Data.IntervalSet

Interval datatype and interval arithmetic.

IntervalSet type

data IntervalSet r

A set comprising zero or more non-empty, disconnected intervals.

Any connected intervals are merged together, and empty intervals are ignored.

Instances

Ord r => IsList (IntervalSet r)

Associated Types

type Item (IntervalSet r) :: *

Methods

fromList :: [Item (IntervalSet r)] -> IntervalSet r

fromListN :: Int -> [Item (IntervalSet r)] -> IntervalSet r

toList :: IntervalSet r -> [Item (IntervalSet r)]

Eq r => Eq (IntervalSet r)

Methods

(==) :: IntervalSet r -> IntervalSet r -> Bool

(/=) :: IntervalSet r -> IntervalSet r -> Bool

(Real r, Fractional r) => Fractional (IntervalSet r)

Methods

(/) :: IntervalSet r -> IntervalSet r -> IntervalSet r

recip :: IntervalSet r -> IntervalSet r

fromRational :: Rational -> IntervalSet r

(Ord r, Data r) => Data (IntervalSet r)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> IntervalSet r -> c (IntervalSet r)

gunfold :: (forall b a. Data b => c (b -> a) -> c a) -> (forall a. a -> c a) -> Constr -> c (IntervalSet r)

toConstr :: IntervalSet r -> Constr

dataTypeOf :: IntervalSet r -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (IntervalSet r))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (IntervalSet r))

gmapT :: (forall b. Data b => b -> b) -> IntervalSet r -> IntervalSet r

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> IntervalSet r -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> IntervalSet r -> r

gmapQ :: (forall d. Data d => d -> u) -> IntervalSet r -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> IntervalSet r -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> IntervalSet r -> m (IntervalSet r)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> IntervalSet r -> m (IntervalSet r)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> IntervalSet r -> m (IntervalSet r)

(Num r, Ord r) => Num (IntervalSet r)

Methods

(+) :: IntervalSet r -> IntervalSet r -> IntervalSet r

(-) :: IntervalSet r -> IntervalSet r -> IntervalSet r

(*) :: IntervalSet r -> IntervalSet r -> IntervalSet r

negate :: IntervalSet r -> IntervalSet r

abs :: IntervalSet r -> IntervalSet r

signum :: IntervalSet r -> IntervalSet r

fromInteger :: Integer -> IntervalSet r

(Ord r, Read r) => Read (IntervalSet r)

Methods

readsPrec :: Int -> ReadS (IntervalSet r)

readList :: ReadS [IntervalSet r]

readPrec :: ReadPrec (IntervalSet r)

readListPrec :: ReadPrec [IntervalSet r]

(Ord r, Show r) => Show (IntervalSet r)

Methods

showsPrec :: Int -> IntervalSet r -> ShowS

show :: IntervalSet r -> String

showList :: [IntervalSet r] -> ShowS

Ord r => Semigroup (IntervalSet r)

Methods

(<>) :: IntervalSet r -> IntervalSet r -> IntervalSet r

sconcat :: NonEmpty (IntervalSet r) -> IntervalSet r

stimes :: Integral b => b -> IntervalSet r -> IntervalSet r

Ord r => Monoid (IntervalSet r)

Methods

mempty :: IntervalSet r

mappend :: IntervalSet r -> IntervalSet r -> IntervalSet r

mconcat :: [IntervalSet r] -> IntervalSet r

NFData r => NFData (IntervalSet r)

Methods

rnf :: IntervalSet r -> ()

Hashable r => Hashable (IntervalSet r)

Methods

hashWithSalt :: Int -> IntervalSet r -> Int

hash :: IntervalSet r -> Int

Ord r => JoinSemiLattice (IntervalSet r)

Methods

(\/) :: IntervalSet r -> IntervalSet r -> IntervalSet r

join :: IntervalSet r -> IntervalSet r -> IntervalSet r

Ord r => MeetSemiLattice (IntervalSet r)

Methods

(/\) :: IntervalSet r -> IntervalSet r -> IntervalSet r

meet :: IntervalSet r -> IntervalSet r -> IntervalSet r

Ord r => Lattice (IntervalSet r)

Ord r => BoundedJoinSemiLattice (IntervalSet r)

Methods

bottom :: IntervalSet r

Ord r => BoundedMeetSemiLattice (IntervalSet r)

Methods

top :: IntervalSet r

Ord r => BoundedLattice (IntervalSet r)

type Item (IntervalSet r)

type Item (IntervalSet r) = Interval r

module Data.ExtendedReal

type EndPoint r = Extended r

Deprecated: EndPoint is deprecated. Please use Extended instead.

Endpoints of intervals

Construction

whole :: Ord r => IntervalSet r

whole real number line (-∞, ∞)

empty :: Ord r => IntervalSet r

empty interval set

singleton :: Ord r => Interval r -> IntervalSet r

single interval

Query

null :: IntervalSet r -> Bool

Is the interval set empty?

member :: Ord r => r -> IntervalSet r -> Bool

Is the element in the interval set?

notMember :: Ord r => r -> IntervalSet r -> Bool

Is the element not in the interval set?

isSubsetOf :: Ord r => IntervalSet r -> IntervalSet r -> Bool

Is this a subset? (is1 `isSubsetOf` is2) tells whether is1 is a subset of is2.

isProperSubsetOf :: Ord r => IntervalSet r -> IntervalSet r -> Bool

Is this a proper subset? (i.e. a subset but not equal).

span :: Ord r => IntervalSet r -> Interval r

convex hull of a set of intervals.

Construction

complement :: Ord r => IntervalSet r -> IntervalSet r

Complement the interval set.

insert :: Ord r => Interval r -> IntervalSet r -> IntervalSet r

Insert a new interval into the interval set.

delete :: Ord r => Interval r -> IntervalSet r -> IntervalSet r

Delete an interval from the interval set.

Combine

union :: Ord r => IntervalSet r -> IntervalSet r -> IntervalSet r

union of two interval sets

unions :: Ord r => [IntervalSet r] -> IntervalSet r

union of a list of interval sets

intersection :: Ord r => IntervalSet r -> IntervalSet r -> IntervalSet r

intersection of two interval sets

intersections :: Ord r => [IntervalSet r] -> IntervalSet r

intersection of a list of interval sets

difference :: Ord r => IntervalSet r -> IntervalSet r -> IntervalSet r

difference of two interval sets

Conversion

List

fromList :: Ord r => [Interval r] -> IntervalSet r

Build a interval set from a list of intervals.

toList :: Ord r => IntervalSet r -> [Interval r]

Convert a interval set into a list of intervals.

Ordered list

toAscList :: Ord r => IntervalSet r -> [Interval r]

Convert a interval set into a list of intervals in ascending order.

toDescList :: Ord r => IntervalSet r -> [Interval r]

Convert a interval set into a list of intervals in descending order.

fromAscList :: Ord r => [Interval r] -> IntervalSet r

Build a map from an ascending list of intervals. The precondition is not checked.