Re: [Haskell-cafe] Faster set intersections?

That does seem to be what the source code says. The code only handles non-empty sets, but I *believe* the Maybe-wrapped version can handle intersections, albeit inefficiently. Can a version that looks like (a -> Bool) -> Maybe a work? On Sun, Dec 9, 2018, 1:41 PM MigMit

My guess — by finding a member that satisfies a predicate, if it's at all possible, and any member if the predicate is const False. It's actually pretty awesome.

...

On 9 Dec 2018, at 19:36, Brandon Allbery wrote:

Naïvely, a set implemented as a predicate determining membership?

On Sun, Dec 9, 2018 at 1:32 PM Siddharth Bhat wrote: I don't understand, how does

(a -> Bool) -> a

model a set?

Thanks Siddharth

On Sun, 9 Dec, 2018, 22:08 Olaf Klinke, wrote:

...

Note that a concrete set "concretizes" anything it touches. Don't take unions of these sets, though, it'll just be a mess.

Won't a union just be the same as intersection but using || instead of && ?

-Jan-Willem Maessen

Unions of predicates and concrete sets are easy, thanks to Set.member:

union (Pred p) (Concrete s) = Pred (\k -> p k || member k s)

What you can not do, of course, is enumerate and fold these sets. There is a set type [1] which supports a litte bit more:

Set a = Maybe ((a -> Bool) -> a)

It has unions, intersections and a Monad instance and can represent infinite sets. If the base type has an Ord instance, the set can be enumerated. If the base type has an Eq instance, so has (Set a). Some functions usually implemented using Foldable are also possible, e.g. minimum and maximum. Caveat: Performance can be poor, depending on how the function inside the set was defined.

Cheers, Olaf

[1] http://hackage.haskell.org/package/infinite-search _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post. -- Sending this from my phone, please excuse any typos! _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.

-- brandon s allbery kf8nh allbery.b@gmail.com _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.

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