Safe Haskell	Safe
Language	Haskell2010

Data.Dioid.Interval

Description

Synopsis

Documentation

Instances

Eq a => Eq (Interval a) Source #
Instance details Defined in Data.Dioid.Interval Methods (==) :: Interval a -> Interval a -> Bool # (/=) :: Interval a -> Interval a -> Bool #
Show a => Show (Interval a) Source #
Instance details Defined in Data.Dioid.Interval Methods showsPrec :: Int -> Interval a -> ShowS # show :: Interval a -> String # showList :: [Interval a] -> ShowS #
Ord a => Prd (Interval a) Source #
Instance details 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 Source #

Construct an interval from a pair of points.

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

Obtain the endpoints of an interval.

Construct an interval containing a single point.

>>> singleton 1
1 ... 1

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

Construct the upper set of an element x.

This function is monotone wrt the containment order.

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

Construct the lower set of an element x.

This function is antitone wrt the containment order.

The empty interval.

>>> empty
Empty