Verifying the correctness of a program using an interactive proof assistant involves first defining in the proof assistant the semantics of the involved programming language. Once mechanized, the semantics serves as the basis for the whole proof development, as it is referred to by all subsequent theorems. Traditionally, semantic judgments are mechanized using recursive inductive predicates, matching the pen-and-paper inference rules of operational semantics. However, the shape of these judgments may make proof engineering and maintenance tedious, requiring complex proof automation frameworks. This problem is especially acute when iterating during the language design period.

Abstract Legal expert systems routinely rely on date computations to determine the eligibility of a citizen to social benefits or whether an application has been filed on time. Unfortunately, date arithmetic exhibits many corner cases, which are handled differently from one library to the other, making faithfully transcribing the law into code error-prone, and possibly leading to heavy financial and legal consequences for users. In this work, we aim to provide a solid foundation for date arithmetic working on days, months and years. We first present a novel, formal semantics for date computations, and formally establish several semantic properties through a mechanization in the F $$^\star $$ ⋆ proof assistant. Building upon this semantics, we then propose a static analysis by abstract interpretation to automatically detect ambiguities in date computations. We finally integrate our approach in the Catala language, a recent domain-specific language for formalizing computational law, and use it to analyze the Catala implementation of the French housing benefits, leading to the discovery of several date-related ambiguities.

In France, income tax is computed from taxpayers' individual returns, using an algorithm that is authored, designed and maintained by the French Public Finances Directorate (DGFiP). This algorithm relies on a legacy custom language and compiler originally designed in 1990, which unlike French wine, did not age well with time. Owing to the shortcomings of the input language and the technical limitations of the compiler, the algorithm is proving harder and harder to maintain, relying on ad-hoc behaviors and workarounds to implement the most recent changes in tax law. Competence loss and aging code also mean that the system does not benefit from any modern compiler techniques that would increase confidence in the implementation.

Steel is a language for developing and proving concurrent programs embedded in F ⋆ , a dependently typed programming language and proof assistant. Based on SteelCore, a concurrent separation logic (CSL) formalized in F ⋆ , our work focuses on exposing the proof rules of the logic in a form that enables programs and proofs to be effectively co-developed. Our main contributions include a new formulation of a Hoare logic of quintuples involving both separation logic and first-order logic, enabling efficient verification condition (VC) generation and proof discharge using a combination of tactics and SMT solving. We relate the VCs produced by our quintuple system to solving a system of associativity-commutativity (AC) unification constraints and develop tactics to (partially) solve these constraints using AC-matching modulo SMT-dischargeable equations. Our system is fully mechanized and implemented in F ⋆ . We evaluate it by developing several verified programs and libraries, including various sequential and concurrent linked data structures, proof libraries, and a library for 2-party session types. Our experience leads us to conclude that our system enables a mixture of automated and interactive proof, making it productive to build programs foundationally verified against a highly expressive, state-of-the-art CSL.

Law at large underpins modern society, codifying and governing many aspects of citizens' daily lives. Oftentimes, law is subject to interpretation, debate and challenges throughout various courts and jurisdictions. But in some other areas, law leaves little room for interpretation, and essentially aims to rigorously describe a computation, a decision procedure or, simply said, an algorithm. Unfortunately, prose remains a woefully inadequate tool for the job. The lack of formalism leaves room for ambiguities; the structure of legal statutes, with many paragraphs and sub-sections spread across multiple pages, makes it hard to compute the intended outcome of the algorithm underlying a given text; and, as with any other piece of poorly-specified critical software, the use of informal, natural language leaves corner cases unaddressed. We introduce Catala, a new programming language that we specifically designed to allow a straightforward and systematic translation of statutory law into an executable implementation. Notably, Catala makes it natural and easy to express the general case / exceptions logic that permeates statutory law. Catala aims to bring together lawyers and programmers through a shared medium, which together they can understand, edit and evolve, bridging a gap that too often results in dramatically incorrect implementations of the law. We have implemented a compiler for Catala, and have proven the correctness of its core compilation steps using the F* proof assistant. We evaluate Catala on several legal texts that are algorithms in disguise, notably section 121 of the US federal income tax and the byzantine French family benefits; in doing so, we uncover a bug in the official implementation of the French benefits. We observe as a consequence of the formalization process that using Catala enables rich interactions between lawyers and programmers, leading to a greater understanding of the original legislative intent, while producing a correct-by-construction executable specification reusable by the greater software ecosystem. Doing so, Catala increases trust in legal institutions, and mitigates the risk of societal damage due to incorrect implementations of the law.

Much recent research has been devoted to modeling effects within type theory. Building on this work, we observe that effectful type theories can provide a foundation on which to build semantics for more complex programming constructs and program logics, extending the reasoning principles that apply within the host effectful type theory itself. Concretely, our main contribution is a semantics for concurrent separation logic (CSL) within the F ⋆ proof assistant in a manner that enables dependently typed, effectful F ⋆ programs to make use of concurrency and to be specified and verified using a full-featured, extensible CSL. In contrast to prior approaches, we directly derive the partial-correctness Hoare rules for CSL from the denotation of computations in the effectful semantics of non-deterministically interleaved atomic actions. Demonstrating the flexibility of our semantics, we build generic, verified libraries that support various concurrency constructs, ranging from dynamically allocated, storable spin locks, to protocol-indexed channels. We conclude that our effectful semantics provides a simple yet expressive basis on which to layer domain-specific languages and logics for verified, concurrent programming.

After suffering decades of high-profile attacks, the need for formal verification of security-critical software has never been clearer. Verification-oriented programming languages like F* are now being used to build high-assurance cryptographic libraries and implementations of standard protocols like TLS. In this paper, we seek to apply these verification techniques to modern Web applications, like WhatsApp, that embed sophisticated custom cryptographic components. The problem is that these components are often implemented in JavaScript, a language that is both hostile to cryptographic code and hard to reason about. So we instead target WebAssembly, a new instruction set that is supported by all major JavaScript runtimes. We present a new toolchain that compiles Low*, a low-level subset of the F* programming language, into WebAssembly. Unlike other WebAssembly compilers like Emscripten, our compilation pipeline is focused on compactness and auditability: we formalize the full translation rules in the paper and implement it in a few thousand lines of OCaml. Using this toolchain, we present two case studies. First, we build WHACL*, a WebAssembly version of the existing, verified HACL* cryptographic library. Then, we present LibSignal*, a brand new, verified implementation of the Signal protocol in WebAssembly, that can be readily used by messaging applications like WhatsApp, Skype, and Signal.