The parametric continuation monad

摘要

Every dialogue category comes equipped with a continuation monad defined byrnapplying the negation functor twice. In this paper, we advocate that this doublernnegation monad should be understood as part of a larger parametric monad (or a laxrnaction) with parameter taken in the opposite of the dialogue category. This alternativernpoint of view has one main conceptual benefit: it reveals that the strength of therncontinuation monad is the fragment of a more fundamental and symmetric structure –rnprovided by a distributivity law between the parametric continuation monad and therncanonical action of the dialogue category over itself. The purpose of this work is torndescribe the formal properties of this parametric continuation monad and of itsrndistributivity law.