Deep neural networks for natural language processing tasks are vulnerable to adversarial input perturbations. In this paper, we present a versatile language for programmatically specifying string transformations---e.g., insertions, deletions, substitutions, swaps, etc.---that are relevant to the task at hand. We then present an approach to adversarially training models that are robust to such user-defined string transformations. Our approach combines the advantages of search-based techniques for adversarial training with abstraction-based techniques. Specifically, we show how to decompose a set of user-defined string transformations into two component specifications, one that benefits from search and another from abstraction. We use our technique to train models on the AG and SST2 datasets and show that the resulting models are robust to combinations of user-defined transformations mimicking spelling mistakes and other meaning-preserving transformations.