Update Monads: Cointerpreting Directed Containers

Authors Danel Ahman, Tarmo Uustalu

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Danel Ahman
Tarmo Uustalu

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Danel Ahman and Tarmo Uustalu. Update Monads: Cointerpreting Directed Containers. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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.
  • monads and distributive laws
  • reader
  • writer and state monads
  • monoids and monoid actions
  • directed containers


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