|Maintainer||Luke Palmer <email@example.com>|
An implementation of nonempty searchable sets, i.e. sets s which admit a
search s :: (a -> Bool) -> Maybe a.
bit = pair True False cantor = sequence (repeat bit) take 5 $ search cantor (\s -> not (s !! 3) && (s !! 4)) -- gives [True, True, True, False, True]
This module is based on the paper Exhaustible sets in higher-type computation by Martin Escardo, and is almost identical to the code in his his expository blog post on the subject: http:math.andrej.com20081121a-haskell-monad-for-infinite-search-in-finite-time/
- data Set a
- search :: Set a -> (a -> Bool) -> Maybe a
- bigUnion :: Set (Set a) -> Set a
- contains :: Eq a => Set a -> a -> Bool
- member :: Eq a => a -> Set a -> Bool
- forsome :: Set a -> (a -> Bool) -> Bool
- forevery :: Set a -> (a -> Bool) -> Bool
- singleton :: a -> Set a
- doubleton :: a -> a -> Set a
- union :: Set a -> Set a -> Set a
Set a is a nonempty searchable set of a's.
There is no Monoid or MonadPlus instance, since
we lack the ability to represent the empty set,
which would be the units of those structures.
Choose a member of the set satisfying a predicate.
search s p = Just x then
p x = True.
Tests whether the set contains an element.
contains s x = forsome s (== x).
forsome s p returns True iff there is some element
s such that
p x = True.
forevery s p returns True iff every element
p x =