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Linked Open Data (LOD) sources on the Web are increasingly becoming a mainstream method to publish and consume data. For real-life applications, mechanisms to describe the structure of the data and to provide guarantees are needed, as recently emphasized by the W3C in its Data Shape Working Group. Using such mechanisms, data providers will be able to validate their data, assuring that it is structured in a way expected by data consumers. In turn, data consumers can design and optimize their applications to match the data format to be processed. In this paper, we present several crucial aspects of RDD, our language for expressing RDF constraints. We introduce the formal semantics and describe how RDD constraints can be translated into SPARQL for constraint checking. Based on our fully working validator, we evaluate the feasibility and efficiency of this checking process using two popular, state-of-the-art RDF triple stores. The results indicate that even a naive implementation of RDD based on SPARQL 1.0 will incur only a moderate overhead on the RDF loading process, yet some constraint types contribute an outsize share and scale poorly. Incorporating several preliminary optimizations, some of them based on SPARQL 1.1, we provide insights on how to overcome these limitations.