Re: Monoid over XOR or XNOR, and Monoid lifted by Applicative.

There are several packagings of lattices and semilattices strewn across hackage, and not much convergence on any single one. Sent from my iPhone

On May 5, 2018, at 4:54 PM, Matthew Farkas-Dyck wrote:

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On 5/5/18, Edward Kmett wrote: In that same light, we're also missing packaged monoids for the bitwise (.|.), (.&.), xor (and the non-existent xnor) from Data.Bits.

I defined a `BitSet` type in my alg package: http://hackage.haskell.org/package/alg (Building docs failed, so here is the definition: `newtype BitSet a = BitSet { bits :: a }`)

The `Monoid` instance is (`False`, `xor`) (wasn't thinking about xnor, stupid me).

I was also trying to define `Monoid` instances for `Min (BitSet a)` and `Max (BitSet a)` but alas, they overlap, tho `BitSet` is not `Ord` (so usual instances are useless).

Maybe we want a `Lattice` class?