From Strong Amalgamability to Modularity of Quantifier-Free Interpolation

The use of interpolants in verification is gaining more and more importance. Sincetheories used in applications are usually obtained as (disjoint) combinations of simplertheories, it is important to modularly re-use interpolation algorithms for the componenttheories. 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, identify a sufficientcondition, and design a combined quantifier-free interpolation algorithm capable of han-dling both convex and non-convex theories, that subsumes and extends most existing workon combined interpolation.