Locality in Reasoning about Graph Transformations

Strecker, Martin

doi:10.1007/978-3-642-34176-2_15

Cited by 5 publications

(9 citation statements)

References 14 publications

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“…This observation we advocated is also shared by Martin Strecker [5] who notes that simply looking at the left and right sides of a transformation rule does not hold with respect to property-preserving. The source graph is then split into a finite interior region and an arbitrarily large exterior one.…”

Section: Related Workmentioning

confidence: 57%

Towards a Rule-Level Verification Framework for Property-Preserving Graph Transformations

Tran

Percebois

2012

2012 IEEE Fifth International Conference on Software Testing, Verification and Validation

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Abstract-We report in this paper a method for proving that a graph transformation is property-preserving. Our approach uses a relational representation for graph grammar and a logical representation for graph properties with first-order logic formulas. The presented work consists in identifying the general conditions for a graph grammar to preserve graph properties, in particular structural properties. We aim to implement all the relevant notions of graph grammar in the Isabelle/HOL proof assistant in order to allow a (semi) automatic verification of graph transformation with a reasonable complexity. Given an input graph and a set of graph transformation rules, we can use mathematical induction strategies to verify statically if the transformation preserves a particular property of the initial graph. The main highlight of our approach is that such a verification is done without calculating the resulting graph and thus without using a transformation engine.

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Section: Related Workmentioning

confidence: 57%

Towards a Rule-Level Verification Framework for Property-Preserving Graph Transformations

Tran

Percebois

2012

2012 IEEE Fifth International Conference on Software Testing, Verification and Validation

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show abstract

“…and are unsound in the presence of loops (with no fixed bound on the number of iterations), and those that are sound but require inductive invariants, which are inferred heuristically or provided manually. Sacrificing the expressiveness provided by general-purpose languages (e.g., no transitive closure [Strecker 2011]) allows Seam to verify for loops, with no a priori bound on the number of iterations, soundly, without the need for inductive invariants.…”

Section: Related Workmentioning

confidence: 99%

Seam: provably safe local edits on graphs

Papadakis

Bernstein

Sharma

et al. 2017

Proc. ACM Program. Lang.

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Algorithms that create and mutate graph data structures are challenging to implement correctly. However, verifying even basic properties of low-level implementations, such as referential integrity and memory safety, remains non-trivial. Furthermore, any extension to such a data structure multiplies the complexity of its implementation, while compounding the challenges in reasoning about correctness. We take a language design approach to this problem. We propose Seam, a language for expressing local edits to graph-like data structures, based on a relational data model, and such that data integrity can be verified automatically. We present a verification method that leverages an SMT solver, and prove it sound and precise (complete modulo termination of the SMT solver). We evaluate the verification capabilities of Seam empirically, and demonstrate its applicability to a variety of examples, most notably a new class of verification tasks derived from geometric remeshing operations used in scientific simulation and computer graphics. We describe our prototype implementation of a Seam compiler that generates low-level code, which can then be integrated into larger applications. We evaluate our compiler on a sample application, and demonstrate competitive execution time, compared to handwritten implementations.

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“…One of the strengths of graph grammars is their ability to model complex states (as graphs), and therefore it is to expect that even small specifications may lead to a large number of complex reachable graphs, restricting the possibilities to use model checking techniques. There are few works [21,22,23] that are using theorem provers or proof assistants for graph grammars, but as far we know, none of them are actually performing verification.…”

Section: Final Remarksmentioning

confidence: 99%

“…With Alloy, they only analyse a system for a finite scope, whose size is user-defined. Strecker [21,22,23] has proposed a formalisation of graph transformations in a set-theoretic model using the Isabelle/HOL [16] proof assistant. In [21] he started to define a language for writing graph transformation programs and reasoning about them.…”

Section: Introductionmentioning

confidence: 99%

“…The language was defined with two statements, one to apply a rule repeatedly to a graph, and another to apply several rules in a specific order to a graph. In [22] and [23] he explores how to reason locally about global properties of graph transformations. In particular, he investigate under which conditions reasoning about a graph transformation can be reduced to reasoning about the shape of the transformation rules.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Proof Tactics for Theorem Proving Graph Grammars through Rodin

Lemor¹,

Cavalheiro²,

Foss³

2015

RITA

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Graph grammar is a formal language suitable for the specification of distributed and concurrent systems. Theorem proving is a technique that allows the verification of systems with huge (and infinite) state space. One of the disadvantages of theorem proving graph grammars (and theorem proving in general) is the specific mathematical knowledge required from the user for concluding the proofs. Previous works have proposed proof strategies to help the developer in the verification process when adopting such approach, firstly establishing proof tactics for some properties and after proposing a visual representation for them. This paper extends the set of proposed tactics, with the aim of expanding the available strategies and encouraging the use of such a technique.

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Locality in Reasoning about Graph Transformations

Cited by 5 publications

References 14 publications

Towards a Rule-Level Verification Framework for Property-Preserving Graph Transformations

Towards a Rule-Level Verification Framework for Property-Preserving Graph Transformations

Seam: provably safe local edits on graphs

Proof Tactics for Theorem Proving Graph Grammars through Rodin

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