Related papers: Automated Discovery of Tactic Libraries for Intera…

We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning. The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner. We…

Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…

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…

Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…

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…

The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…

With the remarkable advancement of AI agents, the number of their equipped tools is increasing rapidly. However, integrating all tool information into the limited model context becomes impractical, highlighting the need for efficient tool…

Modern separation logics allow one to prove rich properties of intricate code, e.g. functional correctness and linearizability of non-blocking concurrent code. However, this expressiveness leads to a complexity that makes these logics…

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…

In this paper, we compare different existing approaches employed in data mining of big proof libraries in automated and interactive theorem proving.

We implement a automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation. This knowledge is then used in a Monte…

Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…

Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction…

Humans can develop new theorems to explore broader and more complex mathematical results. While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new…

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…

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…

In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…

Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…

We present a comparison of several online machine learning techniques for tactical learning and proving in the Coq proof assistant. This work builds on top of Tactician, a plugin for Coq that learns from proofs written by the user to…

Most ATP benchmarks embed the final answer within the formal statement -- a convention we call "Easy Mode" -- a design that simplifies the task relative to what human competitors face and may lead to optimistic estimates of model…