Liam O'Connor

Rewriting is a versatile and powerful technique used in many domains. Strategic rewriting allows programmers to control the application of rewrite rules by composing individual rewrite rules into complex rewrite strategies. These strategies are semantically complex, as they may be nondeterministic, they may raise errors that trigger backtracking, and they may not terminate. Given such semantic complexity, it is necessary to establish a formal understanding of rewrite strategies and to enable reasoning about them in order to answer questions like: How do we know that a rewrite strategy terminates? How do we know that a rewrite strategy does not fail because we compose two incompatible rewrites? How do we know that a desired property holds after applying a rewrite strategy? In this paper, we introduce Shoggoth: a formal foundation for understanding, analysing and reasoning about strategic rewriting that is capable of answering these questions. We provide a denotational semantics of System S, a core language for strategic rewriting, and prove its equivalence to our big-step operational semantics, which extends existing work by explicitly accounting for divergence. We further define a location-based weakest precondition calculus to enable formal reasoning about rewriting strategies, and we prove this calculus sound with respect to the denotational semantics. We show how this calculus can be used in practice to reason about properties of rewriting strategies, including termination, that they are well-composed, and that desired postconditions hold. The semantics and calculus are formalised in Isabelle/HOL and all proofs are mechanised.

Systems programmers need fine-grained control over the memory layout of data structures, both to produce performant code and to comply with well-defined interfaces imposed by existing code, standardised protocols or hardware. Code that manipulates these low-level representations in memory is hard to get right. Traditionally, this problem is addressed by the implementation of tedious marshalling code to convert between compiler-selected data representations and the desired compact data formats. Such marshalling code is error-prone and can lead to a significant runtime overhead due to excessive copying. While there are many languages and systems that address the correctness issue, by automating the generation and, in some cases, the verification of the marshalling code, the performance overhead introduced by the marshalling code remains. In particular for systems code, this overhead can be prohibitive. In this work, we address both the correctness and the performance problems. We present a data layout description language and data refinement framework, called Dargent, which allows programmers to declaratively specify how algebraic data types are laid out in memory. Our solution is applied to the Cogent language, but the general ideas behind our solution are applicable to other settings. The Dargent framework generates C code that manipulates data directly with the desired memory layout, while retaining the formal proof that this generated C code is correct with respect to the functional semantics. This added expressivity removes the need for implementing and verifying marshalling code, which eliminates copying, smoothens interoperability with surrounding systems, and increases the trustworthiness of the overall system.