Split Semiring into Semiring and Dioid

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调研方向

The proposal concerns the Semiring type class in purescript-prelude; start by reading its current definition and the five comments on this issue. The discussion asks whether to move zero and one into Dioid, but does not settle the design or name affected files. Done would require a decided design and agreement on how the breaking change and biproduct generalization should work.

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描述

From @mikesol in Discord:

Would it make sense to revamp Semiring so that it had only the operators add and mul and then use Dioid for zero and one? There is some precedent for that: https://en.m.wikipedia.org/wiki/Semiring. It would create a nice symmetry between semigroup/monoid/group and semiring/dioid/ring. It'd be a breaking change for folks using zero and one, but otherwise I think it wouldn't be too disruptive. Also, it would allow for the generalization of semiring to an analogous biproduct class, which now isn't possible because zero and one necessarily leave out all but one of the types in the biproduct or biCCC class. Thoughts?

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