Safe Haskell	None
Language	Haskell2010

NumHask.Range

Description

representation of a continuous range of a type

Synopsis

newtype Range a = Range' (a, a)
pattern Range :: a -> a -> Range a
gridSensible :: (Ord a, FromInteger a, Fractional a, QuotientField a Integer, ExpField a) => Pos -> Range a -> Integer -> [a]

Documentation

newtype Range a #

A continuous range over type a

>>> let a = Range (-1) 1
>>> a
Range -1 1
>>> fmap (+1) (Range 1 2)
Range 2 3
>>> one :: Range Double
Range -0.5 0.5
>>> zero :: Range Double
Range Infinity -Infinity

as a Field instance

>>> Range 0 1 + zero
Range 0.0 1.0
>>> Range 0 1 + Range 2 3
Range 0.0 3.0
>>> Range 1 1 - one
Range 0.5 1.0
>>> Range 0 1 * one
Range 0.0 1.0
>>> Range 0 1 / one
Range 0.0 1.0
>>> P.singleton 2.3 :: Range Double
Range 2.3 2.3
>>> abs (Range 1 0)
Range 0.0 1.0
>>> sign (Range 1 0) == negate one
True

Idempotent

>>> Range 0 2 + Range 0 2
Range 0.0 2.0

as a space instance

>>> project (Range 0 1) (Range 1 4) 0.5
2.5
>>> grid OuterPos (Range 0 10) 5
[0.0,2.0,4.0,6.0,8.0,10.0]
>>> gridSpace (Range 0 1) 4
[Range 0.0 0.25,Range 0.25 0.5,Range 0.5 0.75,Range 0.75 1.0]
>>> gridSensible OuterPos (Range (-12) 23) 6
[-10.0,-5.0,0.0,5.0,10.0,15.0,20.0]

Constructors

Range' (a, a)

