A range has an upper and lower boundary.
 data Ord v => Range v = Range {
 rangeLower :: Boundary v
 rangeUpper :: Boundary v
 emptyRange :: DiscreteOrdered v => Range v
 fullRange :: DiscreteOrdered v => Range v
 rangeIsEmpty :: DiscreteOrdered v => Range v > Bool
 rangeIsFull :: DiscreteOrdered v => Range v > Bool
 rangeOverlap :: DiscreteOrdered v => Range v > Range v > Bool
 rangeEncloses :: DiscreteOrdered v => Range v > Range v > Bool
 rangeSingletonValue :: DiscreteOrdered v => Range v > Maybe v
 rangeHas :: Ord v => Range v > v > Bool
 rangeListHas :: Ord v => [Range v] > v > Bool
 singletonRange :: DiscreteOrdered v => v > Range v
 rangeIntersection :: DiscreteOrdered v => Range v > Range v > Range v
 rangeUnion :: DiscreteOrdered v => Range v > Range v > [Range v]
 rangeDifference :: DiscreteOrdered v => Range v > Range v > [Range v]
 prop_unionRange :: DiscreteOrdered a => Range a > Range a > a > Bool
 prop_unionRangeLength :: DiscreteOrdered a => Range a > Range a > Bool
 prop_intersectionRange :: DiscreteOrdered a => Range a > Range a > a > Bool
 prop_differenceRange :: DiscreteOrdered a => Range a > Range a > a > Bool
 prop_intersectionOverlap :: DiscreteOrdered a => Range a > Range a > Bool
 prop_enclosureUnion :: DiscreteOrdered a => Range a > Range a > Bool
 prop_singletonRangeHas :: DiscreteOrdered a => a > Bool
 prop_singletonRangeHasOnly :: DiscreteOrdered a => a > a > Bool
 prop_singletonRangeConverse :: DiscreteOrdered a => a > Bool
 prop_emptyNonSingleton :: Bool
 prop_fullNonSingleton :: Bool
 prop_nonSingleton :: Double > Double > Property
 prop_intSingleton :: Integer > Integer > Property
Construction
A Range has upper and lower boundaries.
Range  

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 vSource
The empty range
fullRange :: DiscreteOrdered v => Range vSource
The full range. All values are within it.
Predicates
rangeIsEmpty :: DiscreteOrdered v => Range v > BoolSource
A range is empty unless its upper boundary is greater than its lower boundary.
rangeIsFull :: DiscreteOrdered v => Range v > BoolSource
A range is full if it contains every possible value.
rangeOverlap :: DiscreteOrdered v => Range v > Range v > BoolSource
Two ranges overlap if their intersection is nonempty.
rangeEncloses :: DiscreteOrdered v => Range v > Range v > BoolSource
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 vSource
If the range is a singleton, returns Just
the value. Otherwise returns
Nothing
.
Known bug: This always returns Nothing
for ranges including
BoundaryBelowAll
or BoundaryAboveAll
. For bounded types this can be
incorrect. For instance, the following range only contains one value:
Range (BoundaryBelow maxBound) BoundaryAboveAll
Membership
rangeListHas :: Ord v => [Range v] > v > BoolSource
True if the value is within one of the ranges.
Set Operations
singletonRange :: DiscreteOrdered v => v > Range vSource
A range containing a single value
rangeIntersection :: DiscreteOrdered v => Range v > Range v > Range vSource
Intersection of two ranges, if any.
rangeUnion :: DiscreteOrdered v => Range v > Range v > [Range v]Source
Union of two ranges. Returns one or two results.
If there are two results then they are guaranteed to have a nonempty gap in between, but may not be in ascending order.
rangeDifference :: DiscreteOrdered v => Range v > Range v > [Range v]Source
range1
minus range2
. Returns zero, one or two results. Multiple
results are guaranteed to have nonempty gaps in between, but may not be in
ascending order.
QuickCheck properties
prop_unionRange :: DiscreteOrdered a => Range a > Range a > a > BoolSource
The union of two ranges has a value iff either range has it.
prop_unionRange r1 r2 n = (r1 `rangeHas` n  r2 `rangeHas` n) == (r1 `rangeUnion` r2) `rangeListHas` n
prop_unionRangeLength :: DiscreteOrdered a => Range a > Range a > BoolSource
The union of two ranges always contains one or two ranges.
prop_unionRangeLength r1 r2 = (n == 1)  (n == 2) where n = length $ rangeUnion r1 r2
prop_intersectionRange :: DiscreteOrdered a => Range a > Range a > a > BoolSource
The intersection of two ranges has a value iff both ranges have it.
prop_intersectionRange r1 r2 n = (r1 `rangeHas` n && r2 `rangeHas` n) == (r1 `rangeIntersection` r2) `rangeHas` n
prop_differenceRange :: DiscreteOrdered a => Range a > Range a > a > BoolSource
The difference of two ranges has a value iff the first range has it and the second does not.
prop_differenceRange r1 r2 n = (r1 `rangeHas` n && not (r2 `rangeHas` n)) == (r1 `rangeDifference` r2) `rangeListHas` n
prop_intersectionOverlap :: DiscreteOrdered a => Range a > Range a > BoolSource
Iff two ranges overlap then their intersection is nonempty.
prop_intersectionOverlap r1 r2 = (rangeIsEmpty $ rangeIntersection r1 r2) == (rangeOverlap r1 r2)
prop_enclosureUnion :: DiscreteOrdered a => Range a > Range a > BoolSource
Range enclosure makes union an identity function.
prop_enclosureUnion r1 r2 = rangeEncloses r1 r2 == (rangeUnion r1 r2 == [r1])
prop_singletonRangeHas :: DiscreteOrdered a => a > BoolSource
Range Singleton has its member.
prop_singletonRangeHas v = singletonRange v `rangeHas` v
prop_singletonRangeHasOnly :: DiscreteOrdered a => a > a > BoolSource
Range Singleton has only its member.
prop_singletonHasOnly v1 v2 = (v1 == v2) == (singletonRange v1 `rangeHas` v2)
prop_singletonRangeConverse :: DiscreteOrdered a => a > BoolSource
A singleton range can have its value extracted.
prop_singletonRangeConverse v = rangeSingletonValue (singletonRange v) == Just v
prop_emptyNonSingleton :: BoolSource
The empty range is not a singleton.
prop_emptyNonSingleton = rangeSingletonValue emptyRange == Nothing
prop_fullNonSingleton :: BoolSource
The full range is not a singleton.
prop_fullNonSingleton = rangeSingletonValue fullRange == Nothing
prop_nonSingleton :: Double > Double > PropertySource
For real x and y, x < y
implies that any range between them is a
nonsingleton.
prop_intSingleton :: Integer > Integer > PropertySource
For all integers x and y, any range formed from boundaries on either side of x and y is a singleton iff it contains exactly one integer.