{"id":"https://openalex.org/W2161017670","doi":"https://doi.org/10.1145/1183278.1183281","title":"Extensional equivalence and singleton types","display_name":"Extensional equivalence and singleton types","publication_year":2006,"publication_date":"2006-10-01","ids":{"openalex":"https://openalex.org/W2161017670","doi":"https://doi.org/10.1145/1183278.1183281","mag":"2161017670"},"language":"en","primary_location":{"id":"doi:10.1145/1183278.1183281","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1183278.1183281","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"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":"ACM Transactions on Computational Logic","raw_type":"journal-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/A5068034903","display_name":"C. Addison Stone","orcid":"https://orcid.org/0009-0006-5720-3433"},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christopher A. Stone","raw_affiliation_strings":["Harvey Mudd College, Claremont, CA"],"affiliations":[{"raw_affiliation_string":"Harvey Mudd College, Claremont, CA","institution_ids":["https://openalex.org/I133543626"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028720578","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, PA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068034903"],"corresponding_institution_ids":["https://openalex.org/I133543626"],"apc_list":null,"apc_paid":null,"fwci":4.6573,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.94742316,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"7","issue":"4","first_page":"676","last_page":"722"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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"}},"topics":[{"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9914000034332275,"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":0.9801999926567078,"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/decidability","display_name":"Decidability","score":0.8512506484985352},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5674392580986023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5546011924743652},{"id":"https://openalex.org/keywords/singleton","display_name":"Singleton","score":0.5249362587928772},{"id":"https://openalex.org/keywords/type-inference","display_name":"Type inference","score":0.5060767531394958},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.48202574253082275},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.45765507221221924},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4472450315952301},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44398626685142517},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.4324643015861511},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39404428005218506},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.38350915908813477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.361623615026474},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25580471754074097},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.1483553647994995}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8512506484985352},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5674392580986023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5546011924743652},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.5249362587928772},{"id":"https://openalex.org/C198370458","wikidata":"https://www.wikidata.org/wiki/Q586459","display_name":"Type inference","level":3,"score":0.5060767531394958},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.48202574253082275},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.45765507221221924},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4472450315952301},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44398626685142517},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.4324643015861511},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39404428005218506},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.38350915908813477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.361623615026474},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25580471754074097},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.1483553647994995},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2779234561","wikidata":"https://www.wikidata.org/wiki/Q11995","display_name":"Pregnancy","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1183278.1183281","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1183278.1183281","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"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":"ACM Transactions on Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.111.2872","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.2872","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.hmc.edu/~stone/papers/tocl-final.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.2.6294","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.6294","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-2.cs.cmu.edu/~rwh/papers/singletons/tocl-revised.