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1 Automating Coinduction with Case Analysis
"... Abstract. Coinduction is a major technique employed to prove behavioral properties of systems, such as behavioral equivalence. Its automation is highly desirable, despite the fact that most behavioral problems are Π 0 2complete. Circular coinduction, which is at the core of the CIRC prover, automat ..."
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Abstract. Coinduction is a major technique employed to prove behavioral properties of systems, such as behavioral equivalence. Its automation is highly desirable, despite the fact that most behavioral problems are Π 0 2complete. Circular coinduction, which is at the core of the CIRC prover, automates coinduction by systematically deriving new goals and proving existing ones until, hopefully, all goals are proved. Motivated by practical examples, circular coinduction and CIRC have been recently extended with several features, such as special contexts, generalization and simplification. Unfortunately, none of these extensions eliminates the need for case analysis and, consequently, there are still many natural behavioral properties that CIRC cannot prove automatically. This paper presents an extension of circular coinduction with case analysis constructs and reasoning, as well as its implementation in CIRC. To uniformly prove the soundness of this extension, as well as of past and future extensions of circular coinduction and CIRC, this paper also proposes a general correctextension technique based on equational interpolants. 1
Behavioral institutions and refinements in generalized hidden logics
 J. Univers. Comput. Sci
, 2006
"... Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden klogics) to the algebraic specifica ..."
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Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden klogics) to the algebraic specification of object oriented programs. This is achieved through the Leibniz congruence relation and its combinatorial properties. We reformulate the notion of hidden klogic as well as the behavioral logic of a hidden klogic as institutions. We define refinements as hidden signature morphisms having the extra property of preserving logical consequence. A stricter class of refinements, the ones that preserve behavioral consequence, is studied. We establish sufficient conditions for an ordinary signature morphism to be a behavioral refinement.
Morphisms and Semantics for Higher Order Parameterized Programming
, 2002
"... Parameterized programming is extended to higher order modules, by extending views, which fit actual parameters to formal parameters in a flexible way, to morphisms, with higher order module expressions to compose modules into systems. A category theoretic semantics is outlined, and examples in BOBJ ..."
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Parameterized programming is extended to higher order modules, by extending views, which fit actual parameters to formal parameters in a flexible way, to morphisms, with higher order module expressions to compose modules into systems. A category theoretic semantics is outlined, and examples in BOBJ show the power of morphisms.
Communicating Concurrent Objects in HiddenCCS
, 2004
"... In this paper we add valuepassing communication to hiddenCCS, a new formalism proposed in [2] for synchronizing concurrent objects. We use hidden algebra to specify objectoriented systems, and CCS process algebra to describe the coordination aspects. The new specification formalism extends the obj ..."
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In this paper we add valuepassing communication to hiddenCCS, a new formalism proposed in [2] for synchronizing concurrent objects. We use hidden algebra to specify objectoriented systems, and CCS process algebra to describe the coordination aspects. The new specification formalism extends the object specification with synchronization and communication elements associated with methods and attributes of the objects, and use a CCS description of the interaction patterns. The operational semantics of hiddenCCS specifications is based on labeled transition systems which can be specified in rewriting logic. We use Maude as a platform for verification of the communicating concurrent objects specified in hiddenCCS. Triple Modular Redundancy is used as an example of a hiddenCCS specification and its verification in Maude.
Proving Equality of Streams Automatically
"... Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. In this paper we focus on equality of streams, more precisely, for a given set of equations two stream terms are said to be equal if they are equal in every model satisfyi ..."
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Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. In this paper we focus on equality of streams, more precisely, for a given set of equations two stream terms are said to be equal if they are equal in every model satisfying the given equations. We investigate techniques for proving equality of streams suitable for automation. Apart from techniques that were already available in the tool CIRC from Lucanu and Roşu, we also exploit welldefinedness of streams, typically proved by proving productivity. Moreover, our approach does not restrict to behavioral input format and does not require termination. We present a tool Streambox that can prove equality of a wide range of examples fully automatically. Digital Object Identifier 10.4230/LIPIcs.RTA.2011.393
WELLDEFINEDNESS OF STREAMS BY TRANSFORMATION AND TERMINATION
"... Abstract. Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. We propose a transformation from such a stream specification to a term rewriting systems (TRS) in such a way that termination of the resulting TRS implies that t ..."
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Abstract. Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. We propose a transformation from such a stream specification to a term rewriting systems (TRS) in such a way that termination of the resulting TRS implies that the stream specification is welldefined, that is, admits a unique solution. As a consequence, proving welldefinedness of several interesting stream specifications can be done fully automatically using present powerful tools for proving TRS termination. In order to increase the power of this approach, we investigate transformations that preserve semantics and welldefinedness. We give examples for which the above mentioned technique applies for the transformed specification while it fails for the original one. 1.
Webbased Multimedia Support for Distributed Cooperative Software Engineering
 In Proceedings, International Symposium on Multimedia Software Engineering
, 2000
"... The Tatami project is building a system to support software engineering over the internet, exploiting recent advances in web technology, interface design, and specification. Our effort to improve the usability of such systems led us into algebraic semiotics, while our effort to develop better formal ..."
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The Tatami project is building a system to support software engineering over the internet, exploiting recent advances in web technology, interface design, and specification. Our effort to improve the usability of such systems led us into algebraic semiotics, while our effort to develop better formal methods for distributed concurrent systems led us into hidden algebra. We discuss the Tatami system design, especially user interface issues, and sketch an extension of algebraic semiotics for interface dynamics. 1 Introduction The Tatami project has pursued three main goals: 1. explore novel multimedia interface design principles, for easing the use of complex interactive systems; 2. build and use a generic distributed environment for cooperative work; and 3. verify distributed concurrent software. We discuss these goals in turn. The first is motivated by the difficulties many practicing engineers have with formal methods tools. We have taken theorem provers as a typically difficult c...
Behavioral Abstraction is Information Hiding
"... We show that for any behavioral Sigmaspecification B there is an ordinary algebraic specification ~ B over a larger signature, such that a model behaviorally satisfies B if and only if it satisfies ~ B, where is the information hiding operator exporting only the Sigmatheorems of ~ B. The idea is t ..."
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We show that for any behavioral Sigmaspecification B there is an ordinary algebraic specification ~ B over a larger signature, such that a model behaviorally satisfies B if and only if it satisfies ~ B, where is the information hiding operator exporting only the Sigmatheorems of ~ B. The idea is to add machinery for contexts and experiments (sorts, operations and equations), use it, and then hide it. We develop a procedure, called unhiding, that takes a finite B and produces a finite ~ B. The practical aspect of this procedure is that one can use any standard equational or inductive theorem prover to derive behavioral theorems, even if neither equational reasoning nor induction is sound for behavioral satisfaction.
Specification and Verification of Synchronizing
 In E.Boiten, J.Derrick, and G.Smith (Eds.) Integrated Formal Methods 2004, Lecture Notes in Computer Science
, 2004
"... We introduce a new specification formalism which we call hiddenCCS; hidden algebra is used to specify local goals as objects, and CCS is used to describe global goal of the synchronizing concurrent objects. ..."
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We introduce a new specification formalism which we call hiddenCCS; hidden algebra is used to specify local goals as objects, and CCS is used to describe global goal of the synchronizing concurrent objects.
(Co)Inductive semantics for Constraint Handling Rules
"... In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of sta ..."
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In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over the transition system generated by the abstract operational semantics of CHR. Similarly, we demonstrate that the logical reading of states with respect to a set of propagation rules can be characterized by the greatest fixpoint. Then, in order to take advantage of both types of rules without losing fixpoint characterization, we present a new operational semantics with persistent constraints. We finally establish that this semantics can be characterized by two nested fixpoints, and we show that the resulting language is an elegant framework to program using coinductive reasoning.