{"id":"https://openalex.org/W1996381722","doi":"https://doi.org/10.1017/s0956796810000079","title":"Parametricity, type equality, and higher-order polymorphism","display_name":"Parametricity, type equality, and higher-order polymorphism","publication_year":2010,"publication_date":"2010-03-01","ids":{"openalex":"https://openalex.org/W1996381722","doi":"https://doi.org/10.1017/s0956796810000079","mag":"1996381722"},"language":"en","primary_location":{"id":"doi:10.1017/s0956796810000079","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796810000079","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/94D816825934AEAC3E556D5CA0614B83/S0956796810000079a.pdf/div-class-title-parametricity-type-equality-and-higher-order-polymorphism-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,"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":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/94D816825934AEAC3E556D5CA0614B83/S0956796810000079a.pdf/div-class-title-parametricity-type-equality-and-higher-order-polymorphism-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029108294","display_name":"Dimitrios Vytiniotis","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"DIMITRIOS VYTINIOTIS","raw_affiliation_strings":["Microsoft Research Cambridge, 7 JJ Thomson Avenue, Cambridge CB3 0FBUK (e-mail:","Microsoft research cambridge, 7 jj thomson avenue, cambridge cb3 0fbuk (e-mail: dimitris@microsoft.com)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research Cambridge, 7 JJ Thomson Avenue, Cambridge CB3 0FBUK (e-mail:","institution_ids":["https://openalex.org/I4210164937"]},{"raw_affiliation_string":"Microsoft research cambridge, 7 jj thomson avenue, cambridge cb3 0fbuk (e-mail: dimitris@microsoft.com)#TAB#","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049220962","display_name":"Stephanie Weirich","orcid":"https://orcid.org/0000-0002-6756-9168"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"STEPHANIE WEIRICH","raw_affiliation_strings":["University of Pennsylvania, Department of Computer and Information Science, Levine Hall, 3330 Walnut St., Philadelphia PA 19104\u20136389, USA (e-mail:","University of pennsylvania, department of computer and information science, levine hall, 3330 walnut st., philadelphia pa 19104\u20136389, usa (e-mail: sweirich@cis.upenn.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania, Department of Computer and Information Science, Levine Hall, 3330 Walnut St., Philadelphia PA 19104\u20136389, USA (e-mail:","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"University of pennsylvania, department of computer and information science, levine hall, 3330 walnut st., philadelphia pa 19104\u20136389, usa (e-mail: sweirich@cis.upenn.edu)#TAB#","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9696,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.95932773,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"2","first_page":"175","last_page":"210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9937999844551086,"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/system-f","display_name":"System F","score":0.6491334438323975},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.645838737487793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.62209552526474},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.62068110704422},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.606952428817749},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.5682008266448975},{"id":"https://openalex.org/keywords/type-inference","display_name":"Type inference","score":0.5129892230033875},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.44828733801841736},{"id":"https://openalex.org/keywords/functional-programming","display_name":"Functional programming","score":0.4445263743400574},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.41473495960235596},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.41025134921073914},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.4061894416809082},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39346376061439514},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3258345127105713},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2728368639945984},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10930189490318298}],"concepts":[{"id":"https://openalex.org/C55128367","wikidata":"https://www.wikidata.org/wiki/Q2552799","display_name":"System F","level":3,"score":0.6491334438323975},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.645838737487793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.62209552526474},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.62068110704422},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.606952428817749},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.5682008266448975},{"id":"https://openalex.org/C198370458","wikidata":"https://www.wikidata.org/wiki/Q586459","display_name":"Type