Software Model-Checking as Cyclic-Proof Search

Tsukada, Takeshi; Unno, Hiroshi

doi:10.48550/arxiv.2111.05617

Cited by 2 publications

(2 citation statements)

References 61 publications

(94 reference statements)

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“…Specifically, a cyclic proof system for separation logic has been given that automatically verifies that a program terminates [8,50]. Cyclic proof systems have recently been shown to subsume generic modelchecking algorithms such as: lazy-abstraction with interpolants, property-directed reachability, and maximal conservativity for infinite game solving [51]. As with the generic cyclic theorem prover C…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…Since, in general, we cannot expect that there is any syntactical relationship between the node and its ancestor, the formation of cycles is closely related to the use of cuts in the proof. Indeed Tsukada and Unno [51] have demonstrated that many techniques developed for efficient software model checking can be viewed as methods for introducing cuts into a cyclic proof so as to promote the formation of cycles.…”

Section: Introductionmentioning

confidence: 99%

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CycleQ: An Efficient Basis for Cyclic Equational Reasoning

Jones¹,

Ong²,

Ramsay³

2021

Preprint

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We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual substitution as a cut rule. We show that our system, although simple, already subsumes several of the approaches to implicit induction variously known as "inductionless induction", "rewriting induction", and "proof by consistency". By restricting the form of the traces, we show that global correctness in our system can be verified incrementally, taking advantage of the well-known size-change principle, which leads to an efficient implementation of proof search. Our CycleQ tool, accessible as a GHC plugin, shows promising results on a number of standard benchmarks.

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Section: Related Work and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

CycleQ: An Efficient Basis for Cyclic Equational Reasoning

Jones¹,

Ong²,

Ramsay³

2021

Preprint

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Inductive Approach to Spacer

Tsukada,

Unno

2024

Proc. ACM Program. Lang.

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The constrained Horn clause satisfiability problem is at the core of many automated verification methods, and Spacer is one of the most efficient solvers of this problem. The standard description of Spacer is based on an abstract transition system, dividing the whole procedure into small rules. This division makes individual rules easier to understand but, conversely, makes it difficult to discuss the procedure as a whole. As evidence of the difficulty in understanding the whole procedure, we point out that the claimed refutational completeness actually fails for several reasons, some of which were not present in the original version and subsequently added. It is also difficult to grasp the differences between Spacer and another procedure, such as GPDR. This paper aims to provide a better understanding of Spacer by developing a Spacer-like procedure defined by structural induction. We first formulate the problem to be solved inductively, then give its naïve solver and transform it to obtain a Spacer-like procedure. Interestingly, our inductive approach almost unifies Spacer and GPDR, which differ in only one respect in our understanding. To demonstrate the usefulness of our inductive approach in understanding Spacer, we examine Spacer variants in the literature in terms of inductive procedures and discuss why they are not refutationally complete and how to fix them. We also implemented the proposed procedure and evaluated it experimentally.

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Software Model-Checking as Cyclic-Proof Search

Cited by 2 publications

References 61 publications

CycleQ: An Efficient Basis for Cyclic Equational Reasoning

CycleQ: An Efficient Basis for Cyclic Equational Reasoning

Inductive Approach to Spacer

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