Verifying Relational Properties of Functional Programs by First-Order Refinement

Asada, Kazuyuki; Satô, Ryôsuke; Kobayashi, Naoki

doi:10.1145/2678015.2682546

Cited by 16 publications

(14 citation statements)

References 30 publications

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“…However, we have seen less focus on leveraging relational specifications themselves to simplify verification tasks, although this varies according to the verification method used. Some efforts do not reason over product programs at all, relying on techniques based on decomposition [3] or customized theories with theorem proving [4,30] instead. To the best of our knowledge, none of these efforts exploit symmetry in programs or in relational specifications.…”

Section: Related Workmentioning

confidence: 99%

“…Representative efforts include those that target general analysis using relational program logics and frameworks [4,5,8,27,31] or specific applications such as security verification [1,7,9], compiler validation [16,32], and differential program analysis [17,19,[21][22][23]. These efforts are supported by tools that range from automatic verifiers to interactive theorem-provers.…”

Section: Introductionmentioning

confidence: 99%

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Exploiting Synchrony and Symmetry in Relational Verification

Pick

Fedyukovich

Gupta

2018

Computer Aided Verification

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Abstract. Relational safety specifications describe multiple runs of the same program or relate the behaviors of multiple programs. Approaches to automatic relational verification often compose the programs and analyze the result for safety, but a naively composed program can lead to difficult verification problems. We propose to exploit relational specifications for simplifying the generated verification subtasks. First, we maximize opportunities for synchronizing code fragments. Second, we compute symmetries in the specifications to reveal and avoid redundant subtasks. We have implemented these enhancements in a prototype for verifying k-safety properties on Java programs. Our evaluation confirms that our approach leads to a consistent performance speedup on a range of benchmarks.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploiting Synchrony and Symmetry in Relational Verification

Pick

Fedyukovich

Gupta

2018

Computer Aided Verification

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“…This line of works is probably the most related to our work, however RHOL improves over all of them, as also shown by some of the embedding we give in Section 6. Another work related to this direction is the one by Asada et al [2016]. This work proposes a technique to reduce relational refinement to standard first order refinements.…”

Section: Introductionmentioning

confidence: 99%

A relational logic for higher-order programs

Aguirre¹,

Barthe²,

Gaboardi³

et al. 2019

J. Funct. Prog.

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Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for reasoning about a broad range of properties, including equivalence and refinement, and specialized notions such as continuity, information flow security, or relative cost. In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. Relational refinement type systems excel at relating structurally equivalent terms but provide limited support for relating terms with very different structures. We present a logic, called relational higher-order logic (RHOL), for proving relational properties of a simply typed λ-calculus with inductive types and recursive definitions. RHOL retains the type-directed flavor of relational refinement type systems but achieves greater expressivity through rules which simultaneously reason about the two terms as well as rules which only contemplate one of the two terms. We show that RHOL has strong foundations, by proving an equivalence with higher-order logic, and leverage this equivalence to derive key meta-theoretical properties: subject reduction, admissibility of a transitivity rule, and set-theoretical soundness. Moreover, we define sound embeddings for several existing relational type systems such as relational refinement types and type systems for dependency analysis and relative cost, and we verify examples that were out of reach of prior work.

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“…Relational properties are useful when reasoning about program refinement, approximation, equivalence, provenance, as well as many notions of security. A great many relational program analyses have been proposed in the recent literature, including works by Antonopoulos et al (2017); Asada et al (2016); Banerjee et al (2016); Barthe et al (2012Barthe et al ( , 2013bBarthe et al ( , 2014Barthe et al ( , 2015; Beckert et al ( , 2017; Benton et al (2009);Ştefan Ciobâcă et al (2016); Godlin and Strichman (2010); Hedin and Sabelfeld (2012); Kundu et al This work is licensed under a Creative Commons Attribution 4.0 International License © 2018 Copyright held by the owner/author(s).…”

Section: Introductionmentioning

confidence: 99%

A monadic framework for relational verification: applied to information security, program equivalence, and optimizations

Grimm

Maillard

Fournet

et al. 2018

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs

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Relational properties describe multiple runs of one or more programs. They characterize many useful notions of security, program refinement, and equivalence for programs with diverse computational effects, and they have received much attention in the recent literature. Rather than developing separate tools for special classes of effects and relational properties, we advocate using a general purpose proof assistant as a unifying framework for the relational verification of effectful programs. The essence of our approach is to model effectful computations using monads and to prove relational properties on their monadic representations, making the most of existing support for reasoning about pure programs.We apply this method in F ⋆ and evaluate it by encoding a variety of relational program analyses, including information flow control, semantic declassification, program equivalence and refinement at higher order, correctness of program optimizations and game-based cryptographic security. By relying on SMT-based automation, unary weakest preconditions, user-defined effects, and monadic reification, we show that, compared to unary properties, verifying relational properties requires little additional effort from the F ⋆ programmer.

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Verifying Relational Properties of Functional Programs by First-Order Refinement

Cited by 16 publications

References 30 publications

Exploiting Synchrony and Symmetry in Relational Verification

Exploiting Synchrony and Symmetry in Relational Verification

A relational logic for higher-order programs

A monadic framework for relational verification: applied to information security, program equivalence, and optimizations

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