A Counterexample to Tensorability of Effects

@inproceedings{Goncharov2011ACT,
  title={A Counterexample to Tensorability of Effects},
  author={Sergey Goncharov and Lutz Schr{\"o}der},
  booktitle={CALCO},
  year={2011}
}
Monads are widely used in programming semantics and in functional programming to encapsulate notions of side-effect, such as state, exceptions, input/ output, or continuations. One of their advantages is that they allow for a modular treatment of effects, using composition operators such as sum and tensor. Here, the sum represents the non-interacting combination of effects, while the tensor imposes a high degree of interaction in the shape of a commutation law. Although many important effects… 

Powermonads and Tensors of Unranked Effects

The class of uniform effects is introduced, which includes unbounded nondeterminism and continuations, and it is proved that the tensor does always exist if one of the component effects is uniform, thus in particular improving on previous results on tensoring with continuations.

Exploring the Boundaries of Monad Tensorability on Set

It is shown that the tensor of two monads need not in general exist by presenting two counterexamples, one of them involving finite powerset (i.e. the theory of join semilattices); it is also shown that tensors with bounded powerset monads do exist from countable powerset upwards.

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