{"id":"https://openalex.org/W4386350920","doi":"https://doi.org/10.1007/978-3-031-38499-8_25","title":"Theorem Proving in\u00a0Dependently-Typed Higher-Order Logic","display_name":"Theorem Proving in\u00a0Dependently-Typed Higher-Order Logic","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4386350920","doi":"https://doi.org/10.1007/978-3-031-38499-8_25"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-38499-8_25","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-38499-8_25","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-38499-8_25.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-38499-8_25.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078775159","display_name":"Colin Rothgang","orcid":"https://orcid.org/0000-0001-9751-8989"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Colin Rothgang","raw_affiliation_strings":["Mathematics and Computer Science, FU, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science, FU, Berlin, Germany","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091861223","display_name":"Florian Rabe","orcid":"https://orcid.org/0000-0003-3040-3655"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florian Rabe","raw_affiliation_strings":["Computer Science, University Erlangen-N\u00fcrnberg, Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Computer Science, University Erlangen-N\u00fcrnberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055110324","display_name":"Christoph Benzm\u00fcller","orcid":"https://orcid.org/0000-0002-3392-3093"},"institutions":[{"id":"https://openalex.org/I94626330","display_name":"University of Bamberg","ror":"https://ror.org/01c1w6d29","country_code":"DE","type":"education","lineage":["https://openalex.org/I94626330"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Benzm\u00fcller","raw_affiliation_strings":["AI Systems Engineering, University Bamberg, Bamberg, Germany","Mathematics and Computer Science, FU, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"AI Systems Engineering, University Bamberg, Bamberg, Germany","institution_ids":["https://openalex.org/I94626330"]},{"raw_affiliation_string":"Mathematics and Computer Science, FU, Berlin, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078775159"],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":3.7245,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.94180051,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"438","last_page":"455"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9933000206947327,"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":0.9894000291824341,"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/hol","display_name":"HOL","score":0.991870105266571},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.797325611114502},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7362872958183289},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.6679567694664001},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.6384811401367188},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.634519636631012},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.5560754537582397},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.42257165908813477},{"id":"https://openalex.org/keywords/logical-framework","display_name":"Logical framework","score":0.4160165786743164},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3816376328468323},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.3793548345565796},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.24153253436088562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19523558020591736},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17854705452919006},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.09188815951347351}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.991870105266571},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.797325611114502},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7362872958183289},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.6679567694664001},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.6384811401367188},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.634519636631012},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.5560754537582397},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.42257165908813477},{"id":"https://openalex.org/C20693621","wikidata":"https://www.wikidata.org/wiki/Q6667502","display_name":"Logical framework","level":2,"score":0.4160165786743164},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3816376328468323},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3793548345565796},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.24153253436088562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19523558020591736},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17854705452919006},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.09188815951347351},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-38499-8_25","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-38499-8_25","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-38499-8_25.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-38499-8_25","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-38499-8_25","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-38499-8_25.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"No poverty","id":"https://metadata.un.org/sdg/1"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386350920.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W79561349","https://openalex.org/W1464569014","https://openalex.org/W1497011154","https://openalex.org/W1534850143","https://openalex.org/W1565996669","https://openalex.org/W1573992413","https://openalex.org/W1595467526","https://openalex.org/W1727609483","https://openalex.org/W1974190112","https://openalex.org/W1986402635","https://openalex.org/W1996404651","https://openalex.org/W2034155940","https://openalex.org/W2151520617","https://openalex.org/W2903910822","https://openalex.org/W3148132267","https://openalex.org/W4234528212","https://openalex.org/W4299731435","https://openalex.org/W6912586707"],"related_works":["https://openalex.org/W1515169568","https://openalex.org/W2886069053","https://openalex.org/W1553457932","https://openalex.org/W4378498573","https://openalex.org/W183532729","https://openalex.org/W4386350920","https://openalex.org/W2169776427","https://openalex.org/W1532559807","https://openalex.org/W576491636","https://openalex.org/W1518373246"],"abstract_inverted_index":{"Abstract":[0],"Higher-order":[1],"logic":[2],"HOL":[3,64,82,91],"offers":[4,35],"a":[5,37,59,77,87,90,96],"very":[6],"simple":[7],"syntax":[8],"and":[9,13,69,83],"semantics":[10],"for":[11,99],"representing":[12],"reasoning":[14],"about":[15],"typed":[16],"data":[17],"structures.":[18],"But":[19],"its":[20],"type":[21,33,39],"system":[22],"lacks":[23],"advanced":[24],"features":[25],"where":[26],"types":[27],"may":[28],"depend":[29],"on":[30],"terms.":[31],"Dependent":[32],"theory":[34],"such":[36],"rich":[38],"system,":[40],"but":[41],"has":[42],"rather":[43],"substantial":[44],"conceptual":[45,70],"differences":[46],"to":[47,81,89],"HOL,":[48],"as":[49,51,86],"well":[50],"comparatively":[52],"poor":[53],"proof":[54],"automation":[55],"support.":[56],"We":[57],"introduce":[58],"dependently-typed":[60],"extension":[61],"DHOL":[62,80],"of":[63,72],"that":[65],"retains":[66],"the":[67],"style":[68],"framework":[71],"HOL.":[73],"Moreover,":[74],"we":[75],"build":[76],"translation":[78],"from":[79],"implement":[84],"it":[85],"preprocessor":[88],"theorem":[92,97],"prover,":[93],"thereby":[94],"obtaining":[95],"prover":[98],"DHOL.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}