One *could* write
import Data.Universe.Class (Finite (..))
class (Ord a, Finite a) => OrderedFinite a where
orderedFiniteUniverse :: Set a
orderedFiniteUniverse = S.fromList universeF
data SMaybe a = SJust !a | SNothing
wackyIntersections :: OrderedFinite a => [Set a] -> Set a
wackyIntersections = \ss -> foldr go stop ss SNothing
where
stop SNothing = orderedFiniteUniverse
stop (SJust s) = s
go s r SNothing = r (SJust s)
go s r (SJust acc)
| null acc = empty
| otherwise = r (SJust acc `intersection` s)
No such things will be going in `containers`, but perhaps they would
fit in `universe`.
On Mon, Dec 21, 2020 at 5:12 AM Tom Ellis
On Sun, Dec 20, 2020 at 11:05:39PM +0100, Ben Franksen wrote:
Am 06.12.20 um 19:58 schrieb Sven Panne:
To me it's just the other way around: It violates aesthetics if it doesn't follow the mathematical definition in all cases, which is why I don't like NonEmpty here.
I think you've got that wrong.
x `elem` intersections [] = {definition} forall xs in []. x `elem` xs = {vacuous forall} true
Any proposition P(x) is true for all x in []. So the mathematical definition of intersections::[Set a]-> Set a would not be the empty set but the set of all x:a, which in general we have no way to construct.
Yes, and to bring this back to Sven's original claim
| Why NonEmpty? I would expect "intersections [] = Set.empty", because | the result contains all the elements which are in all sets, | i.e. none. That's at least my intuition, is there some law which | this would violate?
the correct definition of "intersections []" should be "all elements which are in all of no sets" i.e. _every_ value of the given type!
Tom _______________________________________________ Libraries mailing list Libraries@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries