{"id":"https://openalex.org/W6929488979","doi":"https://doi.org/10.4230/lipics.fscd.2025.33","title":"Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It","display_name":"Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W6929488979","doi":"https://doi.org/10.4230/lipics.fscd.2025.33"},"language":"en","primary_location":{"id":"pmh:oai:pure.atira.dk:openaire/92105d5d-ab0a-48ef-adeb-f71d4fe24af4","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/92105d5d-ab0a-48ef-adeb-f71d4fe24af4","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stepanenko, S & Timany, A 2025, Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It. in M Fernandez (ed.), 10th International Conference on Formal Structures for Computation and Deduction, FSCD 2025., 33, Dagstuhl Publishing, Leibniz International Proceedings in Informatics, LIPIcs, vol. 337, 10th International Conference on Formal Structures for Computation and Deduction, FSCD 2025, Birmingham, United Kingdom, 14/07/2025. https://doi.org/10.4230/LIPIcs.FSCD.2025.33","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://pure.au.dk/portal/en/publications/92105d5d-ab0a-48ef-adeb-f71d4fe24af4","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Stepanenko, Sergei","orcid":"https://orcid.org/0000-0002-7322-5644"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Stepanenko, Sergei","raw_affiliation_strings":["Aarhus University, Denmark"],"raw_orcid":"https://orcid.org/0000-0002-7322-5644","affiliations":[{"raw_affiliation_string":"Aarhus University, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"last","author":{"id":null,"display_name":"Timany, Amin","orcid":"https://orcid.org/0000-0002-2237-851X"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Timany, Amin","raw_affiliation_strings":["Aarhus University, Denmark"],"raw_orcid":"https://orcid.org/0000-0002-2237-851X","affiliations":[{"raw_affiliation_string":"Aarhus University, Denmark","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22008284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9564999938011169,"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":0.9564999938011169,"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":0.019600000232458115,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/functor","display_name":"Functor","score":0.8867999911308289},{"id":"https://openalex.org/keywords/subcategory","display_name":"Subcategory","score":0.657800018787384},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5447999835014343},{"id":"https://openalex.org/keywords/domain-theory","display_name":"Domain theory","score":0.4519999921321869},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40849998593330383},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.3718000054359436},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.3621000051498413}],"concepts":[{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.8867999911308289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8248999714851379},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.657800018787384},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5447999835014343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47769999504089355},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.4519999921321869},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40849998593330383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4074000120162964},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C153778094","wikidata":"https://www.wikidata.org/wiki/Q357858","display_name":"Adjoint functors","level":3,"score":0.32260000705718994},{"id":"https://openalex.org/C48808802","wikidata":"https://www.wikidata.org/wiki/Q2007878","display_name":"Functor category","level":3,"score":0.322299987077713},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C99633028","wikidata":"https://www.wikidata.org/wiki/Q1442189","display_name":"Natural transformation","level":3,"score":0.259799987077713}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:pure.atira.dk:openaire/92105d5d-ab0a-48ef-adeb-f71d4fe24af4","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/92105d5d-ab0a-48ef-adeb-f71d4fe24af4","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stepanenko, S & Timany, A 2025, Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It. in M Fernandez (ed.), 10th International Conference on Formal Structures for Computation and Deduction, FSCD 2025., 33, Dagstuhl Publishing, Leibniz International Proceedings in Informatics, LIPIcs, vol. 337, 10th International Conference on Formal Structures for Computation and Deduction, FSCD 2025, Birmingham, United Kingdom, 14/07/2025. https://doi.org/10.4230/LIPIcs.FSCD.2025.33","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:drops-oai.dagstuhl.de:23648","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.33","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol337-fscd2025/LIPIcs.FSCD.2025.33/LIPIcs.FSCD.2025.33.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.fscd.2025.33","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.fscd.2025.33","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/92105d5d-ab0a-48ef-adeb-f71d4fe24af4","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/92105d5d-ab0a-48ef-adeb-f71d4fe24af4","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stepanenko, S & Timany, A 2025, Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It. in M Fernandez (ed.), 10th International Conference on Formal Structures for Computation and Deduction, FSCD 2025., 33, Dagstuhl Publishing, Leibniz International Proceedings in Informatics, LIPIcs, vol. 337, 10th International Conference on Formal Structures for Computation and Deduction, FSCD 2025, Birmingham, United Kingdom, 14/07/2025. https://doi.org/10.4230/LIPIcs.FSCD.2025.33","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6851704783","display_name":null,"funder_award_id":"25804","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"},{"id":"https://openalex.org/G899382969","display_name":"Compositional Higher-Order Reasoning about Distributed Systems","funder_award_id":"101096090","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Constructing":[0],"solutions":[1],"to":[2,29,77,94,155,208,224],"recursive":[3],"domain":[4,158],"equations":[5,159],"is":[6,23,48,52,196],"a":[7,25,32,36,113,120,145,153,227],"well-known,":[8],"important":[9],"problem":[10,22,132,160],"in":[11,178,226],"the":[12,21,45,50,57,62,66,131,156,166,179,183,201,204,209,212],"study":[13],"of":[14,31,59,117,124,168,185,203,206,211,214],"programs":[15],"and":[16,65,187,216],"programming":[17],"languages.":[18],"Mathematically":[19],"speaking,":[20],"finding":[24],"fixed":[26],"point":[27],"(up":[28],"isomorphism)":[30],"suitable":[33,37],"functor":[34,51],"over":[35,53,61,79,102,119,126,138,161,165,170,189],"category.":[38],"A":[39],"particularly":[40,121],"useful":[41],"instance,":[42],"inspired":[43],"by":[44],"step-indexing":[46,78,109],"technique,":[47],"where":[49],"(a":[54],"subcategory":[55,123],"of)":[56],"category":[58,167,205,213],"presheaves":[60,125,169,188,215,220],"ordinal":[63,171],"\u03c9":[64],"functors":[67,118,164],"are":[68,191,221],"locally-contractive,":[69],"also":[70],"known":[71],"as":[72,173,175],"guarded":[73,157,163],"functors.":[74],"This":[75],"corresponds":[76],"natural":[80],"numbers.":[81],"However,":[82],"for":[83],"certain":[84],"problems,":[85],"e.g.,":[86],"when":[87],"dealing":[88],"with":[89,136,144],"infinite":[90],"non-determinism,":[91],"one":[92],"needs":[93],"employ":[95],"trans-finite":[96,108],"step-indexing,":[97],"i.e.,":[98],"consider":[99],"presheaf":[100],"categories":[101,184],"higher":[103,127],"ordinals.":[104],"Prior":[105],"work":[106,199],"on":[107],"either":[110],"only":[111],"considers":[112],"very":[114,133],"narrow":[115],"class":[116],"restricted":[122],"ordinals,":[128],"or":[129],"treats":[130],"generally":[134],"working":[135],"sheaves":[137,186,207],"an":[139],"arbitrary":[140],"complete":[141],"Heyting":[142],"algebra":[143],"well-founded":[146],"basis.":[147],"In":[148],"this":[149],"paper":[150],"we":[151],"present":[152],"solution":[154],"all":[162],"numbers,":[172],"well":[174],"its":[176],"mechanization":[177,225],"Rocq":[180],"Prover.":[181],"As":[182],"ordinals":[190],"equivalent,":[192],"our":[193],"main":[194],"contribution":[195],"simplifying":[197],"prior":[198],"from":[200],"setting":[202,210],"mechanizing":[217],"it":[218],"-":[219],"more":[222],"amenable":[223],"proof":[228],"assistant.":[229]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