Instances

Monad Range #
Instance details Defined in NumHask.Range Methods (>>=) :: Range a -> (a -> Range b) -> Range b # (>>) :: Range a -> Range b -> Range b # return :: a -> Range a # fail :: String -> Range a #
Functor Range #
Instance details Defined in NumHask.Range Methods fmap :: (a -> b) -> Range a -> Range b # (<$) :: a -> Range b -> Range a #
Applicative Range #
Instance details Defined in NumHask.Range Methods pure :: a -> Range a # (<>) :: Range (a -> b) -> Range a -> Range b # liftA2 :: (a -> b -> c) -> Range a -> Range b -> Range c # (>) :: Range a -> Range b -> Range b # (<*) :: Range a -> Range b -> Range a #
Foldable Range #
Instance details Defined in NumHask.Range Methods fold :: Monoid m => Range m -> 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 #
Instance details Defined in NumHask.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) #
Distributive Range #
Instance details Defined in NumHask.Range Methods distribute :: Functor f => f (Range a) -> Range (f a) # collect :: Functor f => (a -> Range b) -> f a -> Range (f b) # distributeM :: Monad m => m (Range a) -> Range (m a) # collectM :: Monad m => (a -> Range b) -> m a -> Range (m b) #
Representable Range #
Instance details Defined in NumHask.Range Associated Types type Rep Range :: * # Methods tabulate :: (Rep Range -> a) -> Range a # index :: Range a -> Rep Range -> a #
Eq1 Range #
Instance details Defined in NumHask.Range Methods liftEq :: (a -> b -> Bool) -> Range a -> Range b -> Bool #
Show1 Range #
Instance details Defined in NumHask.Range Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Range a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Range a] -> ShowS #
Singleton Range #
Instance details Defined in NumHask.Range Methods singleton :: a -> Range a #
Traversable1 Range #
Instance details Defined in NumHask.Range Methods traverse1 :: Apply f => (a -> f b) -> Range a -> f (Range b) # sequence1 :: Apply f => Range (f b) -> f (Range b) #
Foldable1 Range #
Instance details Defined in NumHask.Range Methods fold1 :: Semigroup m => Range m -> m # foldMap1 :: Semigroup m => (a -> m) -> Range a -> m # toNonEmpty :: Range a -> NonEmpty a #
Apply Range #
Instance details Defined in NumHask.Range Methods (<.>) :: Range (a -> b) -> Range a -> Range b # (.>) :: Range a -> Range b -> Range b # (<.) :: Range a -> Range b -> Range a # liftF2 :: (a -> b -> c) -> Range a -> Range b -> Range c #
Additive a => AdditiveModule Range a #
Instance details Defined in NumHask.Range Methods (.+) :: Range a -> a -> Range a # (+.) :: a -> Range a -> Range a #
AdditiveGroup a => AdditiveGroupModule Range a #
Instance details Defined in NumHask.Range Methods (.-) :: Range a -> a -> Range a # (-.) :: a -> Range a -> Range a #
Multiplicative a => MultiplicativeModule Range a #
Instance details Defined in NumHask.Range Methods (.) :: Range a -> a -> Range a # (.) :: a -> Range a -> Range a #
MultiplicativeGroup a => MultiplicativeGroupModule Range a #
Instance details Defined in NumHask.Range Methods (./) :: Range a -> a -> Range a # (/.) :: a -> Range a -> Range a #
Additive a => AdditiveBasis Range a #
Instance details Defined in NumHask.Range Methods (.+.) :: Range a -> Range a -> Range a #
AdditiveGroup a => AdditiveGroupBasis Range a #
Instance details Defined in NumHask.Range Methods (.-.) :: Range a -> Range a -> Range a #
Multiplicative a => MultiplicativeBasis Range a #
Instance details Defined in NumHask.Range Methods (.*.) :: Range a -> Range a -> Range a #
MultiplicativeGroup a => MultiplicativeGroupBasis Range a #
Instance details Defined in NumHask.Range Methods (./.) :: Range a -> Range a -> Range a #
Eq a => Eq (Range a) #
Instance details Defined in NumHask.Range Methods (==) :: Range a -> Range a -> Bool # (/=) :: Range a -> Range a -> Bool #
(Ord a, BoundedField a, FromInteger a) => Ord (Range a) #
Instance details Defined in NumHask.Range Methods compare :: Range a -> Range a -> Ordering # (<) :: Range a -> Range a -> Bool # (<=) :: Range a -> Range a -> Bool # (>) :: Range a -> Range a -> Bool # (>=) :: Range a -> Range a -> Bool # max :: Range a -> Range a -> Range a # min :: Range a -> Range a -> Range a #
Show a => Show (Range a) #
Instance details Defined in NumHask.Range Methods showsPrec :: Int -> Range a -> ShowS # show :: Range a -> String # showList :: [Range a] -> ShowS #
Generic (Range a) #
Instance details Defined in NumHask.Range Associated Types type Rep (Range a) :: * -> * # Methods from :: Range a -> Rep (Range a) x # to :: Rep (Range a) x -> Range a #
(Ord a, BoundedField a, FromInteger a) => Semigroup (Range a) #
Instance details Defined in NumHask.Range Methods (<>) :: Range a -> Range a -> Range a # sconcat :: NonEmpty (Range a) -> Range a # stimes :: Integral b => b -> Range a -> Range a #
(Ord a, BoundedField a, FromInteger a) => Monoid (Range a) #
Instance details Defined in NumHask.Range Methods mempty :: Range a # mappend :: Range a -> Range a -> Range a # mconcat :: [Range a] -> Range a #
Arbitrary a => Arbitrary (Range a) #
