{"id":"https://openalex.org/W2075435997","doi":"https://doi.org/10.1017/s0956796800001805","title":"Haskore music notation \u2013 An algebra of music \u2013","display_name":"Haskore music notation \u2013 An algebra of music \u2013","publication_year":1996,"publication_date":"1996-05-01","ids":{"openalex":"https://openalex.org/W2075435997","doi":"https://doi.org/10.1017/s0956796800001805","mag":"2075435997"},"language":"en","primary_location":{"id":"doi:10.1017/s0956796800001805","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796800001805","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/89A16D59034EF5C649F7846635989E2B/S0956796800001805a.pdf/div-class-title-haskore-music-notation-an-algebra-of-music-div.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/89A16D59034EF5C649F7846635989E2B/S0956796800001805a.pdf/div-class-title-haskore-music-notation-an-algebra-of-music-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113456823","display_name":"Paul Hudak","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Hudak","raw_affiliation_strings":["Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040136408","display_name":"Tom Makucevich","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom Makucevich","raw_affiliation_strings":["Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043890058","display_name":"Syam Gadde","orcid":"https://orcid.org/0000-0003-4156-3961"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Syam Gadde","raw_affiliation_strings":["Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032409884","display_name":"Bo Whong","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bo Whong","raw_affiliation_strings":["Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yale University, New Haven, CT 06520, USA (e-mail:","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Dept of Computer Science, Yale Univ., New Haven, CT 06520 USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":3.4334,"has_fulltext":true,"cited_by_count":84,"citation_normalized_percentile":{"value":0.92912471,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":"3","first_page":"465","last_page":"484"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11349","display_name":"Music Technology and Sound Studies","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11349","display_name":"Music Technology and Sound Studies","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9876999855041504,"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/T11309","display_name":"Music and Audio Processing","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.6957486271858215},{"id":"https://openalex.org/keywords/haskell","display_name":"Haskell","score":0.6522225737571716},{"id":"https://openalex.org/keywords/musical-notation","display_name":"Musical notation","score":0.5298765897750854},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5101218819618225},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.49369677901268005},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.45438656210899353},{"id":"https://openalex.org/keywords/transpose","display_name":"Transpose","score":0.4448179304599762},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.44442397356033325},{"id":"https://openalex.org/keywords/musical","display_name":"Musical","score":0.4294529855251312},{"id":"https://openalex.org/keywords/functional-programming","display_name":"Functional programming","score":0.26351815462112427},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.24770745635032654},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.22308090329170227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21890881657600403},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16676297783851624}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6957486271858215},{"id":"https://openalex.org/C2780624054","wikidata":"https://www.wikidata.org/wiki/Q34010","display_name":"Haskell","level":3,"score":0.6522225737571716},{"id":"https://openalex.org/C88639978","wikidata":"https://www.wikidata.org/wiki/Q233861","display_name":"Musical notation","level":3,"score":0.5298765897750854},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5101218819618225},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.49369677901268005},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.45438656210899353},{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.4448179304599762},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.44442397356033325},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.4294529855251312},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.26351815462112427},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.24770745635032654},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.22308090329170227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21890881657600403},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16676297783851624},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":2,"locations":[{"id":"doi:10.1017/s0956796800001805","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796800001805","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/89A16D59034EF5C649F7846635989E2B/S0956796800001805a.pdf/div-class-title-haskore-music-notation-an-algebra-of-music-div.pdf","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.8687","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.8687","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sal.cs.uiuc.edu/~kamin/cs497/papers/haskore.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1017/s0956796800001805","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0956796800001805","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/89A16D59034EF5C649F7846635989E2B/S0956796800001805a.pdf/div-class-title-haskore-music-notation-an-algebra-of-music-div.pdf","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"},"sustainable_development_goals":[{"score":0.5799999833106995,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2075435997.pdf","grobid_xml":"https://content.openalex.org/works/W2075435997.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W147666236","https://openalex.org/W633561280","https://openalex.org/W1977561459","https://openalex.org/W1986108295","https://openalex.org/W1997400383","https://openalex.org/W2020784851","https://openalex.org/W2022907879","https://openalex.org/W2061981200","https://openalex.org/W2062950667","https://openalex.org/W2063961659","https://openalex.org/W2091200401","https://openalex.org/W2295597695","https://openalex.org/W2396258450","https://openalex.org/W2973261767","https://openalex.org/W4242112856"],"related_works":["https://openalex.org/W2156218549","https://openalex.org/W2014970400","https://openalex.org/W1896852351","https://openalex.org/W4320485815","https://openalex.org/W4361757600","https://openalex.org/W1978173276","https://openalex.org/W2765714965","https://openalex.org/W2048023951","https://openalex.org/W1490654608","https://openalex.org/W4378468868"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"have":[2,87],"developed":[3],"a":[4,64,90],"simple":[5,59],"algebraic":[6,82],"approach":[7],"to":[8,31,42,46],"music":[9,129],"description":[10],"and":[11,28,38,40,54,78,120],"composition":[12],"called":[13],"Haskore":[14],".":[15],"In":[16],"this":[17,108],"framework,":[18],"musical":[19,33,44,72,102],"objects":[20,34,45,103],"consist":[21],"of":[22,84,92,96,123,128],"primitive":[23],"notions":[24,60],"such":[25,35,51,67,116],"as":[26,36,52,68,117],"notes":[27],"rests,":[29],"operations":[30,41],"transform":[32],"transpose":[37],"tempo-scaling,":[39],"combine":[43],"form":[47],"more":[48],"complex":[49,71],"ones,":[50],"concurrent":[53],"sequential":[55],"composition.":[56],"When":[57],"these":[58],"are":[61],"embedded":[62],"into":[63],"functional":[65],"language":[66],"Haskell,":[69],"rather":[70],"relationships":[73],"can":[74,104,113],"be":[75,105,114],"expressed":[76],"clearly":[77],"succinctly.":[79],"Exploiting":[80],"the":[81],"properties":[83,112,122],"Haskore,":[85],"we":[86],"further":[88],"defined":[89],"notion":[91],"literal":[93],"performance":[94],"(devoid":[95],"articulation)":[97],"through":[98],"which":[99],"observationally":[100],"equivalent":[101],"determined.":[106],"With":[107],"basis":[109],"many":[110],"useful":[111],"proved,":[115],"commutative,":[118],"associative,":[119],"distributive":[121],"various":[124],"operators.":[125],"An":[126],"algebra":[127],"thus":[130],"surfaces.":[131]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-27T06:14:07.914337","created_date":"2025-10-10T00:00:00"}