Safe Haskell  Safe 

Language  Haskell2010 
A range has an upper and lower boundary.
Synopsis
 data Ord v => Range v = Range {
 rangeLower, 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
data Ord v => Range v Source #
A Range has upper and lower boundaries.
Range  

Instances
DiscreteOrdered a => Eq (Range a) Source #  
DiscreteOrdered a => Ord (Range a) Source #  
(Show a, DiscreteOrdered a) => Show (Range a) Source #  
(Arbitrary v, DiscreteOrdered v, Show v) => Arbitrary (Range v) Source #  
(CoArbitrary v, DiscreteOrdered v, Show v) => CoArbitrary (Range v) Source #  
Defined in Data.Ranged.Ranges coarbitrary :: Range v > Gen b > Gen b # 
emptyRange :: DiscreteOrdered v => Range v Source #
The empty range
fullRange :: DiscreteOrdered v => Range v Source #
The full range. All values are within it.
Predicates
rangeIsEmpty :: DiscreteOrdered v => Range v > Bool Source #
A range is empty unless its upper boundary is greater than its lower boundary.
rangeIsFull :: DiscreteOrdered v => Range v > Bool Source #
A range is full if it contains every possible value.
rangeOverlap :: DiscreteOrdered v => Range v > Range v > Bool Source #
Two ranges overlap if their intersection is nonempty.
rangeEncloses :: DiscreteOrdered v => Range v > Range v > Bool Source #
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 Source #
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 > Bool Source #
True if the value is within one of the ranges.
Set Operations
singletonRange :: DiscreteOrdered v => v > Range v Source #
A range containing a single value
rangeIntersection :: DiscreteOrdered v => Range v > Range v > Range v Source #
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 > Bool Source #
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 > Bool Source #
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 > Bool Source #
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 > Bool Source #
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 > Bool Source #
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 > Bool Source #
Range enclosure makes union an identity function.
prop_enclosureUnion r1 r2 = rangeEncloses r1 r2 == (rangeUnion r1 r2 == [r1])
prop_singletonRangeHas :: DiscreteOrdered a => a > Bool Source #
Range Singleton has its member.
prop_singletonRangeHas v = singletonRange v `rangeHas` v
prop_singletonRangeHasOnly :: DiscreteOrdered a => a > a > Bool Source #
Range Singleton has only its member.
prop_singletonHasOnly v1 v2 = (v1 == v2) == (singletonRange v1 `rangeHas` v2)
prop_singletonRangeConverse :: DiscreteOrdered a => a > Bool Source #
A singleton range can have its value extracted.
prop_singletonRangeConverse v = rangeSingletonValue (singletonRange v) == Just v
prop_emptyNonSingleton :: Bool Source #
The empty range is not a singleton.
prop_emptyNonSingleton = rangeSingletonValue emptyRange == Nothing
prop_fullNonSingleton :: Bool Source #
The full range is not a singleton.
prop_fullNonSingleton = rangeSingletonValue fullRange == Nothing