Quantifier-free interpolation in combinations of equality interpolating theories

The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly reuse interpolation algorithms for the component theories. We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the strong (sub-)amalgamation property. Then, we provide an equivalent syntactic characterization and show that such characterization covers most theories commonly employed in verification. Finally, we design a combined quantifier-free interpolation algorithm capable of handling both convex and nonconvex theories; this algorithm subsumes and extends most existing work on combined interpolation