{"id":"https://openalex.org/W2020900140","doi":"https://doi.org/10.2168/lmcs-8(4:1)2012","title":"First steps in synthetic guarded domain theory: step-indexing in the topos of trees","display_name":"First steps in synthetic guarded domain theory: step-indexing in the topos of trees","publication_year":2012,"publication_date":"2012-10-03","ids":{"openalex":"https://openalex.org/W2020900140","doi":"https://doi.org/10.2168/lmcs-8(4:1)2012","mag":"2020900140"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-8(4:1)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:1)2012","pdf_url":"https://lmcs.episciences.org/1041/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/1041/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055959064","display_name":"Lars Birkedal","orcid":"https://orcid.org/0000-0003-1320-0098"},"institutions":[{"id":"https://openalex.org/I83467386","display_name":"IT University of Copenhagen","ror":"https://ror.org/02309jg23","country_code":"DK","type":"education","lineage":["https://openalex.org/I83467386"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Lars Birkedal","raw_affiliation_strings":["IT-UNIVERSITY OF COPENHAGEN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IT-UNIVERSITY OF COPENHAGEN","institution_ids":["https://openalex.org/I83467386"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045780288","display_name":"Rasmus Ejlers M\u00f8gelberg","orcid":"https://orcid.org/0000-0003-0386-4376"},"institutions":[{"id":"https://openalex.org/I83467386","display_name":"IT University of Copenhagen","ror":"https://ror.org/02309jg23","country_code":"DK","type":"education","lineage":["https://openalex.org/I83467386"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Rasmus Ejlers M\u00f8gelberg","raw_affiliation_strings":["IT University of Copenhagen","IT-UNIVERSITY OF COPENHAGEN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IT University of Copenhagen","institution_ids":["https://openalex.org/I83467386"]},{"raw_affiliation_string":"IT-UNIVERSITY OF COPENHAGEN","institution_ids":["https://openalex.org/I83467386"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062310143","display_name":"Jan Schwinghammer","orcid":null},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Schwinghammer","raw_affiliation_strings":["Saarland University","saarland university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University","institution_ids":["https://openalex.org/I91712215"]},{"raw_affiliation_string":"saarland university","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111987405","display_name":"Kristian St\u00f8vring","orcid":null},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Kristian St\u00f8vring","raw_affiliation_strings":["DIKU, University of Copenhagen","[DIKU, Univ. of Copenhagen]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DIKU, University of Copenhagen","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"[DIKU, Univ. of Copenhagen]","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.6343,"has_fulltext":true,"cited_by_count":76,"citation_normalized_percentile":{"value":0.96526686,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"Volume 8, Issue 4","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":0.9998999834060669,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9973999857902527,"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":0.9916999936103821,"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/topos-theory","display_name":"Topos theory","score":0.8428016901016235},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.701468288898468},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.5534473061561584},{"id":"https://openalex.org/keywords/domain-theory","display_name":"Domain theory","score":0.5454427003860474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48146119713783264},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.468152791261673},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.4655393362045288},{"id":"https://openalex.org/keywords/modal-operator","display_name":"Modal operator","score":0.45319944620132446},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.44699183106422424},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.44696566462516785},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.433902770280838},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42794692516326904},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.42303434014320374},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.415658175945282},{"id":"https://openalex.org/keywords/logical-framework","display_name":"Logical framework","score":0.41390925645828247},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.3957650363445282},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3840998709201813},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31379586458206177},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.2095721960067749},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1909770369529724},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.17919012904167175},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.14396551251411438}],"concepts":[{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.8428016901016235},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.701468288898468},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.5534473061561584},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.5454427003860474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48146119713783264},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.468152791261673},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.4655393362045288},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.45319944620132446},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.44699183106422424},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.44696566462516785},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.433902770280838},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42794692516326904},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.42303434014320374},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.415658175945282},{"id":"https://openalex.org/C20693621","wikidata":"https://www.wikidata.org/wiki/Q6667502","display_name":"Logical framework","level":2,"score":0.41390925645828247},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3957650363445282},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3840998709201813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31379586458206177},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.2095721960067749},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1909770369529724},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.17919012904167175},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.14396551251411438},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.2168/lmcs-8(4:1)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:1)2012","pdf_url":"https://lmcs.episciences.org/1041/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1208.3596","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1208.3596","pdf_url":"https://arxiv.org/pdf/1208.3596","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.468","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.468","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.itu.dk/people/birkedal/papers/sgdt-conf.