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Mechanical Analysis of Reliable Communication in the Alternating Bit Protocol Using the Maude Invariant Analyzer Tool

Rocha, Camilo; Meseguer, José (Springer., 2014)

The InvA tool supports the deductive verification of safety properties of infinite-state concurrent systems. Given a concurrent system specified as a rewrite theory and a safety formula to be verified, InvA reduces such a ...
Order-Sorted Equality Enrichments Modulo Axioms

Gutiérrez, Raúl; Meseguer, José; Rocha, Camilo (SpringerBerlin., 2012)

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications ...
Proving Safety Properties of Rewrite Theories

Rocha, Camilo; Meseguer, José (SpringerBerlín, 2011)

Rewrite theories are a general and expressive formalism for specifying concurrent systems in which states are axiomatized by equations and transitions among states are axiomatized by rewrite rules. We present a deductive ...
Tool Interoperability in the Maude Formal Environment

Durán, Francisco; Rocha, Camilo; Álvarez, José María (SpringerBerlín, 2011)

We present the Maude Formal Environment (MFE), an executable formal specification in Maude within which a user can seamlessly interact with the Maude Termination Tool, the Maude Sufficient Completeness Checker, the ...
Towards a Maude Formal Environment

Durán, Francisco; Rocha, Camilo; Álvarez, José María (SpringerBerlín, 2011)

Maude is a declarative and reflective language based on rewriting logic in which computation corresponds to efficient deduction by rewriting. Because of its reflective capabilities, Maude has been useful as a metatool in ...

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Mechanical Analysis of Reliable Communication in the Alternating Bit Protocol Using the Maude Invariant Analyzer Tool
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Rocha, Camilo | 2014

The InvA tool supports the deductive verification of safety properties of infinite-state concurrent systems. Given a concurrent system specified as a rewrite theory and a safety formula to be verified, InvA reduces such a formula to inductive properties of the underlying equational theory by means of the application of a few inference rules. Through the combination of various techniques such as unification, narrowing, equationally-defined equality predicates, and SMT solving, InvA achieves a significant degree of automation, verifying automatically many proof obligations. Maude Inductive Theorem Prover (ITP) can be used to discharge the remaining obligations which are not automatically verified by InvA. Verification of the reliable communication ensured by the Alternating Bit Protocol (ABP) is used as a case study to explain the use of the InvA tool, and to illustrate its effectiveness and degree of automation in a concrete way.

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Order-Sorted Equality Enrichments Modulo Axioms
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Gutiérrez, Raúl | 2012

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for checking key properties such as confluence, termination, and sufficient completeness. Such specifications would instead be amenable to formal analysis if an equationally-defined equality predicate enriching the algebraic data types were to be added to them. Furthermore, having an equationally-defined equality predicate is very useful in its own right, particularly in inductive theorem proving. Is it possible to effectively define a theory transformation E↦E≃ that extends an algebraic specification E to a specification E≃ having an equationally-defined equality predicate? This paper answers this question in the affirmative for a broad class of order-sorted conditional specifications E that are sort-decreasing, ground confluent, and operationally terminating modulo axioms B and have a subsignature of constructors. The axioms B can consist of associativity, or commutativity, or associativity-commutativity axioms, so that the constructors are free modulo B. We prove that the transformation E↦E≃ preserves all the just-mentioned properties of E . The transformation has been automated in Maude using reflection and is used in several Maude formal tools.

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Proving Safety Properties of Rewrite Theories
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Rocha, Camilo | 2011

Rewrite theories are a general and expressive formalism for specifying concurrent systems in which states are axiomatized by equations and transitions among states are axiomatized by rewrite rules. We present a deductive approach for verifying safety properties of rewrite theories in which all formal temporal reasoning about concurrent transitions is ultimately reduced to purely equational inductive reasoning. Narrowing modulo axioms is extensively used in our inference system to further simplify the equational proof obligations to which all proofs of safety formulas are ultimately reduced. In this way, existing equational reasoning techniques and tools can be directly applied to verify safety properties of concurrent systems. We report on the implementation of this deductive system in the Maude Invariant Analyzer tool, which provides a substantial degree of automation and can automatically discharge many proof obligations without user intervention.

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Tool Interoperability in the Maude Formal Environment
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Durán, Francisco | 2011

We present the Maude Formal Environment (MFE), an executable formal specification in Maude within which a user can seamlessly interact with the Maude Termination Tool, the Maude Sufficient Completeness Checker, the Church-Rosser Checker, the Coherence Checker, and the Maude Inductive Theorem Prover. We explain the high-level design decisions behind MFE, give a summarized account of its main features, and illustrate with an example the interoperation of the tools available in its current release.

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Towards a Maude Formal Environment
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Durán, Francisco | 2011

Maude is a declarative and reflective language based on rewriting logic in which computation corresponds to efficient deduction by rewriting. Because of its reflective capabilities, Maude has been useful as a metatool in the development of formal analysis tools for checking specific properties of Maude specifications. This includes tools for checking termination, confluence, and inductive properties of rewrite theories. Nevertheless, most of these tools have been designed to work in isolation, making it difficult, for instance, to exchange data between them and inconvenient to switch between their environments. This paper presents the Maude Formal Environment (MFE), an executable formal specification in Maude within which a user can interact with tools to mechanically verify properties of Maude specifications. One important aspect of this work is that the MFE has been designed to be easily extended with tools having highly heterogeneous designs whilst creating synergy among them. As a proof of concept, we report on the integration of five commonly used formal analysis tools for Maude specifications into MFE and illustrate their interoperability with an example.

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