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

Stability | experimental |

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

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

.

Example usage:

bit = pairSet 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/

# 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`

.
This operation is total whenever `p`

is total.

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

`bigUnion ss`

is the union of all the elemens of `ss`

. In other words,
`x `

iff `member`

bigUnion ss`forsome ss (s -> x `

.
`member`

s)

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

`forsome s p`

returns True iff there is some element `x`

of `s`

such that
`p x = True`

.