The parametric continuation monad

@article{Mellis2017ThePC,
  title={The parametric continuation monad},
  author={Paul-Andr{\'e} Melli{\`e}s},
  journal={Mathematical Structures in Computer Science},
  year={2017},
  volume={27},
  pages={651-680}
}
Every dialogue category comes equipped with a continuation monad defined by applying the negation functor twice. In this paper, we advocate that this double negation monad should be understood as part of a larger parametric monad (or a lax action) with parameter taken in the opposite of the dialogue category. This alternative point of view has one main conceptual benefit: it reveals that the strength of the continuation monad is the fragment of a more fundamental and symmetric structure… CONTINUE READING

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