| Issue |
RAIRO-Theor. Inf. Appl.
Volume 36, Number 2, April/June 2002
Fixed Points in Computer Science (FICS'01)
|
|
|---|---|---|
| Page(s) | 181 - 194 | |
| DOI | https://doi.org/10.1051/ita:2002009 | |
| Published online | 15 December 2002 | |
Feedback, trace and fixed-point semantics
1
Dipartimento di Scienze CC.
FF.MM.,Università degli Studi dell'Insubria, Como, Italy;
nicoletta.sabadini@uninsubria.it.robert.walters@uninsubria.it.
2
School of Mathematics and Statistics,
University of Sydney, NSW 2006, Australia.
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.
Mathematics Subject Classification: 68Q55 / 68Q70 / 18D10
© EDP Sciences, 2002
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