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The Relationship between Craig Interpolation and Recursion-Free Horn Clauses

Despite decades of research, there are still a number of concepts commonly found in software programs that are considered challenging for verification: among others, such concepts include concurrency, and the compositional analysis of programs with procedures. As a promising direction to overcome such difficulties, recently the use of Horn constraints as intermediate representation of software programs has been proposed. Horn constraints are related to Craig interpolation, which is one of the main techniques used to construct and refine abstractions in verification, and to synthesise inductive loop invariants. We give a survey of the different forms of Craig interpolation found in literature, and show that all of them correspond to natural fragments of (recursion-free) Horn constraints. We also discuss techniques for solving systems of recursion-free Horn constraints.