In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (Non-Well-Founded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of non-wellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken

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This article presents an example of correct circuit design through interactive transformation. Interactive transformation differs from traditional hardware design transformation frameworks in that it focuses on the issue of finding suitable hardware architecture for the specified system and the issue of architecture correctness. The transformation framework divides every transformation in designs into two steps. The first step is to find a proper architecture implementation. Although the framework does not guarantee existence of such an implementation, nor its discovery, it does provide a characterization of architectural implementation so that the question "is this a correct implementation?" can be answered by equational rewriting. The framework allows a correct architecture implementation to be automatically incorporated with control descriptions to obtain a new system description. The significance of this transformation framework lies in the fact that it requires simpler mechanism o...

Nearly all listeners consider the subjective aspects of music, such as its emotional tone, to have primary importance. But contemporary philosophers often downplay, ignore, or even deny such aspects of experience. Moreover, traditional philosophies of music try to decontextualize it. Using music as an example, this paper explores the structure of qualitative experience, demonstrating that it is multi-layer emergent, non-compositional, enacted, and situation dependent, among other non-Cartesian properties.

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Inheritance is an important feature of the OO approach that allows a designer to easily build a new derived class that extends the functionality of an existing base class. In order to exploit the full potential of inheritance to build systems incrementally, the designer must also be able to test and reason about the behavior of the derived class in an incremental manner. In this paper we develop a specification-based technique for testing both base and derived classes, with the specification and tests for the derived class being obtained incrementally from those of the base class. Using our approach, given the concrete specification of a method m() of a class, we can mechanically generate a simple test method for m(). We show how our approach can be integrated with a standard testing framework. We illustrate the approach by applying it to a simple example.

Values of an abstract data type (ADT) may be built by some of its functions called constructors. A construction term of an ADT value is an expression which contains only constructors and whose evaluation yields the value. For a given ADT, the abstractor is a function that converts its values to the corresponding construction terms. Abstractors may be used in communicating ADT values in distributed programs. This paper addresses the problem of generating abstractors of types from their algebraic specifications. We classify specifications into two classes: symmetric and asymmetric. We show that for a given type if its specification is symmetric, the abstractor can be automatically generated, and if the specification is asymmetric, it is feasible to generate the abstractors when the specification meets certain conditions,

Due to the unprecedented pace of technology development and the increasing flexibility of manufacturing, there is a growing demand for design automation. Since design often requires creativity or even ingenuity, it is one of the most complex tasks humans perform. Because of its complexity, design automation has been limited to routine and detail design. Recently, however, attention has been shifted towards conceptual and innovative design [Navichandra, 1990]. A number of techniques and methods has been proposed, such as [Mostow, 1985], [Goel, 1989] or [Navichandra, 1991a]. Most of these approaches, however, emphasize implementational issues. Design aids or specification methods still lack conceptual frameworks. The research described in this paper is concerned with the formal specification of the entire design process. The proposed many-sorted first order logic approach provides several advantages, such as modular decomposition, encapsulation, direct implementability and reusability. Its main advantage, however, is the faithful formal representation of the design process. First order many-sorted logic is an extension of classical first order logic. In classical first order logic, the world is represented by a class of models which contain homogeneous sets. A mathematical model in first order logic is, therefore, a homogeneous set with a set of (total) functions and relations. Our design environments, however, are made of different types of objects and for each type we have different sets of relations and operations. Therefore, an adequate representation of the world should contain heterogeneous sets. A heterogeneous or many-sorted model is based on a set of elements divided into subsets or sorts. Each element belongs