arXiv subjects

Ben Caldwell

Publications and source records attributed to Ben Caldwell.

3 recordsLinked to original sources

arXiv2024

ViCAR: Visualizing Categories with Automated Rewriting in Coq

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.

cs.PL↗

arXiv2023

VyZX: Formal Verification of a Graphical Quantum Language

Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded languages. This creates obstacles to formally reasoning about graphical languages, since imposing an inductive structure obfuscates the diagrammatic nature of graphical languages, along with their corresponding equational theories. To address this gap, we present VyZX, a verified library for reasoning about inductively defined graphical languages. These inductive constructs arise naturally from category-theoretic definitions. We developed VyZX to Verify the ZX-calculus, a graphical langauge for reasoning about quantum computation. The ZX-calculus comes with a collection of diagrammatic rewrite rules that preserve the graph's semantic interpretation. We show how inductive graphs in VyZX are used to prove the soundness of the ZX-calculus rewrite rules and apply them in practice using standard proof assistant techniques. We also provide an IDE-integrated visualizer for proof engineers to directly reason about diagrams in graphical form.

cs.PL↗

arXiv2022

VyZX : A Vision for Verifying the ZX Calculus

Optimizing quantum circuits is a key challenge for quantum computing. The PyZX compiler broke new ground by optimizing circuits via the ZX calculus, a powerful graphical alternative to the quantum circuit model. Still, it carries no guarantee of its correctness. To address this, we developed VyZX, a verified ZX-calculus in the Coq proof assistant. VyZX provides two distinct representations of ZX diagrams for ease of programming and proof: A graph-based representation for writing high-level functions on diagrams and a block-based representation for proving ZX diagrams equivalent. Through these two different views, VyZX provides the tools necessary to verify properties and transformations of ZX diagrams. This paper explores the proofs and design choices underlying VyZX and its application and the challenges of verifying a graphical programming language.

quant-ph↗