Related papers: Lean-auto: An Interface between Lean 4 and Automat…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
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…
Automated theorem proving systems built on Lean 4 increasingly rely on parallel tactic search over partially specified proofs, such as those generated by Draft-Sketch-Prove (DSP) pipelines. In current systems, each search branch…
Empirical methods to examine the capability of Large Language Models (LLMs) to use Automated Theorem Prover (ATP) reasoning strategies are studied. We evaluate the performance of State of the Art models from December 2023 and August 2024 on…
Large Language Models (LLMs) have recently advanced the field of Automated Theorem Proving (ATP), attaining substantial performance gains through widely adopted test-time scaling strategies, notably reflective Chain-of-Thought (CoT)…
One important approach to software verification is interactive theorem proving. However, writing formal proofs often requires substantial human effort, making proof automation highly important. Traditionally, proof automation has relied on…
Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis.…
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…
Large Language Models (LLMs), when enhanced through reasoning-oriented post-training, evolve into powerful Large Reasoning Models (LRMs). Tool-Integrated Reasoning (TIR) further extends their capabilities by incorporating external tools,…
We report the development of GPT-4, a large-scale, multimodal model which can accept image and text inputs and produce text outputs. While less capable than humans in many real-world scenarios, GPT-4 exhibits human-level performance on…
We present Leapfrog, a Coq-based framework for verifying equivalence of network protocol parsers. Our approach is based on an automata model of P4 parsers, and an algorithm for symbolically computing a compact representation of a…
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…
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…
The rapid evolution of autonomous, agentic artificial intelligence within financial services has introduced an existential architectural crisis: large language models (LLMs) are probabilistic, non-deterministic systems operating in domains…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
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…
A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant. In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…