Instance details Defined in NumHask.Range Methods arbitrary :: Gen (Range a) # shrink :: Range a -> [Range a] #
NFData a => NFData (Range a) #
Instance details Defined in NumHask.Range Methods rnf :: Range a -> () #
(FromInteger a, AdditiveInvertible a, BoundedField a, Ord a) => Signed (Range a) #
Instance details Defined in NumHask.Range Methods sign :: Range a -> Range a # abs :: Range a -> Range a #
(BoundedField a, Ord a, Epsilon a) => Epsilon (Range a) #
Instance details Defined in NumHask.Range Methods nearZero :: Range a -> Bool # aboutEqual :: Range a -> Range a -> Bool # positive :: Range a -> Bool # veryPositive :: Range a -> Bool # veryNegative :: Range a -> Bool #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeMagma (Range a) #	times may well be some sort of affine projection lurking under the hood
Instance details Defined in NumHask.Range Methods times :: Range a -> Range a -> Range a #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeUnital (Range a) #	The unital object (Range -0.5 0.5) satisfies: width one = one mid zero = zero
Instance details Defined in NumHask.Range Methods one :: Range a #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeAssociative (Range a) #
Instance details Defined in NumHask.Range
(FromInteger a, Ord a, BoundedField a) => MultiplicativeCommutative (Range a) #
Instance details Defined in NumHask.Range
(FromInteger a, Ord a, BoundedField a) => MultiplicativeInvertible (Range a) #
Instance details Defined in NumHask.Range Methods recip :: Range a -> Range a #
(FromInteger a, Ord a, BoundedField a) => Multiplicative (Range a) #
Instance details Defined in NumHask.Range Methods (*) :: Range a -> Range a -> Range a #
(FromInteger a, Ord a, BoundedField a) => MultiplicativeGroup (Range a) #
Instance details Defined in NumHask.Range Methods (/) :: Range a -> Range a -> Range a #
Ord a => AdditiveMagma (Range a) #	convex hull union
Instance details Defined in NumHask.Range Methods plus :: Range a -> Range a -> Range a #
(Ord a, BoundedField a) => AdditiveUnital (Range a) #
Instance details Defined in NumHask.Range Methods zero :: Range a #
Ord a => AdditiveAssociative (Range a) #
Instance details Defined in NumHask.Range
Ord a => AdditiveCommutative (Range a) #
Instance details Defined in NumHask.Range
Ord a => AdditiveInvertible (Range a) #
Instance details Defined in NumHask.Range Methods negate :: Range a -> Range a #
(Ord a, BoundedField a) => Additive (Range a) #
Instance details Defined in NumHask.Range Methods (+) :: Range a -> Range a -> Range a #
(Ord a, BoundedField a) => AdditiveGroup (Range a) #
Instance details Defined in NumHask.Range Methods (-) :: Range a -> Range a -> Range a #
(FromInteger a, Ord a, BoundedField a) => Space (Range a) #
Instance details Defined in NumHask.Range Associated Types type Element (Range a) :: * # type Grid (Range a) :: * # Methods lower :: Range a -> Element (Range a) # upper :: Range a -> Element (Range a) # mid :: Range a -> Element (Range a) # width :: Range a -> Element (Range a) # singleton :: Element (Range a) -> Range a # singular :: Range a -> Bool # element :: Element (Range a) -> Range a -> Bool # contains :: Range a -> Range a -> Bool # disjoint :: Range a -> Range a -> Bool # intersects :: Range a -> Range a -> Bool # union :: Range a -> Range a -> Range a # nul :: Range a # space :: Foldable f => f (Element (Range a)) -> Range a # project :: Range a -> Range a -> Element (Range a) -> Element (Range a) # grid :: Pos -> Range a -> Grid (Range a) -> [Element (Range a)] # gridSpace :: Range a -> Grid (Range a) -> [Range a] #
AdditiveGroup a => Normed (Range a) a #
Instance details Defined in NumHask.Range Methods normL1 :: Range a -> a # normL2 :: Range a -> a # normLp :: a -> Range a -> a #
(Ord a, AdditiveGroup a) => Metric (Range a) a #
Instance details Defined in NumHask.Range Methods distanceL1 :: Range a -> Range a -> a # distanceL2 :: Range a -> Range a -> a # distanceLp :: a -> Range a -> Range a -> a #
type Rep Range #
Instance details Defined in NumHask.Range type Rep Range = Bool
type Rep (Range a) #
Instance details Defined in NumHask.Range type Rep (Range a) = D1 (MetaData "Range" "NumHask.Range" "numhask-range-0.2.3.1-J89sQYUYBLeKCiE9B8m0BR" True) (C1 (MetaCons "Range'" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a, a))))
type Element (Range a) #
Instance details Defined in NumHask.Range type Element (Range a) = a
type Grid (Range a) #
Instance details Defined in NumHask.Range type Grid (Range a) = Int

pattern Range :: a -> a -> Range a #

A tuple is the preferred concrete implementation of a Range, due to many libraries having substantial optimizations for tuples already (eg Vector). 'Pattern Synonyms' allow us to recover a constructor without the need for tuple syntax.

gridSensible :: (Ord a, FromInteger a, Fractional a, QuotientField a Integer, ExpField a) => Pos -> Range a -> Integer -> [a] #

turn a range into n as pleasing to human sense and sensibility the as may well lie outside the original range as a result