Copyright	Copyright (C) 2006-2018 Bjorn Buckwalter
License	BSD3
Maintainer	bjorn@buckwalter.se
Stability	Stable
Portability	GHC only
Safe Haskell	Safe-Inferred
Language	Haskell2010

Numeric.Units.Dimensional.Prelude

Description

Summary

This module supplies a convenient set of imports for working with the dimensional package, including aliases for common Quantitys and Dimensions, and a comprehensive set of SI units and units accepted for use with the SI.

It re-exports the Prelude, hiding arithmetic functions whose names collide with the dimensionally-typed versions supplied by this package.

Synopsis

type family (a :: Dimension) * (b :: Dimension) where ...
type family (d :: Dimension) ^ (x :: TypeInt) where ...
type family (a :: Dimension) / (d :: Dimension) where ...
type Recip (d :: Dimension) = DOne / d
class KnownVariant (v :: Variant) where
- data Dimensional v :: Dimension -> Type -> Type
type Unit (m :: Metricality) = Dimensional ('DUnit m)
type Quantity = SQuantity One
data Metricality
- = Metric
- | NonMetric
data Dimension = Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt
type family NRoot (d :: Dimension) (x :: TypeInt) where ...
type Sqrt d = NRoot d 'Pos2
type Cbrt d = NRoot d 'Pos3
data Dimension' = Dim' !Int !Int !Int !Int !Int !Int !Int
class HasDynamicDimension a => HasDimension a where
- dimension :: a -> Dimension'
type KnownDimension (d :: Dimension) = HasDimension (Proxy d)
type DOne = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero
type DLength = 'Dim 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero
type DMass = 'Dim 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero
type DTime = 'Dim 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero
type DElectricCurrent = 'Dim 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero
type DThermodynamicTemperature = 'Dim 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero
type DAmountOfSubstance = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero
type DLuminousIntensity = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1
type Dimensionless = Quantity DOne
type Length = Quantity DLength
type Mass = Quantity DMass
type Time = Quantity DTime
type ElectricCurrent = Quantity DElectricCurrent
type ThermodynamicTemperature = Quantity DThermodynamicTemperature
type AmountOfSubstance = Quantity DAmountOfSubstance
type LuminousIntensity = Quantity DLuminousIntensity
(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a
negate :: Num a => Quantity d a -> Quantity d a
(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a
(*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 * d2) a
(^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a
abs :: Num a => Quantity d a -> Quantity d a
signum :: Num a => Quantity d a -> Dimensionless a
sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a
product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a
(/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 / v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 / v2) (d1 / d2) a
recip :: Fractional a => Quantity d a -> Quantity (Recip d) a
atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a
pi :: Floating a => Dimensionless a
exp :: Floating a => Dimensionless a -> Dimensionless a
log :: Floating a => Dimensionless a -> Dimensionless a
sqrt :: Floating a => Quantity d a -> Quantity (Sqrt d) a
(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a
logBase :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a
sin :: Floating a => Dimensionless a -> Dimensionless a
cos :: Floating a => Dimensionless a -> Dimensionless a
tan :: Floating a => Dimensionless a -> Dimensionless a
asin :: Floating a => Dimensionless a -> Dimensionless a
acos :: Floating a => Dimensionless a -> Dimensionless a
atan :: Floating a => Dimensionless a -> Dimensionless a
sinh :: Floating a => Dimensionless a -> Dimensionless a
cosh :: Floating a => Dimensionless a -> Dimensionless a
tanh :: Floating a => Dimensionless a -> Dimensionless a
asinh :: Floating a => Dimensionless a -> Dimensionless a
acosh :: Floating a => Dimensionless a -> Dimensionless a
atanh :: Floating a => Dimensionless a -> Dimensionless a
log1p :: Floating a => Dimensionless a -> Dimensionless a
expm1 :: Floating a => Dimensionless a -> Dimensionless a
log1pexp :: Floating a => Dimensionless a -> Dimensionless a
log1mexp :: Floating a => Dimensionless a -> Dimensionless a
(*~) :: Num a => a -> Unit m d a -> Quantity d a
(/~) :: Fractional a => Quantity d a -> Unit m d a -> a
(^/) :: (KnownTypeInt n, Floating a) => Quantity d a -> Proxy n -> Quantity (NRoot d n) a
nroot :: (KnownTypeInt n, Floating a) => Proxy n -> Quantity d a -> Quantity (NRoot d n) a
cbrt :: Floating a => Quantity d a -> Quantity (Cbrt d) a
(*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a)
(/~~) :: forall f m d a. (Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a
mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a
dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a
nFromTo :: (Fractional a, Integral b) => Quantity d a -> Quantity d a -> b -> [Quantity d a]
_0 :: Num a => Quantity d a
_1 :: Num a => Dimensionless a
_2 :: Num a => Dimensionless a
_3 :: Num a => Dimensionless a
_4 :: Num a => Dimensionless a
_5 :: Num a => Dimensionless a
_6 :: Num a => Dimensionless a
_7 :: Num a => Dimensionless a
_8 :: Num a => Dimensionless a
_9 :: Num a => Dimensionless a
tau :: Floating a => Dimensionless a
siUnit :: forall d a. (KnownDimension d, Num a) => Unit 'NonMetric d a
one :: Num a => Unit 'NonMetric DOne a
mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a
mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a
mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a
name :: Unit m d a -> UnitName m
exactValue :: Unit m d a -> ExactPi
weaken :: Unit m d a -> Unit 'NonMetric d a
strengthen :: Unit m d a -> Maybe (Unit 'Metric d a)
exactify :: Unit m d a -> Unit m d ExactPi
showIn :: (Show a, Fractional a) => Unit m d a -> Quantity d a -> String
changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b
changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b
asLens :: Fractional a => Unit m d a -> forall f. Functor f => (a -> f a) -> Quantity d a -> f (Quantity d a)
module Numeric.Units.Dimensional.Quantities
module Numeric.Units.Dimensional.SIUnits
neg5 :: Proxy 'Neg5
neg4 :: Proxy 'Neg4
neg3 :: Proxy 'Neg3
neg2 :: Proxy 'Neg2
