Categorical Calculus and Algebra for Multi-Model Data

TL;DR

This paper introduces a theoretical framework for multi-model databases using categorical calculus and algebra, establishing their equivalence, optimization rules, and analyzing their expressive power and complexity.

Contribution

It presents the first formal query languages for categorical databases, extending relational calculus and algebra, with proven equivalence and optimization techniques.

Findings

Proposed two formal query languages: categorical calculus and algebra.

Established the equivalence between the two query languages.

Analyzed the expressive power and computational complexity of the languages.

Abstract

Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We propose two formal query languages: categorical calculus and categorical algebra, by extending relational calculus and relational algebra respectively. We demonstrate the equivalence between these two languages of queries. We propose a series of transformation rules of categorical algebra to facilitate query optimization. Finally, we analyze the expressive power and computation complexity for the proposed query languages.