Related papers: Machine-Generated, Machine-Checked Proofs for a Ve…
Proof assistants like Coq are increasingly popular to help mathematicians carry out proofs of the results they conjecture. However, formal proofs remain highly technical and are especially difficult to reuse. In this paper, we present a…
The essence of compiling with continuations is that conversion to continuation-passing style (CPS) is equivalent to a source language transformation converting to administrative normal form (ANF). Taking as source language Moggi's…
Hardware verification is one of the most challenging stages of the hardware design process, requiring significant time and resources to ensure a design is fully validated and production-ready. Verification teams aim to maximize design…
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
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…
We present a two-stage pipeline for AI-assisted improvement of published algorithm implementations. In the first stage, a large language model with research capabilities identifies recently published algorithms satisfying explicit…
Robotics and Autonomous Systems are increasingly deployed in safety-critical domains, so that demonstrating their safety is essential. Assurance Cases (ACs) provide structured arguments supported by evidence, but generating and maintaining…
While LLM-based agents are able to tackle a wide variety of code reasoning questions, the answers are not always correct. This prevents the agent from being useful in situations where high precision is desired: (1) helping a software…
We report on an experiment in which Claude Opus~4.6, equipped with a suite of Model Context Protocol (MCP) tools for the Rocq proof assistant, autonomously proved 10 of 12 problems from the 2025 Putnam Mathematical Competition. The MCP…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
This work studies the applicability of automatic AI agent optimization methods to real-world agents in formal verification settings, focusing on automated theorem proving in Rocq as a representative and challenging domain. We evaluate how…
Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves…
In industrial control systems, the generation and verification of Programmable Logic Controller (PLC) code are critical for ensuring operational efficiency and safety. While Large Language Models (LLMs) have made strides in automated code…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
We present Agentic Retrieval-Augmented Code Synthesis (ARCS), a system that improves LLM-based code generation without fine-tuning. ARCS operates through a budgeted synthesize-execute-repair loop over a frozen model: it retrieves relevant…
As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to…
Foundational verification allows programmers to build software which has been empirically shown to have high levels of assurance in a variety of important domains. However, the cost of producing foundationally verified software remains…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
Certified program synthesis (aka vericoding) is the process of automatically generating a program, its formal specification, and a machine-checkable proof of their alignment from a natural-language description. Two challenges make…