neg1 :: Proxy 'Neg1
zero :: Proxy 'Zero
pos1 :: Proxy 'Pos1
pos2 :: Proxy 'Pos2
pos3 :: Proxy 'Pos3
pos4 :: Proxy 'Pos4
pos5 :: Proxy 'Pos5
class Category (cat :: k -> k -> Type) where
- id :: forall (a :: k). cat a a
- (.) :: forall (b :: k) (c :: k) (a :: k). cat b c -> cat a b -> cat a c
maximum :: (Foldable t, Ord a) => t a -> a
minimum :: (Foldable t, Ord a) => t a -> a
data Int
data Float
data Char
data IO a
data Bool
- = False
- | True
data Double
data Word
data Ordering
- = LT
- | EQ
- | GT
data Maybe a
- = Nothing
- | Just a
class a ~# b => (a :: k) ~ (b :: k)
data Integer
data Either a b
- = Left a
- | Right b
class (Real a, Enum a) => Integral a where
- quot :: a -> a -> a
- rem :: a -> a -> a
- div :: a -> a -> a
- mod :: a -> a -> a
- quotRem :: a -> a -> (a, a)
- divMod :: a -> a -> (a, a)
- toInteger :: a -> Integer
type Rational = Ratio Integer
type String = [Char]
class Read a where
- readsPrec :: Int -> ReadS a
- readList :: ReadS [a]
class Show a where
- showsPrec :: Int -> a -> ShowS
- show :: a -> String
- showList :: [a] -> ShowS
type IOError = IOException
class Bounded a where
- minBound :: a
- maxBound :: a
class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
class Eq a where
- (==) :: a -> a -> Bool
- (/=) :: a -> a -> Bool
class Fractional a => Floating a
class Num a => Fractional a where
- fromRational :: Rational -> a
class Applicative m => Monad (m :: Type -> Type) where
- (>>=) :: m a -> (a -> m b) -> m b
- (>>) :: m a -> m b -> m b
- return :: a -> m a
class Functor (f :: Type -> Type) where
- fmap :: (a -> b) -> f a -> f b
- (<$) :: a -> f b -> f a
class Num a where
- fromInteger :: Integer -> a
class Eq a => Ord a where
- compare :: a -> a -> Ordering
- (<) :: a -> a -> Bool
- (<=) :: a -> a -> Bool
- (>) :: a -> a -> Bool
- (>=) :: a -> a -> Bool
- max :: a -> a -> a
- min :: a -> a -> a
class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
class (Real a, Fractional a) => RealFrac a where
- properFraction :: Integral b => a -> (b, a)
- truncate :: Integral b => a -> b
- round :: Integral b => a -> b
- ceiling :: Integral b => a -> b
- floor :: Integral b => a -> b
class Monad m => MonadFail (m :: Type -> Type) where
- fail :: String -> m a
class Functor f => Applicative (f :: Type -> Type) where
- pure :: a -> f a
- (<*>) :: f (a -> b) -> f a -> f b
- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
- (*>) :: f a -> f b -> f b
- (<*) :: f a -> f b -> f a
class Foldable (t :: Type -> Type) where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- null :: t a -> Bool
- length :: t a -> Int
- elem :: Eq a => a -> t a -> Bool
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
class Semigroup a where
- (<>) :: a -> a -> a
class Semigroup a => Monoid a where
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
type ShowS = String -> String
type ReadS a = String -> [(a, String)]
type FilePath = String
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
even :: Integral a => a -> Bool
(<$>) :: Functor f => (a -> b) -> f a -> f b
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
fst :: (a, b) -> a
uncurry :: (a -> b -> c) -> (a, b) -> c
head :: HasCallStack => [a] -> a
writeFile :: FilePath -> String -> IO ()
getLine :: IO String
putStrLn :: String -> IO ()
filter :: (a -> Bool) -> [a] -> [a]
cycle :: HasCallStack => [a] -> [a]
(++) :: [a] -> [a] -> [a]
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b
concat :: Foldable t => t [a] -> [a]
zip :: [a] -> [b] -> [(a, b)]
print :: Show a => a -> IO ()
otherwise :: Bool
map :: (a -> b) -> [a] -> [b]
fromIntegral :: (Integral a, Num b) => a -> b
realToFrac :: (Real a, Fractional b) => a -> b
(&&) :: Bool -> Bool -> Bool
(||) :: Bool -> Bool -> Bool
not :: Bool -> Bool
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
(=<<) :: Monad m => (a -> m b) -> m a -> m b
const :: a -> b -> a
flip :: (a -> b -> c) -> b -> a -> c
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
until :: (a -> Bool) -> (a -> a) -> a -> a
asTypeOf :: a -> a -> a
subtract :: Num a => a -> a -> a
maybe :: b -> (a -> b) -> Maybe a -> b
tail :: HasCallStack => [a] -> [a]
last :: HasCallStack => [a] -> a
init :: HasCallStack => [a] -> [a]
scanl :: (b -> a -> b) -> b -> [a] -> [b]
scanl1 :: (a -> a -> a) -> [a] -> [a]
scanr :: (a -> b -> b) -> b -> [a] -> [b]
scanr1 :: (a -> a -> a) -> [a] -> [a]
iterate :: (a -> a) -> a -> [a]
repeat :: a -> [a]
replicate :: Int -> a -> [a]
takeWhile :: (a -> Bool) -> [a] -> [a]
dropWhile :: (a -> Bool) -> [a] -> [a]
take :: Int -> [a] -> [a]
drop :: Int -> [a] -> [a]
splitAt :: Int -> [a] -> ([a], [a])
span :: (a -> Bool) -> [a] -> ([a], [a])
break :: (a -> Bool) -> [a] -> ([a], [a])
reverse :: [a] -> [a]
and :: Foldable t => t Bool -> Bool
or :: Foldable t => t Bool -> Bool
any :: Foldable t => (a -> Bool) -> t a -> Bool
all :: Foldable t => (a -> Bool) -> t a -> Bool
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
lookup :: Eq a => a -> [(a, b)] -> Maybe b
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
(!!) :: HasCallStack => [a] -> Int -> a
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
unzip :: [(a, b)] -> ([a], [b])
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
shows :: Show a => a -> ShowS
showChar :: Char -> ShowS
showString :: String -> ShowS
showParen :: Bool -> ShowS -> ShowS
odd :: Integral a => a -> Bool
(^^) :: (Fractional a, Integral b) => a -> b -> a
gcd :: Integral a => a -> a -> a
lcm :: Integral a => a -> a -> a
snd :: (a, b) -> b
curry :: ((a, b) -> c) -> a -> b -> c
lex :: ReadS String
readParen :: Bool -> ReadS a -> ReadS a
either :: (a -> c) -> (b -> c) -> Either a b -> c
reads :: Read a => ReadS a
read :: Read a => String -> a
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
lines :: String -> [String]
unlines :: [String] -> String
words :: String -> [String]
unwords :: [String] -> String
userError :: String -> IOError
ioError :: IOError -> IO a
putChar :: Char -> IO ()
putStr :: String -> IO ()
getChar :: IO Char
getContents :: IO String
interact :: (String -> String) -> IO ()
readFile :: FilePath -> IO String
appendFile :: FilePath -> String -> IO ()
readLn :: Read a => IO a
readIO :: Read a => String -> IO a

Documentation

type family (a :: Dimension) * (b :: Dimension) where ... infixl 7 Source #

Multiplication of dimensions corresponds to addition of the base dimensions' exponents.

