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13
Universal coalgebra: a theory of systems
, 2000
"... 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 certa ..."
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Cited by 386 (41 self)
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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 (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded 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
Automatically Checking an Implementation against Its Formal Specification
 IEEE Transactions on Software Engineering
, 2000
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Modet: Report on the Larch Shared Language, Version 2.3
, 1990
"... work may not be copied or reproduced in whole or in part for any commercial purpose. ..."
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Cited by 28 (1 self)
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work may not be copied or reproduced in whole or in part for any commercial purpose.
An Example of Interactive Hardware Transformation
, 1993
"... 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 issu ..."
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Cited by 10 (1 self)
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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...
Musical Qualia, Context, Time, and Emotion
 Journal of Consciousness Studies
, 2004
"... 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 ..."
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Cited by 7 (3 self)
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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 multilayer emergent, noncompositional, enacted, and situation dependent, among other nonCartesian properties.
SpecificationBased Incremental Testing of Object Oriented Systems
, 2000
"... 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 an ..."
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Cited by 2 (1 self)
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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 specificationbased 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.
Generating abstractors for abstract data types
, 1992
"... 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 ..."
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Cited by 2 (1 self)
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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,
HIGHERORDER ALGEBRA WITH TRANSFINITE TYPES
"... We extend the simple type system of higherorder algebra with transfinite types. We present a general model theory for transfinite higherorder algebra including results on the existence and construction of free and initial models, and a sound and complete equational calculus. We demonstrate the use ..."
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We extend the simple type system of higherorder algebra with transfinite types. We present a general model theory for transfinite higherorder algebra including results on the existence and construction of free and initial models, and a sound and complete equational calculus. We demonstrate the use of transfinite types for modelling polymorphism by specifying a simple polymorphic functional programming language.