Clauses and subgoals in a Datalog program can be given in any order without affecting program meaning. However, practical applications of the language require the use of built-in or external predicates with particular dataflow requirements. These can be expressed as input or output "modes" on arguments. We describe a static analysis of moding for Datalog which calculates how to transform an ill-moded program into a well-moded program by reordering clause subgoals to satisfy dataflow requirements. We describe an incremental algorithm which efficiently finds a reordering if it exists. This frees the programmer to focus on the declarative specification of a program rather than implementation details of external predicates. We prove that our computed reorderings yield well-moded programs (soundness) and if a program can be made well-moded, then we compute a reordering to do so (completeness).

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. Using the inference mode, we found roughly 87,000 targets for specification across roughly 1.1 million lines of code, showing that the vast majority of array computations read from arrays in a pattern with a simple, regular, static shape. We also studied the commit logs of one of our corpus packages, finding past bug fixes for which our specification system distinguishes the change and thus could have been applied to detect such bugs.