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Dafny is a verification-aware programming language that comes with a compiler and static program verifier. However, neither the compiler nor the verifier is proved correct; in fact, soundness bugs have been found in both tools. This paper shows that the aforementioned Dafny tools can be developed with foundational correctness guarantees. We present a functional big-step semantics for an imperative subset of Dafny and, based on this semantics, a verified verification condition generator (VCG) and a verified compiler for Dafny. The subset of Dafny we have formalized includes mutually recursive method calls, while loops, and arrays -- these language features are significant enough to cover challenging examples such as McCarthy's 91 function and array-based programs that are used when teaching Dafny. The verified VCG allows one to prove functional correctness of annotated Dafny programs, while the verified compiler can be used to compile verified Dafny programs to CakeML programs. From there, one can obtain executable machine code via the (already verified) CakeML compiler, all while provably maintaining the functional correctness guarantees that were proved for the source-level Dafny

Program safety (i.e., absence of undefined behaviors) is critical for correct operation of computer systems. It is usually verified at the source level (e.g., by separation logics) and preserved to the target by verified compilers (e.g., CompCert), thereby achieving end-to-end verification of safety. However, modern safe programming languages like Rust pose new problems in achieving end-to-end safety. Because not all functionalities can be implemented in the safe language, mixing safe and unsafe modules is needed. Therefore, verified compilation must preserve a modular notion of safety which can be composed at the target level. Furthermore, certain classes of errors (e.g., memory errors) are automatically excluded by verifying compilation (e.g., borrow checking) for modules written in safe languages. As a result, verified compilation needs to cooperate with verifying compilation to ensure end-to-end safety. To address the above problems, we propose a modular and generic definition of safety called open safety based on program semantics described as open labeled transition systems (LTS). Open safety is composable at the boundary of modules and can be modularly preserved by verified

We present our ongoing work on developing an end-to-end verified Rust compiler based on CompCert. It provides two guarantees: one is semantics preservation from Rust to assembly, i.e., the behaviors of source code includes the behaviors of target code, with which the properties verified at the source can be preserved down to the target; the other is memory safety ensured by the verifying compilation -- the borrow checking pass, which can simplify the verification of Rust programs, e.g., by allowing the verification tools focus on the functional correctness.

Video generative models ( VGMs) have become a new frontier that can be used not just for video generation but for a multitude of downstream tasks, including world modeling. To advance these tasks, a good video model must understand the physical reality of the world. Evaluating this understanding is an emerging field and has led to the Physics-IQ benchmark, which quantifies this explicitly by comparing model-generated videos to real-world videos of physical experiments. In this work, we present a systematic audit of the Physics-IQ benchmark, expose shortcomings and propose three solutions that sharpen how we can measure physical understanding of VGMs. Specifically, we improve prompt and ground-truth quality to reduce the influence of confounding factors and further introduce a sample-level scoring system that weights each sample and metric equally. Our resulting benchmark, Physics-IQ Verified, refines 57.6\% of all samples and improves over 34.8\% of prompts. In a comparison study using six image-to-video generative models, we observe moderate but meaningful ranking changes (Kendall's $τ= 0.46$). We hope Physics-IQ Verified advances the community by providing a more reliable signal

The main issue with most evaluation schemes today is their "static" nature: the same problems are reused repeatedly, allowing for memorization, format exploitation, and eventual saturation. To measure genuine AI progress, we need evaluation that is robust by construction, not by post-hoc detection. In response, we propose VeRA (Verified Reasoning Data Augmentation), a framework that converts benchmark problems into executable specifications, comprising (i) a natural language template with placeholder slots, (ii) a coherent generator that samples valid configurations, and (iii) a deterministic verifier that validates parameters and calculates the corresponding correct answers for each configuration. From a single seed problem, VeRA automatically creates unlimited verified variants with reliable labels at near-zero marginal cost without human involvement. VeRA operates in two complementary modes. VeRA-E (equivalent) rewrites problems while keeping the underlying logic intact, useful for detecting memorization versus genuine reasoning. VeRA-H (hardened) systematically increases complexity while remaining verifiable, enabling reliable creation and labelling of fresh difficult tasks at

Learning reliably safe autonomous control is one of the core problems in trustworthy autonomy. However, training a controller that can be formally verified to be safe remains a major challenge. We introduce a novel approach for learning verified safe control policies in nonlinear neural dynamical systems while maximizing overall performance. Our approach aims to achieve safety in the sense of finite-horizon reachability proofs, and is comprised of three key parts. The first is a novel curriculum learning scheme that iteratively increases the verified safe horizon. The second leverages the iterative nature of gradient-based learning to leverage incremental verification, reusing information from prior verification runs. Finally, we learn multiple verified initial-state-dependent controllers, an idea that is especially valuable for more complex domains where learning a single universal verified safe controller is extremely challenging. Our experiments on five safe control problems demonstrate that our trained controllers can achieve verified safety over horizons that are as much as an order of magnitude longer than state-of-the-art baselines, while maintaining high reward, as well as

