Related papers: Coquet: a Coq library for verifying hardware

Common programming tools, like compilers, debuggers, and IDEs, crucially rely on the ability to analyse program code to reason about its behaviour and properties. There has been a great deal of work on verifying compilers and static…

We address the challenges of scaling verification efforts to match the increasing complexity and size of systems. We propose a research agenda aimed at building a performant proof engine by studying the asymptotic performance of proof…

We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…

We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus of (Co)Inductive Constructions type…

As quantum computing continues to mature, more developers are designing, coding, and simulating quantum circuits. A challenge exists, however, in debugging quantum circuits, particularly as they scale in size and complexity. Given the lack…

In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in an abstract way.…

This paper contains a discussion of a library of formalized mathematics for the proof assistant Coq which the author worked on in 2011-13.

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…

This document contains a guide on how to use the Qudit Cirq library, an extension of Google's Cirq library for qudits. While Cirq provides necessary building blocks for quantum computation on qudits, the gates, curcuits and simulation of…

In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…

In this report we describe a tool framework for certifying properties of PLCs: CERTPLC. CERTPLC can handle PLC descriptions provided in the Sequential Function Chart (SFC) language of the IEC 61131-3 standard. It provides routines to…

In order to help students learn how to write mathematical proofs, we adapt the Coq proof assistant into an educational tool we call Waterproof. Like with other interactive theorem provers, students write out their proofs inside the software…

This work is a part of an ongoing effort to prove the correctness of invertibility conditions for the theory of fixed-width bit-vectors, which are used to solve quantified bit-vector formulas in the Satisfiability Modulo Theories (SMT)…

In recent years, a number of lightweight programs have been deployed in critical domains, such as in smart contracts based on blockchain technology. Therefore, the security and reliability of such programs should be guaranteed by the most…

Good tools can bring mechanical verification to programs written in mainstream functional languages. We use hs-to-coq to translate significant portions of Haskell's containers library into Coq, and verify it against specifications that we…

While the use of formal verification techniques is well established in the development of mission-critical software, it is still rare in the production of most other kinds of software. We share our experience that a formal verification tool…

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from…

We present VOQC, the first fully verified optimizer for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, a simple quantum intermediate…

Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be…

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…