BibTeX
@MISC{Power_combininga,
author = {John Power and Hiroshi Watanabe},
title = {Combining a Monad and a Comonad},
year = {}
}
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Abstract
We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2-category, giving accounts of the Eilenberg-Moore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2-categorical denitions necessary to support this analysis. This work is supported by EPSRC grants GR/J84205: Frameworks for programming language semantics and logic and GR/M56333: The structure of programming languages : syntax and semantics, and British Council grant 747 FCS R34807: Data and program renement using algebraic structure. y The author acknowledges the support of STA through COE budget for Global Information Processing Project. 1 1 Introduction In recent years, th...
