Data.JoinSemilattice.Intersect

When we play games like Guess Who?, we start with a set of possible candidates, and eliminate subsets of them as the game progresses. The Intersect type works in a similar way: each cell stores a list of its potential values, and the merging operation takes the intersect of the current candidates and the new candidates.

Documentation

newtype Intersect (x :: Type)

A set type with intersection as the (<>) operation.

Constructors

Intersect

Fields

• toHashSet :: HashSet x

Instances

Foldable Intersect

Defined in Data.JoinSemilattice.Intersect

Methods

fold :: Monoid m => Intersect m -> m

foldMap :: Monoid m => (a -> m) -> Intersect a -> m

foldMap' :: Monoid m => (a -> m) -> Intersect a -> m

foldr :: (a -> b -> b) -> b -> Intersect a -> b

foldr' :: (a -> b -> b) -> b -> Intersect a -> b

foldl :: (b -> a -> b) -> b -> Intersect a -> b

foldl' :: (b -> a -> b) -> b -> Intersect a -> b

foldr1 :: (a -> a -> a) -> Intersect a -> a

foldl1 :: (a -> a -> a) -> Intersect a -> a

toList :: Intersect a -> [a]

null :: Intersect a -> Bool

length :: Intersect a -> Int

elem :: Eq a => a -> Intersect a -> Bool

maximum :: Ord a => Intersect a -> a

minimum :: Ord a => Intersect a -> a

sum :: Num a => Intersect a -> a

product :: Num a => Intersect a -> a

BooleanR Intersect

Defined in Data.JoinSemilattice.Class.Boolean

Methods

falseR :: Intersect Bool

trueR :: Intersect Bool

notR :: (Intersect Bool, Intersect Bool) -> (Intersect Bool, Intersect Bool)

andR :: (Intersect Bool, Intersect Bool, Intersect Bool) -> (Intersect Bool, Intersect Bool, Intersect Bool)

orR :: (Intersect Bool, Intersect Bool, Intersect Bool) -> (Intersect Bool, Intersect Bool, Intersect Bool)

EqR Intersect

Defined in Data.JoinSemilattice.Class.Eq

Associated Types

type EqC Intersect :: Type -> Constraint

Methods

eqR :: EqC' Intersect x => (Intersect x, Intersect x, Intersect Bool) -> (Intersect x, Intersect x, Intersect Bool)

OrdR Intersect

Defined in Data.JoinSemilattice.Class.Ord

Associated Types

type OrdC Intersect :: Type -> Constraint

Methods

lteR :: OrdC Intersect x => (Intersect x, Intersect x, Intersect Bool) -> (Intersect x, Intersect x, Intersect Bool)

Mapping Intersect Intersectable

Defined in Data.JoinSemilattice.Class.Mapping

Methods

mapR :: (Intersectable x, Intersectable y) => (Maybe (x -> y), Maybe (y -> x)) -> (Intersect x, Intersect y) -> (Intersect x, Intersect y)

Zipping Intersect Intersectable

Defined in Data.JoinSemilattice.Class.Zipping

Methods

zipWithR :: (Intersectable x, Intersectable y, Intersectable z) => (Maybe ((x, y) -> z), Maybe ((x, z) -> y), Maybe ((y, z) -> x)) -> (Intersect x, Intersect y, Intersect z) -> (Intersect x, Intersect y, Intersect z)

Lifting Intersect Intersectable

Defined in Data.JoinSemilattice.Class.Lifting

Methods

lift' :: Intersectable x => x -> Intersect x

FlatMapping Intersect Intersectable

Defined in Data.JoinSemilattice.Class.FlatMapping

Methods

flatMapR :: (Intersectable x, Intersectable y) => (Maybe (x -> Intersect y), Maybe (Intersect y -> x)) -> (Intersect x, Intersect y) -> (Intersect x, Intersect y)

Eq x => Eq (Intersect x)

Defined in Data.JoinSemilattice.Intersect

Methods

(==) :: Intersect x -> Intersect x -> Bool

(/=) :: Intersect x -> Intersect x -> Bool

(Intersectable x, Fractional x) => Fractional (Intersect x)

Defined in Data.JoinSemilattice.Intersect

Methods

(/) :: Intersect x -> Intersect x -> Intersect x

recip :: Intersect x -> Intersect x

fromRational :: Rational -> Intersect x

(Intersectable content, Num content) => Num (Intersect content)

Defined in Data.JoinSemilattice.Intersect

Methods

(+) :: Intersect content -> Intersect content -> Intersect content

(-) :: Intersect content -> Intersect content -> Intersect content

(*) :: Intersect content -> Intersect content -> Intersect content

negate :: Intersect content -> Intersect content

abs :: Intersect content -> Intersect content

signum :: Intersect content -> Intersect content

fromInteger :: Integer -> Intersect content

Ord x => Ord (Intersect x)

Defined in Data.JoinSemilattice.Intersect

Methods

compare :: Intersect x -> Intersect x -> Ordering

(<) :: Intersect x -> Intersect x -> Bool

(<=) :: Intersect x -> Intersect x -> Bool

(>) :: Intersect x -> Intersect x -> Bool

(>=) :: Intersect x -> Intersect x -> Bool

max :: Intersect x -> Intersect x -> Intersect x

min :: Intersect x -> Intersect x -> Intersect x

Show x => Show (Intersect x)

Defined in Data.JoinSemilattice.Intersect

Methods

showsPrec :: Int -> Intersect x -> ShowS

show :: Intersect x -> String

showList :: [Intersect x] -> ShowS

(Eq content, Hashable content) => Semigroup (Intersect content)

