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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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.

Original language	English
Title of host publication	Heterogeneous Data Management, Polystores, and Analytics for Healthcare : VLDB Workshops, Poly 2021 and DMAH 2021
Editors	El Kindi Rezig, Vijay Gadepally, Timothy Mattson, Michael Stonebraker, Tim Kraska, Fusheng Wang, Gang Luo, Jun Kong, Alevtina Dubovitskaya
Publisher	Springer, Cham
Publication date	20 Aug 2021
Pages	14-28
ISBN (Print)	978-3-030-93662-4
ISBN (Electronic)	978-3-030-93663-1
DOIs	https://doi.org/10.1007/978-3-030-93663-1_2
Publication status	Published - 20 Aug 2021
MoE publication type	A4 Article in conference proceedings
Event	VLDB Workshop on Polystore Systems for Heterogeneous Data in Multiple Databases with Privacy and Security Assurances - Duration: 20 Aug 2021 → 20 Aug 2021

Fields of Science

113 Computer and information sciences
multi-model databases
data transformations
category theory

Access to Document

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

Uotila_A Formal categoryFinal published version, 432 KBLicence: Other

https://arxiv.org/abs/2201.04905Licence: 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
Activity: Talk or presentation types › Invited talk

Cite this

Uotila, V. J. E., & Lu, J. (2021). A Formal Category Theoretical Framework for Multi-model Data Transformations. In E. K. Rezig, V. Gadepally, T. Mattson, M. Stonebraker, T. Kraska, F. Wang, G. Luo, J. Kong, & A. Dubovitskaya (Eds.), Heterogeneous Data Management, Polystores, and Analytics for Healthcare: VLDB Workshops, Poly 2021 and DMAH 2021 (pp. 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. editor / El Kindi Rezig ; Vijay Gadepally ; Timothy Mattson ; Michael Stonebraker ; Tim Kraska ; Fusheng Wang ; Gang Luo ; Jun Kong ; Alevtina Dubovitskaya. Springer, Cham, 2021. pp. 14-28

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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.",

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Uotila, VJE & Lu, J 2021, A Formal Category Theoretical Framework for Multi-model Data Transformations. in EK Rezig, V Gadepally, T Mattson, M Stonebraker, T Kraska, F Wang, G Luo, J Kong & A Dubovitskaya (eds), Heterogeneous Data Management, Polystores, and Analytics for Healthcare: VLDB Workshops, Poly 2021 and DMAH 2021. Springer, Cham, pp. 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. ed. / El Kindi Rezig; Vijay Gadepally; Timothy Mattson; Michael Stonebraker; Tim Kraska; Fusheng Wang; Gang Luo; Jun Kong; Alevtina Dubovitskaya. Springer, Cham, 2021. p. 14-28.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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AU - Uotila, Valter Johan Edvard

AU - Lu, Jiaheng

PY - 2021/8/20

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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.

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KW - multi-model databases

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A2 - Rezig, El Kindi

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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

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

A Formal Category Theoretical Framework for Multi-model Data Transformations

Abstract

Fields of Science

Access to Document

Activities

Multi-model Query Processing Meets Category Theory and Functional Programming

Cite this