Related papers: Sharing HOL4 and HOL Light proof knowledge

Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…

Recent studies highlight various machine learning (ML)-based techniques for code clone detection, which can be integrated into developer tools such as static code analysis. With the advancements brought by ML in code understanding, ML-based…

Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…

The progress of deep learning (DL), especially the recent development of automatic design of networks, has brought unprecedented performance gains at heavy computational cost. On the other hand, blockchain systems routinely perform a huge…

Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback…

Humans learn to solve tasks of increasing complexity by building on top of previously acquired knowledge. Typically, there exists a natural progression in the tasks that we learn - most do not require completely independent solutions, but…

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in…

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…

Large language models (LLMs) sometimes demonstrate poor performance on knowledge-intensive tasks, commonsense reasoning is one of them. Researchers typically address these issues by retrieving related knowledge from knowledge graphs or…

Mathematical reasoning recently has been shown as a hard challenge for neural systems. Abilities including expression translation, logical reasoning, and mathematics knowledge acquiring appear to be essential to overcome the challenge. This…

While the problem of hallucinations in neural machine translation has long been recognized, so far the progress on its alleviation is very little. Indeed, recently it turned out that without artificially encouraging models to hallucinate,…

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…

Large Language Models (LLMs) excel at understanding natural language but struggle with explicit commonsense reasoning. A recent trend of research suggests that the combination of LLM with robust symbolic reasoning systems can overcome this…

Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that…

When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…

We evaluate the ability of Large Language Models (LLMs) to discern and express their internal knowledge state, a key factor in countering factual hallucination and ensuring reliable application of LLMs. We observe a robust self-awareness of…

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical…

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…

Small language models (SLMs) often struggle with complex mathematical reasoning due to limited capacity to maintain long chains of intermediate steps and to recover from early errors. We address this challenge by introducing a hint-assisted…