Related papers: OnlineProver: Experience with a Visualisation Tool…
Online exams conducted via video conferencing platforms such as Zoom have become widespread, yet ensuring exam integrity remains challenging due to the difficulty of monitoring multiple video feeds in real time. We present iExam, an online…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
We describe our Natural Deduction Assistant (NaDeA) and the interfaces between the Isabelle proof assistant and NaDeA. In particular, we explain how NaDeA, using a generated prover that has been verified in Isabelle, provides feedback to…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
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…
Auto-active verifiers provide a level of automation intermediate between fully automatic and interactive: users supply code with annotations as input while benefiting from a high level of automation in the back-end. This paper presents…
We discuss a practical method for assessing mathematical proof online. We examine the use of faded worked examples and reading comprehension questions to understand proof. By breaking down a given proof, we formulate a checklist that can be…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…
Visualization plays a relevant role for discovering patterns in big sets of data. In fact, the most common way to help a human with a pattern interpretation is through a graphic. In 2D/3D virtual environments for procedural training the…
Debugging is often a challenging and infuriating experience for secondary school students learning their first text-based programming language. Many students resort to ineffective debugging strategies, making success with solving errors…
Online exams have become widely used to evaluate students' performance in mastering knowledge in recent years, especially during the pandemic of COVID-19. However, it is challenging to conduct proctoring for online exams due to the lack of…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
EvoGrader is a free, online, on-demand formative assessment service designed for use in undergraduate biology classrooms. EvoGrader's web portal is powered by Amazon's Elastic Cloud and run with LightSIDE Lab's open-source machine-learning…
Recent progress in formal theorem proving has benefited from large-scale proof generation and verifier-aware training, but agentic proving is rarely integrated into prover training, appearing only at inference time. We present OProver, a…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
We propose a new online learning model for learning with preference feedback. The model is especially suited for applications like web search and recommender systems, where preference data is readily available from implicit user feedback…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…