Categorical Calculus and Algebra for Multi-Model Data
This provides a theoretical foundation for querying categorical databases, which is incremental as it extends existing relational methods to multi-model contexts.
The paper tackles the problem of querying multi-model databases by proposing categorical calculus and algebra as formal query languages, extending relational approaches, and demonstrates their equivalence, transformation rules for optimization, and analyzes expressive power and complexity.
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.