## Section: New Results

### Static analysis of functional programs using tree automata and term rewriting

Participants : Thomas Genet, Yann Salmon.

We develop a specific theory and the related tools for analyzing programs whose semantics is defined using term rewriting systems. The analysis principle is based on regular approximations of infinite sets of terms reachable by rewriting. The tools we develop use, so-called, Tree Automata Completion to compute a tree automaton recognizing a superset of all reachable terms. This over-approximation is then used to prove properties on the program by showing that some “bad” terms, encoding dangerous or problematic configurations, are not in the superset and thus not reachable. This is a specific form of, so-called, Regular Tree Model Checking. Now, we aim at applying this technique to the static analysis of programming languages whose semantics is based on terms, like functional programming languages. We already shown that static analysis of first order functional programs with a call-by-value evaluation strategy can be automated using tree automata completion [22] . This is the subject of the PhD thesis Yann Salmon has defended [11] . Now, one of the objective is to lift those results to the static analysis of higher-order functions.