Today's large-scale computations, e.g., in the Cloud, are subject to a multitude of risks concerning the divulging and ownership of private data. Privacy risks are mainly addressed using a large variety of encryption-based techniques. However, these are costly to operate, lead to large aggregates of data that are highly valuable attack targets and do not allow to flexibly handle subsets of such aggregates. Furthermore, today's computations have to ensure privacy properties in the context over highly variable and complex software compositions; however, no general support for the declarative definition and implementation of privacy-preserving applications has been put forward. In this article, we present a compositional approach to the declarative and correct composition of privacy-preserving applications in the Cloud. Our approach provides language support for the compositional definition of encryption- and fragmentation-based privacy-preserving algorithms. This language comes equipped with a set of laws that allows us to verify privacy properties. Finally, we introduce implementation support in Scala that ensures certain privacy properties by construction using advanced features of Scala's type system.