Abstract Separation-logic proofs of heap-manipulating programs require careful accounting of objects and pointers in memory. On paper, these proofs are often accompanied by heap-memory diagrams that help authors and readers track the evolution of the program’s abstract state. However, users of interactive theorem provers must instead work with plain-text notations that obscure object relationships. This paper presents the first automatic visualization library for separation-logic heap predicates, mimicking hand-drawn diagrams found in published materials. Four key features make the library practical. First, it supports animating across proof steps. Second, it offers users a DSL to specify how custom predicates should be visualized. Third, it is straightforward to port to new separation logic frameworks. And fourth, it can be used in browsers and IDEs, during and after proof development. We demonstrate these features by implementing support for CFML and Iris and integrating with Alectryon and VsRocq.

As constraint programming (CP) solvers are increasingly used in critical applications, there is a growing need for certification of solver claims of infeasibility and optimality. Recent work has demonstrated that certification is feasible for CP solvers using a multi-stage proof-generation framework; however, the underlying proof system was informal, and verification relied on translation into an external proof format, impacting the trustworthiness. We address these issues by formalising a rigorous, solver-agnostic framework for certifying CP solver claims. We present a formal definition of DRCP, a proof system for CP over integer domains that captures core solver operations, including conflict analysis and heterogeneous propagation, by modular inference rules with precise semantics. We also develop FznDrcpCheck, a formally verified proof checker in Rocq that validates DRCP proofs directly against FlatZinc models. Our evaluation shows that our framework enables practical certification across various benchmarks with negligible overhead during solving and modest proof-checking costs.

Most separation logics hide container-internal pointers for modularity. This makes it difficult to specify container APIs that temporarily expose those pointers to the outside, and to verify programs that use these APIs.

Railroad diagrams (also called "syntax diagrams") are a common, intuitive visualization of grammars, but limited tooling and a lack of formal attention to their layout mostly confines them to hand-drawn documentation. We present the first formal treatment of railroad diagram layout along with a principled, practical implementation. We characterize the problem as compiling a diagram language (specifying conceptual components and how they connect and compose) to a layout language (specifying basic graphical shapes and their sizes and positions). We then implement a compiler that performs line wrapping to meet a target width, as well as vertical alignment and horizontal justification per user-specified policies. We frame line wrapping as optimization, where we describe principled dimensions of optimality and implement corresponding heuristics. For front-end evaluation, we show that our diagram language is well-suited for common applications by describing how regular expressions and Backus-Naur form can be compiled to it. For back-end evaluation, we argue that our compiler is practical by comparing its output to diagrams laid out by hand and by other tools.

We present the first mechanized, succinct, practical, complete, and proven-faithful semantics for a modern regular expression language with backtracking semantics. We ensure its faithfulness by proving it equivalent to a preexisting line-by-line embedding of the official ECMAScript specification of JavaScript regular expressions. We demonstrate its practicality by presenting two real-world applications. First, a new notion of contextual equivalence for modern regular expressions, which we use to prove or disprove rewrites drawn from previous work. Second, the first formal proof of the PikeVM algorithm used in many real-world engines. In contrast with the specification and other formalization work, our semantics captures not only the top-priority match, but a full backtracking tree recording all possible matches and their respective priority. All our definitions and results have been mechanized in the Rocq proof assistant.

Abstract We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical propositional logic in automated reasoning tools. We formalize, in the Coq proof assistant, a proof system in sequent-calculus style for orthologic. We then prove its soundness and completeness with respect to the algebraic variety of ortholattices, and we formalize a cut-elimination theorem. In doing so, we discover and fix a missing case in a previously published proof. We then implement and verify a complete proof search procedure for orthologic. A naive implementation is exponential; to obtain an optimal quadratic run time, we optimize the implementation by memoizing its results and simulating reference equality testing. We leverage the resulting correctness theorem to implement a reflective Coq tactic. We present benchmarks showing that the procedure, under various optimizations, matches its theoretical complexity. Finally, we develop a collection of tactics, including normalization with respect to orthologic and a boolean solver, which we also benchmark. We make tactics available as a standalone Coq plugin.

All critical systems must evolve to meet the needs of a growing and diversifying user base. But supporting that evolution is challenging at increasing scale: Maintainers must find a way to ensure that each change does only what is intended, and will not inadvertently change behavior for existing users. This paper presents how we addressed this challenge for the Amazon Web Services (AWS) authorization engine, invoked 1 billion times per second, by using formal verification. Over a period of four years, we built a new authorization engine, one that behaves functionally the same as its predecessor, using the verification-aware programming language Dafny. We can now confidently deploy enhancements and optimizations while maintaining the highest assurance of both correctness and backward compatibility. We deployed the new engine in 2024 without incident and customers immediately enjoyed a threefold performance improvement. The methodology we followed to build this new engine was not an off-the-shelf application of an existing verification tool, and this paper presents several key insights: 1) Rather than prove correct the existing engine, written in Java, we found it more effective to write a new engine in Dafny, a language built for verification from the ground up, and then compile the result to Java. 2) To ensure performance, debuggability, and to gain trust from stakeholders, we needed to generate readable, idiomatic Java code, essentially a transliteration of the source Dafny. 3) To ensure that the specification matches the system's actual behavior, we performed extensive differential and shadow testing throughout the development process, ultimately comparing against 1015production samples prior to deployment. Our approach demonstrates how formal verification can be effectively applied to evolve critical legacy software at scale.

