Abstract interpretation over non-deterministic finite tree automate for set-based analysis of logic programs

Set-based program analysis has many potential applications, including compiler optimisations, type-checking, debugging, verification and planning. One method of set-based analysis is to solve a set of {\it set constraints} derived directly from the program text. Another approach is based on abstract interpretation (with widening) over an infinite-height domain of regular types. Up till now only deterministic types have been used in abstract interpretations, whereas solving set constraints yields non-deterministic types, which are more precise. It was pointed out by Cousot and Cousot that set constraint analysis of a particular program $P$ could be understood as an abstract interpretation over a finite domain of regular tree grammars, constructed from $P$. In this paper we define such an abstract interpretation for logic programs, formulated over a domain of non-deterministic finite tree automata, and describe its implementation. Both goal-dependent and goal-independent analysis are considered. Variations on the abstract domains operations are introduced, and we discuss the associated tradeoffs of precision and complexity. The experimental results indicate that this approach is a practical way of achieving the precision of set-constraints in the abstract interpretation framework.