Symbolic Computation in Maude: Some Tapas

Meseguer, José

doi:10.1007/978-3-030-68446-4_1

Cited by 5 publications

(2 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Maude can be used as a meta-tool to develop new formal tools because: (i) its underlying equational and rewriting logics are logical -and reflective metalogical-frameworks [7,27,46]; (ii) Maude's efficient support of logical reflection through its META-LEVEL module; (iii) Maude's rewriting, search, model checking, and strategy language features [11,15]; and (iv) Maude's symbolic reasoning features [15,33], the latest reported here. We refer to [11,15,31,33] for references on various Maude-based tools. Many of them can benefit from these new features.…”

Section: Applications and Conclusionmentioning

confidence: 98%

Equational Unification and Matching, and Symbolic Reachability Analysis in Maude 3.2 (System Description)

Durán

Eker

Escobar

et al. 2022

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Equational unification and matching are fundamental mechanisms in many automated deduction applications. Supporting them efficiently for as wide as possible a class of equational theories, and in a typed manner supporting type hierarchies, benefits many applications; but this is both challenging and nontrivial. We present Maude 3.2’s efficient support of these features as well as of symbolic reachability analysis of infinite-state concurrent systems based on them.

show abstract

Section: Applications and Conclusionmentioning

confidence: 98%

Equational Unification and Matching, and Symbolic Reachability Analysis in Maude 3.2 (System Description)

Durán

Eker

Escobar

et al. 2022

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…This kind of advanced, LP-like reasoning capability based on narrowing goes beyond standard, rewrite-based equational reasoning that does not support symbolic reachability analysis because input variables are simply handled as constants. Symbolic reasoning methods that are based on narrowing and their applications are generally discussed in Meseguer (2020) and Meseguer (2021). For a very brief account of Maude's rewriting and narrowing principles, we refer to Alpuente et al (2019b).…”

Section: Introductionmentioning

confidence: 99%

Symbolic Specialization of Rewriting Logic Theories with`Presto`

Alpuente¹,

Escobar²,

Sapiña³

et al. 2022

Theory and Practice of Logic Programming

View full text Add to dashboard Cite

This paper introduces $\tt{{Presto}}$ , a symbolic partial evaluator for Maude’s rewriting logic theories that can improve system analysis and verification. In $\tt{{Presto}}$ , the automated optimization of a conditional rewrite theory $\mathcal{R}$ (whose rules define the concurrent transitions of a system) is achieved by partially evaluating, with respect to the rules of $\mathcal{R}$ , an underlying, companion equational logic theory $\mathcal{E}$ that specifies the algebraic structure of the system states of $\mathcal{R}$ . This can be particularly useful for specializing an overly general equational theory $\mathcal{E}$ whose operators may obey complex combinations of associativity, commutativity, and/or identity axioms, when being plugged into a host rewrite theory $\mathcal{R}$ as happens, for instance, in protocol analysis, where sophisticated equational theories for cryptography are used. $\tt{{Presto}}$ implements different unfolding operators that are based on folding variant narrowing (the symbolic engine of Maude’s equational theories). When combined with an appropriate abstraction algorithm, they allow the specialization to be adapted to the theory termination behavior and bring significant improvement while ensuring strong correctness and termination of the specialization. We demonstrate the effectiveness of $\tt{{Presto}}$ in several examples of protocol analysis where it achieves a significant speed-up. Actually, the transformation provided by $\tt{{Presto}}$ may cut down an infinite folding variant narrowing space to a finite one, and moreover, some of the costly algebraic axioms and rule conditions may be eliminated as well. As far as we know, this is the first partial evaluator for Maude that respects the semantics of functional, logic, concurrent, and object-oriented computations.

show abstract