Defined in Data.JoinSemilattice.Intersect

Methods

(<>) :: Intersect content -> Intersect content -> Intersect content

sconcat :: NonEmpty (Intersect content) -> Intersect content

stimes :: Integral b => b -> Intersect content -> Intersect content

Intersectable content => Monoid (Intersect content)

Defined in Data.JoinSemilattice.Intersect

Methods

mempty :: Intersect content

mappend :: Intersect content -> Intersect content -> Intersect content

mconcat :: [Intersect content] -> Intersect content

Hashable x => Hashable (Intersect x)

Defined in Data.JoinSemilattice.Intersect

Methods

hashWithSalt :: Int -> Intersect x -> Int

hash :: Intersect x -> Int

Intersectable x => Input (Intersect x)

Defined in Data.JoinSemilattice.Intersect

Associated Types

type Raw (Intersect x)

Methods

from :: forall (m :: Type -> Type). Applicative m => Int -> [Raw (Intersect x)] -> Config m (Intersect x)

(Bounded x, Enum x, Ord x, Hashable x) => Merge (Intersect x)

Defined in Data.JoinSemilattice.Class.Merge

Methods

(<<-) :: Intersect x -> Intersect x -> Result (Intersect x)

(Intersectable x, Num x) => SumR (Intersect x)

Defined in Data.JoinSemilattice.Class.Sum

Methods

addR :: (Intersect x, Intersect x, Intersect x) -> (Intersect x, Intersect x, Intersect x)

(Bounded x, Enum x, Ord x, Hashable x, Integral x) => IntegralR (Intersect x)

Defined in Data.JoinSemilattice.Class.Integral

Methods

divModR :: (Intersect x, Intersect x, Intersect x, Intersect x) -> (Intersect x, Intersect x, Intersect x, Intersect x)

(Bounded x, Enum x, Ord x, Fractional x, Hashable x) => FractionalR (Intersect x)

Defined in Data.JoinSemilattice.Class.Fractional

Methods

multiplyR :: (Intersect x, Intersect x, Intersect x) -> (Intersect x, Intersect x, Intersect x)

(Bounded x, Enum x, Ord x, Hashable x, Num x) => AbsR (Intersect x)

Defined in Data.JoinSemilattice.Class.Abs

Methods

absR :: (Intersect x, Intersect x) -> (Intersect x, Intersect x)

type EqC Intersect

Defined in Data.JoinSemilattice.Class.Eq

type EqC Intersect = Intersectable

type OrdC Intersect

Defined in Data.JoinSemilattice.Class.Ord

type OrdC Intersect

type Raw (Intersect x)

Defined in Data.JoinSemilattice.Intersect

type Raw (Intersect x) = x

class (Bounded content, Enum content, Ord content, Hashable content) => Intersectable content

Instances

(Bounded content, Enum content, Ord content, Hashable content) => Intersectable content

Defined in Data.JoinSemilattice.Intersect

Mapping Intersect Intersectable

Defined in Data.JoinSemilattice.Class.Mapping

Methods

mapR :: (Intersectable x, Intersectable y) => (Maybe (x -> y), Maybe (y -> x)) -> (Intersect x, Intersect y) -> (Intersect x, Intersect y)

Zipping Intersect Intersectable

Defined in Data.JoinSemilattice.Class.Zipping

Methods

zipWithR :: (Intersectable x, Intersectable y, Intersectable z) => (Maybe ((x, y) -> z), Maybe ((x, z) -> y), Maybe ((y, z) -> x)) -> (Intersect x, Intersect y, Intersect z) -> (Intersect x, Intersect y, Intersect z)

Lifting Intersect Intersectable

Defined in Data.JoinSemilattice.Class.Lifting

Methods

lift' :: Intersectable x => x -> Intersect x

FlatMapping Intersect Intersectable

Defined in Data.JoinSemilattice.Class.FlatMapping

Methods

flatMapR :: (Intersectable x, Intersectable y) => (Maybe (x -> Intersect y), Maybe (Intersect y -> x)) -> (Intersect x, Intersect y) -> (Intersect x, Intersect y)

lift2 :: (Intersectable this, Intersectable that, Intersectable result) => (this -> that -> result) -> Intersect this -> Intersect that -> Intersect result

fromList :: (Eq x, Hashable x) => [x] -> Intersect x

Create an Intersect from a list of candidates.

toList :: (Bounded x, Enum x, Eq x) => Intersect x -> [x]

Return a list of candidates stored within an Intersect.

decided :: (Applicative m, Intersectable x) => (x -> m ()) -> Intersect x -> m ()

Run an action only if a single candidate remains.

delete :: Intersectable x => x -> Intersect x -> Intersect x

Delete a candidate from an Intersect.

except :: Intersectable x => Intersect x -> Intersect x

Return an Intersect of all possible candidates except those in the given Intersect. The Intersect of all candidates is assumed to be mempty.

filter :: (x -> Bool) -> Intersect x -> Intersect x

Filter an Intersect with a predicate.

fromSet :: (Eq x, Hashable x) => Set x -> Intersect x

Convert a Set to an Intersect.

map :: (Eq y, Hashable y) => (x -> y) -> Intersect x -> Intersect y

Map over an Intersect with a given function.

powerSet :: (Bounded x, Enum x, Hashable x, Ord x) => Intersect x -> Intersect (Intersect x)

singleton :: Hashable x => x -> Intersect x

Create a singleton Intersect.

size :: Intersectable x => Intersect x -> Int

Count the candidates in an Intersect.

toSet :: Ord x => Intersect x -> Set x

Convert an Intersect to a Set.

union :: Intersectable x => Intersect x -> Intersect x -> Intersect x

Merge two Intersect values with set union.

using :: (Applicative m, Intersectable x) => [Intersect x] -> Config m (Intersect x)

Produce a Config with the given initial value, where the refine function just tries each remaining candidate as a singleton.