A conservative implementation of Intervals, mostly for use as keys in
This should really be a typeclass, so you could have a tuple be an instance of Interval, but that is currently not possible in standard Haskell.
The contructor names of the half-open intervals seem somewhat clumsy, and I'm open to suggestions for better names.
- data Interval a
- lowerBound :: Interval a -> a
- upperBound :: Interval a -> a
- leftClosed :: Interval a -> Bool
- rightClosed :: Interval a -> Bool
- isEmpty :: Ord a => Interval a -> Bool
- overlaps :: Ord a => Interval a -> Interval a -> Bool
- subsumes :: Ord a => Interval a -> Interval a -> Bool
- before :: Ord a => Interval a -> Interval a -> Bool
- after :: Ord a => Interval a -> Interval a -> Bool
- compareByUpper :: Ord a => Interval a -> Interval a -> Ordering
- below :: Ord a => a -> Interval a -> Bool
- inside :: Ord a => a -> Interval a -> Bool
- above :: Ord a => a -> Interval a -> Bool
Intervals with endpoints of type
Show use mathematical notation with square brackets for closed
and parens for open intervals.
This is better for human readability, but is not a valid Haskell expression.
Closed intervals look like a list, open intervals look like a tuple,
and half-open intervals look like mismatched parens.
|IntervalCO !a !a|
Including lower bound, excluding upper
|ClosedInterval !a !a|
Closed at both ends
|OpenInterval !a !a|
Open at both ends
|IntervalOC !a !a|
Excluding lower bound, including upper
Does the first interval completely contain the second?
Interval strictly before another? True if the upper bound of the first interval is below the lower bound of the second.
Interval strictly after another? Same as 'flip before'.
compare, but considering the upper bound first.