ViCAR: Visualizing Categories with Automated Rewriting in Coq

Published in arXiv, 2019

Recommended citation: Bhakti Shah, William Spencer, Laura Zielinski, Ben Caldwell, Adrian Lehmann, Robert Rand (2024). "ViCAR: Visualizing Categories with Automated Rewriting in Coq". To appear in ACT 2024

We present ViCAR, a library for working with monoidal categories in the Coq proof assistant. ViCAR provides definitions for categorical structures that users can instantiate with their own verification projects. Upon verifying relevant coherence conditions, ViCAR gives a set of lemmas and tactics for manipulating categorical structures. We also provide a visualizer that can display any composition and tensor product of morphisms as a string diagram, showing its categorical structure. This enables graphical reasoning and automated rewriting for Coq projects with monoidal structures.