Variant-Based Satisfiability in Initial Algebras

Meseguer, José

doi:10.1007/978-3-319-29510-7_1

Cited by 22 publications

(65 citation statements)

References 68 publications

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“…There are preliminary results for particular classes of theories such as shallow theories [26] and forwardclosed theories [24]. For these particular classes of theories, a mutation-based approach [21] or a variant-based approach [22,29,38] can be successfully applied to solve the (combined) unification problem, but we believe it is always interesting to point out a combination-based alternative when the background theory is a union of "separable" theories. As shown here with the matching problem, some particular decision problems can admit non-disjoint combination methods.…”

Section: Resultsmentioning

confidence: 99%

Building and Combining Matching Algorithms

Ringeissen¹

2019

Lecture Notes in Computer Science

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The concept of matching is ubiquitous in declarative programming and in automated reasoning. For instance, it is a key mechanism to run rule-based programs and to simplify clauses generated by theorem provers. A matching problem can be seen as a particular conjunction of equations where each equation has a ground side. We give an overview of techniques that can be applied to build and combine matching algorithms. First, we survey mutation-based techniques as a way to build a generic matching algorithm for a large class of equational theories. Second, combination techniques are introduced to get combined matching algorithms for disjoint unions of theories. Then we show how these combination algorithms can be extended to handle non-disjoint unions of theories sharing only constructors. These extensions are possible if an appropriate notion of normal form is computable.

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Section: Resultsmentioning

confidence: 99%

Building and Combining Matching Algorithms

Ringeissen¹

2019

Lecture Notes in Computer Science

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“…Besides the applications outlined in this article, further applications could benefit from variant generation in GLINTS. Actually, an important number of applications (and tools) are currently based on variant generation: for instance, the protocol analyzers Maude-NPA (Escobar et al 2009) and Tamarin (Meier et al 2013), proofs of coherence and local confluence (Durán and Meseguer 2012), termination provers (Durán et al 2009), variant-based satisfiability checkers (Meseguer 2015), the partial evaluator Victoria (Alpuente et al 2017), and different applications of symbolic reachability analyses (Bae et al 2013). As an application example, protocol analysis tools that rely on variant computation could identify all the intermediate variant states that are associated to a concrete protocol state and how one is generated from the other (which is convoluted in the output provided by Maude), thereby allowing deep optimizations to cut down the search space.…”

Section: Discussionmentioning

confidence: 99%

“…As future work, we plan to address several extensions of GLINTS, such as computing constructor variants (Meseguer 2015) and irredundant variants (Clavel et al 2016), and supporting irreducibility constraints (Erbatur et al 2012).…”

Section: Discussionmentioning

confidence: 99%

“…The theory BOOL is FVP, whereas the theory NAT-VARIANT does not have the finite variant property since there is an infinite number of variants in NAT-VARIANT for the term X:Nat + 0. It is generally undecidable whether an equational theory has the FVP (Bouchard et al 2013); a semi-decision procedure is given by Meseguer (2015) that works well in practice and another technique based on the dependency pair framework is given by Escobar et al (2012). The procedure by Meseguer (2015) works by computing the variants of all flat terms f (X 1 , .…”

Section: Examplementioning

confidence: 99%

“…. , X n (of the corresponding sort); the theory does have the FVP iff there is a finite number of most general variants for every such term (Meseguer 2015).…”

Section: Examplementioning

confidence: 99%

See 2 more Smart Citations

Inspecting Maude variants with`GLINTS`

Alpuente

Escobar

Sapiña

et al. 2017

Theory and Practice of Logic Programming

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This paper introducesGLINTS, a graphical tool for exploring variant narrowing computations in Maude. The most recent version of Maude, version 2.7.1, provides quite sophisticated unification features, including order-sorted equational unification for convergent theories modulo axioms such as associativity, commutativity, and identity. This novel equational unification relies on built-in generation of the set ofvariantsof a termt, i.e., the canonical form oftσ for a computed substitution σ. Variant generation relies on a novel narrowing strategy calledfolding variant narrowingthat opens up new applications in formal reasoning, theorem proving, testing, protocol analysis, and model checking, especially when the theory satisfies thefinite variant property, i.e., there is a finite number of most general variants for every term in the theory. However, variant narrowing computations can be extremely involved and are simply presented in text format by Maude, often being too heavy to be debugged or even understood. TheGLINTSsystem provides support for (i) determining whether a given theory satisfies the finite variant property, (ii) thoroughly exploring variant narrowing computations, (iii) automatic checking of nodeembeddingandclosednessmodulo axioms, and (iv) querying and inspecting selected parts of the variant trees.

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Rule-Based Unification in Combined Theories and the Finite Variant Property

Eeralla

Erbatur

Marshall

et al. 2019

Language and Automata Theory and Applications

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We investigate the unification problem in theories defined by rewrite systems which are both convergent and forward-closed. These theories are also known in the context of protocol analysis as theories with the finite variant property and admit a variant-based unification algorithm. In this paper, we present a new rule-based unification algorithm which can be seen as an alternative to the variant-based approach. In addition, we define forward-closed combination to capture the union of a forward-closed convergent rewrite system with another theory, such as the Associativity-Commutativity, whose function symbols may occur in right-hand sides of the rewrite system. Finally, we present a combination algorithm for this particular class of non-disjoint unions of theories.

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Variant-Based Satisfiability in Initial Algebras

Cited by 22 publications

References 68 publications

Building and Combining Matching Algorithms

Building and Combining Matching Algorithms

Inspecting Maude variants with`GLINTS`

Rule-Based Unification in Combined Theories and the Finite Variant Property

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Variant-Based Satisfiability in Initial Algebras

Cited by 22 publications

References 68 publications

Building and Combining Matching Algorithms

Building and Combining Matching Algorithms

Inspecting Maude variants withGLINTS

Rule-Based Unification in Combined Theories and the Finite Variant Property

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Product

Resources

About

Inspecting Maude variants with`GLINTS`