Cyclic Abduction of Inductively Defined Safety and Termination Preconditions

Brotherston, J G.; Gorogiannis, Nikos

doi:10.1007/978-3-319-10936-7_5

Cited by 25 publications

(42 citation statements)

References 23 publications

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“…[2]) extended with user-defined (inductive) predicates, typically needed to express data structures in the memory. We omit the schema for inductive predicates and their interpretations here, since they are identical to those used, e.g., in [7,9,8,27]. Definition 1.…”

Section: Programs and Assertionsmentioning

confidence: 99%

“…The logical rules comprise standard rules for the logical connectives and standard unfolding rules for the temporal operators and inductive predicates in memory assertions. For brevity, we omit here the somewhat complex unfolding rule for inductive predicates, but similar rules can be found in, e.g., [7,9,8,27].…”

Section: A Cyclic Proof System For Verifying Ctl Propertiesmentioning

confidence: 99%

“…The following definitions, adaptations of similar notions in e.g. [6,7,9,8,27], formalise this notion. A pre-proof P = (D, L) can be seen as a finite cyclic graph by identifying each open leaf of D with its companion.…”

Section: A Cyclic Proof System For Verifying Ctl Propertiesmentioning

confidence: 99%

“…Roughly speaking, a precondition trace tracks an occurrence of an inductive predicate in the preconditions of the judgements along the path, progressing whenever the predicate occurrence is unfolded. Again, see [7,9,8,27] for similar notions.…”

Section: A Cyclic Proof System For Verifying Ctl Propertiesmentioning

confidence: 99%

See 3 more Smart Citations

Automatically Verifying Temporal Properties of Pointer Programs with Cyclic Proof

Tellez

Brotherston

2017

Automated Deduction – CADE 26

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Abstract. We propose a deductive reasoning approach to the automatic verification of temporal properties of pointer programs, based on cyclic proof. We present a proof system whose judgements express that a program has a certain temporal property over memory state assertions in separation logic, and whose rules operate directly on the temporal modalities as well as symbolically executing programs. Cyclic proofs in our system are, as usual, finite proof graphs subject to a natural, decidable soundness condition, encoding a form of proof by infinite descent. We present a proof system tailored to proving CTL properties of nondeterministic pointer programs, and then adapt this system to handle fair execution conditions. We show both systems to be sound, and provide an implementation of each in the Cyclist theorem prover, yielding an automated tool that is capable of automatically discovering proofs of (fair) temporal properties of heap-aware programs. Experimental evaluation of our tool indicates that our approach is viable, and offers an interesting alternative to traditional model checking techniques.

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Section: Programs and Assertionsmentioning

confidence: 99%

Section: A Cyclic Proof System For Verifying Ctl Propertiesmentioning

confidence: 99%

Section: A Cyclic Proof System For Verifying Ctl Propertiesmentioning

confidence: 99%

Section: A Cyclic Proof System For Verifying Ctl Propertiesmentioning

confidence: 99%

See 2 more Smart Citations

Automatically Verifying Temporal Properties of Pointer Programs with Cyclic Proof

Tellez

Brotherston

2017

Automated Deduction – CADE 26

Self Cite

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show abstract

“…[11,15,21,22]). This fragment is much more expressive than the simple linked-list fragment, but is also computationally much harder.…”

Section: Introductionmentioning

confidence: 99%

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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Shape Analysis via Second-Order Bi-Abduction

Gherghina

Qin

et al. 2014

Lecture Notes in Computer Science

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Abstract. We present a new modular shape analysis that can synthesize heap memory specification on a per method basis. We rely on a second-order biabduction mechanism that can give interpretations to unknown shape predicates. There are several novel features in our shape analysis. Firstly, it is grounded on second-order bi-abduction. Secondly, we distinguish unknown pre-predicates in pre-conditions, from unknown post-predicates in post-condition; since the former may be strengthened, while the latter may be weakened. Thirdly, we provide a new heap guard mechanism to support more precise preconditions for heap specification. Lastly, we formalise a set of derivation and normalization rules to give concise definitions for unknown predicates. Our approach has been proven sound and is implemented on top of an existing automated verification system. We show its versatility in synthesizing a wide range of intricate shape specifications.

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Cyclic Abduction of Inductively Defined Safety and Termination Preconditions

Cited by 25 publications

References 23 publications

Automatically Verifying Temporal Properties of Pointer Programs with Cyclic Proof

Automatically Verifying Temporal Properties of Pointer Programs with Cyclic Proof

Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

Shape Analysis via Second-Order Bi-Abduction

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