相关论文: Online Machine Learning Techniques for Coq: A Comp…

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…

The Tactician's Web is a platform offering a large web of strongly interconnected, machine-checked, formal mathematical knowledge conveniently packaged for machine learning, analytics, and proof engineering. Built on top of the Coq proof…

We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant. In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic…

In proof assistants, the physical proximity between two formal mathematical concepts is a strong predictor of their mutual relevance. Furthermore, lemmas with close proximity regularly exhibit similar proof structures. We show that this…

We report the results of the first experiments with learning proof dependencies from the formalizations done with the Coq system. We explain the process of obtaining the dependencies from the Coq proofs, the characterization of formulas…

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…

The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…

We have developed an alternative approach to teaching computer science students how to prove. First, students are taught how to prove theorems with the Coq proof assistant. In a second, more difficult, step students will transfer their…

Proof assistants enable users to develop machine-checked proofs regarding software-related properties. Unfortunately, the interactive nature of these proof assistants imposes most of the proof burden on the user, making formal verification…

In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…

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…

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…

Enabling more concise and modular proofs is essential for advancing formal reasoning using interactive theorem provers (ITPs). Since many ITPs, such as Rocq and Lean, use tactic-style proofs, learning higher-level custom tactics is crucial…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

We present Q-chunking, a simple yet effective recipe for improving reinforcement learning (RL) algorithms for long-horizon, sparse-reward tasks. Our recipe is designed for the offline-to-online RL setting, where the goal is to leverage an…

Online field experiments are the gold-standard way of evaluating changes to real-world interactive machine learning systems. Yet our ability to explore complex, multi-dimensional policy spaces - such as those found in recommendation and…

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…

This paper presents an online reinforcement-learning framework for safe gain scheduling of a nonlinear quadcopter controller. Rather than learning thrust and torque commands directly, the proposed method selects gain vectors online from a…

In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…

This study has proposed an E-textbook platform, MetaCQ, which integrates ITS and OLM to enable users to monitor their study progress. The platform adopts a chatbot to generate MCQs and manage learners' study data and their learning model.…