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.204.9707","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.204.9707","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.itu.dk/%7Ebirkedal/papers/sgdt-conf.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.221.2713","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.2713","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.itu.dk/%7Ebirkedal/papers/sgdt-journal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.298.7637","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.7637","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.it-c.dk/~birkedal/papers/sgdt-journal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.359.7078","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.359.7078","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.itu.dk/people/birkedal/papers/sgdt-journal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.755.3685","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.755.3685","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1208.3596.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:5bc5287ee86c491ca6b70f696b4b6227","is_oa":true,"landing_page_url":"https://doaj.org/article/5bc5287ee86c491ca6b70f696b4b6227","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 8, Issue 4 (2012)","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/766f3e77-511c-4704-a310-4b7c383069b7","is_oa":false,"landing_page_url":"https://pure.itu.dk/portal/da/publications/766f3e77-511c-4704-a310-4b7c383069b7","pdf_url":null,"source":{"id":"https://openalex.org/S4377196680","display_name":"IT University Of Copenhagen (IT University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83467386","host_organization_name":"IT University of Copenhagen","host_organization_lineage":["https://openalex.org/I83467386"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Birkedal, L, M\u00f8gelberg, R E, Schwinghammer, J & St\u00f8vring, K 2012, 'First steps in synthetic guarded domain theory: step-indexing in the topos of trees', Logical Methods in Computer Science, vol. 8, no. 4. https://doi.org/10.2168/LMCS-8(4:1)2012","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.2168/lmcs-8(4:1)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:1)2012","pdf_url":"https://lmcs.episciences.org/1041/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.5400000214576721,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2020900140.pdf","grobid_xml":"https://content.openalex.org/works/W2020900140.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W16477519","https://openalex.org/W79336753","https://openalex.org/W1486558830","https://openalex.org/W1534018603","https://openalex.org/W1546369567","https://openalex.org/W1565457335","https://openalex.org/W1608782706","https://openalex.org/W1810446968","https://openalex.org/W1828583149","https://openalex.org/W1965602413","https://openalex.org/W1983905931","https://openalex.org/W2017778827","https://openalex.org/W2024873396","https://openalex.org/W2049362364","https://openalex.org/W2060852846","https://openalex.org/W2078959232","https://openalex.org/W2079103712","https://openalex.org/W2100559921","https://openalex.org/W2109084333","https://openalex.org/W2121213425","https://openalex.org/W2121306658","https://openalex.org/W2123329569","https://openalex.org/W2130505204","https://openalex.org/W2132181573","https://openalex.org/W2143623703","https://openalex.org/W2145840053","https://openalex.org/W2153128836"],"related_works":["https://openalex.org/W1507779663","https://openalex.org/W2137868378","https://openalex.org/W2983885771","https://openalex.org/W2024873396","https://openalex.org/W1483105844","https://openalex.org/W2077809881","https://openalex.org/W4300454881","https://openalex.org/W2953362051","https://openalex.org/W3103660633","https://openalex.org/W2399399745"],"abstract_inverted_index":{"We":[0,13,59],"present":[1],"the":[2,15,62,68,72,109,141,156],"topos":[3,142],"S":[4,21,25,66],"of":[5,10,20,41,65,75,78,81,97,112,121,123,143,150],"trees":[6],"as":[7,36],"a":[8,95,98,138,148],"model":[9,96,149],"guarded":[11,125,152],"recursion.":[12],"study":[14],"internal":[16,63,110],"dependently-typed":[17],"higher-order":[18,102],"logic":[19,64,111],"and":[22,32,44,84,104,128],"show":[23,49,91],"that":[24,61],"models":[26,80,122],"two":[27],"modal":[28],"operators,":[29],"on":[30],"predicates":[31],"types,":[33],"which":[34],"serve":[35],"guards":[37],"in":[38],"recursive":[39,53,105],"definitions":[40],"terms,":[42],"predicates,":[43],"types.":[45,58],"In":[46],"particular,":[47],"we":[48,90,115],"how":[50,92],"to":[51,93],"solve":[52],"type":[54],"equations":[55],"involving":[56],"dependent":[57],"propose":[60],"provides":[67],"right":[69],"setting":[70],"for":[71,131,158],"synthetic":[73,124,151],"construction":[74],"abstract":[76],"versions":[77],"step-indexed":[79],"programming":[82,99],"languages":[83],"program":[85],"logics.":[86],"As":[87],"an":[88,117],"example,":[89],"construct":[94],"language":[100],"with":[101,137],"store":[103],"types":[106],"entirely":[107],"inside":[108],"S.":[113,159],"Moreover,":[114],"give":[116],"axiomatic":[118],"categorical":[119],"treatment":[120],"domain":[126,153],"theory":[127],"prove":[129],"that,":[130],"any":[132],"complete":[133],"Heyting":[134],"algebra":[135],"A":[136,146],"well-founded":[139],"basis,":[140],"sheaves":[144],"over":[145],"forms":[147],"theory,":[154],"generalizing":[155],"results":[157]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}