rewalt
(archaic) to overturn, throw down
a library for rewriting, algebra, and topology, developed in Tallinn (aka Reval)
rewalt is a toolkit for higher-dimensional diagram rewriting, with applications in
higher and monoidal category theory,
homotopical algebra,
combinatorial topology,
and more. Thanks to its visualisation features, it can also be used as a structure-aware string diagram editor, supporting TikZ output so the string diagrams can be directly embedded in your LaTeX files.
It implements diagrammatic sets which, by the “higher-dimensional rewriting” paradigm, double as a model of
higher-dimensional rewrite systems, and of
directed cell complexes.
This model is “topologically sound”: a diagrammatic set built in rewalt presents a finite CW complex, and a diagram constructed in the diagrammatic set presents a valid homotopy in this CW complex.
A diagrammatic set can be seen as a generalisation of a simplicial set or of a cubical set with many more “cell shapes”. As a result, rewalt also contains a full implementation of finitely presented simplicial sets and cubical sets with connections.
Installation
rewalt is available for Python 3.7 and higher. You can install it with the command
pip install rewalt
If you want the bleeding edge, you can check out the GitHub repository.
Getting started
To get started, we recommend you check the Notebooks, which contain a number of worked examples from category theory, algebra, and homotopy theory.
Further reading
For a first introduction to the ideas of higher-dimensional rewriting, diagrammatic sets, and “topological soundness”, you may want to watch these presentations at the CIRM meeting on Higher Structures and at the GETCO 2022 conference.
A nice overview of the general landscape of higher-dimensional rewriting is Yves Guiraud’s mémoire d’habilitation.
So far there are two papers on the theory of diagrammatic sets: the first one containing the foundations, the second one containing some developments applied to categorical universal algebra.
A description and complexity analysis of some of the data structures and algorithms behind rewalt will be published in the proceedings of ACT 2022.
License
rewalt is distributed under the BSD 3-clause license.
Contributing
Currently, the only active developer of rewalt is Amar Hadzihasanovic.
Contributions are welcome. Please reach out either by sending me an email, or by opening an issue.
Notebooks