Ilinva: Using Abduction to Generate Loop Invariants

Abstract

We describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize inductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large set of programming languages and application domains; and lazy, in the sense that it only generates invariants that allow one to derive the required properties. It relies on an existing system called GPiD for abductive reasoning modulo theories [14], and on the platform for program verification Why3 [16]. Experiments show evidence of the practical relevance of our approach.

Learning to Find Proofs and Theorems by Learning to Refine Search Strategies: The Case of Loop Invariant Synthesis

“…The abduct procedure may itself be nondeterministic and rely on the choose operator internally. The use of abductive reasoning for theorem proving and loop invariant synthesis specifically has been proposed in the past [16,17]. However, abduction is hard [18] and hard to scale in the absence of good heuristics to rank and filter abduction candidates.…”

An Interactive SMT Tactic in Coq using Abductive Reasoning

“…Given a set of formulas H (taken as a conjunction), a goal G, and a theory T , an abduct is a formula ϕ such that (1) H ∧ ϕ is T -satisfiable and (2) H ∧ ϕ |= T G. Abduction has applications in program verification and static analysis, including: loop invariant generation [24,18]; specification inference [36,2]; and compositional analysis [13,19], among others [17,21].…”