Lingva: Generating and Proving Program Properties Using Symbol Elimination

Dragan, Ioan; Kovács, Laura

doi:10.1007/978-3-662-46823-4_6

Cited by 4 publications

(21 citation statements)

References 13 publications

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“…Our work uses symbol elimination and consequence nding in Vampire and extends Vampire with a new framework for reasoning about loops. Compared to the earlier implementation [6] of invariant generation in Vampire, our tool is independent of the language in which the loops are expressed, simplies symbol elimination in saturation theorem proving, and provides various ways to generate a relevant set of loop invariants. The overall workow of our tool is given in Figure 1 Input.…”

Section: Invariant Generation In Vampirementioning

confidence: 99%

“…Formulas in L extd that are valid at any loop iteration are called extended loop properties. Compared to [6], we simplied L extd as we do not use extended expressions describing loop iteration properties or update predicates over arrays. Figure 2, the following formula describing a monotonically increasing behavior of k is one of the generated properties:…”

Section: Invariant Generation In Vampirementioning

confidence: 99%

“…Symbol elimination allows the generation of quantied invariants, possibly with quantier alternations, for programs with unbounded data structures, such as arrays. While experiments of invariant generation in Vampire show that symbol elimination generates non-trivial invariants, the initial implementation [6] of program analysis and invariant generation in Vampire has various disadvantages: it can only be used with programs written in C, the number of generated invariants is too large, and generating relevant invariants did not take This work was partially supported by the Wallenberg Academy Fellowship 2014, the Swedish VR grant D0497701 and the Austrian research project FWF S11409-N23.…”

Section: Introductionmentioning

confidence: 99%

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Reasoning About Loops Using Vampire in KeY

Ahrendt

Kovács

Robillard

2015

Logic for Programming, Artificial Intelligence, and Reasoning

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We describe symbol elimination and consequence nding in the rst-order theorem prover Vampire for automatic generation of quantied invariants, possibly with quantier alternations, of loops with arrays. Unlike the previous implementation of symbol elimination in Vampire, our work is not limited to a specic programming language but provides a generic framework by relying on a simple guarded command representation of the input loop. We also improve the loop analysis part in Vampire by generating loop properties more easily handled by the saturation engine of Vampire. Our experiments show that, with our changes, the number of generated invariants is decreased, in some cases, by a factor of 20. We also provide a framework to use our approach to invariant generation in conjunction with pre-and post-conditions of program loops. We use the program specication to nd relevant invariants as well as to verify the partial correctness of the loop. As a case study, we demonstrate how symbol elimination in Vampire can be used as an interface for realistic imperative languages, by integrating our tool in the KeY verication system, thus allowing reasoning about loops in Java programs in a fully automated way, without any user guidance.

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Section: Invariant Generation In Vampirementioning

confidence: 99%

Section: Invariant Generation In Vampirementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reasoning About Loops Using Vampire in KeY

Ahrendt

Kovács

Robillard

2015

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

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“…Our approach is not constrained to the inference of invariants of a given shape, in contrast with the approach of [25]. We can handle program with any control-flow structure, as opposed to [17], and we exploit SMT-based interpolating procedures for the refinement of inductive invariant: this differentiates our work from those exploiting first-order theorem provers [24]. In contrast to [19], our approach is not based on machine-learning.…”

Section: Related Workmentioning

confidence: 99%

“…The approach presented here can infer invariants like (1) completely automatically, and can successfully verify many programs with arrays that are still out of reach for state-ofthe-art software model-checkers (e.g., [7,11,14,16,17,19]). …”

Section: Introductionmentioning

confidence: 99%

Polyhedra to the rescue of array interpolants

Alberti

Monniaux

2015

Proceedings of the 30th Annual ACM Symposium on Applied Computing

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We propose a new approach to the automated verification of the correctness of programs handling arrays. An abstract interpreter supplies auxiliary numeric invariants to an interpolation-based refinement procedure suited to array programs. Experiments show that this combination approach, implemented in an enhanced version of the Booster software model-checker, performs better than the pure interpolation-based approach, at no additional cost.

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A First Class Boolean Sort in First-Order Theorem Proving and TPTP

Kotelnikov

Kovács

Воронков

2015

Lecture Notes in Computer Science

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To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem provers can be used to prove program properties efficiently. However, in the TPTP language, the input language of automated first-order theorem provers, the use of the boolean sort is limited compared to other sorts, thus hindering the use of first-order theorem provers in program analysis and verification. In this paper, we present an extension FOOL of many-sorted first-order logic, in which the boolean sort is treated as a first-class sort. Boolean terms are indistinguishable from formulas and can appear as arguments to functions. In addition, FOOL contains if-then-else and let-in constructs. We define the syntax and semantics of FOOL and its model-preserving translation to first-order logic. We also introduce a new technique of dealing with boolean sorts in superposition-based theorem provers. Finally, we discuss how the TPTP language can be changed to support FOOL

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Lingva: Generating and Proving Program Properties Using Symbol Elimination

Cited by 4 publications

References 13 publications

Reasoning About Loops Using Vampire in KeY

Reasoning About Loops Using Vampire in KeY

Polyhedra to the rescue of array interpolants

A First Class Boolean Sort in First-Order Theorem Proving and TPTP

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