Partiality and Container Monads

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10695)


We investigate monads of partiality in Martin-Löf type theory, following Moggi’s general monad-based method for modelling effectful computations. These monads are often called lifting monads and appear in category theory with different but related definitions. In this paper, we unveil the relationship between containers and lifting monads. We show that the lifting monads usually employed in type theory can be specified in terms of containers. Moreover, we give a precise characterization of containers whose interpretations carry a lifting monad structure. We show that these conditions are tightly connected with Rosolini’s notion of dominance. We provide several examples, putting particular emphasis on Capretta’s delay monad and its quotiented variant, the non-termination monad.



We are thankful to Thorsten Altenkirch and Martín Escardó for discussions and valuable hints.

This research was supported by the ERDF funded Estonian national CoE project EXCITE and the Estonian Ministry of Education and Research institutional research grant IUT33-13.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Software ScienceTallinn University of TechnologyTallinnEstonia
  2. 2.IT University of CopenhagenCopenhagen SDenmark

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