The current multi-model database management systems (MMDBS) are becoming more complex. We propose category theory as a foundation for a new query language design, query processing, and transformation frameworks for MMDBS. We describe the recent challenges of MMDBS and represent possible solutions to them. Finally, we propose a category theory-inspired prototype system.
The multi-model database management systems (MMDBS) [9,10] are gradually becoming more complex, which creates an urgent need for a better theory to formalize the systems. We identify that the end-user's experience is often poorly addressed in the design and implementation of the systems. For example, NoSQL is mainly targeted at developers. Technology is supposed to evolve according to the business and end-user's needs. Higher-level abstraction can simplify the systems and enable a better user experience.
The theory should be a standard across different domains and it should be powerful enough to express a wide variety of concepts on a suitable abstraction level. We believe that a candidate to be such a theory is category theory. Liu et al. [8] proposed this role to category theory to reason about declarative constructions and transformations between various data models. The standard introduction to category theory is MacLane [6] and other good are [11,12].
David Spivak [13] has applied category theory to model relational databases in order to category theoretically migrate relational data. The commercial application of this category theory-based relational database framework is implemented by Conexus [1,2]. expressions, and other complex data structures. It is required that MMDBS implement a single declarative query language that enables users to execute cross-model queries. Another wanted feature is a unified indexing mechanism that can index multiple data instances across different models. MMDBS should have the capability to perform extensive data transformations which automatically create views and materialize data between different models. Oracle converged database [3] is an example of a commercial MMDBS.
Historically, we had hierarchical and network data models, and then the relational data model. Now, in addition to the relational model, we have re-invented the hierarchical models as JSON/XML, and the network models as RDF and property graphs. NoSQL system complicates the matter by forcing users to access data without declarative language in a very loose transactional system. All of these efforts have regressed the usability of DBMS.
The principle of DBMS is that there is no single data model that is the best or the worst. Therefore, it is time to introduce the concept of a virtual data model. Virtual data model design is similar to the concept of virtual memory in classical OS design and virtual machine in modern cloud computing environment design.
The modern DBMS needs to follow both schema-first or schemalater paradigms and also support temporal aspects of data [4]. The temporal dimension of data is often poorly implemented in DBMS. For example, a part of temporality is event detection which could be tackled by developing calculus logic on top of queries. The modern DBMS would benefit from the unification of meta-data and data to define schema-flexible storing, indexing, and querying features [7].
We have developed a demonstration system called MultiCategory [15,16] to demonstrate our solutions. The system's backend is implemented with Haskell. It offers a fold function-based query processing mechanism which is a method to model queries from a category theoretical perspective [5]. A multi-model schema is represented as a category that is mapped to the multi-model instance. Formally our approach for modeling MMDBS and data transformations using category theory is represented in [14].
Our future work includes researching data integration, migration, transformation, temporal, and virtual data model challenges using category theory. Recent progress in applied category theory has shown that category theory is a very powerful framework to model and formally define complex systems.
This paper is partially supported by Finnish Academy Project 310321 and Oracle ERO gift funding.