Equations

DOne * d = d
d * DOne = d
('Dim l m t i th n j) * ('Dim l' m' t' i' th' n' j') = 'Dim (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j')

type family (d :: Dimension) ^ (x :: TypeInt) where ... infixr 8 Source #

Powers of dimensions correspond to multiplication of the base dimensions' exponents by the exponent.

We limit ourselves to integer powers of Dimensionals as fractional powers make little physical sense.

Equations

DOne ^ x = DOne
d ^ 'Zero = DOne
d ^ 'Pos1 = d
('Dim l m t i th n j) ^ x = 'Dim (l * x) (m * x) (t * x) (i * x) (th * x) (n * x) (j * x)

type family (a :: Dimension) / (d :: Dimension) where ... infixl 7 Source #

Division of dimensions corresponds to subtraction of the base dimensions' exponents.

Equations

d / DOne = d
d / d = DOne
('Dim l m t i th n j) / ('Dim l' m' t' i' th' n' j') = 'Dim (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j')

type Recip (d :: Dimension) = DOne / d Source #

The reciprocal of a dimension is defined as the result of dividing DOne by it, or of negating each of the base dimensions' exponents.

class KnownVariant (v :: Variant) Source #

A KnownVariant is one whose term-level Dimensional values we can represent with an associated data family instance and manipulate with certain functions, not all of which are exported from the package.

Each validly constructed type of kind Variant has a KnownVariant instance.

Minimal complete definition

extractValue, extractName, injectValue, dmap

Associated Types

data Dimensional v :: Dimension -> Type -> Type Source #

A dimensional value, either a Quantity or a Unit, parameterized by its Dimension and representation.

Instances

Instances details

KnownVariant ('DQuantity s) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Associated Types data Dimensional ('DQuantity s) :: Dimension -> Type -> Type Source # type ScaleFactor ('DQuantity s) :: ExactPi' Methods extractValue :: forall (d :: Dimension) a. Dimensional ('DQuantity s) d a -> (a, Maybe ExactPi) extractName :: forall (d :: Dimension) a. Dimensional ('DQuantity s) d a -> Maybe (UnitName 'NonMetric) injectValue :: forall a (d :: Dimension). Maybe (UnitName 'NonMetric) -> (a, Maybe ExactPi) -> Dimensional ('DQuantity s) d a dmap :: forall a1 a2 (d :: Dimension). (a1 -> a2) -> Dimensional ('DQuantity s) d a1 -> Dimensional ('DQuantity s) d a2 Source #
Typeable m => KnownVariant ('DUnit m) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Associated Types data Dimensional ('DUnit m) :: Dimension -> Type -> Type Source # type ScaleFactor ('DUnit m) :: ExactPi' Methods extractValue :: forall (d :: Dimension) a. Dimensional ('DUnit m) d a -> (a, Maybe ExactPi) extractName :: forall (d :: Dimension) a. Dimensional ('DUnit m) d a -> Maybe (UnitName 'NonMetric) injectValue :: forall a (d :: Dimension). Maybe (UnitName 'NonMetric) -> (a, Maybe ExactPi) -> Dimensional ('DUnit m) d a dmap :: forall a1 a2 (d :: Dimension). (a1 -> a2) -> Dimensional ('DUnit m) d a1 -> Dimensional ('DUnit m) d a2 Source #

type Unit (m :: Metricality) = Dimensional ('DUnit m) Source #

A unit of measurement.

type Quantity = SQuantity One Source #

A dimensional quantity.

data Metricality Source #

Encodes whether a unit is a metric unit, that is, whether it can be combined with a metric prefix to form a related unit.

Constructors

Metric	Capable of receiving a metric prefix.
NonMetric	Incapable of receiving a metric prefix.

Instances

Instances details

Data Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Metricality -> c Metricality # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Metricality # toConstr :: Metricality -> Constr # dataTypeOf :: Metricality -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Metricality) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Metricality) # gmapT :: (forall b. Data b => b -> b) -> Metricality -> Metricality # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r # gmapQ :: (forall d. Data d => d -> u) -> Metricality -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Metricality -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality #
Generic Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Associated Types type Rep Metricality :: Type -> Type # Methods from :: Metricality -> Rep Metricality x # to :: Rep Metricality x -> Metricality #
NFData Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods rnf :: Metricality -> () #
Eq Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods (==) :: Metricality -> Metricality -> Bool # (/=) :: Metricality -> Metricality -> Bool #
Ord Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants Methods compare :: Metricality -> Metricality -> Ordering # (<) :: Metricality -> Metricality -> Bool # (<=) :: Metricality -> Metricality -> Bool # (>) :: Metricality -> Metricality -> Bool # (>=) :: Metricality -> Metricality -> Bool # max :: Metricality -> Metricality -> Metricality # min :: Metricality -> Metricality -> Metricality #
type Rep Metricality Source #
Instance details Defined in Numeric.Units.Dimensional.Variants type Rep Metricality = D1 ('MetaData "Metricality" "Numeric.Units.Dimensional.Variants" "dimensional-1.6.1-ELRyWwWitPHC8LaQvCwLfc" 'False) (C1 ('MetaCons "Metric" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "NonMetric" 'PrefixI 'False) (U1 :: Type -> Type))

data Dimension Source #

Represents a physical dimension in the basis of the 7 SI base dimensions, where the respective dimensions are represented by type variables using the following convention:

l: Length
m: Mass
t: Time
i: Electric current
th: Thermodynamic temperature
n: Amount of substance
j: Luminous intensity

For the equivalent term-level representation, see Dimension'

Constructors

Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt

Instances

Instances details

(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy ('Dim l m t i th n j)) Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel Methods dimension :: Proxy ('Dim l m t i th n j) -> Dimension' Source #
(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDynamicDimension (Proxy ('Dim l m t i th n j)) Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel Methods dynamicDimension :: Proxy ('Dim l m t i th n j) -> DynamicDimension Source #

type family NRoot (d :: Dimension) (x :: TypeInt) where ... Source #

Roots of dimensions correspond to division of the base dimensions' exponents by the order of the root.

Equations

NRoot DOne x = DOne
NRoot d 'Pos1 = d
NRoot ('Dim l m t i th n j) x = 'Dim (l / x) (m / x) (t / x) (i / x) (th / x) (n / x) (j / x)

type Sqrt d = NRoot d 'Pos2 Source #

Square root is a special case of NRoot with order 2.

type Cbrt d = NRoot d 'Pos3 Source #

Cube root is a special case of NRoot with order 3.

data Dimension' Source #

A physical dimension, encoded as 7 integers, representing a factorization of the dimension into the 7 SI base dimensions. By convention they are stored in the same order as in the Dimension data kind.

