A Formal Category Theoretical Framework for Multi-model Data Transformations

Valter Johan Edvard Uotila; Jiaheng Lu

doi:10.1007/978-3-030-93663-1_2

A Formal Category Theoretical Framework for Multi-model Data Transformations

Forskningsoutput: Kapitel i bok/rapport/konferenshandling › Konferensbidrag › Vetenskaplig › Peer review

Sammanfattning

Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema transformation field is scattered with multiple different transformation frameworks, tools, and mappings. These are usually domain-specific and lack solid theoretical foundations. Our first goal is to define category theoretical foundations for relational, graph, and hierarchical data models and instances. Each data instance is represented as a category theoretical mapping called a functor. We formalize data and schema transformations as Kan lifts utilizing the functorial representation for the instances. A Kan lift is a category theoretical construction consisting of two mappings satisfying the certain universal property. In this work, the two mappings correspond to schema transformation and data transformation.

Originalspråk	engelska
Titel på värdpublikation	Heterogeneous Data Management, Polystores, and Analytics for Healthcare : VLDB Workshops, Poly 2021 and DMAH 2021
Redaktörer	El Kindi Rezig, Vijay Gadepally, Timothy Mattson, Michael Stonebraker, Tim Kraska, Fusheng Wang, Gang Luo, Jun Kong, Alevtina Dubovitskaya
Förlag	Springer, Cham
Utgivningsdatum	20 aug. 2021
Sidor	14-28
ISBN (tryckt)	978-3-030-93662-4
ISBN (elektroniskt)	978-3-030-93663-1
DOI	https://doi.org/10.1007/978-3-030-93663-1_2
Status	Publicerad - 20 aug. 2021
MoE-publikationstyp	A4 Artikel i en konferenspublikation
Evenemang	VLDB Workshop on Polystore Systems for Heterogeneous Data in Multiple Databases with Privacy and Security Assurances - Varaktighet: 20 aug. 2021 → 20 aug. 2021

Vetenskapsgrenar

113 Data- och informationsvetenskap

Åtkomst av dokument

10.1007/978-3-030-93663-1_2

Uotila_A Formal categorySlutlig publicerad version, 432 KBLicens: !!Other

https://arxiv.org/abs/2201.04905Licens: CC BY-NC-ND

1 !!Invited talk

Multi-model Query Processing Meets Category Theory and Functional Programming
Valter Johan Edvard Uotila (!!Speaker), Jiaheng Lu (!!Speaker), Dieter Gawlick (!!Speaker), Zhen Hua Liu (!!Speaker), Souripriya Das (!!Speaker) & Gregory Pogossiants (!!Speaker)
20 aug. 2021
Aktivitet: Typer för tal eller presentation › !!Invited talk

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Uotila, V. J. E., & Lu, J. (2021). A Formal Category Theoretical Framework for Multi-model Data Transformations. I E. K. Rezig, V. Gadepally, T. Mattson, M. Stonebraker, T. Kraska, F. Wang, G. Luo, J. Kong, & A. Dubovitskaya (Red.), Heterogeneous Data Management, Polystores, and Analytics for Healthcare: VLDB Workshops, Poly 2021 and DMAH 2021 (s. 14-28). Springer, Cham. https://doi.org/10.1007/978-3-030-93663-1_2

Uotila, Valter Johan Edvard ; Lu, Jiaheng. / A Formal Category Theoretical Framework for Multi-model Data Transformations. Heterogeneous Data Management, Polystores, and Analytics for Healthcare: VLDB Workshops, Poly 2021 and DMAH 2021. redaktör / El Kindi Rezig ; Vijay Gadepally ; Timothy Mattson ; Michael Stonebraker ; Tim Kraska ; Fusheng Wang ; Gang Luo ; Jun Kong ; Alevtina Dubovitskaya. Springer, Cham, 2021. s. 14-28

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title = "A Formal Category Theoretical Framework for Multi-model Data Transformations",

abstract = "Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema transformation field is scattered with multiple different transformation frameworks, tools, and mappings. These are usually domain-specific and lack solid theoretical foundations. Our first goal is to define category theoretical foundations for relational, graph, and hierarchical data models and instances. Each data instance is represented as a category theoretical mapping called a functor. We formalize data and schema transformations as Kan lifts utilizing the functorial representation for the instances. A Kan lift is a category theoretical construction consisting of two mappings satisfying the certain universal property. In this work, the two mappings correspond to schema transformation and data transformation.",

keywords = "113 Computer and information sciences, multi-model databases, data transformations, category theory",

