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OrderSorted Equality Enrichments Modulo Axioms
"... Abstract. Builtin 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 tool ..."
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Abstract. Builtin 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 equationallydefined equality predicate enriching the algebraic data types were to be added to them. Furthermore, having an equationallydefined 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 ≃ where equationallydefined equality predicates have been added? This paper answers this question in the affirmative for a broad class of ordersorted conditional specifications E that are sortdecreasing, ground confluent, and operationally terminating modulo axioms B and have subsignature of constructors. The axioms B can consist of associativity, or commutativity, or associativitycommutativity axioms, so that the constructors are free modulo B. We prove that the transformation E ↦ → E ≃ preserves all the justmentioned properties of E. The transformation has been automated in Maude using reflection and it is used in Maude formal tools. 1
PreProceedings Volume Editors
"... Web services are fundamental to cloud computing and other computing paradigms based on serviceoriented architectures and applications. They make functional and autonomous building blocks available over the Internet, independent of platforms and programming languages, and both within and across orga ..."
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Web services are fundamental to cloud computing and other computing paradigms based on serviceoriented architectures and applications. They make functional and autonomous building blocks available over the Internet, independent of platforms and programming languages, and both within and across organizational boundaries. These can then be described, located, orchestrated, and invoked. Virtualization technology has moreover led to the Software as a Service, Platform as a Service, and Infrastructure as a Service notions. Formal methods can play a fundamental role in research on these concepts. They can help define unambiguous semantics for the languages and protocols that underpin web service infrastructures, and provide a basis for checking the conformance and compliance of bundled services. They can also empower dynamic discovery and binding with compatibility checks against behavioral properties, quality of service requirements, and servicelevel agreements. The resulting possibility of formal verification and analysis of (security) properties and performance (dependability and trustworthiness) is essential to cloud computing
Constructors, Sufficient completeness . . . Generalized Rewrite Theories
, 2010
"... Sufficient completeness has been throughly studied for equational specifications, where function symbols are classified into constructors and defined symbols. But what should sufficient completeness mean for a rewrite theory R = (Σ, E, R) with equations E and nonequational rules R describing concur ..."
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Sufficient completeness has been throughly studied for equational specifications, where function symbols are classified into constructors and defined symbols. But what should sufficient completeness mean for a rewrite theory R = (Σ, E, R) with equations E and nonequational rules R describing concurrent transitions in a system? This work argues that a rewrite theory naturally has two notions of constructor: the usual one for its equations E, and a different one for its rules R. The sufficient completeness of constructors for the rules R turns out to be intimately related with deadlock freedom, i.e., R has no deadlocks outside the constructors for R. The relation between these two notions is studied in the setting of unconditional ordersorted rewrite theories with (i) a frozenness map restricting rewriting with R, and (ii) a contextsensitive map restricting rewriting with the equations E, as it is possible for specifications in the Maude language. Sufficient conditions are given allowing the automatic checking of sufficient completeness, and other related properties, by equational tree automata modulo equational axioms such as associativity, commutativity, and identity. They are used
Verifying ReachabilityLogic Properties on RewritingLogic Specifications
"... Abstract. Reachability Logic is a recently introduced formalism, which is currently used for defining the operational semantics of programming languages and for stating properties about program executions. In this paper we show how Reachability Logic can be adapted for stating properties of transit ..."
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Abstract. Reachability Logic is a recently introduced formalism, which is currently used for defining the operational semantics of programming languages and for stating properties about program executions. In this paper we show how Reachability Logic can be adapted for stating properties of transition systems described by RewritingLogic specifications. We propose an automatic procedure for verifying RewritingLogic specifications against ReachabilityLogic properties. We prove the soundness of the procedure and illustrate it by verifying a communication protocol specified in Maude. 1
OrderSorted Equality Enrichments Modulo
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.