We present TRANX, a transition-based neural semantic parser that maps natural language (NL) utterances into formal meaning representations (MRs). TRANX uses a transition system based on the abstract syntax description language for the target MR, which gives it two major advantages: (1) it is highly accurate, using information from the syntax of the target MR to constrain the output space and model the information flow, and (2) it is highly generalizable, and can easily be applied to new types of MR by just writing a new abstract syntax description corresponding to the allowable structures in the MR. Experiments on four different semantic parsing and code generation tasks show that our system is generalizable, extensible, and effective, registering strong results compared to existing neural semantic parsers.