inference","level":3,"score":0.5129892230033875},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.44828733801841736},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.4445263743400574},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.41473495960235596},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.41025134921073914},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.4061894416809082},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39346376061439514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3258345127105713},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2728368639945984},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10930189490318298},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0956796810000079","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796810000079","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/94D816825934AEAC3E556D5CA0614B83/S0956796810000079a.pdf/div-class-title-parametricity-type-equality-and-higher-order-polymorphism-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,"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:repository.upenn.edu:cis_papers-1675","is_oa":false,"landing_page_url":"https://repository.upenn.edu/cgi/viewcontent.cgi?article=1675&context=cis_papers","pdf_url":null,"source":{"id":"https://openalex.org/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Departmental Papers (CIS)","raw_type":"text"},{"id":"pmh:oai:repository.upenn.edu:20.500.14332/6706","is_oa":false,"landing_page_url":"https://repository.upenn.edu/handle/20.500.14332/6706","pdf_url":null,"source":{"id":"https://openalex.org/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"published","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1017/s0956796810000079","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796810000079","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/94D816825934AEAC3E556D5CA0614B83/S0956796810000079a.pdf/div-class-title-parametricity-type-equality-and-higher-order-polymorphism-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,"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":[],"awards":[{"id":"https://openalex.org/G1101807903","display_name":"CT-T:   Collaborative Research:   Manifest Security","funder_award_id":"0716469","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G235454556","display_name":"A Practical Dependently-Typed Functional Programming Language","funder_award_id":"0702545","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6125997669","display_name":"CAREER:     Type-Directed Programming in Object-Oriented Languages","funder_award_id":"0347289","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1996381722.pdf","grobid_xml":"https://content.openalex.org/works/W1996381722.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W137136619","https://openalex.org/W223002628","https://openalex.org/W326743114","https://openalex.org/W600819829","https://openalex.org/W1480685649","https://openalex.org/W1518331780","https://openalex.org/W1535217452","https://openalex.org/W1561510943","https://openalex.org/W1600772147","https://openalex.org/W1827112781","https://openalex.org/W1949275316","https://openalex.org/W1956373135","https://openalex.org/W1967061556","https://openalex.org/W1968277829","https://openalex.org/W1974398164","https://openalex.org/W1984514567","https://openalex.org/W1991984504","https://openalex.org/W1992889841","https://openalex.org/W2014868111","https://openalex.org/W2021982406","https://openalex.org/W2030916392","https://openalex.org/W2032777378","https://openalex.org/W2033185534","https://openalex.org/W2043740265","https://openalex.org/W2057292961","https://openalex.org/W2058162377","https://openalex.org/W2066166567","https://openalex.org/W2076018351","https://openalex.org/W2089576225","https://openalex.org/W2112121519","https://openalex.org/W2131441325","https://openalex.org/W2131828631","https://openalex.org/W2136177623","https://openalex.org/W2140207165","https://openalex.org/W2140647971","https://openalex.org/W2149412346","https://openalex.org/W2160930653","https://openalex.org/W2491912653","https://openalex.org/W2949436104","https://openalex.org/W3171421481","https://openalex.org/W4233993919","https://openalex.org/W4285719527","https://openalex.org/W4376542588"],"related_works":["https://openalex.org/W2105232714","https://openalex.org/W2095136535","https://openalex.org/W3091937109","https://openalex.org/W1992310464","https://openalex.org/W119268553","https://openalex.org/W1996381722","https://openalex.org/W2466581924","https://openalex.org/W2159526276","https://openalex.org/W2802248566","https://openalex.org/W2096310766"],"abstract_inverted_index":{"Abstract":[0],"Propositions":[1],"that":[2,48],"express":[3],"type":[4,41,52,58],"equality":[5,53,113],"are":[6,30,61,67,72],"a":[7,85],"frequent":[8],"ingredient":[9],"of":[10,51,84],"modern":[11],"functional":[12],"programming":[13],"\u2013":[14],"they":[15,60],"can":[16],"encode":[17],"generic":[18],"functions,":[19],"dynamic":[20],"types,":[21],"and":[22,69,92],"GADTs.":[23],"Via":[24],"the":[25,82],"Curry\u2013Howard":[26],"correspondence,":[27],"these":[28],"propositions":[29,54],"ordinary":[31],"types":[32],"inhabited":[33,63],"by":[34,98],"proof":[35],"terms":[36],",":[37],"computed":[38],"using":[39],"runtime":[40],"representations.":[42],"In":[43],"this":[44,79,106],"paper":[45],"we":[46],"show":[47,78],"two":[49],"examples":[50],"actually":[55],"do":[56],"reflect":[57],"equality;":[59],"only":[62],"when":[64],"their":[65,70],"arguments":[66],"equal":[68],"proofs":[71],"unique":[73],"(up":[74],"to":[75,108],"equivalence.)":[76],"We":[77,103],"result":[80],"in":[81],"context":[83],"strongly":[86],"normalizing":[87],"language":[88],"with":[89],"higher-order":[90],"polymorphism":[91],"primitive":[93],"recursion":[94],"over":[95],"runtime-type":[96],"representations":[97],"proving":[99],"Reynolds's":[100],"abstraction":[101],"theorem.":[102],"then":[104],"use":[105],"theorem":[107],"derive":[109],"\u201cfree\u201d":[110],"theorems":[111],"about":[112],"types.":[114]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-27T06:14:07.914337","created_date":"2025-10-10T00:00:00"}
