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19
Behavioural Satisfaction and Equivalence in Concrete Model Categories
, 1996
"... . We use the wellknown framework of concrete categories to show how much of standard universal algebra may be done in an abstract and still rather intuitive way. This is used to recast the unifying view of behavioural semantics of specications based on behavioural satisfaction and, respectively ..."
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Cited by 30 (9 self)
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. We use the wellknown framework of concrete categories to show how much of standard universal algebra may be done in an abstract and still rather intuitive way. This is used to recast the unifying view of behavioural semantics of specications based on behavioural satisfaction and, respectively, on behavioural equivalence of models abstracting away from many particular features of standard algebras. We also give an explicit representation of behavioural equivalence between models in terms of behavioural correspondences. 1 Introduction Behavioural semantics for specications plays a crucial role in the formalisation of the development process, where a specication need not be implemented exactly but only so that the required system behaviour is achieved  the idea goes back to [GGM76], [Hoa72]; see e.g. [ST95] for the context in which we view it now. There have been two basic approaches to behavioural semantics of speci cations. One introduces a new behavioural satisfaction o...
On Behavioural Abstraction and Behavioural Satisfaction in HigherOrder Logic
, 1996
"... The behavioural semantics of specifications with higherorder logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently g ..."
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Cited by 25 (5 self)
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The behavioural semantics of specifications with higherorder logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently generalized to the case of firstorder logic by Bidoit et al, is further generalized to this case. The fact that higherorder logic is powerful enough to express the indistinguishability relation is used to characterize behavioural satisfaction in terms of ordinary satisfaction, and to develop new methods for reasoning about specifications under behavioural semantics. 1 Introduction An important ingredient in the use of algebraic specifications to describe data abstractions is the concept of behavioural equivalence between algebras, which seems to appropriately capture the "black box" character of data abstractions, see e.g. [GGM76], [GM82], [ST87] and [ST95]. Roughly speaking (since there ...
Hidden Coinduction: Behavioral Correctness Proofs for Objects
 Mathematical Structures in Computer Science
, 1999
"... This paper unveils and motivates an ambitious programme of hidden algebraic research in software engineering, beginning with our general goals, continuing with an overview of results, and including some future plans. The main contribution is powerful hidden coinduction techniques for proving behavio ..."
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Cited by 24 (8 self)
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This paper unveils and motivates an ambitious programme of hidden algebraic research in software engineering, beginning with our general goals, continuing with an overview of results, and including some future plans. The main contribution is powerful hidden coinduction techniques for proving behavioral correctness of concurrent systems; several mechanical proofs are given using OBJ3. We also show how modularization, bisimulation, transition systems, concurrency and combinations of the functional, constraint, logic and object paradigms fit into hidden algebra. 1. Introduction
Extended ML: an institutionindependent framework for formal program development
 PROC. WORKSHOP ON CATEGORY THEORY AND COMPUTER PROGRAMMING
, 1986
"... The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system use ..."
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Cited by 19 (10 self)
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The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system used to write specifications, building on Goguen and Burstall's work on the notion of an institution as a formalisation of the concept of a logical system. One advantage of this is that it permits freedom in the choice of the logic used in writing specifications; an intriguing sideeffect is that it enables Extended ML to be used to develop programs in languages other than Standard ML since we view programs as simply Extended ML specifications which happen to include only "executable" axioms. The semantics of Extended ML is defined in terms of the primitive specificationbuilding operations of the ASL kernel specification language which itself has an institutionindependent semantics. It is no...
Observational Specifications and the Indistinguishability Assumption
 Theoretical Computer Science
, 1995
"... To establish the correctness of some software w.r.t. its formal specification is widely recognized as a difficult task. A first simplification is obtained when the semantics of an algebraic specification is defined as the class of all algebras which correspond to the correct realizations of the spec ..."
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Cited by 17 (0 self)
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To establish the correctness of some software w.r.t. its formal specification is widely recognized as a difficult task. A first simplification is obtained when the semantics of an algebraic specification is defined as the class of all algebras which correspond to the correct realizations of the specification. A software is then declared correct if it corresponds to some algebra of this class. We approach this goal by defining an observational satisfaction relation which is less restrictive than the usual satisfaction relation. Based on this notion we provide an institution for observational specifications. The idea is that the validity of an equational axiom should depend on an observational equality, instead of the usual equality. We show that it is not reasonable to expect an observational equality to be a congruence. We define an observational algebra as an algebra equipped with an observational equality which is an equivalence relation but not necessarily a congruence. We assume th...
A Hidden Herbrand Theorem: Combining the Object and Logic Paradigms
 Principles of Declarative Programming
, 1998
"... : The benefits of the object, logic (or relational), functional, and constraint paradigms ..."
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Cited by 11 (3 self)
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: The benefits of the object, logic (or relational), functional, and constraint paradigms
Hidden Algebra for Software Engineering
 Proceedings Combinatorics, Computation and Logic
, 1999
"... : This paper is an introduction to recent research on hidden algebra and its application to software engineering; it is intended to be informal and friendly, but still precise. We first review classical algebraic specification for traditional "Platonic" abstract data types like integers, vectors, ma ..."
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Cited by 10 (0 self)
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: This paper is an introduction to recent research on hidden algebra and its application to software engineering; it is intended to be informal and friendly, but still precise. We first review classical algebraic specification for traditional "Platonic" abstract data types like integers, vectors, matrices, and lists. Software engineering also needs changeable "abstract machines," recently called "objects," that can communicate concurrently with other objects through visible "attributes" and statechanging "methods." Hidden algebra is a new development in algebraic semantics designed to handle such systems. Equational theories are used in both cases, but the notion of satisfaction for hidden algebra is behavioral, in the sense that equations need only appear to be true under all possible experiments; this extra flexibility is needed to accommodate the clever implementations that software engineers often use to conserve space and/or time. The most important results in hidden algebra are ...
Coalgebras For Binary Methods: Properties Of Bisimulations And Invariants
, 2001
"... Coalgebras for endofunctors C > C can be used to model classes of objectoriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This extension ..."
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Cited by 9 (3 self)
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Coalgebras for endofunctors C > C can be used to model classes of objectoriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard results. 1991 Mathematics Subject Classification. 03E20, 03G30, 68Q55, 68Q65.
Towards an Adequate Notion of Observation
 ESOP '92, 4th European Symposium on Programming
, 1992
"... One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal specification at the semantical level. For this purpose, the semantics of an algebraic specification should be the class of all algebras which correspond to the correct realizations of the specifica ..."
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Cited by 7 (2 self)
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One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal specification at the semantical level. For this purpose, the semantics of an algebraic specification should be the class of all algebras which correspond to the correct realizations of the specification. We approach this goal by defining an observational satisfaction relation which is less restrictive than the usual satisfaction relation. The idea is that the validity of an equational axiom should depend on an observational equality, instead of the usual equality. We show that it is not reasonable to expect an observational equality to be a congruence, hence we define an observational algebra as an algebra equipped with an observational equality which is an equivalence relation but not necessarily a congruence. Since terms may represent computations, our notion of observation depends on a set of observable terms. From a careful case study it follows that this requires to take into acco...
Behavioral algebraization of logics
, 2008
"... Abstract. We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of manysorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL towards providing a meaningful a ..."
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Cited by 4 (4 self)
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Abstract. We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of manysorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL towards providing a meaningful algebraic counterpart also to logics with a manysorted language, and possibly including nontruthfunctional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new algebraic perspective to logics which are algebraizable using the standard tools of AAL. Furthermore, we pave the way towards a robust behavioral theory of AAL, namely by providing a behavioral version of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several wellknown characterization results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach.