相关论文: Coq in a Hurry

We describe the basic notions of co-induction as they are available in the coq system. As an application, we describe arithmetic properties for simple representations of real numbers.

This chapter is a short pedagogical introduction to the use of quantum logic for the simulation of complex quantum systems, including a simulation example on actual quantum hardware.

The goal of this contribution is to provide worksheets in Coq for students to learn about divisibility and binomials. These basic topics are a good case study as they are widely taught in the early academic years (or before in France). We…

A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits…

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…

We have developed an alternative approach to teaching computer science students how to prove. First, students are taught how to prove theorems with the Coq proof assistant. In a second, more difficult, step students will transfer their…

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…

We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…

Sets and relations are very useful concepts for defining denotational semantics. In the Coq proof assistant, curried functions to Prop are used to represent sets and relations, e.g. A -> Prop, A -> B -> Prop, A -> B -> C -> Prop, etc.…

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…

We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…

These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…

We report the results of the first experiments with learning proof dependencies from the formalizations done with the Coq system. We explain the process of obtaining the dependencies from the Coq proofs, the characterization of formulas…

In this paper, we outline the prototype of an automated inference tool, called QUIP, which provides a uniform implementation for several nonmonotonic reasoning formalisms. The theoretical basis of QUIP is derived from well-known results…

The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…

An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…

The work described in this paper improves the reactivity of the Coq system by completely redesigning the way it processes a formal document. By subdividing such work into independent tasks the system can give precedence to the ones of…

This is the first chapter of an introductory text under construction; further chapters are available via the authors' web pages. Our aim is to provide an elementary access to Cox rings and their applications in algebraic and arithmetic…

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…