SPARQL CONSTRUCT queries allow for the specification of data processing pipelines that transform given input graphs into new output graphs. It is now common to constrain graphs through SHACL shapes allowing users to understand which data they can expect and which not. However, it becomes challenging to understand what graph data can be expected at the end of a data processing pipeline without knowing the particular input data: Shape constraints on the input graph may affect the output graph, but may no longer apply literally, and new shapes may be imposed by the query template. In this paper, we study the derivation of shape constraints that hold on all possible output graphs of a given SPARQL CONSTRUCT query. We assume that the SPARQL CONSTRUCT query is fixed, e.g., being part of a program, whereas the input graphs adhere to input shape constraints but may otherwise vary over time and, thus, are mostly unknown. We study a fragment of SPARQL CONSTRUCT queries (SCCQ) and a fragment of SHACL (Simple SHACL). We formally define the problem of deriving the most restrictive set of Simple SHACL shapes that constrain the results from evaluating a SCCQ over any input graph restricted by a given set of Simple SHACL shapes. We propose and implement an algorithm that statically analyses input SHACL shapes and CONSTRUCT queries and prove its soundness and complexity.

Quantitative studies on the border between Mining Software Repository (MSR) and Empirical Software Engineering (ESE) apply data analysis methods, like regression modeling, statistic tests or correlation analysis, to commits or pulls to better understand the software development process. Such studies assure the validity of the reported results by following a sound methodology. However, with increasing complexity, parts of the methodology can still go wrong. This may result in MSR/ESE studies with undetected threats to validity. In this paper, we propose to systematically protect against threats by operationalizing their treatment using simulations. A simulation substitutes observed and unobserved data, related to an MSR/ESE scenario, with synthetic data, carefully defined according to plausible assumptions on the scenario. Within a simulation, unobserved data becomes transparent, which is the key difference to a real study, necessary to detect threats to an analysis methodology. Running an analysis methodology on synthetic data may detect basic technical bugs and misinterpretations, but it also improves the trust in the methodology. The contribution of a simulation is to operationalize testing the impact of important assumptions. Assumptions still need to be rated for plausibility. We evaluate simulation-based testing by operationalizing undetected threats in the context of four published MSR/ESE studies. We recommend that future research uses such more systematic treatment of threats, as a contribution against the reproducibility crisis.