{"id":"https://openalex.org/W2906883693","doi":"https://doi.org/10.1145/3293880.3294091","title":"On synthetic undecidability in Coq, with an application to the Entscheidungsproblem","display_name":"On synthetic undecidability in Coq, with an application to the Entscheidungsproblem","publication_year":2019,"publication_date":"2019-01-04","ids":{"openalex":"https://openalex.org/W2906883693","doi":"https://doi.org/10.1145/3293880.3294091","mag":"2906883693"},"language":"en","primary_location":{"id":"doi:10.1145/3293880.3294091","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3293880.3294091","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},"type":"article","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/A5080496189","display_name":"Yannick Forster","orcid":"https://orcid.org/0000-0002-8676-9819"},"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":true,"raw_author_name":"Yannick Forster","raw_affiliation_strings":["Saarland University, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067282848","display_name":"Dominik Kirst","orcid":"https://orcid.org/0000-0003-4126-6975"},"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":"Dominik Kirst","raw_affiliation_strings":["Saarland University, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073707150","display_name":"Gert Smolka","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":"Gert Smolka","raw_affiliation_strings":["Saarland University, Germany"],"affiliations":[{"raw_affiliation_string":"Saarland University, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080496189"],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":null,"apc_paid":null,"fwci":3.4917,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.93211468,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"38","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991999864578247,"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/T10126","display_name":"Logic, programming, and type systems","score":0.998199999332428,"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":0.9980000257492065,"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/kripke-semantics","display_name":"Kripke semantics","score":0.7552446126937866},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7544997334480286},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.6781802177429199},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.6144755482673645},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.5440300703048706},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.5356789231300354},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.5192999243736267},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5140188932418823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49730589985847473},{"id":"https://openalex.org/keywords/computability-theory","display_name":"Computability theory","score":0.47281160950660706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4467162787914276},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4426640272140503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41400086879730225},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4086475372314453},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4034665524959564},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3355441093444824},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.23677000403404236},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.14803600311279297},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13646313548088074}],"concepts":[{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.7552446126937866},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7544997334480286},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.6781802177429199},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.6144755482673645},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.5440300703048706},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.5356789231300354},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.5192999243736267},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5140188932418823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49730589985847473},{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.47281160950660706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4467162787914276},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4426640272140503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41400086879730225},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4086475372314453},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4034665524959564},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3355441093444824},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.23677000403404236},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.14803600311279297},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13646313548088074},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3293880.3294091","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3293880.3294091","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W50191166","https://openalex.org/W162931075","https://openalex.org/W1510709103","https://openalex.org/W1514516864","https://openalex.org/W1549008998","https://openalex.org/W1579433101","https://openalex.org/W1960494084","https://openalex.org/W1969204136","https://openalex.org/W1987645821","https://openalex.org/W2010146589","https://openalex.org/W2011437767","https://openalex.org/W2027489592","https://openalex.org/W2047144334","https://openalex.org/W2057232741","https://openalex.org/W2064811181","https://openalex.org/W2066815568","https://openalex.org/W2073185604","https://openalex.org/W2085335923","https://openalex.org/W2107589331","https://openalex.org/W2115444569","https://openalex.org/W2115627721","https://openalex.org/W2116976042","https://openalex.org/W2126160338","https://openalex.org/W2133921140","https://openalex.org/W2134419104","https://openalex.org/W2140830696","https://openalex.org/W2144086150","https://openalex.org/W2147202919","https://openalex.org/W2164688709","https://openalex.org/W2288657451","https://openalex.org/W2291208220","https://openalex.org/W2331346174","https://openalex.org/W2402209726","https://openalex.org/W2768826633","https://openalex.org/W2769209754","https://openalex.org/W2798718690","https://openalex.org/W2811265870","https://openalex.org/W2895928777","https://openalex.org/W2896864541","https://openalex.org/W2907653511","https://openalex.org/W3158496506","https://openalex.org/W4238295494"],"related_works":["https://openalex.org/W2277965188","https://openalex.org/W2160135306","https://openalex.org/W2807588908","https://openalex.org/W1602423174","https://openalex.org/W2792955346","https://openalex.org/W2103838550","https://openalex.org/W1988755390","https://openalex.org/W4246430844","https://openalex.org/W2166197034","https://openalex.org/W1511328824"],"abstract_inverted_index":{"We":[0],"formalise":[1,66],"the":[2,19,49,86,101,108],"computational":[3],"undecidability":[4],"of":[5,10,80,88,103],"validity,":[6],"satisfiability,":[7],"and":[8,31,38,43,72,94,112],"provability":[9],"first-order":[11],"formulas":[12],"following":[13],"a":[14,56,77,96],"synthetic":[15,60],"approach":[16],"based":[17],"on":[18],"computation":[20],"native":[21],"to":[22,76],"Coq's":[23],"constructive":[24],"type":[25],"theory.":[26],"Concretely,":[27],"we":[28,65,84],"consider":[29],"Tarski":[30],"Kripke":[32],"semantics":[33],"as":[34,36,107],"well":[35],"classical":[37],"intuitionistic":[39],"natural":[40],"deduction":[41],"systems":[42,111],"provide":[44,95],"compact":[45],"many-one":[46],"reductions":[47],"from":[48],"Post":[50],"correspondence":[51],"problem":[52],"(PCP).":[53],"Moreover,":[54],"developing":[55],"basic":[57],"framework":[58],"for":[59,99],"computability":[61],"theory":[62],"in":[63],"Coq,":[64],"standard":[67],"results":[68],"concerning":[69],"decidability,":[70],"enumerability,":[71],"reducibility":[73],"without":[74],"reference":[75],"concrete":[78],"model":[79],"computation.":[81],"For":[82],"instance,":[83],"prove":[85],"equivalence":[87],"Post's":[89],"theorem":[90],"with":[91],"Markov's":[92],"principle":[93],"convenient":[97],"technique":[98],"establishing":[100],"enumerability":[102],"inductive":[104],"predicates":[105],"such":[106],"considered":[109],"proof":[110],"PCP.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}