Combining continuations with other effects

A fundamental question, in modelling computational effects, is how to give a unified semantic account of modularity, i.e., a mathematical theory that supports the various combinations one naturally makes of computational effects such as exceptions, side-effects, interactive input/output, nondeterminism, and, particularly for this workshop, continuations [2, 3, 5]. We have begun to give such an account over recent years for all of these effects other than continuations [8], describing the sum and the tensor, or commutative combination, of effects, starting from Eugenio Moggi’s proposal to use monads to give semantics for each individual effect [15]. That has yielded the most commonly used combinations of the various effects. Here, we extend our account to include continuations.