Ground interpolation for the theory of equality
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.