Certified Interpolant Generation for EUF

Logical interpolants have found a wide array of applications in automated verification, including symbolic model checking and predicate abstraction. It is often critical to these applications that reported interpolants exhibit desired properties, correctness being first and foremost. In this paper, we introduce a method in which interpolants are computed by type inference within the trusted core of a proof checker. Interpolants produced this way from a proof of the joint unsatisfiability of two formulas are certified as correct by construction. We focus our attention to the quantifier-free theory of equality and uninterpreted functions (EUF) and present an interpolant generating proof calculus that can be encoded in the LFSC proof checking framework with limited reliance upon computational side conditions. Our experimental results show that our method generates certified interpolants with small overhead with respect to solving.