Algebraic Presentation of Semifree Monads

Aloïs Rosset*, Helle Hvid Hansen, Jörg Endrullis

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

Monads and their composition via distributive laws have many applications in program semantics and functional programming. For many interesting monads, distributive laws fail to exist, and this has motivated investigations into weaker notions. In this line of research, Petrişan and Sarkis recently introduced a construction called the semifree monad in order to study semialgebras for a monad and weak distributive laws. In this paper, we prove that an algebraic presentation of the semifree monad Ms on a monad M can be obtained uniformly from an algebraic presentation of M. This result was conjectured by Petrişan and Sarkis. We also show that semifree monads are ideal monads, that the semifree construction is not a monad transformer, and that the semifree construction is a comonad on the category of monads.

Original languageEnglish
Title of host publicationCoalgebraic Methods in Computer Science - 16th IFIP WG 1.3 International Workshop, CMCS 2022, Colocated with ETAPS 2022, Proceedings
EditorsHelle Hvid Hansen, Fabio Zanasi
Place of PublicationCham
PublisherSpringer Science and Business Media Deutschland GmbH
Pages110-132
Number of pages23
ISBN (Electronic)978-3-031-10736-8
ISBN (Print)9783031107351
DOIs
Publication statusPublished - 2022
Event16th IFIP WG 1.3 International Workshop on Coalgebraic Methods in Computer Science, CMCS 2022, colocated with European Joint Conference on Theory and Practice of Software, ETAPS 2022 - Munich, Germany
Duration: 2-Apr-20223-Apr-2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13225 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th IFIP WG 1.3 International Workshop on Coalgebraic Methods in Computer Science, CMCS 2022, colocated with European Joint Conference on Theory and Practice of Software, ETAPS 2022
Country/TerritoryGermany
CityMunich
Period02/04/202203/04/2022

Keywords

  • algebraic presentation
  • algebraic theory
  • monad
  • semifree

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