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Feedback, trace and fixed-point semantics

Published online by Cambridge University Press:  15 December 2002

P. Katis ,
Nicoletta Sabadini  and
Robert F.C. Walters
P. Katis
Affiliation:
Dipartimento di Scienze CC. FF.MM.,Università degli Studi dell'Insubria, Como, Italy; [email protected]@uninsubria.it.
Nicoletta Sabadini
Affiliation:
Dipartimento di Scienze CC. FF.MM.,Università degli Studi dell'Insubria, Como, Italy; [email protected]@uninsubria.it.
Robert F.C. Walters
Affiliation:
Dipartimento di Scienze CC. FF.MM.,Università degli Studi dell'Insubria, Como, Italy; [email protected]@uninsubria.it. School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

We introduce a notion of category with feedback-with-delay, closely related to the notion of traced monoidal category, and show that the Circ construction of [15] is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal et al. [12] we obtain a description of the free compact closed category on a symmetric monoidal category. We thus obtain a categorical analogue of the classical localization of a ring with respect to a multiplicative subset. In this context we define a notion of fixed-point semantics of a category with feedback which is seen to include a variety of classical semantics in computer science.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 2: Fixed Points in Computer Science (FICS'01) , April 2002 , pp. 181 - 194
Copyright
© EDP Sciences, 2002

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