Ground interpolation for the theory of equality

TL;DR

This paper introduces a new method for computing ground interpolants in the theory of equality using colored congruence graphs, resulting in simpler and smaller interpolants compared to existing tools.

Contribution

It presents a novel graph-based approach for interpolation in the theory of equality, leveraging congruence graphs and a generic interpolation game framework.

Findings

Interpolants are simpler and smaller than those from other tools.

The method produces interpolants as conjunctions of Horn clauses.

A generic interpolation game framework is proposed for various theories.

Abstract

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence graphs representing derivations in that theory. These graphs can be produced by conventional congruence closure algorithms in a straightforward manner. By working with graphs, rather than at the level of individual proof steps, we are able to derive interpolants that are pleasingly simple (conjunctions of Horn clauses) and smaller than those generated by other tools. Our interpolation method can be seen as a theory-specific implementation of a cooperative interpolation game between two provers. We present a generic version of the interpolation game, parametrized by the theory T, and define a general method to extract runs of the game from proofs in T and then generate interpolants from these runs.