Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Range

Description

Data type for representing Generic Ranges (Intervals) and functions that work with them.

Synopsis

data EndPoint a
- = Open !a
- | Closed !a
isOpen :: EndPoint a -> Bool
isClosed :: EndPoint a -> Bool
unEndPoint :: Lens (EndPoint a) (EndPoint b) a b
data Range a where
- Range {
  - _lower :: !(EndPoint a)
  - _upper :: !(EndPoint a)
  }
- pattern OpenRange :: a -> a -> Range a
- pattern ClosedRange :: a -> a -> Range a
- pattern Range' :: a -> a -> Range a
prettyShow :: Show a => Range a -> String
lower :: Lens' (Range a) (EndPoint a)
upper :: Lens' (Range a) (EndPoint a)
inRange :: Ord a => a -> Range a -> Bool
width :: Num r => Range r -> r
clipLower :: Ord a => EndPoint a -> Range a -> Maybe (Range a)
clipUpper :: Ord a => EndPoint a -> Range a -> Maybe (Range a)
midPoint :: Fractional r => Range r -> r
clampTo :: Ord r => Range r -> r -> r
isValidRange :: Ord a => Range a -> Bool
covers :: forall a. Ord a => Range a -> Range a -> Bool
shiftLeft :: Num r => r -> Range r -> Range r
shiftRight :: Num r => r -> Range r -> Range r

Documentation

data EndPoint a Source #

Endpoints of a range may either be open or closed.

Constructors

Open !a
Closed !a

Instances

Instances details

Functor EndPoint Source #
Instance details Defined in Data.Range Methods fmap :: (a -> b) -> EndPoint a -> EndPoint b # (<$) :: a -> EndPoint b -> EndPoint a #
Foldable EndPoint Source #
Instance details Defined in Data.Range Methods fold :: Monoid m => EndPoint m -> m # foldMap :: Monoid m => (a -> m) -> EndPoint a -> m # foldMap' :: Monoid m => (a -> m) -> EndPoint a -> m # foldr :: (a -> b -> b) -> b -> EndPoint a -> b # foldr' :: (a -> b -> b) -> b -> EndPoint a -> b # foldl :: (b -> a -> b) -> b -> EndPoint a -> b # foldl' :: (b -> a -> b) -> b -> EndPoint a -> b # foldr1 :: (a -> a -> a) -> EndPoint a -> a # foldl1 :: (a -> a -> a) -> EndPoint a -> a # toList :: EndPoint a -> [a] # null :: EndPoint a -> Bool # length :: EndPoint a -> Int # elem :: Eq a => a -> EndPoint a -> Bool # maximum :: Ord a => EndPoint a -> a # minimum :: Ord a => EndPoint a -> a # sum :: Num a => EndPoint a -> a # product :: Num a => EndPoint a -> a #
Traversable EndPoint Source #
Instance details Defined in Data.Range Methods traverse :: Applicative f => (a -> f b) -> EndPoint a -> f (EndPoint b) # sequenceA :: Applicative f => EndPoint (f a) -> f (EndPoint a) # mapM :: Monad m => (a -> m b) -> EndPoint a -> m (EndPoint b) # sequence :: Monad m => EndPoint (m a) -> m (EndPoint a) #
Read1 EndPoint Source #
Instance details Defined in Data.Range Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (EndPoint a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [EndPoint a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (EndPoint a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [EndPoint a] #
Show1 EndPoint Source #
Instance details Defined in Data.Range Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> EndPoint a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [EndPoint a] -> ShowS #
Eq a => Eq (EndPoint a) Source #
Instance details Defined in Data.Range Methods (==) :: EndPoint a -> EndPoint a -> Bool # (/=) :: EndPoint a -> EndPoint a -> Bool #
Ord a => Ord (EndPoint a) Source #
Instance details Defined in Data.Range Methods compare :: EndPoint a -> EndPoint a -> Ordering # (<) :: EndPoint a -> EndPoint a -> Bool # (<=) :: EndPoint a -> EndPoint a -> Bool # (>) :: EndPoint a -> EndPoint a -> Bool # (>=) :: EndPoint a -> EndPoint a -> Bool # max :: EndPoint a -> EndPoint a -> EndPoint a # min :: EndPoint a -> EndPoint a -> EndPoint a #
Read a => Read (EndPoint a) Source #
Instance details Defined in Data.Range Methods readsPrec :: Int -> ReadS (EndPoint a) # readList :: ReadS [EndPoint a] # readPrec :: ReadPrec (EndPoint a) # readListPrec :: ReadPrec [EndPoint a] #
Show a => Show (EndPoint a) Source #
Instance details Defined in Data.Range Methods showsPrec :: Int -> EndPoint a -> ShowS # show :: EndPoint a -> String # showList :: [EndPoint a] -> ShowS #
Generic (EndPoint a) Source #
Instance details Defined in Data.Range Associated Types type Rep (EndPoint a) :: Type -> Type # Methods from :: EndPoint a -> Rep (EndPoint a) x # to :: Rep (EndPoint a) x -> EndPoint a #
Arbitrary r => Arbitrary (EndPoint r) Source #
Instance details Defined in Data.Range Methods arbitrary :: Gen (EndPoint r) # shrink :: EndPoint r -> [EndPoint r] #
NFData a => NFData (EndPoint a) Source #
Instance details Defined in Data.Range Methods rnf :: EndPoint a -> () #
type Rep (EndPoint a) Source #
Instance details Defined in Data.Range type Rep (EndPoint a) = D1 ('MetaData "EndPoint" "Data.Range" "hgeometry-combinatorial-0.14-4eKKoxfw4Iy23UosEmuxsr" 'False) (C1 ('MetaCons "Open" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)) :+: C1 ('MetaCons "Closed" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))

