Constraint-Based Program Reasoning with Heaps and Separation

Duck, Gregory J.; Jaffar, Joxan; Koh, Nicolas

doi:10.1007/978-3-642-40627-0_24

Cited by 11 publications

(26 citation statements)

References 23 publications

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“…The ↓ binder of HyBBI(↓) also allows us to encode the definition of the overlapping conjunction ∪ * of separation logic, which has been used in specifying and verifying programs manipulating data structures with intrinsic sharing [25,16,13]. In these works, ∪ * is introduced as an new primitive connective, defined by extending the standard forcing relation for BBI (Definition 2.3) as follows:…”

Section: Formulas and Expressivitymentioning

confidence: 99%

Parametric completeness for separation theories

Brotherston

Villard

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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In this paper, we close the logical gap between provability in the logic BBI, which is the propositional basis for separation logic, and validity in an intended class of separation models, as employed in applications of separation logic such as program verification. An intended class of separation models is usually specified by a collection of axioms describing the specific model properties that are expected to hold, which we call a separation theory.Our main contributions are as follows. First, we show that several typical properties of separation theories are not definable in BBI. Second, we show that these properties become definable in a suitable hybrid extension of BBI, obtained by adding a theory of naming to BBI in the same way that hybrid logic extends normal modal logic. The binder-free extension HyBBI captures most of the properties we consider, and the full extension HyBBI(↓) with the usual ↓ binder of hybrid logic covers all these properties. Third, we present an axiomatic proof system for our hybrid logic whose extension with any set of "pure" axioms is sound and complete with respect to the models satisfying those axioms. As a corollary of this general result, we obtain, in a parametric manner, a sound and complete axiomatic proof system for any separation theory from our considered class. To the best of our knowledge, this class includes all separation theories appearing in the published literature.

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Section: Formulas and Expressivitymentioning

confidence: 99%

Parametric completeness for separation theories

Brotherston

Villard

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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“…To this aim we may combine the CHR axiomatization of heaps proposed by [17] with the generalization strategies based on widening and convex-hull considered in this paper.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…Some methods, directly following the approach presented in [41], are based on abstract interpretation [8] and compute an overapproximation of the least model of the CLP program under consideration by a bottom-up evaluation of an abstraction of the program [2,28,39]. Other methods use goal directed evaluation of CLP programs combined with other symbolic techniques such as interpolation [17,20,31,30]. Some other methods, like the ones presented in [5,25,43,45], combine CLP (also called constrained Horn clauses in those papers) with different reasoning techniques developed in the areas of Software Model Checking and Automated Theorem Proving, such as CounterExample-Guided Abstraction Refinement (CEGAR) and Satisfiability Modulo Theory (SMT).…”

Section: Introductionmentioning

confidence: 99%

Program Verification using Constraint Handling Rules and Array Constraint Generalizations*

Angelis

Fioravanti

Pettorossi

et al. 2017

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Abstract. The transformation of constraint logic programs (CLP programs) has been shown to be an effective methodology for verifying properties of imperative programs. By following this methodology, we encode the negation of a partial correctness property of an imperative program prog as a predicate incorrect defined by a CLP program P , and we show that prog is correct by transforming P into the empty program through the application of semantics preserving transformation rules. Some of these rules perform replacements of constraints that encode properties of the data structures manipulated by the program prog. In this paper we show that Constraint Handling Rules (CHR) are a suitable formalism for representing and applying constraint replacements during the transformation of CLP programs. In particular, we consider programs that manipulate integer arrays and we present a CHR encoding of a constraint replacement strategy based on the theory of arrays. We also propose a novel generalization strategy for constraints on integer arrays that combines the CHR constraint replacement strategy with various generalization operators for linear constraints, such as widening and convex hull. Generalization is controlled by additional constraints that relate the variable identifiers in the imperative program prog and the CLP representation of their values. The method presented in this paper has been implemented and we have demonstrated its effectiveness on a set of benchmark programs taken from the literature.

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“…Constraint Logic Programming 1 (CLP) [30] is becoming increasingly popular as a logical basis for developing methods and tools for software verification (see, for instance, [8,16,24,32,39,37]). Indeed, CLP provides a suitable formalism for expressing verification conditions that guarantee the correctness of imperative, functional, or concurrent programs and, moreover, constraints are very useful for encoding properties of data domains such as integers, reals, arrays, and heaps [6,18,11,35]. An advantage of using a CLP representation for verification problems is that we can then combine reasoning techniques and constraint solvers based on the common logical language [22].…”

Section: Introductionmentioning

confidence: 99%

Verification of Programs by Combining Iterated Specialization with Interpolation

Angelis¹,

Fioravanti²,

Navas³

et al. 2014

Electron. Proc. Theor. Comput. Sci.

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We present a verification technique for program safety that combines Iterated Specialization and Interpolating Horn Clause Solving. Our new method composes together these two techniques in a modular way by exploiting the common Horn Clause representation of the verification problem. The Iterated Specialization verifier transforms an initial set of verification conditions by using unfold/fold equivalence preserving transformation rules. During transformation, program invariants are discovered by applying widening operators. Then the output set of specialized verification conditions is analyzed by an Interpolating Horn Clause solver, hence adding the effect of interpolation to the effect of widening. The specialization and interpolation phases can be iterated, and also combined with other transformations that change the direction of propagation of the constraints (forward from the program preconditions or backward from the error conditions). We have implemented our verification technique by integrating the VeriMAP verifier with the FTCLP Horn Clause solver, based on Iterated Specialization and Interpolation, respectively. Our experimental results show that the integrated verifier improves the precision of each of the individual components run separately.

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Constraint-Based Program Reasoning with Heaps and Separation

Cited by 11 publications

References 23 publications

Parametric completeness for separation theories

Parametric completeness for separation theories

Program Verification using Constraint Handling Rules and Array Constraint Generalizations*

Verification of Programs by Combining Iterated Specialization with Interpolation

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