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Title:Combining Effects: Sum and Tensor
Authors: Martin Hyland ; Gordon Plotkin ; John Power
Date: 2006
Publication Title:Theoretical Computer Science (Clifford lectures special issue)
Publication Type:Journal Article Publication Status:Published
Volume No:# 357(1) Page Nos:70-99
We seek a unified account of modularity for computational effects. We begin by reformulating Moggi s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations that produce the effects. Effects qua theories are then combined by appropriate bifunctors on the category of theories. We give a theory for the sum of computational effects, which in particular yields Moggi s exceptions monad transformer and an interactive input/output monad transformer. We further give a theory of the commutative combination of effects, their tensor, which yields Moggi s side-effects monad transformer. Finally we give a theory of operation transformers, for redefining operations when adding new effects; we derive explicit forms for the operation transformers associated to the above monad transformers.
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Bibtex format
author = { Martin Hyland and Gordon Plotkin and John Power },
title = {Combining Effects: Sum and Tensor},
journal = {Theoretical Computer Science (Clifford lectures special issue)},
publisher = {Elsevier},
year = 2006,
volume = {# 357(1)},
pages = {70-99},
doi = {10.1016/j.tcs.2006.03.013},
url = {},

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