Mining generator patterns has raised great research interest in recent years. The main purpose of mining itemset generators is that they can form equivalence classes together with closed itemsets, and can be used to generate simple classification rules according to the MDL principle. In this paper, we devise an efficient algorithm called StreamGen to mine frequent itemset generators over a stream sliding window. We adopt a novel enumeration tree structure to help keep the information of mined generators and the border between generators and non-generators, and propose some optimization techniques to speed up the mining process. We further extend the algorithm to directly mine a set of high quality classification rules over stream sliding windows while keeping high performance. The extensive performance study shows that our algorithm outperforms other state-of-the-art algorithms which perform similar tasks in terms of both runtime and memory usage efficiency, and has high utility in te...