Pointfree foundations for (generic) lossless decomposition
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/24648 |
Resumo: | This report presents a typed, “pointfree” generalization of relational data depen- dency theory expressed not in the standard set-theoretic way, “a` la Codd”, but in the calculus of binary relations which, initiated by De Morgan in the 1860s, is the core of modern algebra of programming. Contrary to the intuition that a binary relation is just a particular case of an n- ary relation, this report shows the effectiveness of the former in “explaining” and reasoning about the latter. Data dependency theory, which is central to relational database design, is addressed in pointfree calculational style instead of reasoning about (sets of) tuples in conventional “implication-first” logic style. It turns out that the theory becomes more general, more structured and sim- pler. Elegant expressions replace lengthy formulæ and easy-to-follow calculations replace pointwise proofs with lots of “· · ·” notation, case analysis and natural lan- guage explanations for “obvious” steps. In particular, attributes are generalized to arbitrary (observation) functions and the principle of lossless decomposition is established for arbitrary such functions. The report concludes by showing how the proposed generalization of data dependency theory paves the way to interesting synergies with other branches of computer science, namely formal modeling and transition systems theory. A number of open topics for research in the field are proposed as future work. |
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Pointfree foundations for (generic) lossless decompositionThis report presents a typed, “pointfree” generalization of relational data depen- dency theory expressed not in the standard set-theoretic way, “a` la Codd”, but in the calculus of binary relations which, initiated by De Morgan in the 1860s, is the core of modern algebra of programming. Contrary to the intuition that a binary relation is just a particular case of an n- ary relation, this report shows the effectiveness of the former in “explaining” and reasoning about the latter. Data dependency theory, which is central to relational database design, is addressed in pointfree calculational style instead of reasoning about (sets of) tuples in conventional “implication-first” logic style. It turns out that the theory becomes more general, more structured and sim- pler. Elegant expressions replace lengthy formulæ and easy-to-follow calculations replace pointwise proofs with lots of “· · ·” notation, case analysis and natural lan- guage explanations for “obvious” steps. In particular, attributes are generalized to arbitrary (observation) functions and the principle of lossless decomposition is established for arbitrary such functions. The report concludes by showing how the proposed generalization of data dependency theory paves the way to interesting synergies with other branches of computer science, namely formal modeling and transition systems theory. A number of open topics for research in the field are proposed as future work.Fundação para a Ciência e a Tecnologia (FCT)Universidade do MinhoOliveira, José Nuno Fonseca2011-112011-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/reportapplication/pdfhttp://hdl.handle.net/1822/24648engOl11Technical Report TR-HASLab:03:2011info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:33:39Zoai:repositorium.sdum.uminho.pt:1822/24648Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:29:12.926660Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Pointfree foundations for (generic) lossless decomposition |
title |
Pointfree foundations for (generic) lossless decomposition |
spellingShingle |
Pointfree foundations for (generic) lossless decomposition Oliveira, José Nuno Fonseca |
title_short |
Pointfree foundations for (generic) lossless decomposition |
title_full |
Pointfree foundations for (generic) lossless decomposition |
title_fullStr |
Pointfree foundations for (generic) lossless decomposition |
title_full_unstemmed |
Pointfree foundations for (generic) lossless decomposition |
title_sort |
Pointfree foundations for (generic) lossless decomposition |
author |
Oliveira, José Nuno Fonseca |
author_facet |
Oliveira, José Nuno Fonseca |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Oliveira, José Nuno Fonseca |
description |
This report presents a typed, “pointfree” generalization of relational data depen- dency theory expressed not in the standard set-theoretic way, “a` la Codd”, but in the calculus of binary relations which, initiated by De Morgan in the 1860s, is the core of modern algebra of programming. Contrary to the intuition that a binary relation is just a particular case of an n- ary relation, this report shows the effectiveness of the former in “explaining” and reasoning about the latter. Data dependency theory, which is central to relational database design, is addressed in pointfree calculational style instead of reasoning about (sets of) tuples in conventional “implication-first” logic style. It turns out that the theory becomes more general, more structured and sim- pler. Elegant expressions replace lengthy formulæ and easy-to-follow calculations replace pointwise proofs with lots of “· · ·” notation, case analysis and natural lan- guage explanations for “obvious” steps. In particular, attributes are generalized to arbitrary (observation) functions and the principle of lossless decomposition is established for arbitrary such functions. The report concludes by showing how the proposed generalization of data dependency theory paves the way to interesting synergies with other branches of computer science, namely formal modeling and transition systems theory. A number of open topics for research in the field are proposed as future work. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-11 2011-11-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/report |
format |
report |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/24648 |
url |
http://hdl.handle.net/1822/24648 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Ol11 Technical Report TR-HASLab:03:2011 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132790567993344 |