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Traces for coalgebraic components

Published online by Cambridge University Press:  25 March 2011

ICHIRO HASUO  and
BART JACOBS
ICHIRO HASUO
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan and PRESTO Research Promotion Program, Japan Science and Technology Agency Email: ichiro@kurims.kyoto-u.ac.jp
BART JACOBS
Affiliation:
Institute for Computing and Information Sciences, Radboud University Nijmegen, P.O.Box 9010, 6500 GL Nijmegen, the Netherlands Email: bart@cs.ru.nl
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Abstract

This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, state-based modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy's tube diagrams, which are an extension of standard string diagrams for monoidal categories, to represent and manipulate component diagrams. The microcosm principle then yields a canonical ‘inner’ traced monoidal structure on the category of resumptions (elements of final coalgebras/components). This generalises an observation by Abramsky, Haghverdi and Scott.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Special Issue 2: Coalgebraic Logic , April 2011 , pp. 267 - 320
Copyright
Copyright © Cambridge University Press 2011

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