isOpen :: EndPoint a -> Bool Source #

True iff EndPoint is open.

isClosed :: EndPoint a -> Bool Source #

True iff EndPoint is closed.

unEndPoint :: Lens (EndPoint a) (EndPoint b) a b Source #

Access lens for EndPoint value regardless of whether it is open or closed.

>>> Open 5 ^. unEndPoint
5
>>> Closed 10 ^. unEndPoint
10
>>> Open 4 & unEndPoint .~ 0
Open 0

data Range a Source #

Data type for representing ranges.

Constructors

Range
Fields _lower :: !(EndPoint a) _upper :: !(EndPoint a)

Bundled Patterns

pattern OpenRange :: a -> a -> Range a
pattern ClosedRange :: a -> a -> Range a
pattern Range' :: a -> a -> Range a	A range from l to u, ignoring/forgetting the type of the endpoints

Instances

Instances details

Functor Range Source #
Instance details Defined in Data.Range Methods fmap :: (a -> b) -> Range a -> Range b # (<$) :: a -> Range b -> Range a #
Foldable Range Source #
Instance details Defined in Data.Range Methods fold :: Monoid m => Range m -> m # foldMap :: Monoid m => (a -> m) -> Range a -> m # foldMap' :: Monoid m => (a -> m) -> Range a -> m # foldr :: (a -> b -> b) -> b -> Range a -> b # foldr' :: (a -> b -> b) -> b -> Range a -> b # foldl :: (b -> a -> b) -> b -> Range a -> b # foldl' :: (b -> a -> b) -> b -> Range a -> b # foldr1 :: (a -> a -> a) -> Range a -> a # foldl1 :: (a -> a -> a) -> Range a -> a # toList :: Range a -> [a] # null :: Range a -> Bool # length :: Range a -> Int # elem :: Eq a => a -> Range a -> Bool # maximum :: Ord a => Range a -> a # minimum :: Ord a => Range a -> a # sum :: Num a => Range a -> a # product :: Num a => Range a -> a #
Traversable Range Source #
Instance details Defined in Data.Range Methods traverse :: Applicative f => (a -> f b) -> Range a -> f (Range b) # sequenceA :: Applicative f => Range (f a) -> f (Range a) # mapM :: Monad m => (a -> m b) -> Range a -> m (Range b) # sequence :: Monad m => Range (m a) -> m (Range a) #
Read1 Range Source #
Instance details Defined in Data.Range Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Range a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Range a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Range a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Range a] #
Show1 Range Source #
Instance details Defined in Data.Range Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Range a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Range a] -> ShowS #
Eq a => Eq (Range a) Source #
Instance details Defined in Data.Range Methods (==) :: Range a -> Range a -> Bool # (/=) :: Range a -> Range a -> Bool #
Read a => Read (Range a) Source #
Instance details Defined in Data.Range Methods readsPrec :: Int -> ReadS (Range a) # readList :: ReadS [Range a] # readPrec :: ReadPrec (Range a) # readListPrec :: ReadPrec [Range a] #
Show a => Show (Range a) Source #
Instance details Defined in Data.Range Methods showsPrec :: Int -> Range a -> ShowS # show :: Range a -> String # showList :: [Range a] -> ShowS #
Generic (Range a) Source #
Instance details Defined in Data.Range Associated Types type Rep (Range a) :: Type -> Type # Methods from :: Range a -> Rep (Range a) x # to :: Rep (Range a) x -> Range a #
(Arbitrary r, Ord r) => Arbitrary (Range r) Source #
Instance details Defined in Data.Range Methods arbitrary :: Gen (Range r) # shrink :: Range r -> [Range r] #
NFData a => NFData (Range a) Source #
Instance details Defined in Data.Range Methods rnf :: Range a -> () #
Ord a => IsIntersectableWith (Range a) (Range a) Source #
Instance details Defined in Data.Range Methods intersect :: Range a -> Range a -> Intersection (Range a) (Range a) Source # nonEmptyIntersection :: proxy (Range a) -> proxy (Range a) -> Intersection (Range a) (Range a) -> Bool Source #
Ord a => HasIntersectionWith (Range a) (Range a) Source #
Instance details Defined in Data.Range Methods intersects :: Range a -> Range a -> Bool Source #
type Rep (Range a) Source #
Instance details Defined in Data.Range type Rep (Range a) = D1 ('MetaData "Range" "Data.Range" "hgeometry-combinatorial-0.14-4eKKoxfw4Iy23UosEmuxsr" 'False) (C1 ('MetaCons "Range" 'PrefixI 'True) (S1 ('MetaSel ('Just "_lower") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (EndPoint a)) :*: S1 ('MetaSel ('Just "_upper") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (EndPoint a))))
type IntersectionOf (Range a) (Range a) Source #
Instance details Defined in Data.Range type IntersectionOf (Range a) (Range a) = '[NoIntersection, Range a]

