License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2013.1
URN: urn:nbn:de:0030-drops-46235
URL: https://drops.dagstuhl.de/opus/volltexte/2014/4623/
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Ahman, Danel ; Uustalu, Tarmo

Update Monads: Cointerpreting Directed Containers

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Abstract

We introduce update monads as a generalization of state monads. Update
monads are the compatible compositions of reader and writer monads
given by a set and a monoid. Distributive laws between such monads are
given by actions of the monoid on the set.

We also discuss a dependently typed generalization of update monads. Unlike simple update monads, they cannot be factored into a reader and writer monad, but rather into similarly looking relative monads.

Dependently typed update monads arise from cointerpreting directed
containers, by which we mean an extension of an interpretation of the
opposite of the category of containers into the category of set
functors.

BibTeX - Entry

@InProceedings{ahman_et_al:LIPIcs:2014:4623,
  author =	{Danel Ahman and Tarmo Uustalu},
  title =	{{Update Monads: Cointerpreting Directed Containers}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{1--23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Ralph Matthes and Aleksy Schubert},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4623},
  URN =		{urn:nbn:de:0030-drops-46235},
  doi =		{10.4230/LIPIcs.TYPES.2013.1},
  annote =	{Keywords: monads and distributive laws,  reader, writer and state monads,  monoids and monoid actions,  directed containers}
}

Keywords: monads and distributive laws, reader, writer and state monads, monoids and monoid actions, directed containers
Collection: 19th International Conference on Types for Proofs and Programs (TYPES 2013)
Issue Date: 2014
Date of publication: 25.07.2014


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