Relational Foundations For Functorial Data Migration

TL;DR

This paper models schemas as categories and introduces a functorial approach to data migration, establishing an algebraic query language FQL that is both expressive and implementable within relational algebra.

Contribution

It presents a novel categorical framework for data schemas and migrations, and develops FQL, a new algebraic query language based on functorial data transformations.

Findings

FQL is closed under composition.

FQL can be implemented with extended relational algebra.

Relational algebra can be implemented within FQL.

Abstract

We study the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations. Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories. A schema $S$ is a finitely-presented category, and the collection of all $S$-instances forms a category, $S$-inst. A functor $F$ between schemas $S$ and $T$, which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, $\Sigma_F:S$-inst$\to T$-inst, $\Pi_F: S$-inst $\to T$-inst, and $\Delta_F:T$-inst $\to S$-inst. We present an algebraic query language FQL based on these functors, prove that FQL is closed under composition, prove that FQL can be implemented with the select-project-product-union relational algebra (SPCU) extended with a key-generation operation, and prove that SPCU can be implemented with FQL.