Data.IntervalMap.Generic.Interval

Type class for IntervalMap keys.

As there is no sensible default, no instances for prelude types are provided (E.g. you might want to have tuples as closed intervals in one case, and open in another).

Empty intervals, i.e. intervals where 'lowerBound >= upperBound' should be avoided if possible. If you must use empty intervals, you need to provide implementations for all operations, as the default implementations do not necessarily work correctly. for example, the default implementation of inside returns True if the point is equal to the lowerBound of a left-closed interval even if it is larger than the upper bound.

Interval type

class Ord e => Interval i e | i -> e where

Intervals with endpoints of type e. A minimal instance declaration for a closed interval needs only to define lowerBound and upperBound.

Minimal complete definition

lowerBound, upperBound

Methods

lowerBound :: i -> e

lower bound

upperBound :: i -> e

upper bound

leftClosed :: i -> Bool

Does the interval include its lower bound? Default is True for all values, i.e. closed intervals.

rightClosed :: i -> Bool

Does the interval include its upper bound bound? Default is True for all values, i.e. closed intervals.

before :: i -> i -> Bool

Interval strictly before another? True if the upper bound of the first interval is below the lower bound of the second.

after :: i -> i -> Bool

Interval strictly after another? Same as 'flip before'.

subsumes :: i -> i -> Bool

Does the first interval completely contain the second?

overlaps :: i -> i -> Bool

Do the two intervals overlap?

below :: e -> i -> Bool

Is a point strictly less than lower bound?

above :: e -> i -> Bool

Is a point strictly greater than upper bound?

inside :: e -> i -> Bool

Does the interval contain a given point?

isEmpty :: i -> Bool

Is the interval empty?

compareUpperBounds :: i -> i -> Ordering

Instances

Ord a => Interval (Interval a) a

Defined in Data.IntervalMap.Generic.Interval

Methods

lowerBound :: Interval a -> a

upperBound :: Interval a -> a

leftClosed :: Interval a -> Bool

rightClosed :: Interval a -> Bool

before :: Interval a -> Interval a -> Bool

after :: Interval a -> Interval a -> Bool

subsumes :: Interval a -> Interval a -> Bool

overlaps :: Interval a -> Interval a -> Bool

below :: a -> Interval a -> Bool

above :: a -> Interval a -> Bool

inside :: a -> Interval a -> Bool

isEmpty :: Interval a -> Bool

compareUpperBounds :: Interval a -> Interval a -> Ordering

helper functions for declaring Eq and Ord instances

genericEquals :: Interval i e => i -> i -> Bool

genericCompare :: Interval i e => i -> i -> Ordering