],"is":[170],"closer":[172],"intuition":[174],"easier":[176],"about.":[179],"tool":[181],"theorems":[184],"derived":[187],"generically":[188],"about":[189],"optics.":[191],"Finally,":[192],"this":[193],"develops":[195],"framework":[197],"ease":[199],"deriving":[200],"encodings":[203],"from":[204],"concrete":[205]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
