We present MiningZinc, a novel system for constraint-based pattern mining. It provides a declarative approach to data mining, where a user specifies a problem in terms of constraints and the system employs advanced techniques to efficiently find solutions. Declarative programming and modeling are common in artificial intelligence and in database systems, but not so much in data mining; by building on ideas from these communities, MiningZinc advances the state-of-the-art of declarative data mining significantly. Key components of the MiningZinc system are (1) a high-level and natural language for formalizing constraint-based itemset mining problems in models, and (2) an infrastructure for executing these models, which supports both specialized mining algorithms as well as generic constraint solving systems. A use case demonstrates the generality of the language, as well as its flexibility towards adding and modifying constraints and data, and the use of different solution methods.