2026-07-24T21:22:24Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:4623 2024-03-06T10:35:09Z ddc:004 open_access

Update Monads: Cointerpreting Directed Containers Ahman, Danel Uustalu, Tarmo monads and distributive laws reader writer and state monads monoids and monoid actions directed containers 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Danel Ahman and Tarmo Uustalu 2014 Is Part Of LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TYPES.2013.1 urn:nbn:de:0030-drops-46235 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.1 eng https://creativecommons.org/licenses/by/3.0/legalcode