We study the dynamic software update problem for programs interacting with an environment that is not necessarily updated. We argue that such updates should be backward compatible. We propose a general definition of backward compatibility and cases of backward compatible program update. Based on our detailed study of real world program evolution, we propose classes of backward compatible update for interactive programs, which are included at an average of 32% of all studied program changes. The definitions of update classes are parameterized by our novel framework of program equivalence, which generalizes existing results on program equivalence to non-terminating executions. Our study of backward compatible updates is based on a typed extension of W language.