{"id":"https://openalex.org/W1494555245","doi":"https://doi.org/10.1007/3-540-61780-9_66","title":"Internal type theory","display_name":"Internal type theory","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1494555245","doi":"https://doi.org/10.1007/3-540-61780-9_66","mag":"1494555245"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-61780-9_66","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-61780-9_66","pdf_url":null,"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":null,"license_id":null,"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":["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/A5053761104","display_name":"Peter Dybjer","orcid":"https://orcid.org/0000-0003-4043-5204"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Peter Dybjer","raw_affiliation_strings":["Department of Computing Science, Chalmers University of Technology, G\u00f6teborg, Sweden","Chalmers University of Technology;"],"affiliations":[{"raw_affiliation_string":"Department of Computing Science, Chalmers University of Technology, G\u00f6teborg, Sweden","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"Chalmers University of Technology;","institution_ids":["https://openalex.org/I66862912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053761104"],"corresponding_institution_ids":["https://openalex.org/I66862912"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.8699,"has_fulltext":false,"cited_by_count":154,"citation_normalized_percentile":{"value":0.6844115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"120","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9790999889373779,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9491999745368958,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.7913216352462769},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7117209434509277},{"id":"https://openalex.org/keywords/algebraic-theory","display_name":"Algebraic theory","score":0.635637104511261},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.6328391432762146},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6249498128890991},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.5841965675354004},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.5796988010406494},{"id":"https://openalex.org/keywords/dependent-type","display_name":"Dependent type","score":0.5112805366516113},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48746395111083984},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4587427079677582},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.4421307146549225},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3230006694793701},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27430182695388794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24070033431053162},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.23164424300193787},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19671615958213806},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.08190900087356567}],"concepts":[{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.7913216352462769},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7117209434509277},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.635637104511261},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6328391432762146},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6249498128890991},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.5841965675354004},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.5796988010406494},{"id":"https://openalex.org/C20528804","wikidata":"https://www.wikidata.org/wiki/Q997433","display_name":"Dependent type","level":3,"score":0.5112805366516113},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48746395111083984},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4587427079677582},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.4421307146549225},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3230006694793701},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27430182695388794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24070033431053162},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.23164424300193787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19671615958213806},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.08190900087356567},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-61780-9_66","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-61780-9_66","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1489565250","https://openalex.org/W1773829243","https://openalex.org/W1828583149","https://openalex.org/W1858353210","https://openalex.org/W2006941708","https://openalex.org/W2022837260","https://openalex.org/W2028419206","https://openalex.org/W2065588545","https://openalex.org/W2088862781","https://openalex.org/W2102151984","https://openalex.org/W2124798629","https://openalex.org/W2177680715","https://openalex.org/W3167950194","https://openalex.org/W6966401951"],"related_works":["https://openalex.org/W2030950371","https://openalex.org/W2005380195","https://openalex.org/W1859146454","https://openalex.org/W223002628","https://openalex.org/W2173548019","https://openalex.org/W2805046018","https://openalex.org/W1494555245","https://openalex.org/W4233993919","https://openalex.org/W1507779663","https://openalex.org/W2175195909"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2025-10-10T00:00:00"}