Data.Ranged.Ranges

A range has an upper and lower boundary.

Construction

data Ord v => Range v

A Range has upper and lower boundaries.

Constructors

Range

Fields

rangeLower :: Boundary v

rangeUpper :: Boundary v

Instances

DiscreteOrdered a => Eq (Range a)

DiscreteOrdered a => Ord (Range a)

(Show a, DiscreteOrdered a) => Show (Range a)

(Arbitrary v, DiscreteOrdered v, Show v) => Arbitrary (Range v)

emptyRange :: DiscreteOrdered v => Range v

The empty range

fullRange :: DiscreteOrdered v => Range v

The full range. All values are within it.

Predicates

rangeIsEmpty :: DiscreteOrdered v => Range v -> Bool

A range is empty unless its upper boundary is greater than its lower boundary.

rangeOverlap :: DiscreteOrdered v => Range v -> Range v -> Bool

Two ranges overlap if their intersection is non-empty.

rangeEncloses :: DiscreteOrdered v => Range v -> Range v -> Bool

The first range encloses the second if every value in the second range is also within the first range. If the second range is empty then this is always true.

rangeSingletonValue :: DiscreteOrdered v => Range v -> Maybe v

If the range is a singleton, returns Just the value. Otherwise returns Nothing.

Membership

rangeHas :: Ord v => Range v -> v -> Bool

True if the value is within the range.

rangeListHas :: Ord v => [Range v] -> v -> Bool

True if the value is within one of the ranges.

Set Operations

singletonRange :: DiscreteOrdered v => v -> Range v

A range containing a single value

rangeIntersection :: DiscreteOrdered v => Range v -> Range v -> Range v

Intersection of two ranges, if any.

rangeUnion :: DiscreteOrdered v => Range v -> Range v -> [Range v]

Union of two ranges. Returns one or two results.

If there are two results then they are guaranteed to have a non-empty gap in between, but may not be in ascending order.

rangeDifference :: DiscreteOrdered v => Range v -> Range v -> [Range v]

range1 minus range2. Returns zero, one or two results. Multiple results are guaranteed to have non-empty gaps in between, but may not be in ascending order.

QuickCheck properties

Range union

 prop_union r1 r2 n =
    (r1 `rangeHas` n || r2 `rangeHas` n) 
    == (r1 `rangeUnion` r2) `rangeListHas` n

Range intersection

 prop_intersection r1 r2 n =
    (r1 `rangeHas` n && r2 `rangeHas` n)
    == (r1 `rangeIntersection` r2) `rangeHas` n

Range difference

 prop_difference r1 r2 n =
    (r1 `rangeHas` n && not (r2 `rangeHas` n))
    == (r1 `rangeDifference` r2) `rangeListHas` n

Singleton range

 prop_singletonHas v =
    singletonRange v `rangeHas` v

 prop_singletonConverse v =
    rangeSingletonValue (singletonRange v) == Just v