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38
Metalogical Frameworks
, 1992
"... In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the me ..."
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Cited by 60 (18 self)
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In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the metalogic of the object language being implemented. We also reason about the implementation itself, say to know it is correct; this is done in a programming logic. How do all these logics relate? This paper considers that question and more. We show that by taking the view that the metalogic is primary, these other parts are related in standard ways. The metalogic should be suitably rich so that the object logic can be presented as an abstract data type, and it must be suitably computational (or constructive) so that an instance of that type is an implementation. The data type abstractly encodes all that is relevant for metareasoning, i.e., not only the term constructing functions but also the...
Building Equational Proving Tools by Reflection in Rewriting Logic
 In Cafe: An IndustrialStrength Algebraic Formal Method
, 1998
"... This paper explains the design and use of two equational proving tools, namely an inductive theorem prover  to prove theorems about equational specifications with an initial algebra semantics  and a ChurchRosser checkerto check whether such specifications satisfy the ChurchRosser property. ..."
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Cited by 41 (22 self)
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This paper explains the design and use of two equational proving tools, namely an inductive theorem prover  to prove theorems about equational specifications with an initial algebra semantics  and a ChurchRosser checkerto check whether such specifications satisfy the ChurchRosser property. These tools can be used to prove properties of ordersorted equational specifications in Cafe [11] and of membership equational logic specifications in Maude [7, 6]. The tools have been written entirely in Maude and are in fact executable specifications in rewriting logic of the formal inference systems that they implement.
Development Graphs  Proof Management for Structured Specifications
, 2005
"... Development graphs are a tool for dealing with structured specifications in a formal program development in order to ease the management of change and reusing proofs. In this work, we extend development graphs with hiding (e.g. hidden operations). Hiding is a particularly difficult to realize operat ..."
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Cited by 30 (19 self)
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Development graphs are a tool for dealing with structured specifications in a formal program development in order to ease the management of change and reusing proofs. In this work, we extend development graphs with hiding (e.g. hidden operations). Hiding is a particularly difficult to realize operation, since it does not admit such a good decomposition of the involved specifications as other structuring operations do. We develop both a semantics and proof rules for development graphs with hiding. The rules are proven to be sound, and also complete relative to an oracle for conservative extensions. We also show that an absolutely complete set of rules cannot exist. The whole framework is developed in a way independent of the underlying logical system (and thus also does not prescribe the nature of the parts of a specification that may be hidden). We also show how various other logic independent specification formalisms can be mapped into development graphs; thus, development graphs can serve as a kernel formalism for management of proofs and of change.
Specification and Analysis of the AER/NCA Active Network Protocol Suite in Realtime Maude
, 2006
"... This paper describes the application of the RealTime Maude tool and the Maude formal methodology to the specification and analysis of the AER/NCA suite of active network multicast protocol components. Because of the timesensitive and resourcesensitive behavior, the presence of probabilistic algor ..."
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Cited by 28 (18 self)
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This paper describes the application of the RealTime Maude tool and the Maude formal methodology to the specification and analysis of the AER/NCA suite of active network multicast protocol components. Because of the timesensitive and resourcesensitive behavior, the presence of probabilistic algorithms, and the composability of its components, AER/NCA poses challenging new problems for its formal specification and analysis. RealTime Maude is a natural extension of the Maude rewriting logic language and tool for the specification and analysis of realtime objectbased distributed systems. It supports a wide spectrum of formal methods, including: executable specification; symbolic simulation; breadthfirst search for failures of safety properties in infinitestate systems; and linear temporal logic model checking of timebounded temporal logic formulas. These methods complement those offered by network simulators on the one hand, and timedautomatonbased tools and generalpurpose theorem provers on the other. Our experience shows that RealTime Maude is wellsuited to meet the AER/NCA modeling challenges, and that its methods have proved effective in uncovering subtle and important errors in the informal use case specification.
A formal approach to objectoriented software engineering
 Electronic Notes on Theoretical Computer Science 4
"... We show how formal specifications can be integrated into one of the current pragmatic objectoriented software development methods. Jacobson’s “ObjectOriented Software Engineering ” (OOSE) process is combined with objectoriented algebraic specifications by extending object and interaction diagrams ..."
