Related papers: Lean4Lean: Verifying a Typechecker for Lean, in Le…
LLMs can generate hardware descriptions from natural language specifications, but the resulting Verilog often contains width mismatches, combinational loops, and incomplete case logic that pass syntax checks yet fail in synthesis or…
We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual…
We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and…
The physics community relies on index notation to effectively manipulate types of tensors. This paper introduces the first formally verified implementation of index notation in the interactive theorem prover Lean 4. By integrating index…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
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)…
Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-based proof automation are drawn from mathematics in the Mathlib ecosystem, whereas proofs in…
Interactive theorem proving software is typically designed around a trusted proof-checking kernel, the sole system component capable of authenticating theorems. Untrusted automation procedures reside outside of the kernel, and drive it to…
The chase is a sound, complete, but possibly non-terminating algorithm for reasoning with existential rules (aka. tuple-generating dependencies), a highly expressive knowledge representation language. Although the procedure appears simple,…
We present a framework for verifying the deterministic structured computations surrounding a large language model rather than the model itself, extending a Lean 4 trust-boundary architecture to the generic interfaces of modern LLM…
Formal verification offers a path to provably correct software, but writing verified code remains expensive enough that the technique is rarely used in production. Recent large language models can accelerate this work, and recent benchmarks…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
Large language models (LLMs) can generate plausible code but offer limited guarantees of correctness. Formally verifying that implementations satisfy specifications requires constructing machine-checkable proofs, a task that remains beyond…
We describe a verification pipeline that takes production Rust cryptographic code and produces machine-checked correctness proofs in Lean 4. The pipeline combines three components: symbolic extraction tools (Charon and Aeneas, or Hax) that…
One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the…
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since…
Backward error analysis offers a method for assessing the quality of numerical programs in the presence of floating-point rounding errors. However, techniques from the numerical analysis literature for quantifying backward error require…
We present LLMSTEP, a tool for integrating a language model into the Lean proof assistant. LLMSTEP is a Lean 4 tactic that sends a user's proof state to a server hosting a language model. The language model generates suggestions, which are…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task we call global premise retrieval. Existing tools address adjacent problems: semantic search engines…