Bridging Arrays and ADTs in Recursive Proofs

Fedyukovich, Grigory; Ernst, Gerhard

doi:10.1007/978-3-030-72013-1_2

Cited by 4 publications

(2 citation statements)

References 54 publications

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“…Furthermore, with the recent growth of the use of SMT solvers, it is often tempting to formulate verification conditions using the combination of different theories, e.g., as in [21]. Verification conditions could be expressed using the combination of ADT and the theory of Equality and Uninterpreted Functions (EUF).…”

Section: Introductionmentioning

confidence: 99%

Beyond the elementary representations of program invariants over algebraic data types

Kostyukov¹,

Mordvinov²,

Fedyukovich

2021

Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

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First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some theories, they fail to express many interesting properties of algebraic data types (ADTs). In this paper, we explore three different approaches to represent program invariants of ADTmanipulating programs: tree automata, and first-order formulas with or without size constraints. We compare the expressive power of these representations and prove the negative definability of both first-order representations using the pumping lemmas. We present an approach to automatically infer program invariants of ADT-manipulating programs by a reduction to a finite model finder. The implementation called RInGen has been evaluated against state-of-the-art invariant synthesizers and has been experimentally shown to be competitive. In particular, program invariants represented by automata are capable of expressing more complex properties of computation and their automatic construction is often less expensive.

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Section: Introductionmentioning

confidence: 99%

Beyond the elementary representations of program invariants over algebraic data types

Kostyukov¹,

Mordvinov²,

Fedyukovich

2021

Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

Self Cite

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“…The current SMT and CHC solvers are, however, not very good at reasoning about recursive data structures (such as lists and trees), compared with the capability of reasoning about basic data such as integers and real numbers. Indeed, improving the treatment of recursive data structures has recently been an active research topic, especially for CHC solvers [6,9,13,27].…”

Section: Introductionmentioning

confidence: 99%

Symbolic Automatic Relations and Their Applications to SMT and CHC Solving

Shimoda¹,

Kobayashi²,

Sakayori³

et al. 2021

Preprint

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Despite the recent advance of automated program verification, reasoning about recursive data structures remains as a challenge for verification tools and their backends such as SMT and CHC solvers. To address the challenge, we introduce the notion of symbolic automatic relations (SARs), which combines symbolic automata and automatic relations, and inherits their good properties such as the closure under Boolean operations. We consider the satisfiability problem for SARs, and show that it is undecidable in general, but that we can construct a sound (but incomplete) and automated satisfiability checker by a reduction to CHC solving. We discuss applications to SMT and CHC solving on data structures, and show the effectiveness of our approach through experiments.

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