[Haskell-cafe] Faster set intersections?

[David Feuer]

On Sun, Dec 9, 2018, 2:30 PM Olaf Klinke <olf at aatal-apotheke.de wrote:

>
> But I fail to see how having Maybe on the inside remedies this situation.
> Furthermore, on Eq types these sets are not so interesting, for the
> following reason.
>

With Maybe on the outside, you can't jump straight to defining the
function; you must first determine whether the intersection is empty. To my
mind, a more natural definition for (possibly empty) sets is

data Set a = Set {find :: (a -> Maybe b) -> Maybe b}

which really explains how this is a set.

>
> One can write a function
> Eq a => ((a -> Bool) -> a) -> [a]
> that enumerates the elements of the set. Because we have universal
> quantification, this list can not be infinite. Which makes sense,
> topologically: These so-called searchable sets are topologically compact,
> and the Eq constraint means the space is discrete. Compact subsets of a
> discrete space are finite.
>

I don't understand how that's finite and not just countable.
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