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We consider a new perspective on dialog state tracking (DST), the task of estimating a user's goal through the course of a dialog. By formulating DST as a semantic parsing task over hierarchical representations, we can incorporate semantic compositionality, cross-domain knowledge sharing and co-reference. We present TreeDST, a dataset of 27k conversations annotated with tree-structured dialog states and system acts. We describe an encoder-decoder framework for DST with hierarchical representations, which leads to 20% improvement over state-of-the-art DST approaches that operate on a flat meaning space of slot-value pairs.