Work

ViCAR: Visualizing Categories with Automated Rewriting in Coq

Year: 2025

Type: article

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.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.429.13

Authors: Bhakti Shah, Willam Spencer, Laura Zielinski, Ben Caldwell, Adrian Lehmann, Robert Rand

Institution: University of Chicago

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Collaborative Research: EPiQC: Enabling Practical-Scale Quantum Computation