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13
Circular Coinductive Rewriting
 In Proceedings of Automated Software Engineering 2000
, 2000
"... Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples ..."
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Cited by 54 (11 self)
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Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples demonstrate the surprising power of circular coinductive rewriting. The paper also sketches the underlying hidden algebraic theory and briefly describes BOBJ and some of its algorithms.
Conditional Circular Coinductive Rewriting with Case Analysis
, 2002
"... We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples. ..."
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Cited by 19 (1 self)
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We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples.
An Overview of the Tatami Project
, 2000
"... This paper describes the Tatami project at UCSD, which is developing a system to support distributed cooperative software development over the web, and in particular, the validation of concurrent distributed software. The main components of our current prototype are a proof assistant, a generator fo ..."
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Cited by 13 (8 self)
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This paper describes the Tatami project at UCSD, which is developing a system to support distributed cooperative software development over the web, and in particular, the validation of concurrent distributed software. The main components of our current prototype are a proof assistant, a generator for documentation websites, a database, an equational proof engine, and a communication protocol to support distributed cooperative work. We believe behavioral specification and verification are important for software development, and for this purpose we use first order hidden logic with equational atoms. The paper also briefly describes some novel user interface design methods that have been developed and applied in the project
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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Cited by 8 (6 self)
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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.
Webbased support for cooperative software engineering
 Annals of Software Engineering
, 2001
"... recent advances in web technology, interface design, and specification. Our effort to improve the usability of such systems has led us into algebraic semiotics, while our effort to develop better formal methods for distributed concurrent systems has led us into hidden algebra and fuzzy logic. This p ..."
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Cited by 7 (2 self)
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recent advances in web technology, interface design, and specification. Our effort to improve the usability of such systems has led us into algebraic semiotics, while our effort to develop better formal methods for distributed concurrent systems has led us into hidden algebra and fuzzy logic. This paper discusses the Tatami system design, especially its software architecture, and its user interface principles. New work in the latter area includes an extension of algebraic semiotics to dynamic multimedia interfaces, and integrating Gibsonian affordances with algebraic semiotics. 1
Coinduction for recursive data types: partial orders, metric spaces and Omegacategories
, 2000
"... In this paper we prove coinduction theorems for nal coalgebras of endofunctors on categories of partial orders and (generalized) metric spaces. These results characterize the order, respectively the metric, on a nal coalgebra as maximum amongst all simulations. As suggested in [15], and motivated by ..."
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Cited by 7 (0 self)
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In this paper we prove coinduction theorems for nal coalgebras of endofunctors on categories of partial orders and (generalized) metric spaces. These results characterize the order, respectively the metric, on a nal coalgebra as maximum amongst all simulations. As suggested in [15], and motivated by the idea that partial orders and metric spaces are types of enriched category, the notion of simulation is based on the enriched categorical counterpart of relations, called bimodules. In fact, the results above arise as instances of a coinduction theorem, parametric in a quantale applying to nal coalgebras of endofunctors on the category of all (small) all) 50147 and 186363 Also, we give a condition under which the operational notion of simulation coincides with the denotational notion of nal semantics. 1 Introduction Coinduction is a principle for reasoning about potentially innite or circular elements of recursive data types, like streams, processes or exact reals [14,5,7]. Typ...
Equational reasoning with subtypes
 Iowa State University
, 2002
"... Abstract. Using equational logic as a specification language, we investigate the proof theory of behavioral subtyping for objectoriented abstract data types with immutable objects and deterministic methods that can use multiple dispatch. In particular, we investigate a proof technique for correct b ..."
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Cited by 5 (1 self)
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Abstract. Using equational logic as a specification language, we investigate the proof theory of behavioral subtyping for objectoriented abstract data types with immutable objects and deterministic methods that can use multiple dispatch. In particular, we investigate a proof technique for correct behavioral subtyping in which each subtype’s specification includes terms that can be used to coerce its objects to objects of each of its supertypes. We show that this technique is sound, using our previous work on the model theory of such abstract data types. We also give an example to show that the technique is not complete, even if the methods do not use multiple dispatch, and even if types specified are termgenerated. In preparation for the results on equational subtyping we develop the proof theory of a richer form of equational logic that is suitable for dealing with subtyping and behavioral equivalence. This gives some insight into question of when our proof techniques can be make effectively computable, but in general behavioral consequence is not effectively computable. 1.
Under consideration for publication in Math. Struct. in Comp. Science Behavioral Reasoning for Conditional Equations †
, 2007
"... Abstract. Object oriented (OO) programming techniques can be applied to equational specification logics by distinguishing visible data from hidden data (i.e., by distinguishing the output of methods from the objects to which the methods apply), and then focusing on the behavioral equivalence of hidd ..."
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Abstract. Object oriented (OO) programming techniques can be applied to equational specification logics by distinguishing visible data from hidden data (i.e., by distinguishing the output of methods from the objects to which the methods apply), and then focusing on the behavioral equivalence of hidden data in the sense introduced by H. Reichel in 1984. Equational specification logics structured in this way are called hidden equational logics, HEL’s. The central problem is how to extend the specification of a given HEL to a specification of behavioral equivalence in a computationally effective way. S. Buss and G. Ro¸su showed in 2000 that this is not possible in general, but much work has been done on the partial specification of behavioral equivalence for a wide class of HEL’s. The OO connection suggests the use of coalgebraic methods, and J. Goguen and his collaborators have developed coinductive processes that depend on an appropriate choice of a cobasis, a special set of contexts that generates a subset of the behavioral equivalence relation. In this paper the theoretical aspects of coinduction are investigated, specifically its role as a supplement to standard equational logic for determining behavioral equivalence. Various forms of coinduction are explored. A simple characterization is given of those HEL’s
Behavioral Abstraction is Hiding Information
"... We show that for any behavioral Σspecification B there is an ordinary algebraic specification B ̃ over a larger signature, such that a model behaviorally satisfies B iff it satisfies, in the ordinary sense, the Σtheorems of B̃. The idea is to add machinery for contexts and experiments (sorts, oper ..."
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We show that for any behavioral Σspecification B there is an ordinary algebraic specification B ̃ over a larger signature, such that a model behaviorally satisfies B iff it satisfies, in the ordinary sense, the Σtheorems of B̃. 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, which takes a finite B and produces a finite B̃. The practical aspect of this procedure is that one can use any standard equational inductive theorem prover to derive behavioral theorems, even if neither equational reasoning nor induction is sound for behavioral satisfaction.
Behavioral Abstraction is Hiding Information Abstract
"... We show that for any behavioral Σspecification B there is an ordinary algebraic specification ˜ B over a larger signature, such that a model behaviorally satisfies B iff it satisfies, in the ordinary sense, the Σtheorems of ˜ B. The idea is to add machinery for contexts and experiments (sorts, ope ..."
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We show that for any behavioral Σspecification B there is an ordinary algebraic specification ˜ B over a larger signature, such that a model behaviorally satisfies B iff it satisfies, in the ordinary sense, the Σtheorems 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, which takes a finite B and produces a finite ˜ B. The practical aspect of this procedure is that one can use any standard equational inductive theorem prover to derive behavioral theorems, even if neither equational reasoning nor induction is sound for behavioral satisfaction.