Generalized Rewrite Theories and Coherence Completion

Meseguer, José

doi:10.1007/978-3-319-99840-4_10

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…Comparison with the Conference Paper [72]. This paper substantially extends the conference paper [72] in the following ways:…”

Section: Introductionmentioning

confidence: 88%

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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“…Comparison with the Conference Paper [72]. This paper substantially extends the conference paper [72] in the following ways:…”

Section: Introductionmentioning

confidence: 88%

Generalized rewrite theories, coherence completion, and symbolic methods

Meseguer

2020

Journal of Logical and Algebraic Methods in Programming

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“…Further Reading. Besides [28], the following references may be helpful: (i) for the semantics of rewrite theories [90,19]; for the modeling of concurrent systems, programming languages, and logical systems in rewriting logic [98,94,107,123,108,83]; (iii) for the ground coherence property and how to check it [47]; (iv) for automatically transforming a rewrite theory into a semantically equivalent one that is ground coherent [100]; and for an even more general notion of rewrite theory well suited for symbolic computation [100].…”

Section: Computation = Deductionmentioning

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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“…We assume as usual that the rewrite rules in R a and the rewrite rules in l −→ r if φ lr ∈ R are coherent in the generalized sense [36].…”

Section: Definition 5 (Valuation Semantics Of Constraints) the Valuat...mentioning

confidence: 99%

Operationally-based Program Equivalence Proofs using LCTRSs

Ciobâcă,

Lucanu,

Buruiană

2020

Preprint

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We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our method is its flexibility. We illustrate this flexibility in two applications, which are novel. For the first application, we show how to encode low-level details such as stack size in the language semantics and how to prove equivalence between two programs operating at different levels of abstraction. For our running example, we show how our method can prove equivalence between a recursive function operating with an unbounded stack and its tail-recursive optimized version operating with a bounded stack. This type of equivalence checking can be used to ensure that new, undesirable behavior is not introduced by a more concrete level of abstraction. For the second application, we show how to formalize read-sets and writesets of symbolic expressions and statements by extending the operational semantics in a conservative way. This enables the relational verification of program schemas, which we exploit to prove correctness of compiler optimizations, some of which cannot be proven by existing tools. Our method requires an extension of standard LCTRSs with axiomatized symbols. We also present a prototype implementation that proves the feasibility of both applications that we propose.

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Generalized Rewrite Theories and Coherence Completion

Cited by 6 publications

References 28 publications

Generalized rewrite theories, coherence completion, and symbolic methods

Generalized rewrite theories, coherence completion, and symbolic methods

Programming and symbolic computation in Maude

Operationally-based Program Equivalence Proofs using LCTRSs

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