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We present Lean Refactor, a plug-and-play retrieval-augmented agentic framework for multi-objective, controllable, and version-robust refactoring of Lean proofs. LLM-generated proofs are notoriously correct-but-verbose and brittle across…
This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…
Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods either focus on theorem-only NL-to-FL…
This paper proposes a new concurrent heap algorithm, based on a stateless shape property, which efficiently maintains balance during insert and removeMin operations implemented with hand-over-hand locking. It also provides a O(1)…
Realistic simulations in engineering or in the materials sciences can consume enormous computing resources and thus require the use of massively parallel supercomputers. The probability of a failure increases both with the runtime and with…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in…
Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the…
As LLMs and foundation models scale, checkpoint/restore has become a critical pattern for training and inference. With 3D parallelism (tensor, pipeline, data), checkpointing involves many processes, each managing numerous tensors of varying…
Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate…
Recent progress in formal theorem proving has benefited from large-scale proof generation and verifier-aware training, but agentic proving is rarely integrated into prover training, appearing only at inference time. We present OProver, a…
We present the design and implementation of the Small Scale Reflection proof methodology and tactic language (a.k.a. SSR) for the Lean 4 proof assistant. Like its Coq predecessor SSReflect, our Lean 4 implementation, dubbed LeanSSR,…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Proving mathematical theorems using computer-verifiable formal languages like Lean significantly impacts mathematical reasoning. One approach to formal theorem proving involves generating complete proofs using Large Language Models (LLMs)…
We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…
Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving…
Language Models are extremely susceptible to performance collapse with even small changes to input prompt strings. Libraries such as DSpy (from Stanford NLP) avoid this problem through demonstration-based prompt optimisation. Inspired by…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…
Speculative decoding has emerged as a pivotal technique to accelerate LLM inference by employing a lightweight draft model to generate candidate tokens that are subsequently verified by the target model in parallel. However, while this…
Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI…