A Unified View of Monadic and Applicative Non-determinism

with Exequiel Rivas and Tom Schrijvers. SCP 2018.PDFCode


It is well-known that monads are monoids in the category of endofunctors, and in fact so are applicative functors. Unfortunately, monoids do not have enough structure to account for computational effects with non-determinism operators. This article recovers a unified view of computational effects with non- determinism by extending monoids to near-semirings with both additive and multiplicative structure. This enables us to generically define free constructions as well as a novel double Cayley representation that optimises both left-nested sums and left-nested products.


author    = {Exequiel Rivas and Mauro Jaskelioff and Tom Schrijvers},
title     = {A unified view of monadic and applicative non-determinism},
journal   = {Science of Computer Programming},
volume    = {152},
pages     = {70--98},
year      = {2018},
url       = {https://doi.org/10.1016/j.scico.2017.09.007},
doi       = {10.1016/j.scico.2017.09.007}