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.594.6022","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.594.6022","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mpi-sws.org/~dreyer/tor/papers/stone-harper-tocl.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W13404328","https://openalex.org/W18425853","https://openalex.org/W569543113","https://openalex.org/W1503831567","https://openalex.org/W1541185175","https://openalex.org/W1547527421","https://openalex.org/W1553136405","https://openalex.org/W1571331450","https://openalex.org/W1581498582","https://openalex.org/W1599798327","https://openalex.org/W1663418338","https://openalex.org/W1764939356","https://openalex.org/W1773829243","https://openalex.org/W1989916808","https://openalex.org/W1996726522","https://openalex.org/W2020660597","https://openalex.org/W2027657506","https://openalex.org/W2030916392","https://openalex.org/W2043740265","https://openalex.org/W2048569219","https://openalex.org/W2059914072","https://openalex.org/W2071060021","https://openalex.org/W2089325110","https://openalex.org/W2097166325","https://openalex.org/W2112885424","https://openalex.org/W2118227920","https://openalex.org/W2125600157","https://openalex.org/W2127818463","https://openalex.org/W2133639043","https://openalex.org/W2145945984","https://openalex.org/W2152035046","https://openalex.org/W2167017930","https://openalex.org/W2171691057","https://openalex.org/W2561675875","https://openalex.org/W2795046794","https://openalex.org/W3021792517","https://openalex.org/W4230069141","https://openalex.org/W4285719527","https://openalex.org/W6600760271","https://openalex.org/W6636058808","https://openalex.org/W6682850052"],"related_works":["https://openalex.org/W1597421937","https://openalex.org/W3130884665","https://openalex.org/W179795792","https://openalex.org/W2949482260","https://openalex.org/W4296000674","https://openalex.org/W4287632524","https://openalex.org/W2076653850","https://openalex.org/W4384648301","https://openalex.org/W3110513392","https://openalex.org/W1512812951"],"abstract_inverted_index":{"We":[0,198,263],"study":[1],"the":[2,24,51,80,85,104,110,180,210,225,230,238,277,285,288],"\u03bb":[3,136,214,245],"\u03a0\u03a3":[4,137,215,246],"S":[5,12,138,216,247],"\u2264":[6,139,217,248],"calculus,":[7],"which":[8,115],"contains":[9],"singleton":[10,83],"types":[11,32],"(":[13],"M":[14,26,93,96,116,119],")":[15],"classifying":[16],"terms":[17],"of":[18,50,56,75,82,87,128,132,152,160,209,244,256,287],"base":[19,52],"type":[20,57,66,112,133,192,202,220,257,274,289,294],"provably":[21],"equivalent":[22],"to":[23,65,72,125,236,253,272],"term":[25,129,249],".":[27],"The":[28,54,150,242,280],"system":[29,211],"includes":[30],"dependent":[31],"for":[33,59,145,190,233,259,276,292],"pairs":[34],"and":[35,38,40,108,118,205,222],"functions":[36],"(\u03a3":[37],"\u03a0)":[39],"a":[41,142,170,186,266],"subtyping":[42],"relation":[43],"induced":[44],"by":[45,140,229],"regarding":[46],"singletons":[47],"as":[48],"subtypes":[49],"type.":[53],"decidability":[55,127,243,255],"checking":[58,191,258,295],"this":[60],"language":[61,227],"is":[62,154],"non-obvious,":[63],"since":[64],"check":[67],"we":[68,174],"must":[69],"be":[70],"able":[71],"determine":[73],"equivalence":[74,89,172,182,193,250],"well-formed":[76],"terms.":[77],"But":[78],"in":[79,135,224,296],"presence":[81],"types,":[84],"provability":[86],"an":[88,157],"judgment":[90],"\u0393":[91,107],"\u22a2":[92],"1":[94,117],"\u2261":[95],"2":[97,120],":":[98],"A":[99,113],"can":[100],"depend":[101],"both":[102],"on":[103,109],"typing":[105],"context":[106],"particular":[111],"at":[114],"are":[121,212],"compared.We":[122],"show":[123,200,254],"how":[124],"prove":[126,273],"equivalence,":[130],"hence":[131],"checking,":[134,203],"exhibiting":[141],"type-directed":[143],"algorithm":[144,189],"directly":[146,176],"computing":[147],"normal":[148,196],"forms.":[149,197],"correctness":[151],"normalization":[153],"shown":[155],"using":[156],"unusual":[158],"variant":[159],"Kripke":[161],"logical":[162,171],"relations":[163],"organized":[164],"around":[165],"sets;":[166],"rather":[167],"than":[168],"defining":[169],"relation,":[173],"work":[175],"with":[177],"(subsets":[178],"of)":[179],"corresponding":[181],"classes.We":[183],"then":[184],"provide":[185],"more":[187],"efficient":[188],"without":[194],"constructing":[195],"also":[199,264],"that":[201,269],"subtyping,":[204],"all":[206],"other":[207],"judgments":[208],"decidable.The":[213],"calculus":[218],"models":[219],"constructors":[221],"kinds":[223],"intermediate":[226,261,278],"used":[228,291],"TILT":[231],"compiler":[232],"Standard":[234],"ML":[235],"implement":[237],"SML":[239],"module":[240],"system.":[241],"allows":[251,270],"us":[252,271],"TILT's":[260],"language.":[262,279],"obtain":[265],"consistency":[267],"result":[268],"safety":[275],"algorithms":[281],"derived":[282],"here":[283],"form":[284],"core":[286],"checker":[290],"internal":[293],"TILT.":[297]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}