Building Better Bit-Blasting for Floating-Point Problems

An effective approach to handling the theory of floating-point is to reduce it to the theory of bit-vectors. Implementing the required encodings is complex, error prone and requires a deep understanding of floating-point hardware. This paper presents SymFPU, a library of encodings that can be included in solvers. It also includes a verification argument for its correctness, and experimental results showing that its use in CVC4 out-performs all previous tools. As well as a significantly improved performance and correctness, it is hoped this will give a simple route to add support for the theory of floating-point

Database Constraint Enforcement: A Decompositional Approach.

This thesis presents an efficient and integrated approach to integrity constraint checking for advanced database systems. The proposed approach essentially consists of three phases: constraint decomposition, global enforcement strategy and local enforcement tuning. The central theme of this dissertation is the development of constraint decomposition theory, which can be used to decompose each constraint formula into a set of constraint sub-formulas. The constraint sub-formulas derived from the decomposition satisfy the sufficient conditions imposed by the original constraint and are also much simpler and more efficient to check. The decomposition is done only once for each constraint, at the time of its definition. The global enforcement strategies, with the application of decomposition theory, are studied in both sequential and parallel environments. The physical characteristics of the database state is used to determine the checking order or to make assignment of constraint sub-formulas to processing elements. It is shown that the performance of constraint enforcement, with the application of the decomposition theory, is much better than that without the application of the decomposition theory. Local enforcement tuning methods are developed to further simplify each constraint sub-formula derived at constraint decomposition phase. Because of the simplicity of constraint sub-formulas, more efficient and simple methods can be used. Furthermore, more information, such as update types and update data, are available for the purpose of simplification. The fundamental assumption underlying our approach is that most database updates satisfy integrity constaints. A second assumption is that transactions are localized and database updates are nonuniform in their distribution. Based on these assumptions, the proposed approach will achieve a significant performance increase over previous approaches

Mechanising and evolving the formal semantics of WebAssembly: the Web's new low-level language

WebAssembly is the first new programming language to be supported natively by all major Web browsers since JavaScript. It is designed to be a natural low-level compilation target for languages such as C, C++, and Rust, enabling programs written in these languages to be compiled and executed efficiently on the Web. WebAssembly’s specification is managed by the W3C WebAssembly Working Group (made up of representatives from a number of major tech companies). Uniquely, the language is specified by way of a full pen-and-paper formal semantics. This thesis describes a number of ways in which I have both helped to shape the specification of WebAssembly, and built upon it. By mechanising the WebAssembly formal semantics in Isabelle/HOL while it was being drafted, I discovered a number of errors in the specification, drove the adoption of official corrections, and provided the first type soundness proof for the corrected language. This thesis also details a verified type checker and interpreter, and a security type system extension for cryptography primitives, all of which have been mechanised as extensions of my initial WebAssembly mechanisation. A major component of the thesis is my work on the specification of shared memory concurrency in Web languages: correcting and verifying properties of JavaScript’s existing relaxed memory model, and defining the WebAssembly-specific extensions to the corrected model which have been adopted as the basis of WebAssembly’s official threads specification. A number of deficiencies in the original JavaScript model are detailed. Some errors have been corrected, with the verified fixes officially adopted into subsequent editions of the language specification. However one discovered deficiency is fundamental to the model, an instance of the well-known "thin-air problem". My work demonstrates the value of formalisation and mechanisation in industrial programming language design, not only in discovering and correcting specification errors, but also in building confidence both in the correctness of the language’s design and in the design of proposed extensions.2019 Google PhD Fellowship in Programming Technology and Software Engineering Peterhouse Research Fellowshi

Portable Inter-workgroup Barrier Synchronisation for GPUs

Despite the growing popularity of GPGPU programming, there is not yet a portable and formally-specified barrier that one can use to synchronise across workgroups. Moreover, the occupancy-bound execution model of GPUs breaks assumptions inherent in traditional software execution barriers, exposing them to deadlock. We present an occupancy discovery protocol that dynamically discovers a safe estimate of the occupancy for a given GPU and kernel, allowing for a starvation-free (and hence, deadlock-free) inter-workgroup barrier by restricting the number of workgroups according to this estimate. We implement this idea by adapting an existing, previously non-portable, GPU inter-workgroup barrier to use OpenCL 2.0 atomic operations, and prove that the barrier meets its natural specification in terms of synchronisation. We assess the portability of our approach over eight GPUs spanning four vendors, comparing the performance of our method against alternative methods. Our key findings include: (1) the recall of our discovery protocol is nearly 100%; (2) runtime comparisons vary substantially across GPUs and applications; and (3) our method provides portable and safe inter-workgroup synchronisation across the applications we study

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing