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Don't Try This at Home: No-Go Theorems for Distributive Laws. (arXiv:1811.06460v2 [math.CT] UPDATED)
来源于:arXiv
Beck's distributive laws provide sufficient conditions under which two monads
can be composed, and monads arising from distributive laws have many desirable
theoretical properties. Unfortunately, finding and verifying distributive laws,
or establishing if one even exists, can be extremely difficult and error-prone.
We develop general-purpose techniques for showing when there can be no
distributive law between two monads. Two approaches are presented. The first
widely generalizes ideas from a counterexample attributed to Plotkin, yielding
general-purpose theorems that recover the previously known situations in which
no distributive law can exist. Our second approach is entirely novel,
encompassing new practical situations beyond our generalization of Plotkin's
approach. It negatively resolves the open question of whether the list monad
distributes over itself.
Our approach adopts an algebraic perspective throughout, exploiting a
syntactic characterization of distributive laws. This appr 查看全文>>