Constructors

Dim' !Int !Int !Int !Int !Int !Int !Int

Instances

Instances details

Data Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dimension' -> c Dimension' # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Dimension' # toConstr :: Dimension' -> Constr # dataTypeOf :: Dimension' -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Dimension') # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Dimension') # gmapT :: (forall b. Data b => b -> b) -> Dimension' -> Dimension' # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r # gmapQ :: (forall d. Data d => d -> u) -> Dimension' -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dimension' -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' #
Monoid Dimension' Source #	The monoid of dimensions under multiplication.
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods mempty :: Dimension' # mappend :: Dimension' -> Dimension' -> Dimension' # mconcat :: [Dimension'] -> Dimension' #
Semigroup Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (<>) :: Dimension' -> Dimension' -> Dimension' # sconcat :: NonEmpty Dimension' -> Dimension' # stimes :: Integral b => b -> Dimension' -> Dimension' #
Generic Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Associated Types type Rep Dimension' :: Type -> Type # Methods from :: Dimension' -> Rep Dimension' x # to :: Rep Dimension' x -> Dimension' #
Show Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods showsPrec :: Int -> Dimension' -> ShowS # show :: Dimension' -> String # showList :: [Dimension'] -> ShowS #
NFData Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods rnf :: Dimension' -> () #
HasDimension Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dimension :: Dimension' -> Dimension' Source #
HasDynamicDimension Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dynamicDimension :: Dimension' -> DynamicDimension Source #
Eq Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (==) :: Dimension' -> Dimension' -> Bool # (/=) :: Dimension' -> Dimension' -> Bool #
Ord Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods compare :: Dimension' -> Dimension' -> Ordering # (<) :: Dimension' -> Dimension' -> Bool # (<=) :: Dimension' -> Dimension' -> Bool # (>) :: Dimension' -> Dimension' -> Bool # (>=) :: Dimension' -> Dimension' -> Bool # max :: Dimension' -> Dimension' -> Dimension' # min :: Dimension' -> Dimension' -> Dimension' #
type Rep Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel type Rep Dimension' = D1 ('MetaData "Dimension'" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.6.1-ELRyWwWitPHC8LaQvCwLfc" 'False) (C1 ('MetaCons "Dim'" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int))) :: ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int)) :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int)))))

class HasDynamicDimension a => HasDimension a where Source #

Dimensional values inhabit this class, which allows access to a term-level representation of their dimension.

Methods

dimension :: a -> Dimension' Source #

Obtains a term-level representation of a value's dimension.

Instances

Instances details

HasDimension Dimension' Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dimension :: Dimension' -> Dimension' Source #
HasDimension AnyUnit Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods dimension :: AnyUnit -> Dimension' Source #
HasDimension (AnyQuantity a) Source #
Instance details Defined in Numeric.Units.Dimensional.Dynamic Methods dimension :: AnyQuantity a -> Dimension' Source #
(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy ('Dim l m t i th n j)) Source #
Instance details Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel Methods dimension :: Proxy ('Dim l m t i th n j) -> Dimension' Source #
KnownDimension d => HasDimension (Dimensional v d a) Source #
Instance details Defined in Numeric.Units.Dimensional.Internal Methods dimension :: Dimensional v d a -> Dimension' Source #

type KnownDimension (d :: Dimension) = HasDimension (Proxy d) Source #

A KnownDimension is one for which we can construct a term-level representation. Each validly constructed type of kind Dimension has a KnownDimension instance.

While KnownDimension is a constraint synonym, the presence of KnownDimension d in a context allows use of dimension :: Proxy d -> Dimension'.

type DOne = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero Source #

The type-level dimension of dimensionless values.

type DLength = 'Dim 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero Source #

type DMass = 'Dim 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero Source #

type DTime = 'Dim 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero Source #

type DElectricCurrent = 'Dim 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero Source #

type DThermodynamicTemperature = 'Dim 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero Source #

type DAmountOfSubstance = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero Source #

type DLuminousIntensity = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 Source #

type Dimensionless = Quantity DOne Source #

type Length = Quantity DLength Source #

type Mass = Quantity DMass Source #

type Time = Quantity DTime Source #

type ElectricCurrent = Quantity DElectricCurrent Source #

type ThermodynamicTemperature = Quantity DThermodynamicTemperature Source #

type AmountOfSubstance = Quantity DAmountOfSubstance Source #

type LuminousIntensity = Quantity DLuminousIntensity Source #

(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #

Subtracts one Quantity from another.

negate :: Num a => Quantity d a -> Quantity d a Source #

Negates the value of a Quantity.

(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #

Adds two Quantitys.

(*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 * d2) a infixl 7 Source #

Multiplies two Quantitys or two Units.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NonMetric.

(^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a infixr 8 Source #

Raises a Quantity or Unit to an integer power.

Because the power chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the exponent in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NonMetric.

abs :: Num a => Quantity d a -> Quantity d a Source #

Takes the absolute value of a Quantity.

signum :: Num a => Quantity d a -> Dimensionless a Source #

Takes the sign of a Quantity. The functions abs and signum satisy the law that:

abs x * signum x == x

The sign is either negate _1 (negative), _0 (zero), or _1 (positive).

sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a Source #

The sum of all elements in a foldable structure.

>>> sum ([] :: [Mass Double])
0.0 kg

>>> sum [12.4 *~ meter, 1 *~ foot]
12.7048 m

product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a Source #

The product of all elements in a foldable structure.

>>> product ([] :: [Dimensionless Double])
1.0

>>> product [pi, _4, 0.36 *~ one]
4.523893421169302

(/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 / v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 / v2) (d1 / d2) a infixl 7 Source #

Divides one Quantity by another or one Unit by another.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NonMetric.

recip :: Fractional a => Quantity d a -> Quantity (Recip d) a Source #

Forms the reciprocal of a Quantity, which has the reciprocal dimension.

>>> recip $ 47 *~ hertz
2.127659574468085e-2 s

atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a Source #

The standard two argument arctangent function. Since it interprets its two arguments in comparison with one another, the input may have any dimension.

>>> atan2 _0 _1
0.0

>>> atan2 _1 _0
1.5707963267948966

>>> atan2 _0 (negate _1)
3.141592653589793

>>> atan2 (negate _1) _0
-1.5707963267948966

pi :: Floating a => Dimensionless a Source #

exp :: Floating a => Dimensionless a -> Dimensionless a Source #

log :: Floating a => Dimensionless a -> Dimensionless a Source #

sqrt :: Floating a => Quantity d a -> Quantity (Sqrt d) a Source #

Computes the square root of a Quantity using **.

