Section: New Results

Decision results for solving Horn Clauses with arrays

Participants : Laure Gonnord, Julien Braine.

Many approaches exist for verifying programs operating on Boolean and integer values (e.g. abstract interpretation, counterexample-guided abstraction refinement using interpolants), but transposing them to array properties has been fraught with difficulties. In the context of the Phd of Julien Braine, we propose to work directly on horn clauses, because we think that it is a suitable intermediate representation for verifying programs.

Currently, two techniques strike out to infer very precise quantified invariants on arrays using Horn clauses: a quantifier instantiation method [1] and a cell abstraction method that can be rephrased on Horn clauses. However, the quantifier instantiation method is parametrized by an heuristic and finding a good heuristic is a major challenge, and the cell abstraction method uses an abstract interpretation to completely remove arrays and is limited to linear Horn clauses. We combine these two techniques. We provide an heuristic for the quantifier instantiation method of  [29] by using the ideas from the cell abstraction method of  [48] and discover a requirement such that, when met, the heuristic is complete, that is, there is no loss of information by using that heuristic. Furthermore, we prove that Horn clauses that come from program semantic translation verify the requirement and therefore, we have an optimal instantiation technique for program analysis.

This work is done in collaboration with David Monniaux (Verimag), coadvisor of the PhD of Julien Braine. A journal paper is currently being written for submission early 2020.