prettyShow :: Show a => Range a -> String Source #

Helper function to show a range in mathematical notation.

>>> prettyShow $ OpenRange 0 2
"(0,2)"
>>> prettyShow $ ClosedRange 0 2
"[0,2]"
>>> prettyShow $ Range (Open 0) (Closed 5)
"(0,5]"

lower :: Lens' (Range a) (EndPoint a) Source #

Lens access for the lower part of a range.

upper :: Lens' (Range a) (EndPoint a) Source #

Lens access for the upper part of a range.

inRange :: Ord a => a -> Range a -> Bool Source #

Test if a value lies in a range.

>>> 1 `inRange` (OpenRange 0 2)
True
>>> 1 `inRange` (OpenRange 0 1)
False
>>> 1 `inRange` (ClosedRange 0 1)
True
>>> 1 `inRange` (ClosedRange 1 1)
True
>>> 10 `inRange` (OpenRange 1 10)
False
>>> 10 `inRange` (ClosedRange 0 1)
False

This one is kind of weird

>>> 0 `inRange` Range (Closed 0) (Open 0)
False

width :: Num r => Range r -> r Source #

Get the width of the interval

>>> width $ ClosedRange 1 10
9
>>> width $ OpenRange 5 10
5

clipLower :: Ord a => EndPoint a -> Range a -> Maybe (Range a) Source #

Clip the interval from below. I.e. intersect with the interval {l,infty), where { is either open, (, orr closed, [.

clipUpper :: Ord a => EndPoint a -> Range a -> Maybe (Range a) Source #

Clip the interval from above. I.e. intersect with (-infty, u}, where } is either open, ), or closed, ],

midPoint :: Fractional r => Range r -> r Source #

Compute the halfway point between the start and end of a range.

clampTo :: Ord r => Range r -> r -> r Source #

Clamps a value to a range. I.e. if the value lies outside the range we report the closest value "in the range". Note that if an endpoint of the range is open we report that value anyway, so we return a value that is truely inside the range only if that side of the range is closed.

>>> clampTo (ClosedRange 0 10) 20
10
>>> clampTo (ClosedRange 0 10) (-20)
0
>>> clampTo (ClosedRange 0 10) 5
5
>>> clampTo (OpenRange 0 10) 20
10
>>> clampTo (OpenRange 0 10) (-20)
0
>>> clampTo (OpenRange 0 10) 5
5

isValidRange :: Ord a => Range a -> Bool Source #

Check if the range is valid and nonEmpty, i.e. if the lower endpoint is indeed smaller than the right endpoint. Note that we treat empty open-ranges as invalid as well.

>>> isValidRange $ Range (Open 4) (Closed 4)
False
>>> isValidRange $ Range (Open 5) (Closed 4)
False
>>> isValidRange $ Range (Open 4) (Closed 5)
True
>>> isValidRange $ Range (Closed 5) (Closed 40)
True

covers :: forall a. Ord a => Range a -> Range a -> Bool Source #

Wether or not the first range completely covers the second one

shiftLeft :: Num r => r -> Range r -> Range r Source #

Shift a range x units to the left

>>> prettyShow $ shiftLeft 10 (ClosedRange 10 20)
"[0,10]"
>>> prettyShow $ shiftLeft 10 (OpenRange 15 25)
"(5,15)"

shiftRight :: Num r => r -> Range r -> Range r Source #

Shifts the range to the right

>>> prettyShow $ shiftRight 10 (ClosedRange 10 20)
"[20,30]"
>>> prettyShow $ shiftRight 10 (OpenRange 15 25)
"(25,35)"