GPU hardware implements a SIMT execution model, where small groups of threads, called subgroups (or warps in CUDA), execute synchronously. Languages expose this through high-performance subgroup-level APIs. However, providing precise subgroup semantics in languages is challenging, as compilers may transform the program, potentially disrupting source-level synchronous behavior even if the hardware is synchronous. As a result, no GPU programming language provides rigorous semantics for subgroup execution. In this work, we present SIMT-Step, a formal and flexible operational semantics for subgroup execution. At its core is a new semantic object, dynamic basic blocks, which enables precise specification of converged subgroup execution. SIMT-Step then provides flexibility for the execution of instructions, which can be collective, synchronous, or independent. We propose several candidate instantiations of SIMT-Step and design a suite of idiomatic tests to distinguish them, highlighting counter-intuitive behavior that arises under relaxed variants. We implement SIMT-Step in TLA+ and validate the behavior of the idiomatic tests, all of which can be verified in under one second. Finally, to investigate how closely SIMT-Step models real-world GPU behavior, we conduct a large fuzzing campaign, spanning nine GPUs and seven vendors. Our results show that, despite hesitancy to provide guarantees in official specifications, most GPUs exhibit strongly synchronous behavior. Combined, these contributions provide both a theoretical foundation and practical tools for reasoning about subgroup semantics in GPU programming languages.

We introduce Kuiper, a language for safe and verified efficient CPU/GPU programming embedded as an extensible library within the F* dependently typed language. We rely on F*’s support for dependent types and its associated Pulse concurrent separation logic to develop a program logic in which to prove CPU/GPU programs safe, data-race free, and functionally correct. Our model of the GPU includes several intricacies, including the memory hierarchy, kernel launches, and synchronization within a single comprehensive framework. To do so, we extend the Pulse program logic with a novel notion of located resources and a new connective to structure reasoning about massively parallel programs, and present new proof rules to lift the per-thread view of GPU kernels to an end-to-end correctness specification. We have used Kuiper to program and prove correct a variety of GPU kernels, including full functional correctness proofs of an optimized matrix multiplication using two levels of block tiling and tensor cores. In doing so, we have developed a range of libraries to enable programs and proofs at a high level of abstraction but without imposing any runtime overhead. These allow Kuiper programs to be polymorphic (over types, operations, memory layout, and more) and compile to efficient, specialized CUDA code, while enabling a novel form of verified auto-tuning. Our experimental evaluation confirms that Kuiper programs match the performance of their handwritten CUDA counterparts and are competitive with closed source, state-of-the-art kernels in cuBLAS.

Project Everest began at Microsoft Research in 2016, aiming to spur research in program verification to produce industrial-grade software. In collaboration with INRIA and Carnegie Mellon University, Project Everest’s goal was to produce drop-in verified replacements of secure communications software used in the HTTPS ecosystem, including TLS, the underlying cryptography, and related subprotocols. Now, almost a decade later, we reflect on the project, sharing both its successes and failures, and look ahead to the next decade of program verification research.

Incorrect handling of security-critical data formats, particularly in low-level languages, are the root cause of many security vulnerabilities. Provably correct parsing and serialization tools that target languages like C can help. Towards this end, we present PulseParse, a library of verified parser and serializer combinators for non-malleable binary formats. Specifications and proofs in PulseParse are in separation logic, offering a more abstract and compositional interface, with full support for data validation, parsing, and serialization. PulseParse also supports a class of recursive formats---with a focus on security and handling adversarial inputs, we show how to parse such formats with only a constant amount of stack space.

We introduce SecRef ★ , a secure compilation framework protecting stateful programs verified in F ★ against linked unverified code, with which the program dynamically shares ML-style mutable references. To ease program verification in this setting, we track which references are shareable with the unverified code, and which ones are not shareable and whose contents are thus guaranteed to be unchanged after calling into unverified code. This universal property of non-shareable references is exposed in the interface on which the verified program can rely when calling into unverified code. The remaining refinement types and pre- and post-conditions that the verified code expects from the unverified code are converted into dynamic checks about the shared references by using higher-order contracts. We prove formally in F ★ that this strategy ensures sound and secure interoperability with unverified code. Since SecRef ★ is built on top of the Monotonic State effect of F ★ , these proofs rely on the first monadic representation for this effect, which is a contribution of our work that can be of independent interest. Finally, we use SecRef ★ to build a simple cooperative multi-threading scheduler that is verified and that securely interacts with unverified threads.