Recent advances have shown the effectiveness of self-evolving LLM agents on tasks such as program repair and scientific discovery. In this paradigm, a planner LLM synthesizes an agent program that invokes parametric models, including LLMs, which are then tuned per task to improve performance. However, existing self-evolving agent frameworks provide no formal guarantees of safety or correctness. Because such programs are often executed autonomously on unseen inputs, this lack of guarantees raises reliability and security concerns. We formulate agentic code generation as a constrained learning problem, combining hard formal specifications with soft objectives capturing task utility. We introduce Formally Guarded Generative Models (FGGM), which allow the planner LLM to specify a formal output contract for each generative model call using first-order logic. Each FGGM call wraps the underlying model in a rejection sampler with a verified fallback, ensuring every returned output satisfies the contract for any input and parameter setting. Building on FGGM, we present SEVerA (Self-Evolving Verified Agents), a three-stage framework: Search synthesizes candidate parametric programs containin

Verified explanations are a principled way to explain the decisions taken by neural networks, which are otherwise black-box in nature. However, these techniques face significant scalability challenges, as they require multiple calls to neural network verifiers, each of them with an exponential worst-case complexity. We present FaVeX, a novel algorithm to compute verified explanations. FaVeX accelerates the computation by dynamically combining batch and sequential processing of input features, and by reusing information from previous queries, both when proving invariances with respect to certain input features, and when searching for feature assignments altering the prediction. Furthermore, we present a novel and hierarchical definition of verified explanations, termed verifieroptimal robust explanations, that explicitly factors the incompleteness of network verifiers within the explanation. Our comprehensive experimental evaluation demonstrates the superior scalability of both FaVeX, and of verifier-optimal robust explanations, which together can produce meaningful formal explanation on networks with hundreds of thousands of non-linear activations.

Hamiltonian simulation is a central application of quantum computing, with significant potential in modeling physical systems and solving complex optimization problems. Existing compilers for such simulations typically focus on low-level representations based on Pauli operators, limiting programmability and offering no formal guarantees of correctness across the compilation pipeline. We introduce QBlue, a high-level, formally verified framework for compiling Hamiltonian simulations. QBlue is based on the formalism of second quantization, which provides a natural and expressive way to describe quantum particle systems using creation and annihilation operators. To ensure safety and correctness, QBlue includes a type system that tracks particle types and enforces Hermitian structure. The framework supports compilation to both digital and analog quantum circuits and captures multiple layers of semantics, from static constraints to dynamic evolution. All components of QBlue, including its language design, type system, and compilation correctness, are fully mechanized in the Rocq proof framework, making it the first end-to-end verified compiler for second-quantized Hamiltonian simulation

Continuous double auctions are commonly used to match orders at currency, stock, and commodities exchanges. A verified implementation of continuous double auctions is a useful tool for market regulators as they give rise to automated checkers that are guaranteed to detect errors in the trade logs of an existing exchange if they contain trades that violate the matching rules. We provide an efficient and formally verified implementation of continuous double auctions that takes $O(n \log n)$ time to match $n$ orders. This improves an earlier $O(n^2)$ verified implementation. We also prove a matching $Ω(n\log n)$ lower bound on the running time for continuous double auctions. Our new implementation takes only a couple of minutes to run on ten million randomly generated orders as opposed to a few days taken by the earlier implementation. Our new implementation gives rise to an efficient automatic checker. We use the Coq proof assistant for verifying our implementation and extracting a verified OCaml program. While using Coq's standard library implementation of red-black trees to obtain our improvement, we observed that its specification has serious gaps, which we fill in this work; this

A compiler consists of a sequence of phases going from lexical analysis to code generation. Ideally, the formal verification of a compiler should include the formal verification of each component of the tool-chain. An example is the CompCert project, a formally verified C compiler, that comes with associated tools and proofs that allow to formally verify most of those components. However, some components, in particular the lexer, remain unverified. In fact, the lexer of Compcert is generated using OCamllex, a lex-like OCaml lexer generator that produces lexers from a set of regular expressions with associated semantic actions. Even though there exist various approaches, like CakeML or Verbatim++, to write verified lexers, they all have only limited practical applicability. In order to contribute to the end-to-end verification of compilers, we implemented a generator of verified lexers whose usage is similar to OCamllex. Our software, called Coqlex, reads a lexer specification and generates a lexer equipped with a Coq proof of its correctness. It provides a formally verified implementation of most features of standard, unverified lexer generators. The conclusions of our work are two