The NRoot type family will prevent application where the supplied quantity does not have a square dimension.

(x :: Area Double) >= _0 ==> sqrt x == nroot pos2 x

(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a infixr 8 Source #

Raises a dimensionless quantity to a dimensionless power.

logBase :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a Source #

Takes the logarithm of the second argument in the base of the first.

>>> logBase _2 _8
3.0

sin :: Floating a => Dimensionless a -> Dimensionless a Source #

cos :: Floating a => Dimensionless a -> Dimensionless a Source #

tan :: Floating a => Dimensionless a -> Dimensionless a Source #

asin :: Floating a => Dimensionless a -> Dimensionless a Source #

acos :: Floating a => Dimensionless a -> Dimensionless a Source #

atan :: Floating a => Dimensionless a -> Dimensionless a Source #

sinh :: Floating a => Dimensionless a -> Dimensionless a Source #

cosh :: Floating a => Dimensionless a -> Dimensionless a Source #

tanh :: Floating a => Dimensionless a -> Dimensionless a Source #

asinh :: Floating a => Dimensionless a -> Dimensionless a Source #

acosh :: Floating a => Dimensionless a -> Dimensionless a Source #

atanh :: Floating a => Dimensionless a -> Dimensionless a Source #

log1p :: Floating a => Dimensionless a -> Dimensionless a Source #

expm1 :: Floating a => Dimensionless a -> Dimensionless a Source #

log1pexp :: Floating a => Dimensionless a -> Dimensionless a Source #

log1mexp :: Floating a => Dimensionless a -> Dimensionless a Source #

(*~) :: Num a => a -> Unit m d a -> Quantity d a infixl 7 Source #

Forms a Quantity by multipliying a number and a unit.

(/~) :: Fractional a => Quantity d a -> Unit m d a -> a infixl 7 Source #

Divides a Quantity by a Unit of the same physical dimension, obtaining the numerical value of the quantity expressed in that unit.

(^/) :: (KnownTypeInt n, Floating a) => Quantity d a -> Proxy n -> Quantity (NRoot d n) a infixr 8 Source #

Computes the nth root of a Quantity using **.

The NRoot type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.

Because the root chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the root in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

Also available in prefix form, see nroot.

nroot :: (KnownTypeInt n, Floating a) => Proxy n -> Quantity d a -> Quantity (NRoot d n) a Source #

Computes the nth root of a Quantity using **.

The NRoot type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.

Because the root chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the root in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

n must not be zero. Negative roots are defined such that nroot (Proxy :: Proxy (Negate n)) x == nroot (Proxy :: Proxy n) (recip x).

Also available in operator form, see ^/.

cbrt :: Floating a => Quantity d a -> Quantity (Cbrt d) a Source #

Computes the cube root of a Quantity using **.

The NRoot type family will prevent application where the supplied quantity does not have a cubic dimension.

(x :: Volume Double) >= _0 ==> cbrt x == nroot pos3 x

(*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a) infixl 7 Source #

Applies *~ to all values in a functor.

(/~~) :: forall f m d a. (Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a infixl 7 Source #

Applies /~ to all values in a functor.

mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a Source #

The arithmetic mean of all elements in a foldable structure.

>>> mean [pi, _7]
5.070796326794897

dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a Source #

The length of the foldable data structure as a Dimensionless. This can be useful for purposes of e.g. calculating averages.

>>> dimensionlessLength ["foo", "bar"]
2

nFromTo Source #

Arguments

:: (Fractional a, Integral b)
=> Quantity d a	The initial value.
-> Quantity d a	The final value.
-> b	The number of intermediate values. If less than one, no intermediate values will result.
-> [Quantity d a]

Returns a list of quantities between given bounds.

n <= 0 ==> nFromTo (x :: Mass Double) (y :: Mass Double) n == [x, y]

(x :: Length Double) <= (y :: Length Double) ==> all (\z -> x <= z && z <= y) (nFromTo x y n)

>>> nFromTo _0 _3 2
[0.0,1.0,2.0,3.0]

>>> nFromTo _1 _0 7
[1.0,0.875,0.75,0.625,0.5,0.375,0.25,0.125,0.0]

>>> nFromTo _0 _1 (-5)
[0.0,1.0]

_0 :: Num a => Quantity d a Source #

The constant for zero is polymorphic, allowing it to express zero Length or Capacitance or Velocity etc, in addition to the Dimensionless value zero.

_1 :: Num a => Dimensionless a Source #

_2 :: Num a => Dimensionless a Source #

_3 :: Num a => Dimensionless a Source #

_4 :: Num a => Dimensionless a Source #

_5 :: Num a => Dimensionless a Source #

_6 :: Num a => Dimensionless a Source #

_7 :: Num a => Dimensionless a Source #

_8 :: Num a => Dimensionless a Source #

_9 :: Num a => Dimensionless a Source #

tau :: Floating a => Dimensionless a Source #

Twice pi.

For background on tau see https://tauday.com/tau-manifesto (but also feel free to review https://web.archive.org/web/20200926221249/http://www.thepimanifesto.com/).

siUnit :: forall d a. (KnownDimension d, Num a) => Unit 'NonMetric d a Source #

A polymorphic Unit which can be used in place of the coherent SI base unit of any dimension. This allows polymorphic quantity creation and destruction without exposing the Dimensional constructor.

one :: Num a => Unit 'NonMetric DOne a Source #

The unit one has dimension DOne and is the base unit of dimensionless values.

As detailed in 7.10 "Values of quantities expressed simply as numbers: the unit one, symbol 1" of [1], the unit one generally does not appear in expressions. However, for us it is necessary to use one as we would any other unit to perform the "wrapping" of dimensionless values.

mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is irrational or Approximate. See mkUnitQ for when it is rational and mkUnitZ for when it is an integer.

Note that supplying zero as a definining quantity is invalid, as the library relies upon units forming a group under multiplication.

Supplying negative defining quantities is allowed and handled gracefully, but is discouraged on the grounds that it may be unexpected by other readers.

mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is rational. See mkUnitZ for when it is an integer and mkUnitR for the general case.

For more information see mkUnitR.

mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is an integer. See mkUnitQ for when it is rational and mkUnitR for the general case.

For more information see mkUnitR.

name :: Unit m d a -> UnitName m Source #

Extracts the UnitName of a Unit.

exactValue :: Unit m d a -> ExactPi Source #

Extracts the exact value of a Unit, expressed in terms of the SI coherent derived unit (see siUnit) of the same Dimension.

