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Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…

When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…

This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many…

Weak memory models specify the semantics of concurrent programs on multi-core architectures. Reasoning techniques for weak memory models are often specialized to one fixed model and verification results are hence not transferable to other…

In this report, we present the preliminary work developed for our research project for the APDC (\'Area Pr\'atica de Desenvolvimento Curricular) course. The main goal of this project is to develop a framework, on top of the Why3 tool, for…

One of the major hurdles toward automatic semantic understanding of computer programs is the lack of knowledge about what constitutes functional equivalence of code segments. We postulate that a sound knowledgebase can be used to…

The computing education community has a rich history of pedagogical innovation designed to support students in introductory courses, and to support teachers in facilitating student learning. Very recent advances in artificial intelligence…

Reinforcement Learning (RL) has emerged as a popular training paradigm, particularly when paired with reasoning models. While effective, it primarily focuses on generating responses and lacks mechanisms to explicitly foster critique or…

Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…

Competitive programming (CP) has been increasingly integrated into computer science curricula worldwide due to its efficacy in enhancing students' algorithmic reasoning and problem-solving skills. However, existing CP curriculum designs…

Incorporating computer programming exercises into introductory physics is a delicate task that involves a number of choices that may have an effect on student learning. We present a "hybrid" approach that speaks to a number of common…

Recent research in mathematics education points to an "epistemic clash" when programming and computational thinking (CT) are leveraged alongside more established forms of mathematical thinking (MT). The emergence of generative AI emphasises…

In the last few years appeared pedagogical propositional natural deduction systems. In these systems, one must satisfy the pedagogical constraint: the user must give an example of any introduced notion. First we expose the reasons of such a…

Many undergraduate students of engineering and the exact sciences have difficulty with their mathematics courses due to insufficient proficiency in what we in this paper have termed clear thinking. We believe that this lack of proficiency…

Novice programmers often struggle to understand how code executes and to form the abstract mental models necessary for effective problem-solving, challenges that are amplified in large, diverse introductory courses where students'…

We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…

Environments for systematic construction of logic programs are needed in the academy as well as in the industry. Such environments should support well defined construction methods and should be able to be extended and interact with other…

What would you teach if you had only one course to help students grasp the essence of computation and perhaps inspire a few of them to make computing a subject of further study? Assume they have the standard college prep background. This…

This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…