Automatic induction proofs of data-structures in imperative programs

Chu, Duc-Hiep; Jaffar, Joxan; Trinh, Minh-Thai

doi:10.1145/2737924.2737984

Cited by 32 publications

(44 citation statements)

References 31 publications

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“…To evaluate our technique, we compared our system against state-of-the-art SL provers, including Slide [15,16], Spen [13], Sleek [10] and Cyclist [5,7], which had participated in the recent SL competition SL-COMP [30]. We are however unable to make direct comparison with the induction-based proof technique presented in [11] as their prover was not publicly available. Our evaluation was performed on an Ubuntu 14.04 machine with CPU Intel E5-2620 (2.4GHz) and RAM 64GB.…”

Section: Methodsmentioning

confidence: 99%

“…Consequently, a soundness condition needs to be checked globally on proof trees. On the other hand, Chu et al [11] apply structural induction on inductive heap predicates for proving SL entailments. During proof search, this technique dynamically uses derived entailments as induction hypotheses.…”

Section: Introductionmentioning

confidence: 99%

“…Cyclic proof [5,7] and induction proof in [11] are most closely related to our approach. We recall the aforementioned comments that cyclic proof requires soundness condition to be checked globally on proof trees, whereas proof technique in [11] restricts that induction hypotheses collected from one path of proof tree cannot be used to prove entailments in other paths. Our work differs from them as we not only allow soundness condition to be checked locally at inference rule level, but also support mutual induction where entailments from different proof paths can be used as hypotheses to prove each other.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Automated Mutual Explicit Induction Proof in Separation Logic

Khoo

et al. 2016

Lecture Notes in Computer Science

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We present a sequent-based deductive system for automatically proving entailments in separation logic by using mathematical induction. Our technique, called mutual explicit induction proof, is an instance of Noetherian induction. Specifically, we propose a novel induction principle on a well-founded relation of separation logic model, and follow the explicit induction methods to implement this principle as inference rules, so that it can be easily integrated into a deductive system. We also support mutual induction, a natural feature of implicit induction, where the goal entailment and other entailments derived during the proof search can be used as hypotheses to prove each other. We have implemented a prototype prover and evaluated it on a benchmark of handcrafted entailments as well as benchmarks from a separation logic competition.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Automated Mutual Explicit Induction Proof in Separation Logic

Khoo

et al. 2016

Lecture Notes in Computer Science

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“…We evaluate Art on two dimensions: the first demonstrates that it is expressive enough to verify a variety of sophisticated properties for linked structures; the second that it provides a significant automation over the state-of-the-art, represented by the SMT-based VCDryad system. VCDryad has annotations comparable to other recent tools that use specialized decision procedures to discharge Separation Logic VCs [10]. Our benchmarks are available at [1].…”

Section: Methodsmentioning

confidence: 99%

Predicate Abstraction for Linked Data Structures

Bakst

Jhala

2015

Lecture Notes in Computer Science

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We present Alias Refinement Types (Art), a new approach that uses predicate-abstraction to automate the verification of correctness properties of linked data structures. While there are many techniques for checking that a heap-manipulating program adheres to its specification, they often require that the programmer annotate the behavior of each procedure, for example, in the form of loop invariants and pre-and post-conditions. We introduce a technique that lifts predicate abstraction to the heap by factoring the analysis of data structures into two orthogonal components: (1) Alias Types, which reason about the physical shape of heap structures, and (2) Refinement Types, which use simple predicates from an SMT decidable theory to capture the logical or semantic properties of the structures. We evaluate Art by implementing a tool that performs type inference for an imperative language, and empirically show, using a suite of data-structure benchmarks, that Art requires only 21% of the annotations needed by other state-of-the-art verification techniques.

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“…(Due to space limit, the work on SLID without data constraints will be skipped.) In [7,8,23], SLID with set/multiset/size data constraints were considered, but only (incomplete) heuristics were provided. To reason about invariants of data values stored in lists, SL with list segment predicates and data constraints in universally quantified Presburger arithmetic was considered [1].…”

Section: Introductionmentioning

confidence: 99%

Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

Gao

Chen

Zhang

2019

SOFSEM 2019: Theory and Practice of Computer Science

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We identify difference-bound set constraints (DBS), an analogy of difference-bound arithmetic constraints for sets. DBS can express not only set constraints but also arithmetic constraints over set elements. We integrate DBS into separation logic with linearly compositional inductive predicates, obtaining a logic thereof where set data constraints of linear data structures can be specified. We show that the satisfiability of this logic is decidable. A crucial step of the decision procedure is to compute the transitive closure of DBS-definable set relations, to capture which we propose an extension of quantified set constraints with Presburger Arithmetic (RQSPA). The satisfiability of RQSPA is then shown to be decidable by harnessing advanced automata-theoretic techniques.

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Automatic induction proofs of data-structures in imperative programs

Cited by 32 publications

References 31 publications

Automated Mutual Explicit Induction Proof in Separation Logic

Automated Mutual Explicit Induction Proof in Separation Logic

Predicate Abstraction for Linked Data Structures

Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

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