{"id":"https://openalex.org/W4402425258","doi":"https://doi.org/10.1007/978-3-031-71162-6_28","title":"Proving Functional Program Equivalence via\u00a0Directed Lemma Synthesis","display_name":"Proving Functional Program Equivalence via\u00a0Directed Lemma Synthesis","publication_year":2024,"publication_date":"2024-09-10","ids":{"openalex":"https://openalex.org/W4402425258","doi":"https://doi.org/10.1007/978-3-031-71162-6_28"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-71162-6_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-71162-6_28","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-71162-6_28.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/10.1007/978-3-031-71162-6_28.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091706559","display_name":"Yican Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yican Sun","raw_affiliation_strings":["Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059555100","display_name":"Ruyi Ji","orcid":"https://orcid.org/0000-0002-0150-8629"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruyi Ji","raw_affiliation_strings":["Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073833609","display_name":"Jian Fang","orcid":"https://orcid.org/0000-0002-1077-3686"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Fang","raw_affiliation_strings":["Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111322403","display_name":"Xuanlin Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuanlin Jiang","raw_affiliation_strings":["Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043436285","display_name":"Mingshuai Chen","orcid":"https://orcid.org/0000-0001-9663-7441"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingshuai Chen","raw_affiliation_strings":["Zhejiang University, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101363861","display_name":"Yingfei Xiong","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yingfei Xiong","raw_affiliation_strings":["Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China","Zhongguancun Laboratory, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of High Confidence Software Technologies (Peking University), Ministry of Education; School of Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"Zhongguancun Laboratory, Beijing, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101363861"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.3717,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.82636893,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"538","last_page":"557"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9994999766349792,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/computer-science","display_name":"Computer science","score":0.7707191705703735},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.7264695763587952},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6688205003738403},{"id":"https://openalex.org/keywords/functional-equivalence","display_name":"Functional equivalence","score":0.5710007548332214},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.5303436517715454},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3975059986114502},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3796535134315491},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3644527792930603},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3202432692050934},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18255656957626343},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08457052707672119}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7707191705703735},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7264695763587952},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6688205003738403},{"id":"https://openalex.org/C2988012377","wikidata":"https://www.wikidata.org/wiki/Q29966452","display_name":"Functional equivalence","level":2,"score":0.5710007548332214},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.5303436517715454},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3975059986114502},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3796535134315491},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3644527792930603},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3202432692050934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18255656957626343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08457052707672119},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-71162-6_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-71162-6_28","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-71162-6_28.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:10.1007/978-3-031-71162-6_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-71162-6_28","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-71162-6_28.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":[],"awards":[{"id":"https://openalex.org/G4869734229","display_name":null,"funder_award_id":"2022YFB4501902","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8821883043","display_name":null,"funder_award_id":"62161146003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402425258.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W123460044","https://openalex.org/W145069693","https://openalex.org/W174956004","https://openalex.org/W1464569014","https://openalex.org/W1480909796","https://openalex.org/W1541587797","https://openalex.org/W1553511155","https://openalex.org/W1856554806","https://openalex.org/W2076667206","https://openalex.org/W2091723900","https://openalex.org/W2109261022","https://openalex.org/W2124141583","https://openalex.org/W2130427425","https://openalex.org/W2139626883","https://openalex.org/W2164778826","https://openalex.org/W2580272185","https://openalex.org/W2749302087","https://openalex.org/W2780276625","https://openalex.org/W2921114217","https://openalex.org/W2945675489","https://openalex.org/W2956182160","https://openalex.org/W2974174239","https://openalex.org/W3001530932","https://openalex.org/W3039412221","https://openalex.org/W3185574054","https://openalex.org/W4206670752","https://openalex.org/W4210917167","https://openalex.org/W4254459063","https://openalex.org/W4297415612","https://openalex.org/W4379534296","https://openalex.org/W4387667038","https://openalex.org/W4391840543","https://openalex.org/W6600547436","https://openalex.org/W6911662583"],"related_works":["https://openalex.org/W3118866054","https://openalex.org/W2056882394","https://openalex.org/W2379789703","https://openalex.org/W2383806832","https://openalex.org/W2050092215","https://openalex.org/W2391201265","https://openalex.org/W2392210095","https://openalex.org/W2384861189","https://openalex.org/W2391858393","https://openalex.org/W2366800561"],"abstract_inverted_index":{"Abstract":[0],"Proving":[1],"equivalence":[2,51,115,193],"between":[3],"functional":[4],"programs":[5],"is":[6,46],"a":[7,39,60,82,167],"fundamental":[8],"problem":[9],"in":[10],"program":[11,122,174],"verification,":[12],"which":[13],"often":[14,47],"amounts":[15],"to":[16,58,74,113,137,166,191],"reasoning":[17],"about":[18],"algebraic":[19],"data":[20],"types":[21],"(ADTs)":[22],"and":[23,70,95,150,171,207],"compositions":[24],"of":[25,62,84,87,131,140,169,187,216],"structural":[26,33,40],"recursions":[27],".":[28],"Modern":[29],"theorem":[30,45],"provers":[31],"provide":[32],"induction":[34,41],"for":[35,49,92],"such":[36,54],"reasoning,":[37],"but":[38],"on":[42,205],"the":[43,76,138,141,155,185,217],"original":[44,77],"insufficient":[48],"many":[50],"theorems.":[52],"In":[53],"cases,":[55],"one":[56],"has":[57],"invent":[59],"set":[61,168],"lemmas,":[63,152],"prove":[64,75],"these":[65,72,97],"lemmas":[66,73,89,98,120],"by":[67,117],"additional":[68],"induction,":[69],"use":[71],"theorem.":[78],"There":[79],"is,":[80],"however,":[81],"lack":[83],"systematic":[85],"understanding":[86],"what":[88],"are":[90],"needed":[91],"inductive":[93],"proofs":[94,116],"how":[96],"can":[99,178],"be":[100,179],"synthesized":[101],"automatically.":[102],"This":[103],"paper":[104],"presents":[105],"directed":[106,199],"lemma":[107,164,197,200],"synthesis":[108,123,165,175,201],",":[109],"an":[110,213],"effective":[111],"approach":[112],"automating":[114],"discovering":[118],"critical":[119],"using":[121],"techniques.":[124],"We":[125,143],"first":[126],"identify":[127],"two":[128,146],"induction-friendly":[129,159],"forms":[130],"propositions":[132],"that":[133,148,177],"give":[134],"formal":[135],"guarantees":[136],"progress":[139],"proof.":[142],"then":[144],"propose":[145],"tactics":[147,162],"synthesize":[149],"apply":[151],"thereby":[153],"transforming":[154],"proof":[156],"goal":[157],"into":[158],"forms.":[160],"Both":[161],"reduce":[163],"independent":[170],"typically":[172],"small":[173],"problems":[176],"efficiently":[180],"solved.":[181],"Experimental":[182],"results":[183],"demonstrate":[184],"effectiveness":[186],"our":[188],"approach:":[189],"Compared":[190],"state-of-the-art":[192],"checkers":[194],"employing":[195],"heuristic-based":[196],"enumeration,":[198],"saves":[202],"95.47%":[203],"runtime":[204],"average":[206],"solves":[208],"38":[209],"more":[210],"tasks":[211],"over":[212],"extended":[214],"version":[215],"standard":[218],"benchmark":[219],"set.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}