Model Finding for Recursive Functions in SMT

SMT solvers have recently been extended with techniques for finding models in presence of universally quantified formulas in some restricted fragments. This paper introduces a translation which reduces axioms specifying a large class of recursive functions, including well-founded (terminating) functions, to universally quantified formulas for which these techniques are applicable. An empirical evaluation confirms that the approach improves the performance of existing solvers on benchmarks from three sources. The translation is implemented as a preprocessor in the CVC4 solver and in a new higher-order model finder called Nunchaku.