Data.Dioid.Interval

https://en.wikipedia.org/wiki/Partially_ordered_set#Intervals

Documentation

data Interval a

Instances

Eq a => Eq (Interval a)

Defined in Data.Dioid.Interval

Methods

(==) :: Interval a -> Interval a -> Bool

(/=) :: Interval a -> Interval a -> Bool

Show a => Show (Interval a)

Defined in Data.Dioid.Interval

Methods

showsPrec :: Int -> Interval a -> ShowS

show :: Interval a -> String

showList :: [Interval a] -> ShowS

Ord a => Prd (Interval a)

Defined in Data.Dioid.Interval

Methods

(<~) :: Interval a -> Interval a -> Bool

(>~) :: Interval a -> Interval a -> Bool

(=~) :: Interval a -> Interval a -> Bool

(?~) :: Interval a -> Interval a -> Bool

pcompare :: Interval a -> Interval a -> Maybe Ordering

(...) :: Prd a => a -> a -> Interval a infix 3

Construct an interval from a pair of points.

If a <~ b then a ... b = Empty.

endpts :: Interval a -> Maybe (a, a)

Obtain the endpoints of an interval.

singleton :: a -> Interval a

Construct an interval containing a single point.

>>> singleton 1
1 ... 1

upset :: Max a => a -> Interval a

\( X_\geq(x) = \{ y \in X | y \geq x \} \)

Construct the upper set of an element x.

This function is monotone wrt the containment order.

dnset :: Min a => a -> Interval a

\( X_\leq(x) = \{ y \in X | y \leq x \} \)

Construct the lower set of an element x.

This function is antitone wrt the containment order.

empty :: Interval a

The empty interval.

>>> empty
Empty