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Premonoidal categories and notions of computation

Published online by Cambridge University Press:  01 October 1997

JOHN POWER  and
EDMUND ROBINSON
JOHN POWER
Affiliation:
Department of Computer Science, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, Scotland
EDMUND ROBINSON
Affiliation:
Department of Computer Science, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, UK
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Abstract

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We introduce the notions of premonoidal category and premonoidal functor, and show how these can be used in the denotational semantics of programming languages. We characterize the semantic definitions of Eugenio Moggi's monads as notions of computation, exhibit a representation theorem for our premonoidal setting in terms of monads, and give a fibrational setting for the structure.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 7 , Issue 5 , October 1997 , pp. 453 - 468
Copyright
1997 Cambridge University Press