ViCAR: Visualizing Categories with Automated Rewriting in Coq
arXiv:2404.08163 · doi:10.4204/EPTCS.429.13
Abstract
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.
arXiv commentIn Proceedings ACT 2024, arXiv:2509.18357
References in corpus (6)
- A survey of graphical languages for monoidal categories
- PyZX: Large Scale Automated Diagrammatic Reasoning
- A Verified Optimizer for Quantum Circuits
- Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions
- Tactics for Reasoning modulo AC in Coq
- Experience Implementing a Performant Category-Theory Library in Coq