Control Flow Semantics. Foundations of Computing Series. (1996)

by Jaco W de Bakker, Erik P de Vink
Results 1 - 10 of 27

Universal coalgebra: a theory of systems

by J. J. M. M. Rutten , 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 ..."
Abstract - Cited by 408 (42 self) - Add to MetaCart
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

Automata and coinduction (an exercise in coalgebra

by J. J. M. M. Rutten - LNCS , 1998
"... The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which ..."
Abstract - Cited by 86 (19 self) - Add to MetaCart
The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.
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Generalized Metric Spaces: Completion, Topology, and Powerdomains via the Yoneda Embedding

by M.M. Bonsangue, F. van Breugel, J. J. M. M. Rutten , 1996
"... Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere 1973). Combining Lawvere's (1973) enriched-categorical and Smyth' (1988, 1991) topological view on generalized metric spaces, it is shown how to construct 1. completion, 2. topology, and ..."
Abstract - Cited by 30 (3 self) - Add to MetaCart
Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere 1973). Combining Lawvere's (1973) enriched-categorical and Smyth' (1988, 1991) topological view on generalized metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ordinary metric spaces, these constructions yield, respectively: 1. chain completion and Cauchy completion; 2. the Alexandroff and the Scott topology, and the ffl-ball topology; 3. lower, upper, and convex powerdomains, and the hyperspace of compact subsets. All constructions are formulated in terms of (a metric version of) the Yoneda (1954) embedding.
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The Essence of Multitasking

by William L. Harrison - Proceedings of the 11th International Conference on Algebraic Methodology and Software Technology, volume 4019 of Lecture Notes in Computer Science , 2006
"... Abstract. This article demonstrates how a powerful and expressive abstraction from concurrency theory—monads of resumptions—plays a dual rôle as a programming tool for concurrent applications. The article demonstrates how a wide variety of typical OS behaviors may be specified in terms of resumption ..."
Abstract - Cited by 13 (5 self) - Add to MetaCart
Abstract. This article demonstrates how a powerful and expressive abstraction from concurrency theory—monads of resumptions—plays a dual rôle as a programming tool for concurrent applications. The article demonstrates how a wide variety of typical OS behaviors may be specified in terms of resumption monads known heretofore exclusively in the literature of programming language semantics. We illustrate the expressiveness of the resumption monad with the construction of an exemplary multitasking kernel in the pure functional language Haskell. 1
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Generalized distance functions in the theory of computation

by Anthony Karel Seda, Pascal Hitzler - Computer Journal
"... We discuss a number of distance functions encountered in the theory of computation, including ..."
Abstract - Cited by 11 (0 self) - Add to MetaCart
We discuss a number of distance functions encountered in the theory of computation, including
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Congruence for SOS with data

by Mohammadreza Mousavi, Michel Reniers, Jan Friso Groote - In Proceedings of LICS’04 , 2004
"... While studying the specification of the operational semantics of different programming languages and formalisms, one can observe the following three facts. Firstly, Plotkin’s style of Structured Operational Semantics (SOS) has become a standard in defining operational semantics. Secondly, congruence ..."
Abstract - Cited by 10 (5 self) - Add to MetaCart
While studying the specification of the operational semantics of different programming languages and formalisms, one can observe the following three facts. Firstly, Plotkin’s style of Structured Operational Semantics (SOS) has become a standard in defining operational semantics. Secondly, congruence with respect to some notion of bisimilarity is an interesting property for such languages and it is essential in reasoning about them. Thirdly, there are numerous languages that contain an explicit data part in the state of the operational semantics. The first two facts, have resulted in a line of research exploring syntactic formats of operational rules to derive the desired congruence property for free. However, the third point (in combination with the first two) is not sufficiently addressed and there is no standard congruence format for operational semantics with an explicit data state. In this paper, we address this problem by studying the implications of the presence of a data state on the notion of bisimilarity. Furthermore, we propose a number of formats for congruence. 1

Coalgebra, Concurrency, and Control

by J. J. M. M. Rutten - PROCEEDINGS OF THE 5TH WORKSHOP ON DISCRETE EVENT SYSTEMS (WODES 2000 , 1999
"... Coalgebra is used to generalize notions and techniques from concurrency theory, in order to apply them to problems concerning the supervisory control of discrete event systems. The main ingredients of this approach are the characterization of controllability in terms of (a variant of) the notion of ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
Coalgebra is used to generalize notions and techniques from concurrency theory, in order to apply them to problems concerning the supervisory control of discrete event systems. The main ingredients of this approach are the characterization of controllability in terms of (a variant of) the notion of bisimulation, and the observation that the family of (partial) languages carries a final coalgebra structure. This allows for a pervasive use of coinductive definition and proof principles, leading to a conceptual unification and simplification and, in a number of cases, to more general and more efficient algorithms.
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A metric model of PCF

by Martín Hötzel Escardó , 1998
"... We introduce a computationally adequate metric model of PCF, based on the fact that the category of non-expansive maps of complete bounded ultrametric spaces is cartesian closed. The model captures certain temporal aspects of higher-type computation and contains both extensional and intensional func ..."
Abstract - Cited by 6 (0 self) - Add to MetaCart
We introduce a computationally adequate metric model of PCF, based on the fact that the category of non-expansive maps of complete bounded ultrametric spaces is cartesian closed. The model captures certain temporal aspects of higher-type computation and contains both extensional and intensional functions. We show that Scott’s model arises as its extensional collapse. The intensional aspects of the metric model are illustrated via a Gödel-number-free version of Kleene’s T-predicate.
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Themes in Final Semantics

by Marina Lenisa - Dipartimento di Informatica, Università di , 1998
"... C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: "C'era una volta un re seduto in canap`e ..."
Abstract - Cited by 6 (2 self) - Add to MetaCart
C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: "C'era una volta un re seduto in canap`e

A Theory of Metric Labelled Transition Systems

by Franck Van Breugel - Papers on General Topology and Applications: 11th Summer Conference at the University of Southern Maine, volume 806 of Annals of the New York Academy of Sciences , 1995
"... Labelled transition systems are useful for giving semantics to programming languages. Kok and Rutten have developed some theory to prove semantic models defined by means of labelled transition systems to be equal to other semantic models. Metric labelled transition systems are labelled transition sy ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
Labelled transition systems are useful for giving semantics to programming languages. Kok and Rutten have developed some theory to prove semantic models defined by means of labelled transition systems to be equal to other semantic models. Metric labelled transition systems are labelled transition systems with the configurations and actions endowed with metrics. The additional metric structure allows us to generalize the theory developed by Kok and Rutten. Introduction The classical result due to Banach [Ban22] that a contractive function from a nonempty complete metric space to itself has a unique fixed point plays an important role in the theory of metric semantics for programming languages. Metric spaces and Banach's theorem were first employed by Nivat [Niv79] to give semantics to recursive program schemes. Inspired by the work of Nivat, De Bakker and Zucker [BZ82] gave semantics to concurrent languages by means of metric spaces. The metric spaces they used were defined as solutio...
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