2024

  1. Correspondence Between Composite Theories and Distributive Laws
    RossetAloı̈s, Maaike Zwart, Helle Hvid Hansen, and Jörg Endrullis
    In: Coalgebraic Methods in Computer Science - 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024, Luxembourg City, Luxembourg, April 6-7, 2024, Proceedings König, Barbara and Urbat, Henning (eds.) , pp. 194–215 , Springer (2024)
    paper

    Summary

    Composite theories are the algebraic equivalent of distributive laws. In this paper, we delve into the details of this correspondence and concretely show how to construct a composite theory from a distributive law and vice versa. Using term rewriting methods, we also describe when a minimal set of equations axiomatises the composite theory.

    Bibtex

    @inproceedings{monads:composite:theories:2024,
  author = {Rosset, Alo{\"{\i}}s and Zwart, Maaike and Hansen, Helle Hvid and Endrullis, J{\"{o}}rg},
  editor = {K{\"{o}}nig, Barbara and Urbat, Henning},
  title = {Correspondence Between Composite Theories and Distributive Laws},
  booktitle = {Coalgebraic Methods in Computer Science - 17th {IFIP} {WG} 1.3 International
                    Workshop, {CMCS} 2024, Colocated with {ETAPS} 2024, Luxembourg City,
                    Luxembourg, April 6-7, 2024, Proceedings},
  series = {Lecture Notes in Computer Science},
  volume = {14617},
  pages = {194--215},
  publisher = {Springer},
  year = {2024},
  url = {https://doi.org/10.1007/978-3-031-66438-0\_10},
  doi = {10.1007/978-3-031-66438-0\_10},
  biburl = {https://dblp.org/rec/conf/cmcs/RossetZHE24.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org},
  keywords = {coalgebra, rewriting},
  type = {workshop}
}

    Digital Object Identifier

    10.1007/978-3-031-66438-0_10

2022

  1. Algebraic Presentation of Semifree Monads
    RossetAloı̈s, Helle Hvid Hansen, and Jörg Endrullis
    In: Coalgebraic Methods in Computer Science - 16th IFIP WG 1.3 International Workshop, CMCS 2022, Colocated with ETAPS 2022, Munich, Germany, April 2-3, 2022, Proceedings Hansen, Helle Hvid and Zanasi, Fabio (eds.) , pp. 110–132 , Springer (2022)
    paper

    Summary

    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 M^s 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.

    Bibtex

    @inproceedings{monads:semifree:2022,
  author = {Rosset, Alo{\"{\i}}s and Hansen, Helle Hvid and Endrullis, J{\"{o}}rg},
  editor = {Hansen, Helle Hvid and Zanasi, Fabio},
  title = {Algebraic Presentation of Semifree Monads},
  booktitle = {Coalgebraic Methods in Computer Science - 16th {IFIP} {WG} 1.3 International
                    Workshop, {CMCS} 2022, Colocated with {ETAPS} 2022, Munich, Germany,
                    April 2-3, 2022, Proceedings},
  series = {Lecture Notes in Computer Science},
  volume = {13225},
  pages = {110--132},
  publisher = {Springer},
  year = {2022},
  url = {https://doi.org/10.1007/978-3-031-10736-8\_6},
  doi = {10.1007/978-3-031-10736-8\_6},
  biburl = {https://dblp.org/rec/conf/cmcs/RossetHE22.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org},
  keywords = {coalgebra},
  type = {workshop}
}

    Digital Object Identifier

    10.1007/978-3-031-10736-8_6