Note that the actual value may in some cases be approximate, for example if the unit is defined by experiment.

weaken :: Unit m d a -> Unit 'NonMetric d a Source #

Discards potentially unwanted type level information about a Unit.

strengthen :: Unit m d a -> Maybe (Unit 'Metric d a) Source #

Attempts to convert a Unit which may or may not be Metric to one which is certainly Metric.

exactify :: Unit m d a -> Unit m d ExactPi Source #

Forms the exact version of a Unit.

showIn :: (Show a, Fractional a) => Unit m d a -> Quantity d a -> String Source #

Shows the value of a Quantity expressed in a specified Unit of the same Dimension.

Uses non-breaking spaces between the value and the unit, and within the unit name.

>>> putStrLn $ showIn watt $ (37 *~ volt) * (4 *~ ampere)
148.0 W

changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b Source #

Convenient conversion between numerical types while retaining dimensional information.

>>> let x = (37 :: Rational) *~ poundMass
>>> changeRep x :: Mass Double
16.78291769 kg

changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b Source #

Convenient conversion from exactly represented values while retaining dimensional information.

asLens :: Fractional a => Unit m d a -> forall f. Functor f => (a -> f a) -> Quantity d a -> f (Quantity d a) Source #

Converts a Unit into a lens from Quantitys to values.

module Numeric.Units.Dimensional.Quantities

module Numeric.Units.Dimensional.SIUnits

neg5 :: Proxy 'Neg5 #

neg4 :: Proxy 'Neg4 #

neg3 :: Proxy 'Neg3 #

neg2 :: Proxy 'Neg2 #

neg1 :: Proxy 'Neg1 #

zero :: Proxy 'Zero #

pos1 :: Proxy 'Pos1 #

pos2 :: Proxy 'Pos2 #

pos3 :: Proxy 'Pos3 #

pos4 :: Proxy 'Pos4 #

pos5 :: Proxy 'Pos5 #

class Category (cat :: k -> k -> Type) where #

A class for categories. Instances should satisfy the laws

Right identity: f . id = f
Left identity: id . f = f
Associativity: f . (g . h) = (f . g) . h

Methods

id :: forall (a :: k). cat a a #

the identity morphism

(.) :: forall (b :: k) (c :: k) (a :: k). cat b c -> cat a b -> cat a c infixr 9 #

morphism composition

Instances

Instances details

Monad m => Category (Kleisli m :: Type -> Type -> Type)	Since: base-3.0
Instance details Defined in Control.Arrow Methods id :: forall (a :: k). Kleisli m a a # (.) :: forall (b :: k) (c :: k) (a :: k). Kleisli m b c -> Kleisli m a b -> Kleisli m a c #
Category (Coercion :: k -> k -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). Coercion a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). Coercion b c -> Coercion a b -> Coercion a c #
Category ((:~:) :: k -> k -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). a :~: a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~: c) -> (a :~: b) -> a :~: c #
Category (->)	Since: base-3.0
Instance details Defined in Control.Category Methods id :: forall (a :: k). a -> a # (.) :: forall (b :: k) (c :: k) (a :: k). (b -> c) -> (a -> b) -> a -> c #
Category ((:~~:) :: k -> k -> Type)	Since: base-4.10.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). a :~~: a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~~: c) -> (a :~~: b) -> a :~~: c #

maximum :: (Foldable t, Ord a) => t a -> a #

The largest element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.

Examples

Expand

Basic usage:

>>> maximum [1..10]
10

>>> maximum []
*** Exception: Prelude.maximum: empty list

>>> maximum Nothing
*** Exception: maximum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

minimum :: (Foldable t, Ord a) => t a -> a #

The least element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.

Examples

Expand

Basic usage:

>>> minimum [1..10]
1

>>> minimum []
*** Exception: Prelude.minimum: empty list

>>> minimum Nothing
*** Exception: minimum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

