{"id":"https://openalex.org/W2014175609","doi":"https://doi.org/10.1145/2535838.2535885","title":"Proofs that count","display_name":"Proofs that count","publication_year":2014,"publication_date":"2014-01-08","ids":{"openalex":"https://openalex.org/W2014175609","doi":"https://doi.org/10.1145/2535838.2535885","mag":"2014175609"},"language":"en","primary_location":{"id":"doi:10.1145/2535838.2535885","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2535838.2535885","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","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/A5016276143","display_name":"Azadeh Farzan","orcid":"https://orcid.org/0000-0001-9005-2653"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Azadeh Farzan","raw_affiliation_strings":["University of Toronto, Toronto, ON, Canada","University of Toronto, Toronto, On, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"University of Toronto, Toronto, On, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041698482","display_name":"Zachary Kincaid","orcid":"https://orcid.org/0000-0002-7294-9165"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zachary Kincaid","raw_affiliation_strings":["University of Toronto, Toronto, ON, Canada","University of Toronto, Toronto, On, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"University of Toronto, Toronto, On, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062411838","display_name":"Andreas Podelski","orcid":"https://orcid.org/0000-0003-2540-9489"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Podelski","raw_affiliation_strings":["University of Freiburg, Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"University of Freiburg, Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016276143"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":7.8338,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.97807063,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"151","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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":0.9998000264167786,"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/T11567","display_name":"semigroups and automata theory","score":0.9947999715805054,"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/mathematical-proof","display_name":"Mathematical proof","score":0.8939945697784424},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7301645278930664},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6512326598167419},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.5633200407028198},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.5433477163314819},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.471760094165802},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.46105778217315674},{"id":"https://openalex.org/keywords/formal-proof","display_name":"Formal proof","score":0.4516708552837372},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44998642802238464},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4345993399620056},{"id":"https://openalex.org/keywords/formal-methods","display_name":"Formal methods","score":0.4289943277835846},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3482394218444824},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29749906063079834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2540433406829834}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8939945697784424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7301645278930664},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6512326598167419},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.5633200407028198},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.5433477163314819},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.471760094165802},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.46105778217315674},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.4516708552837372},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44998642802238464},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4345993399620056},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.4289943277835846},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3482394218444824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29749906063079834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2540433406829834},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2535838.2535885","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2535838.2535885","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W69918202","https://openalex.org/W335576746","https://openalex.org/W1485572331","https://openalex.org/W1511206757","https://openalex.org/W1514194201","https://openalex.org/W1516842532","https://openalex.org/W1527710292","https://openalex.org/W1536946401","https://openalex.org/W1549166962","https://openalex.org/W1555742330","https://openalex.org/W1561112849","https://openalex.org/W1563374593","https://openalex.org/W1565898282","https://openalex.org/W1573633114","https://openalex.org/W1575098094","https://openalex.org/W1577235157","https://openalex.org/W1592314966","https://openalex.org/W1606022702","https://openalex.org/W1783679080","https://openalex.org/W1810198311","https://openalex.org/W1841626152","https://openalex.org/W1853246977","https://openalex.org/W1855789069","https://openalex.org/W1861590051","https://openalex.org/W1881102326","https://openalex.org/W1933255669","https://openalex.org/W1940110491","https://openalex.org/W1965662337","https://openalex.org/W1967917857","https://openalex.org/W1982900911","https://openalex.org/W1989788631","https://openalex.org/W2028113097","https://openalex.org/W2031276295","https://openalex.org/W2033942886","https://openalex.org/W2036526834","https://openalex.org/W2039812824","https://openalex.org/W2042876806","https://openalex.org/W2048880957","https://openalex.org/W2053685668","https://openalex.org/W2078521778","https://openalex.org/W2096199323","https://openalex.org/W2102236203","https://openalex.org/W2106001218","https://openalex.org/W2128453996","https://openalex.org/W2133055577","https://openalex.org/W2141957585","https://openalex.org/W2147269402","https://openalex.org/W2149030441","https://openalex.org/W2149706659","https://openalex.org/W2155487709","https://openalex.org/W2170487018","https://openalex.org/W2914181030","https://openalex.org/W4236040576","https://openalex.org/W4243742593","https://openalex.org/W4249920159","https://openalex.org/W6639142308","https://openalex.org/W6679998460"],"related_works":["https://openalex.org/W3168779796","https://openalex.org/W3037184231","https://openalex.org/W4295798319","https://openalex.org/W1819460135","https://openalex.org/W1515562936","https://openalex.org/W2044402378","https://openalex.org/W47204537","https://openalex.org/W187835144","https://openalex.org/W84189497","https://openalex.org/W2508333642"],"abstract_inverted_index":{"Counting":[0],"arguments":[1,44,71],"are":[2,18,45,55],"among":[3],"the":[4,12],"most":[5],"basic":[6],"proof":[7],"methods":[8],"in":[9,47,68],"mathematics.":[10],"Within":[11],"field":[13],"of":[14,34,51],"formal":[15],"verification,":[16],"they":[17],"useful":[19],"for":[20,97],"reasoning":[21],"about":[22],"programs":[23,29,38],"with":[24,30,39],"infinite":[25],"control,":[26],"such":[27,52],"as":[28],"an":[31],"unbounded":[32],"number":[33],"threads,":[35],"or":[36],"(concurrent)":[37],"recursive":[40],"procedures.":[41],"While":[42],"counting":[43,62,70,86,102],"common":[46],"informal,":[48],"hand-written":[49],"proofs":[50],"programs,":[53],"there":[54],"no":[56],"fully":[57],"automated":[58],"techniques":[59],"to":[60,74,82,108],"construct":[61],"arguments.":[63],"The":[64],"key":[65],"questions":[66],"involved":[67],"automating":[69],"are:":[72],"how":[73,81],"decide":[75,83],"what":[76],"should":[77],"be":[78],"counted?,":[79],"and":[80,100],"when":[84],"a":[85,95],"argument":[87],"is":[88],"valid?":[89],"In":[90],"this":[91],"paper,":[92],"we":[93],"present":[94],"technique":[96],"automatically":[98],"constructing":[99],"checking":[101],"arguments,":[103],"which":[104],"includes":[105],"novel":[106],"solutions":[107],"these":[109],"questions.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
