Related papers: Maths with Coq in L1, a pedagogical experiment
In this paper, we discuss the educational value of a few mid-size and one large applied research projects at the Computer Science Department of Okanagan College (OC) and at the Universities of Paris East Creteil (LACL) and Orleans (LIFO) in…
Capitalizing on previous encodings and formal developments about nominal calculi and type systems, we propose a weak Higher-Order Abstract Syntax formalization of the type language of pure System F<: within Coq, a proof assistant based on…
The reform of the upper secondary school in Italy has recently introduced physics in the curricula of professional schools, in realities where it was previously absent. Many teachers, often with a temporary position, are obliged to teaching…
As quantum information science and technology (QIST) is becoming more prevalent and occurring not only in research labs but also in industry, many educators are considering how best to incorporate learning about quantum mechanics into…
In this work, we conduct an experiment using state-of-the-art LLMs to translate MiniF2F into Rocq. The translation task focuses on generating a Rocq theorem based on three sources: a natural language description, the Lean formalization, and…
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.
A set of virtual experiments were designed to use with introductory physics I (analytical and general) class, which covers kinematics, Newton laws, energy, momentum, and rotational dynamics. Virtual experiments were based on video analysis…
In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
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…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
In this work, we describe our experience in learning the use of a computer proof assistant - specifically, Lean - from scratch, through proving formulae for the solutions of polynomial equations. Specifically, in this work we characterize…
This paper is presenting a set of laboratory classes to be taught as a part of a 1-year calculus-based physics class. It is composed out of 7 modules designed to bring together experiments and computer simulations (numerical simulations).…
Integration, just as much as differentiation, is a fundamental calculus tool that is widely used in many scientific domains. Formalizing the mathematical concept of integration and the associated results in a formal proof assistant helps in…
The recent, widespread availability of Large Language Models (LLMs) like ChatGPT and GitHub Copilot may impact introductory programming courses (CS1) both in terms of what should be taught and how to teach it. Indeed, recent research has…
Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools…
With the surge in data-centric AI and its increasing capabilities, AI applications have become a part of our everyday lives. However, misunderstandings regarding their capabilities, limitations, and associated advantages and disadvantages…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…