data Int #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Instances details

Data Int	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int # toConstr :: Int -> Constr # dataTypeOf :: Int -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) # gmapT :: (forall b. Data b => b -> b) -> Int -> Int # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r # gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int #
Storable Int	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int -> Int # alignment :: Int -> Int # peekElemOff :: Ptr Int -> Int -> IO Int # pokeElemOff :: Ptr Int -> Int -> Int -> IO () # peekByteOff :: Ptr b -> Int -> IO Int # pokeByteOff :: Ptr b -> Int -> Int -> IO () # peek :: Ptr Int -> IO Int # poke :: Ptr Int -> Int -> IO () #
Bits Int	Since: base-2.1
Instance details Defined in GHC.Bits Methods (.&.) :: Int -> Int -> Int # (.\|.) :: Int -> Int -> Int # xor :: Int -> Int -> Int # complement :: Int -> Int # shift :: Int -> Int -> Int # rotate :: Int -> Int -> Int # zeroBits :: Int # bit :: Int -> Int # setBit :: Int -> Int -> Int # clearBit :: Int -> Int -> Int # complementBit :: Int -> Int -> Int # testBit :: Int -> Int -> Bool # bitSizeMaybe :: Int -> Maybe Int # bitSize :: Int -> Int # isSigned :: Int -> Bool # shiftL :: Int -> Int -> Int # unsafeShiftL :: Int -> Int -> Int # shiftR :: Int -> Int -> Int # unsafeShiftR :: Int -> Int -> Int # rotateL :: Int -> Int -> Int # rotateR :: Int -> Int -> Int # popCount :: Int -> Int #
FiniteBits Int	Since: base-4.6.0.0
Instance details Defined in GHC.Bits Methods finiteBitSize :: Int -> Int # countLeadingZeros :: Int -> Int # countTrailingZeros :: Int -> Int #
Bounded Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int # maxBound :: Int #
Enum Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int # pred :: Int -> Int # toEnum :: Int -> Int # fromEnum :: Int -> Int # enumFrom :: Int -> [Int] # enumFromThen :: Int -> Int -> [Int] # enumFromTo :: Int -> Int -> [Int] # enumFromThenTo :: Int -> Int -> Int -> [Int] #
Num Int	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int # (-) :: Int -> Int -> Int # (*) :: Int -> Int -> Int # negate :: Int -> Int # abs :: Int -> Int # signum :: Int -> Int # fromInteger :: Integer -> Int #
Read Int	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int # readList :: ReadS [Int] # readPrec :: ReadPrec Int # readListPrec :: ReadPrec [Int] #
Integral Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # div :: Int -> Int -> Int # mod :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) # divMod :: Int -> Int -> (Int, Int) # toInteger :: Int -> Integer #
Real Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational #
Show Int	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS # show :: Int -> String # showList :: [Int] -> ShowS #
NFData Int
Instance details Defined in Control.DeepSeq Methods rnf :: Int -> () #
Eq Int
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool # (/=) :: Int -> Int -> Bool #
Ord Int
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering # (<) :: Int -> Int -> Bool # (<=) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool # (>=) :: Int -> Int -> Bool # max :: Int -> Int -> Int # min :: Int -> Int -> Int #
AEq Int
Instance details Defined in Data.AEq Methods (===) :: Int -> Int -> Bool # (~==) :: Int -> Int -> Bool #
Unbox Int
Instance details Defined in Data.Vector.Unboxed.Base
Lift Int
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Int -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Int -> Code m Int #
Vector Vector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s Int -> ST s (Vector Int) # basicUnsafeThaw :: Vector Int -> ST s (Mutable Vector s Int) # basicLength :: Vector Int -> Int # basicUnsafeSlice :: Int -> Int -> Vector Int -> Vector Int # basicUnsafeIndexM :: Vector Int -> Int -> Box Int # basicUnsafeCopy :: Mutable Vector s Int -> Vector Int -> ST s () # elemseq :: Vector Int -> Int -> b -> b #
MVector MVector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Int -> MVector s Int # basicOverlaps :: MVector s Int -> MVector s Int -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Int) # basicInitialize :: MVector s Int -> ST s () # basicUnsafeReplicate :: Int -> Int -> ST s (MVector s Int) # basicUnsafeRead :: MVector s Int -> Int -> ST s Int # basicUnsafeWrite :: MVector s Int -> Int -> Int -> ST s () # basicClear :: MVector s Int -> ST s () # basicSet :: MVector s Int -> Int -> ST s () # basicUnsafeCopy :: MVector s Int -> MVector s Int -> ST s () # basicUnsafeMove :: MVector s Int -> MVector s Int -> ST s () # basicUnsafeGrow :: MVector s Int -> Int -> ST s (MVector s Int) #
Generic1 (URec Int :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Int) :: k -> Type # Methods from1 :: forall (a :: k0). URec Int a -> Rep1 (URec Int) a # to1 :: forall (a :: k0). Rep1 (URec Int) a -> URec Int a #
Foldable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # toList :: UInt a -> [a] # null :: UInt a -> Bool # length :: UInt a -> Int # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # minimum :: Ord a => UInt a -> a # sum :: Num a => UInt a -> a # product :: Num a => UInt a -> a #
Traversable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) # sequenceA :: Applicative f => UInt (f a) -> f (UInt a) # mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) # sequence :: Monad m => UInt (m a) -> m (UInt a) #
Functor (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
Generic (URec Int p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Int p) :: Type -> Type # Methods from :: URec Int p -> Rep (URec Int p) x # to :: Rep (URec Int p) x -> URec Int p #
Show (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Int p -> ShowS # show :: URec Int p -> String # showList :: [URec Int p] -> ShowS #
Eq (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Int p -> URec Int p -> Bool # (/=) :: URec Int p -> URec Int p -> Bool #
Ord (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Int p -> URec Int p -> Ordering # (<) :: URec Int p -> URec Int p -> Bool # (<=) :: URec Int p -> URec Int p -> Bool # (>) :: URec Int p -> URec Int p -> Bool # (>=) :: URec Int p -> URec Int p -> Bool # max :: URec Int p -> URec Int p -> URec Int p # min :: URec Int p -> URec Int p -> URec Int p #
newtype Vector Int
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int = V_Int (Vector Int)
data URec Int (p :: k)	Used for marking occurrences of `Int#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Int (p :: k) = UInt { uInt# :: Int# }
newtype MVector s Int
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int = MV_Int (MVector s Int)
type Rep1 (URec Int :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Int :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: k -> Type)))
type Rep (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Int p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: Type -> Type)))

data Float #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Instances details

