Related papers: CoqPyt: Proof Navigation in Python in the Era of L…

Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…

HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…

For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…

ML4PG is an extension of the Proof General interface, allowing the user to invoke machine-learning algorithms and find proof similarities in Coq/SSReect libraries. In this paper, we present three new improvements to ML4PG. First, a new…

Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed…

Data analysis is challenging as it requires synthesizing domain knowledge, statistical expertise, and programming skills. Assistants powered by large language models (LLMs), such as ChatGPT, can assist analysts by translating natural…

Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…

Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they…

Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…

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 describe a method for building composable and extensible verification procedures within the Coq proof assistant. Unlike traditional methods that rely on run-time generation and checking of proofs, we use verified-correct procedures with…

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…

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…

Natural language (NL) programming has become more approachable due to the powerful code-generation capability of large language models (LLMs). This shift to using NL to program enhances collaborative programming by reducing communication…

Chain-of-thought (CoT) prompting enables large language models (LLMs) to solve complex reasoning tasks by generating an explanation before the final prediction. Despite it's promising ability, a critical downside of CoT prompting is that…

We introduce SIMCOPILOT, a benchmark that simulates the role of large language models (LLMs) as interactive, "copilot"-style coding assistants. Targeting both completion (finishing incomplete methods or code blocks) and infill tasks…

We present LLMSTEP, a tool for integrating a language model into the Lean proof assistant. LLMSTEP is a Lean 4 tactic that sends a user's proof state to a server hosting a language model. The language model generates suggestions, which are…

When engineers train deep learning models, they are very much 'flying blind'. Commonly used methods for real-time training diagnostics, such as monitoring the train/test loss, are limited. Assessing a network's training process solely…

Large Language Models (LLMs) have gained widespread popularity due to their ability to perform ad-hoc Natural Language Processing (NLP) tasks with a simple natural language prompt. Part of the appeal for LLMs is their approachability to the…

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…