A Coinductive Approach to Proving Reachability Properties in Logically Constrained Term Rewriting Systems

Ciobâcă, Ștefan; Lucanu, Dorel

doi:10.1007/978-3-319-94205-6_20

Cited by 18 publications

(22 citation statements)

References 31 publications

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“…Another body of inductive theorem proving work, perhaps the most closely related to the present one, is that on reachability logic [92,93,64,91,78,63,23]. In equational inductive theorem proving one reasons about validity of formulas in an initial algebra T Σ{EZB , whereas in reachability logic one reasons about validity of reachability formulas in the initial model T R of a generalized rewrite theory R. Although originally developed for purposes of verifying properties of programs in a programming language from their rewriting logic semantics [92,93], it has later been extended to verify reachability properties in general rewrite theories [64,91,63,23]. This subsequent development is the one most closely related to the present work.…”

Section: Related Work and Conclusionmentioning

confidence: 89%

Generalized rewrite theories, coherence completion, and symbolic methods

Meseguer

2020

Journal of Logical and Algebraic Methods in Programming

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A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion in [19] is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those in [33] for standard rewrite theories, including a generalized notion of coherence, are given. Symbolic executability, including coherence, is both ensured and made available for a wide class of such theories by automatable theory transformations. Using these foundations, several symbolic reasoning methods using generalized rewrite theories are studied, including: (i) symbolic description of sets of terms by pattern predicates; (ii) reasoning about universal reachability properties by generalized rewriting; (iii) reasoning about existential reachability properties by constrained narrowing; and (iv) symbolic verification of safety properties such as invariants and stability properties.

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Section: Related Work and Conclusionmentioning

confidence: 89%

Generalized rewrite theories, coherence completion, and symbolic methods

Meseguer

2020

Journal of Logical and Algebraic Methods in Programming

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“…Moreover, our definition of total correctness (Definition 3.2) generalizes the usual definition of total correctness, as it can also be used to reason about nonterminating programs that are guaranteed to reach a desired configuration (which could be nonterminating) in a finite number of steps. We have implemented our approach in the RMT tool [10,8]. Instructions on obtaining RMT are available at at http://profs.info.uaic.ro/~stefan.ciobaca/wpte2018, along with several examples for total correctness (including our running example).…”

Section: Discussionmentioning

confidence: 99%

Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Buruiana

Ciobâcă

2019

Electron. Proc. Theor. Comput. Sci.

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We give a language-parametric solution to the problem of total correctness, by automatically reducing it to the problem of partial correctness, under the assumption that an expression whose value decreases with each program step in a well-founded order is provided. Our approach assumes that the programming language semantics is given as a rewrite theory. We implement a prototype on top of the RMT tool and we show that it works in practice on a number of examples.

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“…The most recent Maude-based work on reachability logic provers closest to the work in [125] is that in [80] and, even more so, in [23]. The approach in [80] adopts a semantic framework for models similar to the already-discussed work in [131,132], i.e., state properties are specified using matching logic and assume a given first-order logic model.…”

Section: Generalization Homeomorphic Embedding and Partial Evaluationmentioning

confidence: 99%

Programming and symbolic computation in Maude

Durán

Eker

Escobar

et al. 2020

Journal of Logical and Algebraic Methods in Programming

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Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite theories. Maude has also a formal environment of verification tools. Symbolic computation is a powerful technique for reasoning about the correctness of concurrent systems and for increasing the power of formal tools. We present several new symbolic features of Maude that enhance formal reasoning about Maude programs and the effectiveness of formal tools. They include: (i) very general unification modulo user-definable equational theories, and (ii) symbolic reachability analysis of concurrent systems using narrowing. The paper does not focus just on symbolic features: it also describes several other new Maude features, including: (iii) Maude's strategy language for controlling rewriting, and (iv) external objects that allow flexible interaction of Maude object-based concurrent systems with the external world. In particular, metainterpreters are external objects encapsulating Maude interpreters that can interact with many other objects. To make the paper self-contained and give a reasonably complete language overview, we also review the basic Maude features for equational rewriting and rewriting with rules, Maude programming of concurrent object systems, and reflection. Furthermore, we include many examples illustrating all the Maude notions and features described in the paper.

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A Coinductive Approach to Proving Reachability Properties in Logically Constrained Term Rewriting Systems

Cited by 18 publications

References 31 publications

Generalized rewrite theories, coherence completion, and symbolic methods

Generalized rewrite theories, coherence completion, and symbolic methods

Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Programming and symbolic computation in Maude

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