The process isolation enforceable by commodity hardware and operating systems is too weak to protect secrets from malicious code running on the same machine: attacks exploit timing side channels derived from contention on shared microarchitectural resources to extract secrets. With appropriate hardware support, however, we can construct isolated enclaves and safeguard independent processes from interference through timing side channels, a step towards confidentiality and integrity guarantees.

Systems code is challenging to verify, because it uses constructs (like raw pointers, pointer arithmetic, and bit twiddling) that are hard for tools to reason about. Existing approaches either sacrifice programmer friendliness, by demanding significant manual effort and verification expertise, or generality, by restricting the programming language or requiring that the code adapt to the verification tool.

Modern regex languages have strayed far from well-understood traditional regular expressions: they include features that fundamentally transform the matching problem. In exchange for these features, modern regex engines at times suffer from exponential complexity blowups, a frequent source of denial-of-service vulnerabilities in JavaScript applications. Worse, regex semantics differ across languages, and the impact of these divergences on algorithmic design and worst-case matching complexity has seldom been investigated. This paper provides a novel perspective on JavaScript’s regex semantics by identifying a larger-than-previously-understood subset of the language that can be matched with linear time guarantees. In the process, we discover several cases where state-of-the-art algorithms were either wrong (semantically incorrect), inefficient (suffering from superlinear complexity) or excessively restrictive (assuming certain features could not be matched linearly). We introduce novel algorithms to restore correctness and linear complexity. We further advance the state-of-the-art in linear regex matching by presenting the first nonbacktracking algorithms for matching lookarounds in linear time: one supporting captureless lookbehinds in any regex language, and another leveraging a JavaScript property to support unrestricted lookaheads and lookbehinds. Finally, we describe new time and space complexity tradeoffs for regex engines. All of our algorithms are practical: we validated them in a prototype implementation, and some have also been merged in the V8 JavaScript implementation used in Chrome and Node.js.

Modern software needs fine-grained compartmentalization, i.e., intra-process isolation. A particularly important reason for it are supply-chain attacks, the need for which is aggravated by modern applications depending on hundreds or even thousands of libraries. Object capabilities are a particularly salient approach to compartmentalization, but they require the entire program to assume a lack of ambient authority. Most of existing code was written under no such assumption; effectively, existing applications need to undergo a rewrite-the-world migration to reap the advantages of ocap. We propose gradual compartmentalization , an approach which allows gradually migrating an application to object capabilities, component by component in arbitrary order, all the while continuously enjoying security guarantees. The approach relies on runtime authority enforcement and tracking the authority of objects the type system. We present Gradient, a proof-of- concept gradual compartmentalization extension to Scala which uses Enclosures and Capture Tracking as its key components. We evaluate our proposal by migrating the standard XML library of Scala to Gradient.

We present verification of a bare-metal server built using diverse implementation techniques and languages against a whole-system input-output specification in terms of machine code, network packets, and mathematical specifications of elliptic-curve cryptography. We used very different formal-reasoning techniques throughout the stack, ranging from computer algebra, symbolic execution, and verification-condition generation to interactive verification of functional programs including compilers for C-like and functional languages. All these component specifications and domain-specific reasoning techniques are defined and justified against common foundations in the Coq proof assistant. Connecting these components is a minimalistic specification style based on functional programs and assertions over simple objects, omnisemantics for program execution, and basic separation logic for memory layout. This design enables us to bring the components together in a top-level correctness theorem that can be audited without understanding or trusting the internal interfaces and tools. Our case study is a simple cryptographic server for flipping of a bit of state through public-key authenticated network messages, and its proof shows total functional correctness including static bounds on memory usage. This paper also describes our experiences with the specific verification tools we build upon, along with detailed analysis of reasons behind the widely varying levels of productivity we experienced between combinations of tools and tasks.

