Our starting point is set-based program analysis. In logic or functional programs, this analysis produces a recursive description of the set of terms corresponding to each variable in the program. This has many potential applications, including compiler optimisations, program specialisation, type-checking, debugging, verification and planning. We present a new practical algorithm for computing set-based descriptions with different degrees of precision, obtained by an abstract interpretation over non-deterministic tree grammars. Then we outline the abstract domain of tree grammars combined with arithmetic constraints, and discuss the precision and practicality of this extension.