{"id":"https://openalex.org/W2007054034","doi":"https://doi.org/10.1016/s1571-0661(05)80726-1","title":"On propositions-as-types in realizability models","display_name":"On propositions-as-types in realizability models","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2007054034","doi":"https://doi.org/10.1016/s1571-0661(05)80726-1","mag":"2007054034"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(05)80726-1","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80726-1","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(05)80726-1","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055959064","display_name":"Lars Birkedal","orcid":"https://orcid.org/0000-0003-1320-0098"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lars Birkedal","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055959064"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10297693,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":null,"first_page":"52","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9850000143051147,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9850000143051147,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9843999743461609,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9692000150680542,"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/realizability","display_name":"Realizability","score":0.9666762351989746},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.9038701057434082},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5894491076469421},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.5487015843391418},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.5479046702384949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5466079115867615},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5231702923774719},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5073422789573669},{"id":"https://openalex.org/keywords/dependent-type","display_name":"Dependent type","score":0.48607686161994934},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.4183278977870941},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3740193843841553},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37105050683021545},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3371521830558777},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.23651883006095886},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23078295588493347},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2120576798915863}],"concepts":[{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.9666762351989746},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.9038701057434082},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5894491076469421},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.5487015843391418},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.5479046702384949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5466079115867615},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5231702923774719},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5073422789573669},{"id":"https://openalex.org/C20528804","wikidata":"https://www.wikidata.org/wiki/Q997433","display_name":"Dependent type","level":3,"score":0.48607686161994934},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.4183278977870941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3740193843841553},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37105050683021545},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3371521830558777},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.23651883006095886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23078295588493347},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2120576798915863},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0661(05)80726-1","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80726-1","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(05)80726-1","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80726-1","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2952065348","https://openalex.org/W4299815640","https://openalex.org/W2096221521","https://openalex.org/W2473161270","https://openalex.org/W2073738669","https://openalex.org/W1802255488","https://openalex.org/W2007054034","https://openalex.org/W1983399101","https://openalex.org/W2158086586","https://openalex.org/W2043740265"],"abstract_inverted_index":{"It":[0],"is":[1],"well-known":[2],"that":[3,51],"one":[4,35,45],"can":[5,36,46],"build":[6],"models":[7],"of":[8,16,62],"full":[9],"higher-order":[10],"dependent":[11],"type":[12],"theory":[13],"(a.k.a.":[14],"calculus":[15],"constructions)":[17],"using":[18,87],"partial":[19,26],"equivalence":[20],"relations":[21],"and":[22,42,58,69],"assemblies":[23,52],"over":[24],"a":[25,55,82],"combinatory":[27],"algebra.":[28],"Using":[29],"the":[30,40,49,60,63,88,93,98],"propositions":[31],"as":[32,71,95],"types":[33,41,68],"paradigm,":[34],"then":[37],"reason":[38,66],"about":[39,67],"kinds.":[43],"But":[44],"also":[47],"use":[48,59],"fact":[50],"embed":[53],"into":[54],"realizability":[56],"topos":[57,64,89],"logic":[61,90],"to":[65,92],"kinds,":[70],"done":[72],"by":[73],"Reus":[74],"in":[75,81],"his":[76],"dissertation.":[77],"We":[78],"show":[79],"that,":[80],"suitably":[83],"precise":[84],"sense,":[85],"reasoning":[86,96],"amounts":[91],"same":[94],"via":[97],"propositions-as-types":[99],"method.":[100]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}