{"id":"https://openalex.org/W7169851626","doi":"https://doi.org/10.48550/arxiv.2607.16372","title":"AoA: Theorem Proving Agent over Abstract Syntax Tree of Redesigned Language","display_name":"AoA: Theorem Proving Agent over Abstract Syntax Tree of Redesigned Language","publication_year":2026,"publication_date":"2026-07-17","ids":{"openalex":"https://openalex.org/W7169851626","doi":"https://doi.org/10.48550/arxiv.2607.16372"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.16372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.16372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.16372","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040102430","display_name":"Qiyuan Xu","orcid":"https://orcid.org/0000-0002-9196-3237"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Qiyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114335069","display_name":"Joshua Ong Jun Leang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leang, Joshua Ong Jun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5141257066","display_name":"Renxi Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Renxi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5141273612","display_name":"Wenda Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Wenda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5141230667","display_name":"Haonan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Haonan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5141244233","display_name":"Luke Ong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ong, Luke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060197721","display_name":"Conrad Watt","orcid":"https://orcid.org/0000-0002-0596-877X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Watt, Conrad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9057999849319458,"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":0.9057999849319458,"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":0.009999999776482582,"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.009100000374019146,"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":0.8070999979972839},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.6913999915122986},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.6675000190734863},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.6536999940872192},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6115999817848206},{"id":"https://openalex.org/keywords/abstract-syntax-tree","display_name":"Abstract syntax tree","score":0.5902000069618225},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.5706999897956848},{"id":"https://openalex.org/keywords/gas-meter-prover","display_name":"Gas meter prover","score":0.5388000011444092},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5202999711036682}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8070999979972839},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.7458999752998352},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7325000166893005},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.6913999915122986},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.6675000190734863},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.6536999940872192},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6115999817848206},{"id":"https://openalex.org/C58646249","wikidata":"https://www.wikidata.org/wiki/Q127380","display_name":"Abstract syntax tree","level":3,"score":0.5902000069618225},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.5706999897956848},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.5388000011444092},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5202999711036682},{"id":"https://openalex.org/C11742125","wikidata":"https://www.wikidata.org/wiki/Q1195374","display_name":"Syntax error","level":4,"score":0.5084999799728394},{"id":"https://openalex.org/C114408938","wikidata":"https://www.wikidata.org/wiki/Q333373","display_name":"Abstract syntax","level":3,"score":0.4327000081539154},{"id":"https://openalex.org/C548217200","wikidata":"https://www.wikidata.org/wiki/Q251","display_name":"Java","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C2780416260","wikidata":"https://www.wikidata.org/wiki/Q2063","display_name":"JSON","level":2,"score":0.3864000141620636},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.3449999988079071},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32690000534057617},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C13766981","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Automated proof checking","level":3,"score":0.3068000078201294},{"id":"https://openalex.org/C129131279","wikidata":"https://www.wikidata.org/wiki/Q1931259","display_name":"Predicative expression","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.27070000767707825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.16372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.16372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.16372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.16372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.43714672327041626,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Interactive":[0],"theorem":[1],"proving":[2,98],"(ITP)":[3],"underpins":[4],"program":[5],"verification":[6,224],"and":[7,29,56,70,76,118,141,153,187,205,210],"formalized":[8],"mathematics,":[9],"but":[10,24,99],"its":[11,163],"manual":[12],"effort":[13],"limits":[14],"scalability.":[15],"LLM-based":[16,97],"proof":[17,58,91,151,157],"agents":[18,45],"promise":[19],"to":[20,40,137],"ease":[21],"this":[22,38,174],"effort,":[23],"their":[25],"heavy":[26],"token":[27],"consumption":[28],"API":[30,194],"cost":[31,39,195],"remain":[32],"a":[33,41,89,146],"major":[34],"obstacle.":[35],"We":[36,107,172],"trace":[37],"shared":[42],"root:":[43],"current":[44],"operate":[46],"on":[47,81,96,185,221],"serialized":[48],"concrete":[49,82],"syntax,":[50],"emitting":[51],"proofs":[52,128],"as":[53,129],"source":[54,116],"text":[55,117],"recovering":[57],"states":[59,154],"through":[60,145],"separate,":[61],"line-number-based":[62],"queries,":[63],"so":[64,159],"every":[65],"edit":[66],"shifts":[67],"later":[68],"lines":[69],"forces":[71],"repeated":[72],"relocation":[73],"of":[74,87,132],"errors":[75],"states.":[77],"This":[78],"same":[79],"dependence":[80],"syntax":[83,122],"also":[84,216],"blocks":[85],"adoption":[86],"Minilang,":[88],"recent":[90],"language":[92],"that":[93,149],"reaches":[94],"SOTA":[95],"is":[100],"too":[101],"new":[102],"for":[103],"LLMs'":[104],"training":[105],"corpora.":[106],"address":[108],"both":[109],"problems":[110,220],"by":[111,196],"lifting":[112],"the":[113,120,125,143,170,222],"agent":[114],"off":[115,169],"onto":[119],"abstract":[121],"tree":[123],"(AST):":[124],"model":[126,148],"supplies":[127],"JSON":[130],"representations":[131],"Minilang's":[133],"AST":[134],"--":[135,140,214],"native":[136],"tool-calling":[138],"LLMs":[139],"drives":[142],"prover":[144],"tree-edit":[147],"fuses":[150],"operations":[152],"into":[155],"one":[156],"tree,":[158],"each":[160],"operation":[161],"carries":[162],"own":[164],"subgoal's":[165],"state,":[166],"readable":[167],"directly":[168],"tree.":[171],"realize":[173],"design":[175],"in":[176],"\\emph{Agent":[177],"over":[178],"AST}":[179],"(AoA).":[180],"Against":[181],"Amazon's":[182],"Isabelle":[183],"Agent":[184],"miniF2F":[186],"NTP4VC-Pearl":[188],"common":[189],"success":[190],"sets,":[191],"AoA":[192],"cuts":[193],"2.3--4.7x":[197],"(normalized":[198],"input-cache":[199],"accounting),":[200],"uses":[201],"2.9--6.9x":[202],"fewer":[203,207],"tokens":[204],"3.9--8.9x":[206],"tool":[208],"calls,":[209],"finishes":[211],"1.4--2.0x":[212],"faster":[213],"while":[215],"solving":[217],"far":[218],"more":[219],"harder":[223],"benchmark.":[225]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-22T00:00:00"}