# CQL: Categorical Databases

> Source: <https://categoricaldata.net/>
> Published: 2026-05-30 11:18:04+00:00

# Categorical Databases

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## A principled way to transform data

Open-source CQL and its integrated development environment (IDE) performs data-related tasks — such as querying, combining, migrating, and evolving databases — using [category theory](https://en.wikipedia.org/wiki/Applied_category_theory), a branch of mathematics that has revolutionized several areas of computer science. Open-source CQL is production-ready for single-node in-memory data processing workloads, such as [integrating data for data science](http://arxiv.org/abs/1903.10579). It is being commercialized by [Conexus AI](https://conexus.com); for inquiries, contact [Ryan Wisnesky](https://wisnesky.net).

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## Value Proposition

**Reduce risk of failure through artificial intelligence**. CQL contains an embedded automated theorem prover that guarantees the correctness of CQL programs. For example,[a CQL program cannot materialize an instance that violates a data integrity constraint](fk.html). Such errors are detected at compile time, when they are easiest to fix.**Preserve data quality**. High-quality data is expensive to obtain, so it is important to preserve that quality throughout the data life-cycle. CQL programs evolve and migrate data in a mathematically universal way, with zero degradation. As such, data integrated by CQL has many advantages, including perfect provenance:[every row in the output of an CQL program contains a lineage that describes exactly how that row was obtained from input data](joinless.html).**Increased developer productivity through higher-level abstractions**. CQL generalizes concepts from SQL using powerful principles from category theory. For example,[CQL generalizes SQL's select-from-where queries from returning single tables to returning many tables related by foreign keys](fk.html). Such higher-level abstractions enable developers to be more productive.

## Key Features

**Flexible I/O:** data can be imported into and exported out of CQL[by JDBC-SQL](jdbc.html), CSV, and more.**Visualization:** CQL[schemas](images/shot2.png),[databases](images/shot3.png), etc. can be displayed graphically.**Rich data integrity constraints:** CQL schemas contain entities, attributes, and foreign keys - as well as[equations between them](eqs.html). One use of equations is for[denormalization without the need to manually enforce the consistency of redundant data](denorm.html).**Computational schemas:**[user-defined functions are part of CQL schemas](unitconv.html)and can be specified using java, javascript, or purely equationally. CQL's theorem prover can reason about user-defined functions and how they relate to data integrity constraints.**More principled than SQL:** relational concepts such as[foreign keys re-appear, in a more principled form, in CQL](joinless.html). And[CQL provides primitives that SQL lacks](quotient.html).**100% java**. User-defined functions can be written in java or javascript, and a deep embedding of CQL into Haskell, in collaboration with[Statebox](https://statebox.org), is under development.**Stateless**. CQL is not a database management system: it neither stores nor updates data. It is a[canonical functional programming language](https://categoricaldata.net/cql/fql_def.pdf)and IDE whose scalability is similar to that of SQL and[chase engines](https://www.cs.ox.ac.uk/boris.motik/pubs/bkmmpst17becnhmarking-chase.pdf).

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[Kan extensions / Silmarils / applied category theory](https://silmarils.tech). CQL provides a reference implementation of David Spivak's

[ologs (ontology logs)](https://arxiv.org/abs/1102.1889).

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