TY - GEN
T1 - Algebraic Presentation of Semifree Monads
AU - Rosset, Aloïs
AU - Hansen, Helle Hvid
AU - Endrullis, Jörg
N1 - Funding Information:
We thank Ralph Sarkis, and Roy Overbeek for useful discussion, suggestions and corrections. We also thank all anonymous reviewers for their valuable feedback and suggestions. Aloïs Rosset and Jörg Endrullis received funding from the Netherlands Organization for Scientific Research (NWO) under the Innovational Research Incentives Scheme Vidi (project. No. VI.Vidi.192.004).
Publisher Copyright:
© 2022, IFIP International Federation for Information Processing.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - algebraic presentation
KW - algebraic theory
KW - monad
KW - semifree
UR - http://www.scopus.com/inward/record.url?scp=85135018645&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-10736-8_6
DO - 10.1007/978-3-031-10736-8_6
M3 - Conference contribution
AN - SCOPUS:85135018645
SN - 9783031107351
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 110
EP - 132
BT - Coalgebraic Methods in Computer Science - 16th IFIP WG 1.3 International Workshop, CMCS 2022, Colocated with ETAPS 2022, Proceedings
A2 - Hansen, Helle Hvid
A2 - Zanasi, Fabio
PB - Springer Science and Business Media Deutschland GmbH
CY - Cham
T2 - 16th 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
Y2 - 2 April 2022 through 3 April 2022
ER -