Verifying Spatial Properties of Array Computations

Arrays computations are at the core of numerical modelling and computational science applications. However, low-level manipulation of array indices is a source of program error. Many practitioners are aware of the need to ensure program correctness, yet very few of the techniques from the programming research community are applied by scientists. We aim to change that by providing targetted lightweight verification techniques for scientific code. We focus on the all too common mistake of array offset errors as a generalisation of off-by-one errors. Firstly, we report on a code analysis study on eleven real-world computational science code base, identifying common idioms of array usage and their spatial properties. This provides much needed data on array programming idioms common in scientific code. From this data, we designed a lightweight declarative specification language capturing the majority of array access patterns via a small set of combinators. We detail a semantic model, and the design and implementation of a verification tool for our specification language, which both checks and infers specifications. We evaluate our tool on our corpus of scientific code and give verification case studies of bug fixes that are detected by our approach. We found roughly 80,000 targets for specification across roughly 1.4 million lines of code, showing that the vast majority of array computations read from arrays in a pattern with a simple, regular, static shape.