Related papers: Lean4Lean: Verifying a Typechecker for Lean, in Le…
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…
We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4. Key to our approach is reflection: a Boolean checker function whose soundness is fully proved in Lean and executed as compiled native code.…
MerLean-Prover is an end-to-end Lean4 theorem prover that replaces sorry declarations with kernel-checkable proofs. It is built from three agent types (Planning, Check, and Lean) composed by a recursive outer loop whose unit of revision is…
We present Lean Finder, a semantic search engine for Lean and mathlib that understands and aligns with the intents of mathematicians. Progress in formal theorem proving is often hindered by the difficulty of locating relevant theorems and…
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,…
The interactive theorem prover Lean enables the verification of formal mathematical proofs and is backed by an expanding community. Central to this ecosystem is its mathematical library, mathlib4, which lays the groundwork for the…
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…
We introduce ${\rm C{\small LEVER}}$, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out…
Neural networks are increasingly deployed in scientific, safety critical, and mission critical pipelines, yet verification and analysis are often performed outside the programming environment that defines and runs the model. This creates a…
Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…
We introduce CSLib, an open-source framework for proving computer-science-related theorems and writing formally verified code in the Lean proof assistant. CSLib aims to be for computer science what Lean's Mathlib is for mathematics. Mathlib…
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…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
AI-driven autoformalization of mathematics is advancing rapidly. However, the type checker of a proof assistant guarantees only the logical correctness of proofs; it does not verify whether propositions and definitions faithfully capture…
Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…
Automatic and efficient verification of multiplier designs, especially through a provably correct method, is a difficult problem. We show how to utilize a theorem prover, ACL2, to implement an efficient rewriting algorithm for multiplier…
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…
We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…
The expanding Lean 4 ecosystem poses challenges for navigating its vast libraries. This paper introduces LeanExplore, a search engine for Lean 4 declarations. LeanExplore enables users to semantically search for statements, both formally…
Traditional approaches for validating molecular simulations rely on making software open source and transparent, incorporating unit testing, and generally employing human oversight. We propose an approach that eliminates software errors…