author = "Uotila, {Valter Johan Edvard} and Jiaheng Lu",

year = "2021",

month = aug,

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doi = "10.1007/978-3-030-93663-1_2",

language = "English",

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editor = "Rezig, {El Kindi} and Vijay Gadepally and Timothy Mattson and Michael Stonebraker and Tim Kraska and Fusheng Wang and Gang Luo and Jun Kong and Alevtina Dubovitskaya",

booktitle = "Heterogeneous Data Management, Polystores, and Analytics for Healthcare",

publisher = "Springer, Cham",

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note = "VLDB Workshop on Polystore Systems for Heterogeneous Data in Multiple Databases with Privacy and Security Assurances ; Conference date: 20-08-2021 Through 20-08-2021",

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Uotila, VJE & Lu, J 2021, A Formal Category Theoretical Framework for Multi-model Data Transformations. i EK Rezig, V Gadepally, T Mattson, M Stonebraker, T Kraska, F Wang, G Luo, J Kong & A Dubovitskaya (red), Heterogeneous Data Management, Polystores, and Analytics for Healthcare: VLDB Workshops, Poly 2021 and DMAH 2021. Springer, Cham, s. 14-28, VLDB Workshop on Polystore Systems for Heterogeneous Data in Multiple Databases with Privacy and Security Assurances, 20/08/2021. https://doi.org/10.1007/978-3-030-93663-1_2

A Formal Category Theoretical Framework for Multi-model Data Transformations. / Uotila, Valter Johan Edvard ; Lu, Jiaheng.
Heterogeneous Data Management, Polystores, and Analytics for Healthcare: VLDB Workshops, Poly 2021 and DMAH 2021. red. / El Kindi Rezig; Vijay Gadepally; Timothy Mattson; Michael Stonebraker; Tim Kraska; Fusheng Wang; Gang Luo; Jun Kong; Alevtina Dubovitskaya. Springer, Cham, 2021. s. 14-28.

Forskningsoutput: Kapitel i bok/rapport/konferenshandling › Konferensbidrag › Vetenskaplig › Peer review

TY - GEN

T1 - A Formal Category Theoretical Framework for Multi-model Data Transformations

AU - Uotila, Valter Johan Edvard

AU - Lu, Jiaheng

PY - 2021/8/20

Y1 - 2021/8/20

N2 - Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema transformation field is scattered with multiple different transformation frameworks, tools, and mappings. These are usually domain-specific and lack solid theoretical foundations. Our first goal is to define category theoretical foundations for relational, graph, and hierarchical data models and instances. Each data instance is represented as a category theoretical mapping called a functor. We formalize data and schema transformations as Kan lifts utilizing the functorial representation for the instances. A Kan lift is a category theoretical construction consisting of two mappings satisfying the certain universal property. In this work, the two mappings correspond to schema transformation and data transformation.

AB - Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema transformation field is scattered with multiple different transformation frameworks, tools, and mappings. These are usually domain-specific and lack solid theoretical foundations. Our first goal is to define category theoretical foundations for relational, graph, and hierarchical data models and instances. Each data instance is represented as a category theoretical mapping called a functor. We formalize data and schema transformations as Kan lifts utilizing the functorial representation for the instances. A Kan lift is a category theoretical construction consisting of two mappings satisfying the certain universal property. In this work, the two mappings correspond to schema transformation and data transformation.

KW - 113 Computer and information sciences

KW - multi-model databases

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BT - Heterogeneous Data Management, Polystores, and Analytics for Healthcare

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A2 - Gadepally, Vijay

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A2 - Stonebraker, Michael

A2 - Kraska, Tim

A2 - Wang, Fusheng

A2 - Luo, Gang

A2 - Kong, Jun

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PB - Springer, Cham

T2 - VLDB Workshop on Polystore Systems for Heterogeneous Data in Multiple Databases with Privacy and Security Assurances

Y2 - 20 August 2021 through 20 August 2021

ER -

Uotila VJE , Lu J. A Formal Category Theoretical Framework for Multi-model Data Transformations. I Rezig EK, Gadepally V, Mattson T, Stonebraker M, Kraska T, Wang F, Luo G, Kong J, Dubovitskaya A, redaktörer, Heterogeneous Data Management, Polystores, and Analytics for Healthcare: VLDB Workshops, Poly 2021 and DMAH 2021. Springer, Cham. 2021. s. 14-28 doi: 10.1007/978-3-030-93663-1_2

A Formal Category Theoretical Framework for Multi-model Data Transformations

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Aktiviteter

Multi-model Query Processing Meets Category Theory and Functional Programming

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