{"id":"https://openalex.org/W4405259879","doi":"https://doi.org/10.1017/s095679682400011x","title":"An example of goal-directed, calculational proof","display_name":"An example of goal-directed, calculational proof","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4405259879","doi":"https://doi.org/10.1017/s095679682400011x"},"language":"en","primary_location":{"id":"doi:10.1017/s095679682400011x","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s095679682400011x","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A20D6BD38245A04263684CFDC5375C0D/S095679682400011Xa.pdf/div-class-title-an-example-of-goal-directed-calculational-proof-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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A20D6BD38245A04263684CFDC5375C0D/S095679682400011Xa.pdf/div-class-title-an-example-of-goal-directed-calculational-proof-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037876376","display_name":"Roland Backhouse","orcid":"https://orcid.org/0000-0002-0140-8089"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"ROLAND CARL BACKHOUSE","raw_affiliation_strings":["School of Computer Science, University of Nottingham, Nottingham NG8 1BB, UK (e-mail:"],"raw_orcid":"https://orcid.org/0000-0002-0140-8089","affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Nottingham, Nottingham NG8 1BB, UK (e-mail:","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071961816","display_name":"Walter Guttmann","orcid":"https://orcid.org/0000-0003-2969-1688"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"WALTER GUTTMANN","raw_affiliation_strings":["Computer Science and Software Engineering, University of Canterbury, Christchurch, New Zealand (e-mail:"],"raw_orcid":"https://orcid.org/0000-0003-2969-1688","affiliations":[{"raw_affiliation_string":"Computer Science and Software Engineering, University of Canterbury, Christchurch, New Zealand (e-mail:","institution_ids":["https://openalex.org/I185492890"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063657067","display_name":"Michael Winter","orcid":"https://orcid.org/0000-0003-0847-0448"},"institutions":[{"id":"https://openalex.org/I186803428","display_name":"Brock University","ror":"https://ror.org/056am2717","country_code":"CA","type":"education","lineage":["https://openalex.org/I186803428"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"MICHAEL WINTER","raw_affiliation_strings":["Department of Computer Science, Brock University, St. Catharines, Ontario, Canada (e-mail:"],"raw_orcid":"https://orcid.org/0000-0003-0847-0448","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Brock University, St. Catharines, Ontario, Canada (e-mail:","institution_ids":["https://openalex.org/I186803428"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2660,"currency":"USD","value_usd":2660},"apc_paid":{"value":2660,"currency":"USD","value_usd":2660},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15946334,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9814000129699707,"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/T11567","display_name":"semigroups and automata theory","score":0.9729999899864197,"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":0.8536949157714844},{"id":"https://openalex.org/keywords/proof-of-concept","display_name":"Proof of concept","score":0.638491690158844},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.39586973190307617}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8536949157714844},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.638491690158844},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.39586973190307617},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s095679682400011x","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s095679682400011x","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A20D6BD38245A04263684CFDC5375C0D/S095679682400011Xa.pdf/div-class-title-an-example-of-goal-directed-calculational-proof-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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Functional Programming","raw_type":"journal-article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:42836553","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/42836553","pdf_url":"https://nottingham-repository.worktribe.com/file/42836553/1/an-example-of-goal-directed-calculational-proof","source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1017/s095679682400011x","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s095679682400011x","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A20D6BD38245A04263684CFDC5375C0D/S095679682400011Xa.pdf/div-class-title-an-example-of-goal-directed-calculational-proof-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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Functional Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405259879.pdf","grobid_xml":"https://content.openalex.org/works/W4405259879.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2147543351","https://openalex.org/W2561675875","https://openalex.org/W3206621927"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"equivalence":[2,68],"relation":[3,12,23,27,39],"can":[4],"be":[5],"constructed":[6],"from":[7],"a":[8,99,102,126,134],"given":[9,26],"(homogeneous,":[10],"binary)":[11],"in":[13,43,109],"two":[14],"steps:":[15],"first,":[16],"construct":[17,35],"the":[18,25,31,36,44,47,53,82,106,121,131],"smallest":[19],"reflexive":[20,58],"and":[21,59,65,87,94],"transitive":[22,60],"containing":[24],"(the":[28],"\u201cstar\u201d":[29],"of":[30,46,85,125,133],"relation)":[32],"and,":[33],"second,":[34],"largest":[37],"symmetric":[38],"that":[40,52,81,104,119],"is":[41,56,70,115],"included":[42],"result":[45,55],"first":[48],"step.":[49],"The":[50,112],"fact":[51],"final":[54],"also":[57],"(as":[61],"well":[62,129],"as":[63,128,130],"symmetric),":[64],"thus":[66],"an":[67,143],"relation,":[69],"not":[71],"immediately":[72],"obvious,":[73],"although":[74],"straightforward":[75],"to":[76,117],"prove.":[77],"Rather":[78],"than":[79],"prove":[80],"defining":[83],"properties":[84],"reflexivity":[86,93],"transitivity":[88,95],"are":[89],"satisfied,":[90],"we":[91],"establish":[92],"constructively":[96],"by":[97],"exhibiting":[98],"starth":[100],"root\u2014in":[101],"way":[103],"emphasises":[105],"creative":[107],"process":[108],"its":[110,137],"construction.":[111],"resulting":[113],"construction":[114],"fundamental":[116],"algorithms":[118],"determine":[120],"strongly":[122,138],"connected":[123,139],"components":[124,140],"graph":[127,135,145],"decomposition":[132],"into":[136],"together":[141],"with":[142],"acyclic":[144],"connecting":[146],"such":[147],"components.":[148]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