Formally verified compilers and formally verified static analyzers are a solution to the problem that certain industries face when they have to demonstrate to authorities that the object code they run truly corresponds to its source code and that it satisfies certain properties. From a scientific and technological point of view, they are a challenge: not only a number of nontrivial invariants and algorithms must be proved to be correct, but also the implementation must be reasonably effective so that the tools operate within reasonable time. Many optimizations in compilers rely on static analysis, and thus a formally verified compiler entails formally verified static analyses.In this article, we explain some difficulties, possible solutions, design choices and trade-offs pertaining to verified static analysis, in particular when the solution of the analysis is expressed as some form of tree, map or set.

Differential privacy (DP) has become the gold standard for privacy-preserving data analysis, but implementing it correctly has proven challenging. Prior work has focused on verifying DP at a high level, assuming the foundations are correct and a perfect source of randomness is available. However, the underlying theory of differential privacy can be very complex and subtle. Flaws in basic mechanisms and random number generation have been a critical source of vulnerabilities in real-world DP systems. In this paper, we present SampCert, the first comprehensive, mechanized foundation for differential privacy. SampCert is written in Lean with over 12,000 lines of proof. It offers a generic and extensible notion of DP, a framework for constructing and composing DP mechanisms, and formally verified implementations of Laplace and Gaussian sampling algorithms. SampCert provides (1) a mechanized foundation for developing the next generation of differentially private algorithms, and (2) mechanically verified primitives that can be deployed in production systems. Indeed, SampCert's verified algorithms power the DP offerings of Amazon Web Services (AWS), demonstrating its real-world impact. Sam

Domain-specific languages (DSLs) are integral to various software workflows. Such languages offer domain-specific optimizations and abstractions that improve code readability and maintainability. However, leveraging these languages requires developers to rewrite existing code using the specific DSL's API. While large language models (LLMs) have shown some success in automatic code transpilation, none of them provide any functional correctness guarantees on the transpiled code. Another approach for automating this task is verified lifting, which relies on program synthesis to find programs in the target language that are functionally equivalent to the source language program. While several verified lifting tools have been developed for various application domains, they are specialized for specific source-target languages or require significant expertise in domain knowledge to make the search efficient. In this paper, leveraging recent advances in LLMs, we propose an LLM-based approach (LLMLift) to building verified lifting tools. We use the LLM's capabilities to reason about programs to translate a given program into its corresponding equivalent in the target language. Additionally,

This technical report contains the full set of definitions and projection rules of the paper ``Verified Parameterized Choreographies'' by Rubbens et al. It also supplements the artefact.

We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified implementation. The implementation is evaluated on benchmark problems to show its practicability. As part of the refinement, we develop verified software to certify Linear Programming solutions. The algorithm builds on a diverse library of formalized mathematics and pushes existing methodologies for interactive theorem provers to the limits. We discuss the process of the verification project and the modifications to the algorithm needed for formal verification.

The Weighted Path Order of Yamada is a powerful technique for proving termination. It is also supported by CeTA, a certifier for checking untrusted termination proofs. To be more precise, CeTA contains a verified function that computes for two terms whether one of them is larger than the other for a given WPO, i.e., where all parameters of the WPO have been fixed. The problem of this verified function is its exponential runtime in the worst case. Therefore, in this work we develop a polynomial time implementation of WPO that is based on memoization. It also improves upon an earlier verified implementation of the Recursive Path Order: the RPO-implementation uses full terms as keys for the memory, a design which simplified the soundness proofs, but has some runtime overhead. In this work, keys are just numbers, so that the lookup in the memory is faster. Although trivial on paper, this change introduces some challenges for the verification task.

Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much harder problem. This paper reports work-in-progress to do such verification in Lean.

In this article we review standard null-move pruning and introduce our extended version of it, which we call verified null-move pruning. In verified null-move pruning, whenever the shallow null-move search indicates a fail-high, instead of cutting off the search from the current node, the search is continued with reduced depth. Our experiments with verified null-move pruning show that on average, it constructs a smaller search tree with greater tactical strength in comparison to standard null-move pruning. Moreover, unlike standard null-move pruning, which fails badly in zugzwang positions, verified null-move pruning manages to detect most zugzwangs and in such cases conducts a re-search to obtain the correct result. In addition, verified null-move pruning is very easy to implement, and any standard null-move pruning program can use verified null-move pruning by modifying only a few lines of code.