Related papers: An Extensible Ad Hoc Interface between Lean and Ma…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
The paper advocates for LLMs to enhance the accessibility, usage and explainability of rule-based legal systems, contributing to a democratic and stakeholder-oriented view of legal technology. A methodology is developed to explore the…
We present Lean Refactor, a plug-and-play retrieval-augmented agentic framework for multi-objective, controllable, and version-robust refactoring of Lean proofs. LLM-generated proofs are notoriously correct-but-verbose and brittle across…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
We introduce a new software toolbox for agent-based simulation. Facilitating rapid prototyping by offering a user-friendly Python API, its core rests on an efficient C++ implementation to support simulation of large-scale multi-agent…
The proof assistant Lean has support for abstract polynomials, but this is not necessarily the same as support for computations with polynomials. Lean is also a functional programming language, so it should be possible to implement…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
AI-driven autoformalization of mathematics is advancing rapidly. However, the type checker of a proof assistant guarantees only the logical correctness of proofs; it does not verify whether propositions and definitions faithfully capture…
The Edinburgh Logical Framework (LF) is a dependently type lambda calculus that can be used to encode formal systems. The versatility of LF allows specifications to be constructed also about the encoded systems. The Twelf system exploits…
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…
Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential.…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
We introduce a machine-learning-based tool for the Lean proof assistant that suggests relevant premises for theorems being proved by a user. The design principles for the tool are (1) tight integration with the proof assistant, (2) ease of…
We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes…
Procedural activity assistants potentially support humans in a variety of settings, from our daily lives, e.g., cooking or assembling flat-pack furniture, to professional situations, e.g., manufacturing or biological experiments. Despite…
With the growing popularity of Large Reasoning Models and their results in solving mathematical problems, it becomes crucial to measure their capabilities. We introduce a pipeline for both automatic and interactive verification as a more…