Related papers: Waterproof: Educational Software for Learning How …
This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present…
Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
We present CoqPilot, a VS Code extension designed to help automate writing of Coq proofs. The plugin collects the parts of proofs marked with the admit tactic in a Coq file, i.e., proof holes, and combines LLMs along with…
Software piracy, the illegal using, copying, and resale of applications is a major concern for anyone develops software. Software developers also worry about their applications being reverse engineered by extracting data structures and…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
We present a light formalism for proofs that encodes their inferential structure, along with a system that transforms these representations into flow-chart diagrams. Such diagrams should improve the comprehensibility of proofs. We discuss…
Diproche ("Didactical Proof Checking") is an automatic system for supporting the acquistion of elementary proving skills in the initial phase of university education in mathematics. A key feature of Diproche - which is designed by the…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read…
We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…
Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…
The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express…
Formally reasoning about functional programs is supposed to be straightforward and elegant, however, it is not typically done as a matter of course. Reasoning in a proof assistant requires "reimplementing" the code in those tools, which is…
We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical…
The most effective techniques to detect LLM-generated text rely on inserting a detectable signature -- or watermark -- during the model's decoding process. Most existing watermarking methods require access to the underlying LLM's logits,…
While loops are present in virtually all imperative programming languages. They are important both for practical reasons (performing a number of iterations not known in advance) and theoretical reasons (achieving Turing completeness). In…
As educators push for students to learn science by doing science, there is a need for computational scaffolding to assist students' evaluation of scientific evidence and argument building. In this paper, we present a pilot study of SciNote,…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
We present Tactician, a tactic learner and prover for the Coq Proof Assistant. Tactician helps users make tactical proof decisions while they retain control over the general proof strategy. To this end, Tactician learns from previously…