Towards Static Analysis of Functional Programs using Tree Automata Completion

This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of terms reachable by a rewriting relation. The completion algorithm we focus on is parameterized by a set \(E\) of equations controlling the precision of the approximation and influencing its termination. For completion to be used as a static analysis, the first step is to guarantee its termination. In this work, we thus give a sufficient condition on \(E\) and \(\mathcal{T(F)}\) for completion algorithm to always terminate. In the particular setting of functional programs, this condition can be relaxed into a condition on \(E\) and \(\mathcal{T(C)}\) (terms built on the set of constructors) that is closer to what is done in the field of static analysis, where abstractions are performed on data.

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