Abstract
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. • A unified model of monadic and applicative non-determinism. • General free constructions and Cayley representations. • Different non-determinism constructions from existing monads and applicatives. • Example applications to combinatorial search and interleaving parsers.
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