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Combining Computational Effects: Commutativity and Sum
, 2002
"... We begin to develop a unified account of modularity for computational effects. We use the notion of enriched Lawvere theory, together with its relationship with strong monads, to reformulate Moggi's paradigm for modelling computational effects; we emphasise the importance here of the operations ..."
Abstract

Cited by 19 (4 self)
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We begin to develop a unified account of modularity for computational effects. We use the notion of enriched Lawvere theory, together with its relationship with strong monads, to reformulate Moggi's paradigm for modelling computational effects; we emphasise the importance here of the operations that induce computational effects. Effects qua theories are then combined by appropriate bifunctors (on the category of theories). We give a theory of the commutative combination of effects, which in particular yields Moggi's sideeffects monad transformer (an application is the combination of sideeffects with nondeterminism). And we give a theory...
Pseudodistributive laws
, 2004
"... We address the question of how elegantly to combine a number of different structures, such as finite product structure, monoidal structure, and colimiting structure, on a category. Extending work of Marmolejo and Lack, we develop the definition of a pseudodistributive law between pseudomonads, and ..."
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Cited by 13 (1 self)
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We address the question of how elegantly to combine a number of different structures, such as finite product structure, monoidal structure, and colimiting structure, on a category. Extending work of Marmolejo and Lack, we develop the definition of a pseudodistributive law between pseudomonads, and we show how the definition and the main theorems about it may be used to model several such structures simultaneously. Specifically, we address the relationship between pseudodistributive laws and the lifting of one pseudomonad to the 2category of algebras and to the Kleisli bicategory of another. This, for instance, sheds light on the preservation of some structures but not others along the Yoneda embedding. Our leading examples are given by the use of open maps to model bisimulation and by the logic of bunched implications.