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Cited by 22 (2 self)
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We show how formal specifications can be integrated into one of the current pragmatic objectoriented software development methods. Jacobson’s “ObjectOriented Software Engineering ” (OOSE) process is combined with objectoriented algebraic specifications by extending object and interaction diagrams with formal annotations. The specifications are based on Meseguer’s rewriting logic and are written in a metalevel extension of the language Maude by process expressions. As a result any such diagram can be associated with a formal specification, proof obligations ensuring invariant properties can be automatically generated, and the refinement relations between documents at different abstraction levels can be formally stated and proved. 1
Mapping modular SOS to rewriting logic
 12th International Symposium on LogicBased Program Synthesis and Transformation (LOPSTR’02), volume 2664 of Lecture Notes in Computer Science
, 2002
"... Abstract. Modular SOS (MSOS) is a framework created to improve the modularity of structural operational semantics specifications, a formalism frequently used in the fields of programming languages semantics and process algebras. With the objective of defining formal tools to support the execution a ..."
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Cited by 20 (3 self)
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Abstract. Modular SOS (MSOS) is a framework created to improve the modularity of structural operational semantics specifications, a formalism frequently used in the fields of programming languages semantics and process algebras. With the objective of defining formal tools to support the execution and verification of MSOS specifications, we have defined a mapping, named MtoR, from MSOS to rewriting logic (RWL), a logic which has been proposed as a logical and semantic framework. We have proven the correctness ofMtoR and implemented it as a prototype, the MSOSSL Interpreter, in the Maude system, a highperformance implementation of RWL. In this paper we characterize the MtoR mapping and the MSOSSL Interpreter. The reader is assumed to have some basic knowledge of structural operational semantics and objectoriented concepts. 1
Reflection in membership equational logic, manysorted equational logic, horn logic with equality, and rewriting logic
 In Gadducci and Montanari [33
, 2002
"... We show that the generalized variant of rewriting logic where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational log ..."
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Cited by 20 (6 self)
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We show that the generalized variant of rewriting logic where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational logic, manysorted equational logic, and Horn logic with equality are likewise reflective. These results provide logical foundations for reflective languages and tools based on these logics, and in particular for the Maude language itself. 1
Structured Theories and Institutions
, 1999
"... Category theory provides an excellent foundation for studying structured specifications and their composition. For example, theories can be structured together in a diagram, and their composition can be obtained as a colimit. There is, however, a growing awareness, both in theory and in specificatio ..."
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Cited by 15 (4 self)
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Category theory provides an excellent foundation for studying structured specifications and their composition. For example, theories can be structured together in a diagram, and their composition can be obtained as a colimit. There is, however, a growing awareness, both in theory and in specification practice, that structured theories should not be viewed just as the "scaffolding" used to build unstructured theories: they should become firstclass citizens in the specification process. Given a logic formalized as an institution I, we therefore ask whether there is a good definition of the category of Istructured theories, and whether they can be naturally regarded as the ordinary theories of an appropriate institution S(I) generalizing the original institution I. We answer both question in the affirmative, and study good properties of the institution I inherited by S(I). We show that, under natural conditions, a number of important properties are indeed inherited, including cocompleteness of the category of theories, liberality, and extension of the basic framework by freeness constraints. The results presented here have been used as a foundation for the module algebra of the Maude language, and seem promising as a semantic basis for a generic module algebra that could be both specified and executed within the logical framework of rewriting logic. 1
Software Specification and Verification in Rewriting Logic
, 2003
"... One can distinguish two specification levels: a system specification level, in which the computational system of interest is specified; and a property specification level, in which the relevant properties are specified. These lectures present an approach to executable system specification based on e ..."
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Cited by 13 (4 self)
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One can distinguish two specification levels: a system specification level, in which the computational system of interest is specified; and a property specification level, in which the relevant properties are specified. These lectures present an approach to executable system specification based on equational logic for deterministic systems and on rewriting logic for concurrent systems that is seamlessly integrated with a property specification level using firstorder, inductive, and temporal logics. This integration is directly supported by formal verification tools in the formal environment of the Maude rewriting logic language. We show how this approach and the supporting tools can be applied to the specification and verification of a wide variety of programs, that can be either declarative or imperative, and either deterministic or concurrent.
Specification and Analysis of RealTime and Hybrid Systems in Rewriting Logic
, 2000
"... 2 Dedicated with affection to my beloved parents Cecilia and Miklós 3 4 ..."
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Cited by 12 (5 self)
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2 Dedicated with affection to my beloved parents Cecilia and Miklós 3 4