WCFG to PCFG Conversion The algorithm of converting a WCFG to its equivalent PCFG is shown in Algorithm 1. Full proof of this equivalence can be found in Smith and Johnson [1]. Proof of the Dynamic Programming for Marginal Inference We prove the correctness of the dynamic programming algorithm for computing the marginal permutation matrix of separable permutations by induction as follows. As a base case, each word (i.e., segment with length 1) is associated with an identity permutation matrix 1 . In the structured reordering module, we compute the scores for BTG production rules using span 2 Figure 1: The detailed architecture of our seq2seq model for semantic parsing (view in color). First, the structured reordering module genearates a (relaxed) permutation matrix given the input utterrance.