A framework for applied category theory in the Julia language
https://algebraicjulia.github.io/Catlab.jl/latest/

You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.

4.6 KiB

Catlab.jl is a framework for applied and computational category theory, written in the Julia language. Catlab provides a programming library and interactive interface for applications of category theory to scientific and engineering fields. It emphasizes monoidal categories due to their wide applicability but can support any categorical structure that is formalizable as a generalized algebraic theory.

The documentation contains several example notebooks, as well as partial API docs. However, we readily acknowledge that the documentation is not as well developed as it should be. Feel free to ask questions! Besides the GitHub issues, we have a #catlab.jl stream on the Julia Zulip (preferred) and also a #catlab channel on the Julia Slack (less preferred).

Catlab is experimental software and is missing many features, big and small. Moreover, the computational aspects of category theory are generally underdeveloped, both theoretically and practically. On the flip side, this means that there are lots of opportunities to do new and interesting things! Applied category theory is a young field and is likely to grow significantly.

We welcome contributions and are committed to supporting prospective contributors, regardless of experience level with category theory. If you are interested in contributing, please let us know.

Catlab is, or will eventually be, the following things.

**Programming library**: First and foremost, Catlab provides data structures,
algorithms, and serialization for applied category theory. Macros offer a
convenient syntax for specifying categorical doctrines and type-safe symbolic
manipulation systems. Wiring diagrams (aka string diagrams) are supported
through specialized data structures and can be serialized to and from GraphML
(an XML-based format) and JSON.

**Interactive computing environment**: Catlab can also be used interactively in
Jupyter notebooks. Symbolic expressions are displayed
using LaTeX and wiring diagrams are visualized using
Compose.jl,
Graphviz, or TikZ.

**Computer algebra system**: Catlab will serve as a computer algebra system for
categorical algebra. Unlike most computer algebra systems, all expressions are
typed using fragment of dependent type theory called generalized algebraic
theories. We will
implement core algorithms for solving word problems and reducing expressions to
normal form with respect to several important doctrines, such as those of
categories and of symmetric monoidal categories. For the computer algebra of
classical abstract algebra, see
AbstractAlgebra.j and
Nemo.jl.

Catlab is *not* currently any of the following things, although we do not rule
out that it could eventually evolve in these directions.

**Automated theorem prover**: Although there is some overlap between computer
algebra and automated theorem proving, Catlab cannot be considered a theorem
prover because it does not produce formal certificates of correctness
(aka proofs).

**Proof assistant**: Likewise, Catlab is not a proof assistant because it does
not produce formally verifiable proofs. Formal verification is not within scope
of the project.

**Graphical user interface**: Catlab does not provide a wiring diagram editor
or other graphical user interface. It is primarily a programming library, not a
user-facing application. However, it could be used as the backend for such an
application.