- Abstract:
-
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.
- Links To Paper
- 1st Link
- Bibtex format
- @Article{EDI-INF-RR-0599,
- 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 = {http://homepages.inf.ed.ac.uk/gdp/publications/Comb_Effects_Jour.pdf},
- }
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