Higher-Order Program Verification via HFL Model Checking

Kobayashi, Naoki; Tsukada, Takeshi; Watanabe, Kojiro

doi:10.1007/978-3-319-89884-1_25

Cited by 28 publications

(42 citation statements)

References 54 publications

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“…It would be very interesting to find an inverse reduction that preserves the structure of fixpoints, depends only on the nesting of fixpoints and not the size of the transition system. A recent paper of Kobayashi, Tsukada, and Watanabe [36] makes a strong case for HFL-MC.…”

Section: Discussionmentioning

confidence: 99%

Lambda Y-Calculus With Priorities

Walukiewicz

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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The lambdaY-calculus with priorities is a variant of the simplytyped lambda calculus designed for higher-order model-checking. The higher-order model-checking problem asks if a given parity tree automaton accepts the Böhm tree of a given term of the simply-typed lambda calculus with recursion. We show that this problem can be reduced to the same question but for terms of lambdaY-calculus with priorities and visibly parity automata; a subclass of parity automata. The latter question can be answered by evaluating terms in a simple powerset model with least and greatest fixpoints. We prove that the recognizing power of powerset models and visibly parity automata are the same. So, up to conversion to the lambdaY-calculus with priorities, powerset models with least and greatest fixpoints are indeed the right semantic framework for the model-checking problem. The reduction to lambdaY-calculus with priorities is also efficient algorithmically: it gives an algorithm of the same complexity as direct approaches to the higher-order model-checking problem. This indicates that the task of calculating the value of a term in a powerset model is a central algorithmic problem for higher-order model-checking.

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Section: Discussionmentioning

confidence: 99%

Lambda Y-Calculus With Priorities

Walukiewicz

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…Moreover, many of the transformations from program to grammar incur a large blow-up in size. Two promising evolutions of higher-order model checking are the approach of Kobayashi, Tsukada, and Watanabe [2018] based on the higher-order fixpoint logic of Viswanathan and Viswanathan [2004] and that of Cathcart Burn, Ong, and Ramsay [2017] via higher-order constrained Horn clauses.…”

Section: Related Workmentioning

confidence: 99%

Intensional datatype refinement: with application to scalable verification of pattern-match safety

Jones

Ramsay

2021

Proc. ACM Program. Lang.

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The pattern-match safety problem is to verify that a given functional program will never crash due to non-exhaustive patterns in its function definitions. We present a refinement type system that can be used to solve this problem. The system extends ML-style type systems with algebraic datatypes by a limited form of structural subtyping and environment-level intersection. We describe a fully automatic, sound and complete type inference procedure for this system which, under reasonable assumptions, is worst-case linear-time in the program size. Compositionality is essential to obtaining this complexity guarantee. A prototype implementation for Haskell is able to analyse a selection of packages from the Hackage database in a few hundred milliseconds.

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“…Several works have explored how to automate the verification of higher-order programs by means of techniques inspired by model checking and Horn clause solving. Some of the recent works in this direction (Kobayashi et al, 2017(Kobayashi et al, , 2018 have focused on the use of higher-order modal fixed point logics (HFL). In this approach, a program is translated to an HFL formula expressing the correctness of the program with respect to a particular property, and the verification is performed via HFL model checking.…”

Section: Related Workmentioning

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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Higher-Order Program Verification via HFL Model Checking

Cited by 28 publications

References 54 publications

Lambda Y-Calculus With Priorities

Lambda Y-Calculus With Priorities

Intensional datatype refinement: with application to scalable verification of pattern-match safety

A relational logic for higher-order programs

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