Ranged-sets-0.1.1: Ranged sets for HaskellSource codeContentsIndex
Data.Ranged.Ranges
Contents
Construction
Predicates
Membership
Set Operations
QuickCheck properties
Description
A range has an upper and lower boundary.
Synopsis
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
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]
Construction
data Ord v => Range v Source
A Range has upper and lower boundaries.
Constructors
Range
rangeLower :: Boundary v
rangeUpper :: Boundary v
show/hide Instances
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.
rangeOverlap :: DiscreteOrdered v => Range v -> Range v -> BoolSource
Two ranges overlap if their intersection is non-empty.
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.
Membership
rangeHas :: Ord v => Range v -> v -> BoolSource
True if the value is within the range.
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 non-empty 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 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
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