Portability | portable |
---|---|

Stability | experimental |

Maintainer | Luke Palmer <lrpalmer@gmail.com> |

An implementation of nonempty searchable (compact and overt) sets, i.e. sets s
which admit a total operation `search s :: (a -> Bool) -> Maybe a`

.

Example usage:

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.com/2008/11/21/a-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

# Documentation

`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.

search :: Set a -> (a -> Bool) -> Maybe aSource

Choose a member of the set satisfying a predicate.
If `search s p = Just x`

then `p x = True`

.

bigUnion :: Set (Set a) -> Set aSource

`bigUnion ss`

is the union of all the elemens of `ss`

. In other words,
`x `member` bigUnion ss`

iff `forsome ss (s -> x `member` s)`

.

contains :: Eq a => Set a -> a -> BoolSource

Tests whether the set contains an element. `contains s x = forsome s (== x)`

.

forsome :: Set a -> (a -> Bool) -> BoolSource

`forsome s p`

returns True iff there is some element `x`

of `s`

such that
`p x = True`

.