Modular reasoning about heap paths via effectively propositional formulas

ItzhakyShachar,; BanerjeeAnindya,; ImmermanNeil,; LahavOri,; NanevskiAleksandar,; SagivMooly,

doi:10.1145/2578855.2535854

Cited by 13 publications

(22 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this context, adapting our technique within the automata-theoretic technique of [15,17,16,12,10] seems most promising. Second, there are several program verification techniques that use EPR, and in several of these, EPR is used mainly to establish a linear order on the universe [20]. Automatically verifying such programs using our technique is worth exploring.…”

Section: Discussionmentioning

confidence: 99%

“…EPR-based reasoning has been proved powerful for verification of large-scale systems [32,28,38] and the Ivy [33,29] system is one of the most notable framework that exploits EPR based reasoning for verifying program snippets without recursion. EPR encoding of order axioms such as reflexivity, symmetry, transitivity and total orders has been used in proving programs working over heaps [20].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

What’s Decidable About Program Verification Modulo Axioms?

Mathur

Madhusudan

Viswanathan

2020

Tools and Algorithms for the Construction and Analysis of Systems

View full text Add to dashboard Cite

We consider the decidability of the verification problem of programs modulo axioms -automatically verifying whether programs satisfy their assertions, when the function and relation symbols are interpreted as arbitrary functions and relations that satisfy a set of first-order axioms. Though verification of uninterpreted programs (with no axioms) is already undecidable, a recent work introduced a subclass of coherent uninterpreted programs, and showed that they admit decidable verification [26]. We undertake a systematic study of various natural axioms for relations and functions, and study the decidability of the coherent verification problem. Axioms include relations being reflexive, symmetric, transitive, or total order relations, functions restricted to being associative, idempotent or commutative, and combinations of such axioms as well. Our comprehensive results unearth a rich landscape that shows that though several axiom classes admit decidability for coherent programs, coherence is not a panacea as several others continue to be undecidable. 1 We adapt the definition in a way that preserves the spirit of the definition of coherence. Moreover, if we do not adapt the definition, essentially all axioms classes we study in this paper would be undecidable.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

What’s Decidable About Program Verification Modulo Axioms?

Mathur

Madhusudan

Viswanathan

2020

Tools and Algorithms for the Construction and Analysis of Systems

View full text Add to dashboard Cite

show abstract

“…Our work was inspired by Itzhaky et al [2014Itzhaky et al [ , 2013. Their verification technique allows one to prove reachability properties in various forms of list data structures.…”

Section: Related Workmentioning

confidence: 99%

Modular verification of heap reachability properties in separation logic

Ter-Gabrielyan

Summers

Müller

2019

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

The correctness of many algorithms and data structures depends on reachability properties, that is, on the existence of chains of references between objects in the heap. Reasoning about reachability is difficult for two main reasons. First, any heap modification may affect an unbounded number of reference chains, which complicates modular verification, in particular, framing. Second, general graph reachability is not supported by SMT solvers, which impedes automatic verification.In this paper, we present a modular specification and verification technique for reachability properties in separation logic. For each method, we specify reachability only locally within the fragment of the heap on which the method operates. A novel form of reachability framing for relatively convex subheaps allows one to extend reachability properties from the heap fragment of a callee to the larger fragment of its caller, enabling precise procedure-modular reasoning. Our technique supports practically important heap structures, namely acyclic graphs with a bounded outdegree as well as (potentially cyclic) graphs with at most one path (modulo cycles) between each pair of nodes. The integration into separation logic allows us to reason about reachability and other properties in a uniform way, to verify concurrent programs, and to automate our technique via existing separation logic verifiers. We demonstrate that our verification technique is amenable to SMT-based verification by encoding a number of benchmark examples into the Viper verification infrastructure.

show abstract

“…There exists a more general treatment of the frame predicate that preserves reachability information and does not make assumptions about the set S. The details can be found in [20,33]. Since the footprints of tree manipulating programs are typically defined by tree predicates and hence parent-closed, we stick to the simpler definition given by formula (12).…”

Section: The Grit Logicmentioning

confidence: 99%

Automating Separation Logic with Trees and Data

Piskač

Wies

Zufferey³

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Separation logic (SL) is a widely used formalism for verifying heap manipulating programs. Existing SL solvers focus on decidable fragments for list-like structures. More complex data structures such as trees are typically unsupported in implementations, or handled by incomplete heuristics. While complete decision procedures for reasoning about trees have been proposed, these procedures suffer from high complexity, or make global assumptions about the heap that contradict the separation logic philosophy of local reasoning. In this paper, we present a fragment of classical first-order logic for local reasoning about tree-like data structures. The logic is decidable in NP and the decision procedure allows for combinations with other decidable first-order theories for reasoning about data. Such extensions are essential for proving functional correctness properties. We have implemented our decision procedure and, building on earlier work on translating SL proof obligations into classical logic, integrated it into an SL-based verification tool. We successfully used the tool to verify functional correctness of tree-based data structure implementations. Contributions. In this paper, we give a positive answer to this question. Our solution builds on our earlier work on reducing entailment checking in separation logic to satisfiability checking in classical first-order logic [32]. Our main technical contribution therefore lies in the identification of a fragment of first-order logic that (1) supports reasoning about mutable tree data structures; (2) is sufficiently expressive to serve as AE Supported in part by NSF grant CCS-1320583. AEAE Supported by DARPA (Grant FA8650-11-C-7192).

show abstract

Modular reasoning about heap paths via effectively propositional formulas

Cited by 13 publications

References 30 publications

What’s Decidable About Program Verification Modulo Axioms?

What’s Decidable About Program Verification Modulo Axioms?

Modular verification of heap reachability properties in separation logic

Automating Separation Logic with Trees and Data

Contact Info

Product

Resources

About