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https://github.com/AlgebraicJulia/Catlab.jl

A framework for applied category theory in the Julia language
https://github.com/AlgebraicJulia/Catlab.jl

applied-category-theory category-theory compositionality julia string-diagrams wiring-diagrams

Last synced: 25 days ago
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A framework for applied category theory in the Julia language

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# ![Catlab.jl](docs/src/assets/logo.png) Catlab.jl



[![Stable Docs](https://img.shields.io/badge/docs-stable-blue.svg)](https://algebraicjulia.github.io/Catlab.jl/stable)

[![Dev Docs](https://img.shields.io/badge/docs-dev-blue.svg)](https://algebraicjulia.github.io/Catlab.jl/dev)

[![Julia CI/CD](https://github.com/AlgebraicJulia/Catlab.jl/actions/workflows/julia_ci.yml/badge.svg)](https://github.com/AlgebraicJulia/Catlab.jl/actions/workflows/julia_ci.yml)

[![Code Coverage](https://codecov.io/gh/AlgebraicJulia/Catlab.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/AlgebraicJulia/Catlab.jl)

[![DOI](https://img.shields.io/badge/DOI-10.17605%2FOSF.IO%2FHMNFE-blue)](https://doi.org/10.17605/OSF.IO/HMNFE)



Catlab.jl is a framework for applied and computational category theory, written

in the [Julia](https://julialang.org) 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.



## Getting started



The [documentation](https://algebraicjulia.github.io/Catlab.jl/latest) 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](https://julialang.zulipchat.com/#narrow/stream/230248-catlab.2Ejl)

stream on the [Julia Zulip](https://julialang.zulipchat.com/) (preferred) and

also a [#catlab](https://julialang.slack.com/archives/CQNUDDF5L) channel on the

[Julia Slack](https://julialang.org/slack/) (less preferred).



### Contributing



Applied category theory is a young and growing field, and Catlab is too the

subject of ongoing research and development. This means that there are lots of

opportunities to do new and interesting things!



We welcome contributions to Catlab, regardless of your experience level with

category theory or the Julia language. For more information, see the

[CONTRIBUTING](CONTRIBUTING.md) file.



## What is Catlab?



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](http://jupyter.org). Symbolic expressions are displayed

using LaTeX and wiring diagrams are visualized using

[Compose.jl](https://github.com/GiovineItalia/Compose.jl),

[Graphviz](http://www.graphviz.org), or [TikZ](https://github.com/pgf-tikz/pgf).



**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](https://ncatlab.org/nlab/show/generalized+algebraic+theory). 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.jl](https://github.com/wbhart/AbstractAlgebra.jl) and

[Nemo.jl](https://github.com/wbhart/Nemo.jl).



### What is Catlab not?



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, there is another project in the AlgebraicJulia

ecosystem, [Semagrams.jl](https://github.com/AlgebraicJulia/Semagrams.jl)

which does provide graphical user interfaces for interacting with wiring

diagrams, Petri nets, and the like.