The Delay Monad and Restriction Categories

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10580)


We continue the study of Capretta’s delay monad as a means of introducing non-termination from iteration into Martin-Löf type theory. In particular, we explain in what sense this monad provides a canonical solution. We discuss a class of monads that we call \(\omega \)-complete pointed classifying monads. These are monads whose Kleisli category is an \(\omega \)-complete pointed restriction category where pure maps are total. All such monads support non-termination from iteration: this is because restriction categories are a general framework for partiality; the presence of an \(\omega \)-join operation on homsets equips a restriction category with a uniform iteration operator. We show that the delay monad, when quotiented by weak bisimilarity, is the initial \(\omega \)-complete pointed classifying monad in our type-theoretic setting. This universal property singles it out from among other examples of such monads.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Software ScienceTallinn University of TechnologyTallinnEstonia

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