Model checking for symbolic-heap separation logic with inductive predicates

BrotherstonJames,; GorogiannisNikos,; KanovichMax,; RoweReuben,

doi:10.1145/2914770.2837621

Cited by 12 publications

(32 citation statements)

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“…We run BBeye in an iterative deepening way, and the time counted for BBeye is the total time it spends. Formulae (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) are used by Park et al to test their prover BBeye for BBI [51]. We can see that for formulae (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) the performance of Separata is comparable with the heuristic based prover for FVLS BBI .…”

Section: Methodsmentioning

confidence: 94%

Modular Labelled Sequent Calculi for Abstract Separation Logics

Hóu

Clouston

Goré

et al. 2018

ACM Trans. Comput. Logic

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separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete resource model. Their assertion languages, called propositional abstract separation logics (PASLs), extend the logic of (Boolean) Bunched Implications (BBI) in various ways. In particular, these logics contain the connectives * and − * , denoting the composition and extension of resources respectively. This added expressive power comes at a price since the resulting logics are all undecidable. Given their wide applicability, even a semi-decision procedure for these logics is desirable. Although several PASLs and their relationships with BBI are discussed in the literature, the proof theory of, and automated reasoning for, these logics were open problems solved by the conference version of this paper, which developed a modular proof theory for various PASLs using cut-free labelled sequent calculi. This paper non-trivially improves upon this previous work by giving a general framework of calculi on which any new axiom in the logic satisfying a certain form corresponds to an inference rule in our framework, and the completeness proof is generalised to consider such axioms.Our base calculus handles Calcagno et al. 's original logic of separation algebras by adding sound rules for partial-determinism and cancellativity, while preserving cut-elimination. We then show that many important properties in separation logic, such as indivisible unit, disjointness, splittability, and cross-split, can be expressed in our general axiom form. Thus our framework offers inference rules and completeness for these properties for free. Finally, we show how our calculi reduce to calculi with global label substitutions, enabling more efficient implementation. emp in some literature), and separating implication − * , also called magic wand, from the logic of Bunched Implications (BI) [50]. Moreover, the assertion language introduces the points-to predicate E → E ′ on expressions, along with the usual quantifiers and predicates of first-order logic with equality and arithmetic. The additive connectives may be either intuitionistic, as for BI, or classical, as for the logic of Boolean Bunched Implications (BBI). Classical additives are more expressive as they support reasoning about non-monotonic commands such as memory de-allocation, and assertions such as "the heap is empty" [36]. In this paper we consider classical additives only.The concrete memory model for SL is given in terms of heaps, where a heap is a finite partial function from addresses to values. A heap satisfies P * Q iff it can be partitioned into heaps satisfying P and Q respectively; it satisfies ⊤ * iff it is empty; it satisfies P − * Q iff any extension with a heap that satisfies P must then satisfy Q; and it satisfies E → E ′ iff it is a singleton map sending the address specified by the expression E to the value specified by the expression E ′ . Wh...

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Section: Methodsmentioning

confidence: 94%

Modular Labelled Sequent Calculi for Abstract Separation Logics

Hóu

Clouston

Goré

et al. 2018

ACM Trans. Comput. Logic

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“…Another possible line of future work, building on the very recent development of a model checking procedure for our logic [12], is to explore the possibility of disproving entailments by directly generating and checking potential countermodels. However, such an analysis might be significantly more expensive than the one we present here.…”

Section: Discussionmentioning

confidence: 99%

“…This approach has only just become potentially viable at the time of going to press, following the very recent development of a model checking procedure for our logic [12]. However, this approach still presents some fairly significant obstacles.…”

Section: An Algorithm For Entailment Disproofmentioning

confidence: 99%

“…That is to say, there are infinitely many distinct models of a given size, and so some quotienting over these values is required so as to restrict these models to finitely many "representative cases". Secondly, this approach also seems likely to be quite expensive even in average cases, since the model checking problem itself, according to [12], is EXPTIME-complete: Many models would be generated and most of them would inevitably fail to be countermodels (e.g., for the trivial reason that they do not satisfy A). Finally, any complete enumeration-based approach will, in general, fail to terminate.…”

Section: An Algorithm For Entailment Disproofmentioning

confidence: 99%

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Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

Brotherston

Gorogiannis

2015

Lecture Notes in Computer Science

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Abstract. We give a procedure for establishing the invalidity of logical entailments in the symbolic heap fragment of separation logic with user-defined inductive predicates, as used in program verification. This disproof procedure attempts to infer the existence of a countermodel to an entailment by comparing computable model summaries, a.k.a. bases (modified from earlier work), of its antecedent and consequent. Our method is sound and terminating, but necessarily incomplete. Experiments with the implementation of our disproof procedure indicate that it can correctly identify a substantial proportion of the invalid entailments that arise in practice, at reasonably low time cost. Accordingly, it can be used, e.g., to improve the output of theorem provers by returning "no" answers in addition to "yes" and "unknown" answers to entailment questions, and to speed up proof search or automated theory exploration by filtering out invalid entailments.

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“…The decisive condition is that in every definition clause, all existential variables must occur in − → u where the definition clause has x → ( − → u ). It is similar to the constructively valued condition in [11]. This condition guarantees that the cell at address x decides the content of every existential variable.…”

Section: Languagementioning

confidence: 94%

Completeness of Cyclic Proofs for Symbolic Heaps with Inductive Definitions

Tatsuta

Nakazawa

Kimura

2019

Programming Languages and Systems

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Separation logic is successful for software verification in both theory and practice. Decision procedure for symbolic heaps is one of the key issues. This paper proposes a cyclic proof system for symbolic heaps with general form of inductive definitions, and shows its soundness and completeness. The decision procedure for entailments of symbolic heaps with inductive definitions is also given. Decidability for entailments of symbolic heaps with inductive definitions is an important question. Completeness of cyclic proof systems is also an important question. The results of this paper answer both questions. The decision procedure is feasible since it is nondeterministic double-exponential time complexity.We define F (m) as obtained from a formula F by replacing every inductive predicate P by P (m) .We define ( = (T 1 , T 2 )) as t1∈T1,t2∈T2,t1 ≡t2 t 1 = t 2 . We write x = T for ( = ({x}, T )).We define ( = (T )) as ( = (T ∪ {nil}, T ∪ {nil})). SemanticsThis subsection gives semantics of the language. We define the following structure: Val = N , Locs = {x ∈ N |x > 0}, Heaps = Locs → f in Val n cell , Stores = Vars → Val. Each s ∈ Stores is called a store. Each h ∈ Heaps is called a heap, and Dom(h) is the domain of h, and Range(h) is the range of h. We write h = h 1 + h 2 when Dom(h 1 ) and Dom(h 2 ) are disjoint and the graph of h is the union of those of h 1 and h 2 . A pair (s, h) is called a heap model, which means a memory state. The value s(x) means the value of the variable x in the model (s, h). Each value a ∈ Dom(h) means an address, and the value of h(a) is the content of the memory cell at address a in the heap h. We suppose each memory cell has n cell elements as its content.The interpretation s(t) for any term t is defined as 0 for nil and s(x) for the variable x.For a formula F we define the interpretation s, h |= F as follows.

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Model checking for symbolic-heap separation logic with inductive predicates

Cited by 12 publications

References 30 publications

Modular Labelled Sequent Calculi for Abstract Separation Logics

Modular Labelled Sequent Calculi for Abstract Separation Logics

Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

Completeness of Cyclic Proofs for Symbolic Heaps with Inductive Definitions

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