PulseCore is a new program logic suitable for intrinsic proofs of higher-order, stateful, concurrent, dependently typed programs. It provides many of the features of a modern, concurrent separation logic, including dynamically allocated impredicative invariants, higher-order ghost state, step-indexing with later credits, and support for user-defined ghost state constructions. PulseCore is developed foundationally within the F ⋆ programming language with fully mechanized proofs, and is applicable to F ⋆ programs itself. To evaluate our work, we use Pulse , a surface language within F ⋆ for PulseCore , to develop a range of program proofs. Illustrating its suitability for proving higher-order concurrent programs, we present a verified library for task pools in the style of OCaml5, together with some verified task-parallel programs. Next, we present various data structures and synchronization primitives, including a barrier that requires the use of higher-order ghost state. Finally, we present a verified implementation of the DICE Protection Environment, an industry standard secure boot protocol. Taken together, our evaluation consists of more than 31,000 lines of verified code in a range of settings, providing evidence that PulseCore is both highly expressive as well as practical for a variety of program proof applications.

We introduce SCIO ⋆ , a formally secure compilation framework for statically verified programs performing input-output (IO). The source language is an F ⋆ subset in which a verified program interacts with its IO-performing context via a higher-order interface that includes refinement types as well as pre- and post-conditions about past IO events. The target language is a smaller F ⋆ subset in which the compiled program is linked with an adversarial context that has an interface without refinement types, pre-conditions, or concrete post-conditions. To bridge this interface gap and make compilation and linking secure we propose a formally verified combination of higher-order contracts and reference monitoring for recording and controlling IO operations. Compilation uses contracts to convert the logical assumptions the program makes about the context into dynamic checks on each context-program boundary crossing. These boundary checks can depend on information about past IO events stored in the state of the monitor. But these checks cannot stop the adversarial target context before it performs dangerous IO operations. Therefore linking in SCIO ⋆ additionally forces the context to perform all IO actions via a secure IO library, which uses reference monitoring to dynamically enforce an access control policy before each IO operation. We prove in F ⋆ that SCIO ⋆ soundly enforces a global trace property for the compiled verified program linked with the untrusted context. Moreover, we prove in F ⋆ that SCIO ⋆ satisfies by construction Robust Relational Hyperproperty Preservation, a very strong secure compilation criterion. Finally, we illustrate SCIO ⋆ at work on a simple web server example.

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.

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.

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.

This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism between a computational monad and a specification monad gives rise to a Dijkstra monad, which provides great flexibility for obtaining Dijkstra monads tailored to the verification task at hand. We moreover show that a large variety of specification monads can be obtained by applying monad transformers to various base specification monads, including predicate transformers and Hoare-style pre- and postconditions. For defining correct monad transformers, we propose a language inspired by Moggi's monadic metalanguage that is parameterized by a dependent type theory. We also develop a notion of algebraic operations for Dijkstra monads, and start to investigate two ways of also accommodating effect handlers. We implement our framework in both Coq and F*, and illustrate that it supports a wide variety of verification styles for effects such as exceptions, nondeterminism, state, input-output, and general recursion.

Dijkstra monads enable a dependent type theory to be enhanced with support for specifying and verifying effectful code via weakest preconditions. Together with their closely related counterparts, Hoare monads, they provide the basis on which verification tools like F*, Hoare Type Theory (HTT), and Ynot are built. We show that Dijkstra monads can be derived "for free" by applying a continuation-passing style (CPS) translation to the standard monadic definitions of the underlying computational effects. Automatically deriving Dijkstra monads in this way provides a correct-by-construction and efficient way of reasoning about user-defined effects in dependent type theories. We demonstrate these ideas in EMF*, a new dependently typed calculus, validating it via both formal proof and a prototype implementation within F*. Besides equipping F* with a more uniform and extensible effect system, EMF* enables a novel mixture of intrinsic and extrinsic proofs within F*.