We present an executable, proven-safe, faithful, and future-proof Coq mechanization of JavaScript regular expression (regex) matching, as specified by the latest published edition of ECMA-262 section 22.2. This is, to our knowledge, the first time that an industrial-strength regex language has been faithfully mechanized in an interactive theorem prover. We highlight interesting challenges that arose in the process (including issues of encoding, corner cases, and executability), and we document the steps that we took to ensure that the result is straightforwardly auditable and that our understanding of the specification aligns with existing implementations. We demonstrate the usability and versatility of the mechanization through a broad collection of analyses, case studies, and experiments: we prove that JavaScript regex matching always terminates and is safe (no assertion failures); we identify subtle corner cases that led to mistakes in previous publications; we verify an optimization extracted from a state-of-the-art regex engine; we show that some classic properties described in automata textbooks and used in derivatives-based matchers do not hold in JavaScript regexes; and we demonstrate that the cost of updating the mechanization to account for changes in the original specification is reasonably low. Our mechanization can be extracted to OCaml and JavaScript and linked with Unicode libraries to produce an executable regex engine that passes the relevant parts of the official Test262 conformance test suite.

There are typically two ways to compile and run a purely functional program verified using an interactive theorem prover (ITP): automatically extracting it to a similar language (typically an unverified process, like Coq to OCaml) or manually proving it equivalent to a lower-level reimplementation (like a C program). Traditionally, only the latter produced both excellent performance and end-to-end proofs.

Rule-based hardware-design languages (RHDLs) promise to enhance developer productivity by offering convenient abstractions. Advanced compiler technology keeps the cost of these abstractions low, generating circuits with excellent area and timing properties.

The Bluespec hardware-description language presents a significantly higher-level view than hardware engineers are used to, exposing a simpler concurrency model that promotes formal proof, without compromising on performance of compiled circuits. Unfortunately, the cost model of Bluespec has been unclear, with performance details depending on a mix of user hints and opaque static analysis of potential concurrency conflicts within a design. In this paper we present Koika, a derivative of Bluespec that preserves its desirable properties and yet gives direct control over the scheduling decisions that determine performance. Koika has a novel and deterministic operational semantics that uses dynamic analysis to avoid concurrency anomalies. Our implementation includes Coq definitions of syntax, semantics, key metatheorems, and a verified compiler to circuits. We argue that most of the extra circuitry required for dynamic analysis can be eliminated by compile-time BSV-style static analysis.

Proof assistants like Coq, Lean, or HOL4 rely heavily on stateful meta-programs called scripts to assemble proofs. Unlike pen-and-paper proofs, proof scripts only describe the steps to take (induct on x, apply a theorem, …), not the states that these steps lead to; as a result, plain proof scripts are essentially incomprehensible without the assistance of an interactive user interface able to run the script and show the corresponding proof states.

We introduce Meta-F $$^{\star }$$ , a tactics and metaprogramming framework for the F $$^\star $$ program verifier. The main novelty of Meta-F $$^\star $$ is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them into well-behaved SMT fragments. Plus, Meta-F $$^\star $$ can be used to generate verified code automatically. Meta-F $$^\star $$ is implemented as an F $$^\star $$ effect, which, given the powerful effect system of F $$^{\star }$$ , heavily increases code reuse and even enables the lightweight verification of metaprograms. Metaprograms can be either interpreted, or compiled to efficient native code that can be dynamically loaded into the F $$^\star $$ type-checker and can interoperate with interpreted code. Evaluation on realistic case studies shows that Meta-F $$^\star $$ provides substantial gains in proof development, efficiency, and robustness.

It is a neat result from functional programming that libraries of parser combinators can support rapid construction of decoders for quite a range of formats. With a little more work, the same combinator program can denote both a decoder and an encoder. Unfortunately, the real world is full of gnarly formats, as with the packet formats that make up the standard Internet protocol stack. Most past parser-combinator approaches cannot handle these formats, and the few exceptions require redundancy – one part of the natural grammar needs to be hand-translated into hints in multiple parts of a parser program. We show how to recover very natural and nonredundant format specifications, covering all popular network packet formats and generating both decoders and encoders automatically. The catch is that we use the Coq proof assistant to derive both kinds of artifacts using tactics, automatically, in a way that guarantees that they form inverses of each other. We used our approach to reimplement packet processing for a full Internet protocol stack, inserting our replacement into the OCaml-based MirageOS unikernel, resulting in minimal performance degradation.

We present Fiat, a library for the Coq proof assistant supporting refinement of declarative specifications into efficient functional programs with a high degree of automation. Each refinement process leaves a proof trail, checkable by the normal Coq kernel, justifying its soundness. We focus on the synthesis of abstract data types that package methods with private data. We demonstrate the utility of our framework by applying it to the synthesis of query structures -- abstract data types with SQL-like query and insert operations. Fiat includes a library for writing specifications of query structures in SQL-inspired notation, expressing operations over relations (tables) in terms of mathematical sets. This library includes a suite of tactics for automating the refinement of specifications into efficient, correct-by-construction OCaml code. Using these tactics, a programmer can generate such an implementation completely automatically by only specifying the equivalent of SQL indexes, data structures capturing useful views of the abstract data. Throughout we speculate on the new programming modularity possibilities enabled by an automated refinement system with proved-correct rules.