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The delay monad and restriction categories

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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 ω-complete pointed classifying monads. These are monads whose Kleisli category is an ω-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 ω-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 ω-complete pointed classifying monad in our type-theoretic setting. This universal property singles it out from among other examples of such monads.
Original languageEnglish
Title of host publicationTheoretical Aspects of Computing - ICTAC 2017: 14th International Colloquium, Hanoi, Vietnam, October 23-27, 2017, Proceedings
EditorsDang Van Hung, Deepak Kapur
Number of pages19
Place of PublicationCham
PublisherSpringer
Publication date2017
Pages32-50
ISBN (Print)978-3-319-67729-3
DOIs
Publication statusPublished - 2017
Externally publishedYes
Event14th International Colloquium on Theoretical Aspects of Computing, 2017 -
Duration: 23 Oct 201727 Oct 2017

Conference

Conference14th International Colloquium on Theoretical Aspects of Computing, 2017
Periode23/10/201727/10/2017
SeriesLecture Notes in Computer Science
Volume10580
ISSN0302-9743

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