Beyond the elementary representations of program invariants over algebraic data types

Kostyukov, Yurii; Mordvinov, Dmitry; Fedyukovich, Grigory

doi:10.1145/3453483.3454055

Cited by 18 publications

(25 citation statements)

References 60 publications

(109 reference statements)

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“…In contrast to Racer, HoIce does not provide progress guarantees nor always generates a counterexample. The RInGen [Kostyukov et al 2021] solver infers solutions to CHCs modulo ADTs by treating all symbols as uninterpreted (thus, it does not support arithmetic). It uses a finite model finder to infer a finite model for the resulting FoL formula and extends it to a solution expressed using a tree automaton.…”

Section: Implementation and Evaluationmentioning

confidence: 99%

Solving constrained Horn clauses modulo algebraic data types and recursive functions

Shoham

Gurfinkel

2022

Proc. ACM Program. Lang.

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This work addresses the problem of verifying imperative programs that manipulate data structures, e.g., Rust programs. Data structures are usually modeled by Algebraic Data Types (ADTs) in verification conditions. Inductive invariants of such programs often require recursively defined functions (RDFs) to represent abstractions of data structures. From the logic perspective, this reduces to solving Constrained Horn Clauses (CHCs) modulo both ADT and RDF. The underlying logic with RDFs is undecidable. Thus, even verifying a candidate inductive invariant is undecidable. Similarly, IC3-based algorithms for solving CHCs lose their progress guarantee: they may not find counterexamples when the program is unsafe. We propose a novel IC3-inspired algorithm Racer for solving CHCs modulo ADT and RDF (i.e., automatically synthesizing inductive invariants, as opposed to only verifying them as is done in deductive verification). Racer ensures progress despite the undecidability of the underlying theory, and is guaranteed to terminate with a counterexample for unsafe programs. It works with a general class of RDFs over ADTs called catamorphisms. The key idea is to represent catamorphisms as both CHCs, via relationification , and RDFs, using novel abstractions . Encoding catamorphisms as CHCs allows learning inductive properties of catamorphisms, as well as preserving unsatisfiabilty of the original CHCs despite the use of RDF abstractions, whereas encoding catamorphisms as RDFs allows unfolding the recursive definition, and relying on it in solutions. Abstractions ensure that the underlying theory remains decidable. We implement our approach in Z3 and show that it works well in practice.

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Section: Implementation and Evaluationmentioning

confidence: 99%

Solving constrained Horn clauses modulo algebraic data types and recursive functions

Shoham

Gurfinkel

2022

Proc. ACM Program. Lang.

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“…Benchmarks used in the ADT-nonlin track were preprocessed by eliminating all theory constraints and recursively-defined functions. The transformation was performed using the feature of the RINGEN tool [13]. This way, we were able to satisfy the input-language constraints for all four tools entering the competition in this track.…”

Section: Benchmark Processing In Adt-nonlinmentioning

confidence: 99%

“…Algorithm. RINGEN stands for a Regular Invariant Generator, where regular invariants [13] are represented by finite tree automata. While invariant representations based on first-order logic (FOL) can only access finitely many subterms, regular invariants have an ability to "scan" an ADT term to the unbounded depth via automaton rules.…”

Section: Golemmentioning

confidence: 99%

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Competition Report: CHC-COMP-21

Fedyukovich

Rümmer

2021

Electron. Proc. Theor. Comput. Sci.

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CHC-COMP-21 1 is the fourth competition of solvers for Constrained Horn Clauses. In this year, 7 solvers participated at the competition, and were evaluated in 7 separate tracks on problems in linear integer arithmetic, linear real arithmetic, arrays, and algebraic data-types. The competition was run in March 2021 using the StarExec computing cluster. This report gives an overview of the competition design, explains the organisation of the competition, and presents the competition results.

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“…Recent work by Kostyukov et al [36] proposes a method for proving the satisfiability of CHCs over ADTs by computing models represented by finite tree automata. The tool based on this approach, called RegInv, is applied to the problem of computing invariants of programs that manipulate ADTs and it is shown to be more practical, in some cases, than state-of-the-art CHC solvers that compute invariants represented by first-order logic formulas.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Satisfiability of Constrained Horn Clauses on Algebraic Data Types: A Transformation-based Approach

Angelis¹,

Fioravanti²,

Pettorossi³

et al. 2021

Preprint

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We address the problem of checking the satisfiability of Constrained Horn Clauses (CHCs) defined on Algebraic Data Types (ADTs), such as lists and trees. We propose a new technique for transforming CHCs defined on ADTs into CHCs where the arguments of the predicates have only basic types, such as integers and booleans. Thus, our technique avoids, during satisfiability checking, the explicit use of proof rules based on induction over the ADTs. The main extension over previous techniques for ADT removal is a new transformation rule, called differential replacement, which allows us to introduce auxiliary predicates, whose definitions correspond to lemmas that are used when making inductive proofs. We present an algorithm that performs the automatic removal of ADTs by applying the new rule, together with the traditional folding/unfolding rules. We prove that, under suitable hypotheses, the set of the transformed clauses is satisfiable if and only if so is the set of the original clauses. By an experimental evaluation, we show that the use of the new rule significantly improves the effectiveness of ADT removal. We also show that our approach is competitive with respect to tools that extend CHC solvers with the use of inductive rules.

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Beyond the elementary representations of program invariants over algebraic data types

Cited by 18 publications

References 60 publications

Solving constrained Horn clauses modulo algebraic data types and recursive functions

Solving constrained Horn clauses modulo algebraic data types and recursive functions

Competition Report: CHC-COMP-21

Satisfiability of Constrained Horn Clauses on Algebraic Data Types: A Transformation-based Approach

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