Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematics

• URL: http://arxiv.org/abs/2606.17581v1
• Date: Tue, 16 Jun 2026 06:43:08 GMT
• Title: Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematics
• Abstract summary: We present a dependent-type-based prover designed around the way LLMs (and humans) tend to write mathematics.<n>Its core design choices are a surface that imitates mathematical natural language and a rule-driven automation layer that closes the routine steps a textbook would omit.<n>Early experiments suggest that, even without any prover-specific training data, LLMs can learn to use it effectively on the miniF2F benchmark.
• Score: 32.09940762546616
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a dependent-type-based prover designed around the way LLMs (and humans) tend to write mathematics, complementing existing systems such as Lean and Rocq. Its core design choices are a surface that imitates mathematical natural language and a rule-driven automation layer that closes the routine steps a textbook would omit, so that an accepted proof can be re-emitted as a checked Lean file. Early experiments suggest that, even without any prover-specific training data, LLMs can learn to use it effectively on the miniF2F benchmark. Lean output excerpts: https://github.com/xiyuzhai-husky-lang/visored/

Related papers

• TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts [26.98890165420689]
  TheoremLlama is an end-to-end framework that trains a general-purpose Lean4 expert. Our framework achieves cumulative accuracies of 36.48% and 33.61% on MiniF2F-Valid and Test datasets respectively.
  arXiv  Detail & Related papers  (2024-07-03T15:36:18Z)
• Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean [81.94024084598598]
  We introduce Lean Copilot, a framework for running LLM inference in Lean.<n>We build tools that suggest proof steps, complete proof goals, and select relevant premises.<n>When assisting humans, Lean Copilot requires only 2.08 manually-entered proof steps on average (3.86 required by aesop)<n>When automating the theorem proving process, Lean Copilot 74.2% proof steps on average, 85% better than aesop (40.1%).
  arXiv  Detail & Related papers  (2024-04-18T22:54:08Z)
• $\orall$uto$\exists$val: Autonomous Assessment of LLMs in Formal Synthesis and Interpretation Tasks [21.12437562185667]
  This paper presents a new approach for scaling LLM assessment in translating formal syntax to natural language. We use context-free grammars (CFGs) to generate out-of-distribution datasets on the fly. We also conduct an assessment of several SOTA closed and open-source LLMs to showcase the feasibility and scalability of this paradigm.
  arXiv  Detail & Related papers  (2024-03-27T08:08:00Z)
• Tuna: Instruction Tuning using Feedback from Large Language Models [74.04950416204551]
  We propose finetuning an instruction-tuned large language model using our novel textitprobabilistic ranking and textitcontextual ranking approaches. Probabilistic ranking enables the instruction-tuned model to inherit the relative rankings of high-quality and low-quality responses from the teacher LLM. On the other hand, learning with contextual ranking allows the model to refine its own response distribution using the contextual understanding ability of stronger LLMs.
  arXiv  Detail & Related papers  (2023-10-20T09:55:06Z)
• Assessing the Reliability of Large Language Model Knowledge [78.38870272050106]
  Large language models (LLMs) have been treated as knowledge bases due to their strong performance in knowledge probing tasks. How do we evaluate the capabilities of LLMs to consistently produce factually correct answers? We propose MOdel kNowledge relIabiliTy scORe (MONITOR), a novel metric designed to directly measure LLMs' factual reliability.
  arXiv  Detail & Related papers  (2023-10-15T12:40:30Z)
• Large Language Model-Aware In-Context Learning for Code Generation [75.68709482932903]
  Large language models (LLMs) have shown impressive in-context learning (ICL) ability in code generation. We propose a novel learning-based selection approach named LAIL (LLM-Aware In-context Learning) for code generation.
  arXiv  Detail & Related papers  (2023-10-15T06:12:58Z)
• LeanDojo: Theorem Proving with Retrieval-Augmented Language Models [72.54339382005732]
  Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. Existing methods are difficult to reproduce or build on, due to private code, data, and compute requirements. This paper introduces LeanDojo: an open-source Lean toolkit consisting of toolkits, data, models. We develop ReProver: an LLM-based prover augmented with retrieval for selecting premises from a vast math library.
  arXiv  Detail & Related papers  (2023-06-27T17:05:32Z)
• Coarse-Tuning Models of Code with Reinforcement Learning Feedback [0.0]
  Large Language Models (LLMs) pre-trained on code have emerged as the dominant approach to program synthesis. We propose RLCF, that further trains a pre-trained LLM via reinforcement learning, using feedback from a grounding function that scores the quality of the code.
  arXiv  Detail & Related papers  (2023-05-25T22:09:08Z)
• Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning [101.26814728062065]
  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 problem-solving.
  arXiv  Detail & Related papers  (2023-05-20T22:25:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.