Convex polyhedral abstractions, specialisation and property-based predicate splitting in Horn clause verification

TL;DR

This paper introduces a combined approach using convex polyhedral abstract interpretation, predicate specialisation, and refinement via interpolant-driven predicate splitting to improve Horn clause verification.

Contribution

It demonstrates how to effectively integrate abstract interpretation, specialisation, and predicate splitting for enhanced Horn clause analysis, including a novel refinement technique using interpolants.

Findings

Convex polyhedral analysis derives sophisticated invariants.

Predicate splitting improves analysis precision.

Iterative refinement enhances verification success.

Abstract

We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of query-answer transformed clauses, and refinement by splitting predicates. The purpose of the work is to investigate how analysis and transformation tools developed for constraint logic programs (CLP) can be applied to the Horn clause verification problem. Abstract interpretation over convex polyhedra is capable of deriving sophisticated invariants and when used in conjunction with specialisation for propagating constraints it can frequently solve challenging verification problems. This is a contribution in itself, but refinement is needed when it fails, and the question of how to refine convex polyhedral analyses has not been studied much. We present a refinement technique based on interpolants derived from a counterexample trace; these are used to drive a property-based specialisation that splits predicates, leading in turn to more precise convex polyhedral analyses. The process of specialisation, analysis and splitting can be repeated, in a manner similar to the CEGAR and iterative specialisation approaches.