Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot

Authors Paul Blain Levy , Sergey Goncharov

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Author Details

Paul Blain Levy
  • University of Birmingham, UK
Sergey Goncharov
  • FAU Erlangen-Nürnberg, Germany

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Paul Blain Levy and Sergey Goncharov. Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We introduce a new notion of "guarded Elgot monad", that is a monad equipped with a form of iteration. It requires every guarded morphism to have a specified fixpoint, and classical equational laws of iteration to be satisfied. This notion includes Elgot monads, but also further examples of partial non-unique iteration, emerging in the semantics of processes under infinite trace equivalence. We recall the construction of the "coinductive resumption monad" from a monad and endofunctor, that is used for modelling programs up to bisimilarity. We characterize this construction via a universal property: if the given monad is guarded Elgot, then the coinductive resumption monad is the guarded Elgot monad that freely extends it by the given endofunctor.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
  • Theory of computation → Axiomatic semantics
  • Guarded iteration
  • guarded monads
  • coalgebraic resumptions


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