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Sketch-Oriented Databases

Dominique Duval, Rachid Echahed

TL;DR

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 and introduces stuttering sketches, whose aim is to facilitate modular composition and scalable model growth.

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.

Sketch-Oriented Databases

TL;DR

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 and introduces stuttering sketches, whose aim is to facilitate modular composition and scalable model growth.

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.
Paper Structure (14 sections, 2 theorems, 27 equations)

This paper contains 14 sections, 2 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Sketch-oriented databases
  3. Finite-limit sketches
  4. Sketch-oriented databases
  5. Some sketch-oriented database paradigms
  6. Sketch-oriented inference
  7. Localizers of sketches
  8. Sketch-oriented inference systems
  9. Paths
  10. Stuttering sketches
  11. Pointwise colimits of models
  12. Stuttering sketches
  13. Conclusion
  14. Relational databases

Key Result

Theorem 1

Let $D$ be a diagram, $C_0=(\underline{p_0}:V_0\to D)$ the limit of $D$ and $C=(\underline{p}:V\to D)$ any commutative cone on $D$. Let $v:V\to V_0$ be the unique arrow such that $p_X=p_{0,X}\circ v:V\to X$ for each point $X$ of $D$. Then $v$ is a mono if and only if $\mathit{Stt}(C)$ is the limit o

Theorems & Definitions (23)

  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Remark 1
  • Example 5
  • Example 6
  • Definition 1
  • Example 7
  • Example 8
  • ...and 13 more