{"id":"https://openalex.org/W3047945087","doi":"https://doi.org/10.1017/s0956796820000222","title":"A focused solution to the avoidance problem","display_name":"A focused solution to the avoidance problem","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3047945087","doi":"https://doi.org/10.1017/s0956796820000222","mag":"3047945087"},"language":"en","primary_location":{"id":"doi:10.1017/s0956796820000222","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0956796820000222","pdf_url":null,"source":{"id":"https://openalex.org/S12266929","display_name":"Journal of Functional Programming","issn_l":"0956-7968","issn":["0956-7968","1469-7653"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Functional Programming","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/A5045900536","display_name":"Karl Crary","orcid":"https://orcid.org/0000-0002-1556-2183"},"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":"KARL CRARY","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, 15213, USA, (e-mail:"],"raw_orcid":"https://orcid.org/0000-0002-1556-2183","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, 15213, USA, (e-mail:","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045900536"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.272,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.642749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","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":0.9998000264167786,"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/T11450","display_name":"Model-Driven Software Engineering Techniques","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.9703999757766724,"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/computer-science","display_name":"Computer science","score":0.7969979047775269},{"id":"https://openalex.org/keywords/metatheory","display_name":"Metatheory","score":0.7743458151817322},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6495364904403687},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.639335036277771},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.582683265209198},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.56130051612854},{"id":"https://openalex.org/keywords/scope","display_name":"Scope (computer science)","score":0.5459011793136597},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.49357569217681885},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.47237280011177063},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.46620476245880127},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.41580644249916077},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30836614966392517},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14624911546707153}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7969979047775269},{"id":"https://openalex.org/C39387531","wikidata":"https://www.wikidata.org/wiki/Q1096708","display_name":"Metatheory","level":2,"score":0.7743458151817322},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6495364904403687},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.639335036277771},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.582683265209198},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.56130051612854},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.5459011793136597},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49357569217681885},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.47237280011177063},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.46620476245880127},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.41580644249916077},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30836614966392517},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14624911546707153},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0956796820000222","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0956796820000222","pdf_url":null,"source":{"id":"https://openalex.org/S12266929","display_name":"Journal of Functional Programming","issn_l":"0956-7968","issn":["0956-7968","1469-7653"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Functional Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W326743114","https://openalex.org/W1498395593","https://openalex.org/W1514385560","https://openalex.org/W1542954600","https://openalex.org/W1545449210","https://openalex.org/W1561824685","https://openalex.org/W1571331450","https://openalex.org/W1574919925","https://openalex.org/W1581498582","https://openalex.org/W1597824249","https://openalex.org/W1720741243","https://openalex.org/W1829244603","https://openalex.org/W1970673141","https://openalex.org/W1974190112","https://openalex.org/W1980302687","https://openalex.org/W1987755707","https://openalex.org/W1989916808","https://openalex.org/W2014889169","https://openalex.org/W2023132547","https://openalex.org/W2034676877","https://openalex.org/W2048569219","https://openalex.org/W2053070172","https://openalex.org/W2058193465","https://openalex.org/W2059054133","https://openalex.org/W2070324762","https://openalex.org/W2096970061","https://openalex.org/W2104204098","https://openalex.org/W2107440213","https://openalex.org/W2110196404","https://openalex.org/W2118229393","https://openalex.org/W2118567331","https://openalex.org/W2121993468","https://openalex.org/W2125422552","https://openalex.org/W2133171398","https://openalex.org/W2133639043","https://openalex.org/W2144747140","https://openalex.org/W2145945984","https://openalex.org/W2154044723","https://openalex.org/W2154148405","https://openalex.org/W2156876717","https://openalex.org/W2160728467","https://openalex.org/W2161017670","https://openalex.org/W2165264979","https://openalex.org/W2167017930","https://openalex.org/W2293455754","https://openalex.org/W2560961062","https://openalex.org/W2798868568","https://openalex.org/W2899867207","https://openalex.org/W2908243715","https://openalex.org/W3004658589","https://openalex.org/W3033613823","https://openalex.org/W3045454762","https://openalex.org/W3055243769","https://openalex.org/W4244706347","https://openalex.org/W4248372752","https://openalex.org/W4285719527","https://openalex.org/W6633707562","https://openalex.org/W6634349929","https://openalex.org/W6637416062","https://openalex.org/W6903439633"],"related_works":["https://openalex.org/W1756852158","https://openalex.org/W2750284450","https://openalex.org/W3122371259","https://openalex.org/W2020092927","https://openalex.org/W4247547597","https://openalex.org/W2566728714","https://openalex.org/W2322423074","https://openalex.org/W1995210049","https://openalex.org/W1562622185","https://openalex.org/W2142558882"],"abstract_inverted_index":{"Abstract":[0],"In":[1,56,185],"ML-style":[2],"module":[3],"type":[4,13,173],"theory,":[5],"sealing":[6],"often":[7],"leads":[8],"to":[9,177],"situations":[10],"in":[11,30,76,94,171,182,197,213],"which":[12,95,109],"variables":[14,71],"must":[15],"leave":[16],"scope,":[17],"and":[18],"this":[19,187],"creates":[20],"a":[21,39,65,85,92,116,120,143,172,189],"need":[22],"for":[23,69,192],"signatures":[24],"that":[25,37,129,166],"avoid":[26],"such":[27],"variables.":[28],"Unfortunately,":[29],"general,":[31],"there":[32],"is":[33,51,99,130,140],"no":[34],"best":[35,117],"signature":[36,128],"avoids":[38],"variable,":[40],"so":[41,72],"modules":[42],"do":[43],"not":[44,147],"always":[45],"enjoy":[46],"principal":[47],"signatures.":[48],"This":[49,138,152],"observation":[50],"called":[52],"the":[53,57,59,96,102,106,131,155,167,178,193,198,202,209],"avoidance":[54],"problem.":[55],"past,":[58],"problem":[60],"has":[61,146],"been":[62,149],"circumvented":[63],"using":[64,158],"variety":[66],"of":[67,135,201,205],"devices":[68,79,180],"moving":[70],"they":[73],"can":[74,114],"remain":[75],"scope.":[77],"These":[78],"work,":[80],"but":[81,142],"have":[82,89],"heretofore":[83],"lacked":[84,91],"logical":[86],"foundation.":[87],"They":[88],"also":[90],"presentation":[93],"dynamic":[97],"semantics":[98,204],"given":[100],"on":[101],"same":[103],"phrases":[104],"as":[105],"static":[107,203],"semantics,":[108],"limits":[110],"their":[111],"applications.":[112],"We":[113,164],"provide":[115],"supersignature":[118],"avoiding":[119],"variable":[121],"by":[122,124],"fiat,":[123],"adding":[125],"an":[126],"existential":[127],"least":[132],"upper":[133],"bound":[134],"its":[136],"instances.":[137],"idea":[139],"old,":[141],"workable":[144],"metatheory":[145],"previously":[148],"worked":[150],"out.":[151],"work":[153],"resolves":[154],"metatheoretic":[156],"issues":[157],"ideas":[159],"borrowed":[160],"from":[161],"focused":[162],"logic.":[163],"show":[165],"new":[168],"theory":[169],"results":[170],"discipline":[174],"very":[175],"similar":[176],"aforementioned":[179],"used":[181,196],"prior":[183],"work.":[184],"passing,":[186],"gives":[188],"type-theoretic":[190],"justification":[191],"generative":[194],"stamps":[195],"early":[199],"days":[200],"ML":[206],"modules.":[207],"All":[208],"proofs":[210],"are":[211],"formalized":[212],"Coq.":[214]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}