{"id":"https://openalex.org/W7109589747","doi":"https://doi.org/10.1145/3776673","title":"Abstraction Functions as Types: Modular Verification of Cost and Behavior in Dependent Type Theory","display_name":"Abstraction Functions as Types: Modular Verification of Cost and Behavior in Dependent Type Theory","publication_year":2026,"publication_date":"2026-01-08","ids":{"openalex":"https://openalex.org/W7109589747","doi":"https://doi.org/10.1145/3776673"},"language":"en","primary_location":{"id":"doi:10.1145/3776673","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3776673","pdf_url":null,"source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1145/3776673","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Harrison Grodin","orcid":"https://orcid.org/0000-0002-0947-3520"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Harrison Grodin","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Runming Li","orcid":"https://orcid.org/0000-0001-7600-9069"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Runming Li","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":null,"display_name":"Robert Harper","orcid":"https://orcid.org/0000-0002-9400-2941"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Harper","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":89.4774,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.99747062,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"10","issue":"POPL","first_page":"895","last_page":"922"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.8544999957084656,"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":0.8544999957084656,"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/T10260","display_name":"Software Engineering Research","score":0.04540000110864639,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10639","display_name":"Advanced Software Engineering Methodologies","score":0.018400000408291817,"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/modularity","display_name":"Modularity (biology)","score":0.6909000277519226},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6313999891281128},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.6291000247001648},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5430999994277954},{"id":"https://openalex.org/keywords/refinement-calculus","display_name":"Refinement calculus","score":0.46320000290870667},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4334999918937683},{"id":"https://openalex.org/keywords/abstract-data-type","display_name":"Abstract data type","score":0.41440001130104065},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.3723999857902527},{"id":"https://openalex.org/keywords/data-type","display_name":"Data type","score":0.36890000104904175}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7269999980926514},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.6909000277519226},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6313999891281128},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.6291000247001648},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5430999994277954},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4860000014305115},{"id":"https://openalex.org/C90483712","wikidata":"https://www.wikidata.org/wiki/Q7307205","display_name":"Refinement calculus","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.46129998564720154},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C175971053","wikidata":"https://www.wikidata.org/wiki/Q827335","display_name":"Abstract data type","level":2,"score":0.41440001130104065},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C138958017","wikidata":"https://www.wikidata.org/wiki/Q190087","display_name":"Data type","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.3472000062465668},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.34459999203681946},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.33180001378059387},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C160713754","wikidata":"https://www.wikidata.org/wiki/Q1389965","display_name":"Maintainability","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C97686452","wikidata":"https://www.wikidata.org/wiki/Q7604153","display_name":"Static analysis","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C116253237","wikidata":"https://www.wikidata.org/wiki/Q1437424","display_name":"Formal specification","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C134537474","wikidata":"https://www.wikidata.org/wiki/Q17144832","display_name":"Naturalness","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3776673","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3776673","pdf_url":null,"source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2502.20496","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.20496","pdf_url":"https://arxiv.org/pdf/2502.20496","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1145/3776673","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3776673","pdf_url":null,"source":{"id":"https://openalex.org/S4210216081","display_name":"Proceedings of the ACM on Programming Languages","issn_l":"2475-1421","issn":["2475-1421"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Programming Languages","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Partnerships for the goals","score":0.4378841519355774,"id":"https://metadata.un.org/sdg/17"}],"awards":[{"id":"https://openalex.org/G3043146079","display_name":null,"funder_award_id":"FA9550-23-1-0434","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G405945890","display_name":null,"funder_award_id":"FA9550-21-0009","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Software":[0],"development":[1,199],"depends":[2],"on":[3,17,56],"the":[4,41,52,91,140,144,149,159,222],"use":[5],"of":[6,81,93,124,156,161,175,200,211,220,226],"libraries":[7],"whose":[8],"public":[9],"specifications":[10,219],"inform":[11],"client":[12,162],"code":[13],"and":[14,47,62,121,133,202,224],"impose":[15],"obligations":[16],"private":[18,189,209],"implementations;":[19],"it":[20],"follows":[21],"that":[22,70,113,126,207],"verification":[23,155],"at":[24],"scale":[25],"must":[26],"also":[27],"be":[28,181],"modular,":[29],"preserving":[30],"such":[31,44],"abstraction.":[32],"Hoare's":[33,82],"influential":[34],"methodology":[35,54,83],"uses":[36],"abstraction":[37,94,116],"functions":[38,95],"to":[39,109,154,165,180,214],"demonstrate":[40],"coherence":[42],"between":[43,60],"concrete":[45,132],"implementations":[46],"their":[48],"abstract":[49,134],"specifications.":[50],"However,":[51],"Hoare":[53],"relies":[55],"a":[57,78,103,110,119,122,128,166,205],"conventional":[58],"separation":[59],"implementation":[61,179],"specification,":[63],"providing":[64],"no":[65,212],"linguistic":[66],"support":[67],"for":[68],"ensuring":[69],"this":[71],"convention":[72],"is":[73,100],"obeyed.":[74],"This":[75,99,151],"paper":[76],"proposes":[77],"synthetic":[79],"account":[80],"within":[84,96],"univalent":[85],"dependent":[86],"type":[87,120,129],"theory":[88,196],"by":[89,148,183],"encoding":[90],"data":[92],"types":[97],"themselves.":[98],"achieved":[101],"via":[102],"phase":[104,141],"distinction,":[105],"which":[106],"gives":[107],"rise":[108],"gluing":[111],"construction":[112],"renders":[114],"an":[115,178],"function":[117],"as":[118],"pair":[123],"modalities":[125],"fracture":[127],"into":[130],"its":[131,184],"parts.":[135],"A":[136,169],"noninterference":[137],"theorem":[138],"governing":[139],"distinction":[142],"characterizes":[143],"modularity":[145,174],"guarantees":[146],"provided":[147],"theory.":[150],"approach":[152],"scales":[153],"cost,":[157,176],"allowing":[158],"analysis":[160],"cost":[163,223],"relative":[164],"cost-aware":[167],"specification.":[168],"monadic":[170],"sealing":[171],"effect":[172],"facilitates":[173],"permitting":[177,217],"upper-bounded":[182],"specification":[185],"in":[186,204],"cases":[187],"where":[188],"details":[190,210],"influence":[191],"observable":[192],"cost.":[193],"The":[194],"resulting":[195],"supports":[197],"modular":[198],"programs":[201],"proofs":[203],"manner":[206],"hides":[208],"concern":[213],"clients":[215],"while":[216],"precise":[218],"both":[221],"behavior":[225],"programs.":[227]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-12-07T00:00:00"}
