Sketch-Oriented Databases

TL;DR

This paper presents a categorical framework for sketch-oriented databases, unifying various graph paradigms and features through finite-limit sketches, and introduces inference rules and stuttering sketches for scalable, modular database modeling.

Contribution

It introduces a formal categorical framework for sketch-oriented databases, unifying graph paradigms and features, and proposes inference rules and stuttering sketches for scalable modeling.

Findings

Unified formalism for graph-oriented database paradigms

Inference rules for path computation and conformance tasks

Introduction of stuttering sketches for scalable model composition

Abstract

This paper introduces sketch-oriented databases, a categorical framework that encodes database paradigms as finite-limit sketches and individual databases and schemas as set-valued models. It illustrates the formalism through graph-oriented paradigms such as quivers, RDF triplestores and property graphs. It also shows how common graph features such as labels, attributes, typing, and paths, are uniformly captured by sketch constructions. Because paths play an important role in queries, we propose inference rules formalized via localizers to compute useful paths lazily; such localizers are also useful for tasks like database type conformance. Finally, the paper introduces stuttering sketches, whose aim is to facilitate modular composition and scalable model growth: stuttering sketches are finite-limit sketches in which relations are specified by a single limit instead of two nested limits, and the paper proves that finite unions of models of a stuttering sketch are pointwise colimits.