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On the Duality between Observability and Reachability
 PROC. 4TH INT. CONF. FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS'01
, 2001
"... Observability and reachability are important concepts in formal software development. While observability concepts allow to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper ..."
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Observability and reachability are important concepts in formal software development. While observability concepts allow to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper, we show that there is a duality between observability and reachability, both from a methodological and from a formal point of view. In particular, we establish a correspondence between observer operations and datatype constructors, observational algebras and constructorbased algebras, and observational and inductive properties of specifications. Our study is based on the observational logic institution [11] and on a novel treatment of reachability which introduces the constructorbased logic institution. Both institutions are tailored to capture the semantically correct realizations of a specification from the observational and reachability points of view. The duality between the observability and reachability concepts is then formalized in a categorytheoretic setting.
On specification logics for algebracoalgebra structures: Reconciling reachability and observability
 Proceedings of FoSSaCS 2002, volume 2303 of LNCS
, 2002
"... Abstract. The paper builds on recent results regarding the expressiveness of modal logics for coalgebras in order to introduce a specification framework for coalgebraic structures which offers support for modular specification. An equational specification framework for algebraic structures is obtain ..."
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Abstract. The paper builds on recent results regarding the expressiveness of modal logics for coalgebras in order to introduce a specification framework for coalgebraic structures which offers support for modular specification. An equational specification framework for algebraic structures is obtained in a similar way. The two frameworks are then integrated in order to account for structures comprising both a coalgebraic (observational) component and an algebraic (computational) component. The integration results in logics whose sentences are either coalgebraic (modal) or algebraic (equational) in nature, but whose associated notions of satisfaction take into account both the coalgebraic and the algebraic features of the structures being specified. Each of the logics thus obtained also supports modular specification. 1
ObjectOriented Hybrid Systems of Coalgebras plus Monoid Actions
 Algebraic Methodology and Software Technology (AMAST
, 1996
"... . Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (nontempora ..."
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. Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (nontemporal) objectoriented systems). The monoid action captures the influence of time on the state space, where the monoids that we consider are the natural numbers monoid (N; 0; +) of discrete time, and the positive reals monoid (R0 ; 0; +) of real time. Based on this semantics we develop a hybrid specification formalism with timed method applications: it involves expressions like s:meth@ff, with the following meaning: in state s let the state evolve for ff units of time (according to the monoid action), and then apply the (coalgebraic) method meth. In this formalism we specify various (elementary) hybrid systems, investigate their correctness, and display their behaviour in simulations. We furthe...
doi:10.1093/comjnl/bxm031 On the Behavioral Equivalence Between kdata Structures
"... Throughout this paper we consider data structures as sorted algebras endowed with a designated subset of their visible part, which represents the set of truth values. The originality of our approach is the application of the standard abstract algebraic logic theory of deductive systems to the hidden ..."
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Throughout this paper we consider data structures as sorted algebras endowed with a designated subset of their visible part, which represents the set of truth values. The originality of our approach is the application of the standard abstract algebraic logic theory of deductive systems to the hidden heterogeneous case. We generalize the wellknown equivalence relation between finite automata, which relies on the Nerode equivalence relation between states, to kdata structures. This is obtained via the Leibniz congruence, which can be viewed as a generalization of the Nerode equivalence in automata theory.
Algebraic System Specification and Development: Survey and Annotated Bibliography  Second Edition 
, 1997
"... Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . ..."
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Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.2 Action Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.1 Early Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.2 Recent Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . 55 4.7.3 The Common Framework Initiative. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5 Methodology 57 5.1 Development Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Applica...
On Observability and Reachability
"... Observability and reachability are important concepts in formal software development. While observability concepts allow to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of data type constructors. In this pape ..."
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Observability and reachability are important concepts in formal software development. While observability concepts allow to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of data type constructors. In this paper we show that there is a duality between observability and reachability, both from a methodological and from a formal point of view. In particular, we establish a correspondence between observer operations and data type constructors, observational algebras and constructorbased algebras, and observational and inductive properties of specifications. Our study is based on the observational logic institution [7] and on a novel treatment of reachability which introduces the institution of constructorbased logic. The duality between both concepts is formalised in a categorytheoretic setting.
Observational Truth as a Categorical Modality
"... Abstract We examine the notion of truthuptoobservability in the setting of categorical logic and show that it can be captured by a modal operator. We view socalled `hidden algebras ' as setvalued functors on a category of observations. Our main results extend the KripkeBethJoyal semantic ..."
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Abstract We examine the notion of truthuptoobservability in the setting of categorical logic and show that it can be captured by a modal operator. We view socalled `hidden algebras ' as setvalued functors on a category of observations. Our main results extend the KripkeBethJoyal semantics for the internal logics of functor toposes to the observational modality. We also give a categorical account of coinduction as a proof technique for establishing observational truth, and give a covariety theorem that characterises a class of algebras as equationally definable up to observability iff the class forms a slice topos over a particular form of subobject.
FACS 2005 ComponentBased Specification of Distributed Systems
"... Abstract We suggest that hidden algebra can provide a setting for component specification and composition that has the advantages of algebraic specification, without the disadvantages of objectoriented approaches where communication between components is mediated solely by method invocation. We pro ..."
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Abstract We suggest that hidden algebra can provide a setting for component specification and composition that has the advantages of algebraic specification, without the disadvantages of objectoriented approaches where communication between components is mediated solely by method invocation. We propose a basic composition mechanism for hidden algebraic component specifications that is based on communication through shared subcomponents, and show that this composition mechanism on specifications extends naturally to allow models (or implementations) of the component specifications to be amalgamated into a model of the composite system.
ComponentBased Specification of Distributed Systems Abstract
, 2005
"... We suggest that hidden algebra can provide a setting for component specification and composition that has the advantages of algebraic specification, without the disadvantages of objectoriented approaches where communication between components is mediated solely by method invocation. We propose a ba ..."
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We suggest that hidden algebra can provide a setting for component specification and composition that has the advantages of algebraic specification, without the disadvantages of objectoriented approaches where communication between components is mediated solely by method invocation. We propose a basic composition mechanism for hidden algebraic component specifications that is based on communication through shared subcomponents, and show that this composition mechanism on specifications extends naturally to allow models (or implementations) of the component specifications to be amalgamated into a model of the composite system. As part of a general trend towards decentralisation [16], computer systems tend more and more to be constructed from distributed, selfcontained, and possibly autonomous units. The challenges that this poses to computer science are reflected in the growth of new paradigms such as componentbased, serviceoriented, and aspectoriented software, and of new languages for modelling, specifying, composing, and coordinating these units. The object paradigm certainly helped set these developments moving: code could be organised at the level of classes, architectures at the level of class instances, and both these levels could be seen as comprising selfcontained, even autonomous units. Distributedness is an essential part of the object paradigm, with interaction between instances being mediated by (possibly remote) method invocation, and type systems that include interfaces and abstract classes allow systems of interacting objects to be built from subsystems in a robust and flexible way. Yet it is widely agreed that the basic mechanism of interaction through method invocation does not meet the challenges posed by decentralised software systems. For example, Andrade and Fiadeiro [1], concerned with serviceoriented software, describe (op. cit., p. 380) ‘a gap between the highlevel