Either as a lattice, Maybe as a lattice

haskellari / lattices

Fine-grained lattice primitives for Haskell

BSD 3-Clause "New" or "Revised" License

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Either as a lattice, Maybe as a lattice #98

Closed erykciepiela closed 4 years ago

erykciepiela commented 4 years ago

Add (Lattice a, Lattice b) => Lattice (Either a b) instance constructed by considering all minimal elements of b greater than all maximal elements of a Add Lattice a => Lattice (Maybe a) instance constructed by using Nothing as 0 element

phadej commented 4 years ago

There're Levitated and Dropped, as picking one over other for Maybe is arbitrary (cf Sum and Product Monoids in base)
That instance for Either is not a coproduct in the category of partial orders, so I'd also have a different type for it (c.f. instances for (a,b) and Lexicographic).

phadej commented 4 years ago

To clarify, I'd not object having a type isomorphic to Either which is:

-- The name of this construction is escaping me atm
data SomeName a b = Upper a | Lower b

which your instance, but not for Either.

erykciepiela commented 4 years ago

Thanks for insightful comments. I think I get the point and general spirit of the library now. As for Either instance, in the spirit of Levitated and Dropped I would propose Stacked. Regarding Maybe I would propose conversion functions from Maybe to Dropped and Lifted. All these as part of the other PR #99.