Add Semiring instance

[ozkutuk]

Description of the change

Semiring instance was removed by #20 with response to #18, due to it not satisfying all the semiring laws. This PR re-adds the instance with an implementation that satisfies the laws. The instance passed all the tests provided by Test.QuickCheck.Laws.Data.Semiring. The implementation is roughly the same as the instance from the semirings package on Hackage.

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Checklist:

• Added the change to the changelog's "Unreleased" section with a reference to this PR (e.g. "- Made a change (#0000)")
• Linked any existing issues or proposals that this pull request should close
• Updated or added relevant documentation
• Added a test for the contribution (if applicable)

[JordanMartinez]

In #18,

Changing the definition of zero to be Nothing could fix this but might break other laws, I'm not sure.

I'm assuming the 'other laws' are in reference to the Ring, ModuloRing, DivisionRing, and Num type classes that existed at that time.

By adding this instance back, are either type classes (e.g. Ring) now possible, too?

Otherwise, LGTM.

[ozkutuk]

I don't think having a Ring instance is possible. It requires an additive inverse operation negate such that a + negate a = zero. However, since we have zero = Nothing, there is no reasonable way to have such an inverse:

let a = Just5
a' = negate a -- Just (-5)in a + a' -- Just 0 ≠ Nothing

And since all other ring related classes require Ring as their constraint, they can't be added either. Once again, taking semirings package of Haskell as reference, there is also no Ring instance for Maybe there.

[JordanMartinez]

Makes sense. Thanks for clarifying.