Data Float	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float # toConstr :: Float -> Constr # dataTypeOf :: Float -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) # gmapT :: (forall b. Data b => b -> b) -> Float -> Float # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r # gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float #
Storable Float	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Float -> Int # alignment :: Float -> Int # peekElemOff :: Ptr Float -> Int -> IO Float # pokeElemOff :: Ptr Float -> Int -> Float -> IO () # peekByteOff :: Ptr b -> Int -> IO Float # pokeByteOff :: Ptr b -> Int -> Float -> IO () # peek :: Ptr Float -> IO Float # poke :: Ptr Float -> Float -> IO () #
Floating Float	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Float # exp :: Float -> Float # log :: Float -> Float # sqrt :: Float -> Float # (**) :: Float -> Float -> Float # logBase :: Float -> Float -> Float # sin :: Float -> Float # cos :: Float -> Float # tan :: Float -> Float # asin :: Float -> Float # acos :: Float -> Float # atan :: Float -> Float # sinh :: Float -> Float # cosh :: Float -> Float # tanh :: Float -> Float # asinh :: Float -> Float # acosh :: Float -> Float # atanh :: Float -> Float # log1p :: Float -> Float # expm1 :: Float -> Float # log1pexp :: Float -> Float # log1mexp :: Float -> Float #
RealFloat Float	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # exponent :: Float -> Int # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isNaN :: Float -> Bool # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # isIEEE :: Float -> Bool # atan2 :: Float -> Float -> Float #
Read Float	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float # readList :: ReadS [Float] # readPrec :: ReadPrec Float # readListPrec :: ReadPrec [Float] #
NFData Float
Instance details Defined in Control.DeepSeq Methods rnf :: Float -> () #
Eq Float	Note that due to the presence of `NaN`, `Float`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Float)`False Also note that `Float`'s `Eq` instance does not satisfy extensionality: `>>>` `0 == (-0 :: Float)`True `>>>` `recip 0 == recip (-0 :: Float)`False
Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool # (/=) :: Float -> Float -> Bool #
Ord Float	Note that due to the presence of `NaN`, `Float`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Float)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Float`'s instance: `>>>` `(0/0 :: Float) > 1`False `>>>` `compare (0/0 :: Float) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Float -> Float -> Ordering # (<) :: Float -> Float -> Bool # (<=) :: Float -> Float -> Bool # (>) :: Float -> Float -> Bool # (>=) :: Float -> Float -> Bool # max :: Float -> Float -> Float # min :: Float -> Float -> Float #
AEq Float
Instance details Defined in Data.AEq Methods (===) :: Float -> Float -> Bool # (~==) :: Float -> Float -> Bool #
IEEE Float
Instance details Defined in Numeric.IEEE Methods infinity :: Float # minDenormal :: Float # minNormal :: Float # maxFinite :: Float # epsilon :: Float # copySign :: Float -> Float -> Float # identicalIEEE :: Float -> Float -> Bool # succIEEE :: Float -> Float # predIEEE :: Float -> Float # bisectIEEE :: Float -> Float -> Float # sameSignificandBits :: Float -> Float -> Int # nan :: Float # nanWithPayload :: Word64 -> Float # maxNaNPayload :: Float -> Word64 # nanPayload :: Float -> Word64 #
Unbox Float
Instance details Defined in Data.Vector.Unboxed.Base
Lift Float
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Float -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Float -> Code m Float #
Vector Vector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s Float -> ST s (Vector Float) # basicUnsafeThaw :: Vector Float -> ST s (Mutable Vector s Float) # basicLength :: Vector Float -> Int # basicUnsafeSlice :: Int -> Int -> Vector Float -> Vector Float # basicUnsafeIndexM :: Vector Float -> Int -> Box Float # basicUnsafeCopy :: Mutable Vector s Float -> Vector Float -> ST s () # elemseq :: Vector Float -> Float -> b -> b #
MVector MVector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Float -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Float -> MVector s Float # basicOverlaps :: MVector s Float -> MVector s Float -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Float) # basicInitialize :: MVector s Float -> ST s () # basicUnsafeReplicate :: Int -> Float -> ST s (MVector s Float) # basicUnsafeRead :: MVector s Float -> Int -> ST s Float # basicUnsafeWrite :: MVector s Float -> Int -> Float -> ST s () # basicClear :: MVector s Float -> ST s () # basicSet :: MVector s Float -> Float -> ST s () # basicUnsafeCopy :: MVector s Float -> MVector s Float -> ST s () # basicUnsafeMove :: MVector s Float -> MVector s Float -> ST s () # basicUnsafeGrow :: MVector s Float -> Int -> ST s (MVector s Float) #
Generic1 (URec Float :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Float) :: k -> Type # Methods from1 :: forall (a :: k0). URec Float a -> Rep1 (URec Float) a # to1 :: forall (a :: k0). Rep1 (URec Float) a -> URec Float a #
Foldable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # toList :: UFloat a -> [a] # null :: UFloat a -> Bool # length :: UFloat a -> Int # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # sum :: Num a => UFloat a -> a # product :: Num a => UFloat a -> a #
Traversable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) # sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) # mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) # sequence :: Monad m => UFloat (m a) -> m (UFloat a) #
AEq (Complex Float)
Instance details Defined in Data.AEq Methods (===) :: Complex Float -> Complex Float -> Bool # (~==) :: Complex Float -> Complex Float -> Bool #
Functor (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
Generic (URec Float p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Float p) :: Type -> Type # Methods from :: URec Float p -> Rep (URec Float p) x # to :: Rep (URec Float p) x -> URec Float p #
Show (URec Float p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Float p -> ShowS # show :: URec Float p -> String # showList :: [URec Float p] -> ShowS #
Eq (URec Float p)
Instance details Defined in GHC.Generics Methods (==) :: URec Float p -> URec Float p -> Bool # (/=) :: URec Float p -> URec Float p -> Bool #
Ord (URec Float p)
Instance details Defined in GHC.Generics Methods compare :: URec Float p -> URec Float p -> Ordering # (<) :: URec Float p -> URec Float p -> Bool # (<=) :: URec Float p -> URec Float p -> Bool # (>) :: URec Float p -> URec Float p -> Bool # (>=) :: URec Float p -> URec Float p -> Bool # max :: URec Float p -> URec Float p -> URec Float p # min :: URec Float p -> URec Float p -> URec Float p #
newtype Vector Float
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Float = V_Float (Vector Float)
data URec Float (p :: k)	Used for marking occurrences of `Float#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Float (p :: k) = UFloat { uFloat# :: Float# }
newtype MVector s Float
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Float = MV_Float (MVector s Float)
type Rep1 (URec Float :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))
type Rep (URec Float p)
Instance details Defined in GHC.Generics type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

data Char #

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type Char.

To convert a Char to or from the corresponding Int value defined by Unicode, use toEnum and fromEnum from the Enum class respectively (or equivalently ord and chr).

Instances

Instances details

Data Char	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Char -> c Char # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Char # toConstr :: Char -> Constr # dataTypeOf :: Char -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Char) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Char) # gmapT :: (forall b. Data b => b -> b) -> Char -> Char # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r # gmapQ :: (forall d. Data d => d -> u) -> Char -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Char -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Char -> m Char # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char #
Storable Char	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Char -> Int # alignment :: Char -> Int # peekElemOff :: Ptr Char -> Int -> IO Char # pokeElemOff :: Ptr Char -> Int -> Char -> IO () # peekByteOff :: Ptr b -> Int -> IO Char # pokeByteOff :: Ptr b -> Int -> Char -> IO () # peek :: Ptr Char -> IO Char # poke :: Ptr Char -> Char -> IO () #
Bounded Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Char # maxBound :: Char #
Enum Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Char -> Char # pred :: Char -> Char # toEnum :: Int -> Char # fromEnum :: Char -> Int # enumFrom :: Char -> [Char] # enumFromThen :: Char -> Char -> [Char] # enumFromTo :: Char -> Char -> [Char] # enumFromThenTo :: Char -> Char -> Char -> [Char] #
Read Char	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Char # readList :: ReadS [Char] # readPrec :: ReadPrec Char # readListPrec :: ReadPrec [Char] #
Show Char	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Char -> ShowS # show :: Char -> String # showList :: [Char] -> ShowS #
NFData Char
Instance details Defined in Control.DeepSeq Methods rnf :: Char -> () #
Eq Char
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool # (/=) :: Char -> Char -> Bool #
Ord Char
Instance details Defined in GHC.Classes Methods compare :: Char -> Char -> Ordering # (<) :: Char -> Char -> Bool # (<=) :: Char -> Char -> Bool # (>) :: Char -> Char -> Bool # (>=) :: Char -> Char -> Bool # max :: Char -> Char -> Char # min :: Char -> Char -> Char #
AEq Char
Instance details Defined in Data.AEq Methods (===) :: Char -> Char -> Bool # (~==) :: Char -> Char -> Bool #
Unbox Char
Instance details Defined in Data.Vector.Unboxed.Base
TestCoercion SChar	Since: base-4.18.0.0
Instance details Defined in GHC.TypeLits Methods testCoercion :: forall (a :: k) (b :: k). SChar a -> SChar b -> Maybe (Coercion a b) #
TestEquality SChar	Since: base-4.18.0.0
Instance details Defined in GHC.TypeLits Methods testEquality :: forall (a :: k) (b :: k). SChar a -> SChar b -> Maybe (a :~: b) #
Lift Char
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Char -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Char -> Code m Char #
Vector Vector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s Char -> ST s (Vector Char) # basicUnsafeThaw :: Vector Char -> ST s (Mutable Vector s Char) # basicLength :: Vector Char -> Int # basicUnsafeSlice :: Int -> Int -> Vector Char -> Vector Char # basicUnsafeIndexM :: Vector Char -> Int -> Box Char # basicUnsafeCopy :: Mutable Vector s Char -> Vector Char -> ST s () # elemseq :: Vector Char -> Char -> b -> b #
MVector MVector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Char -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Char -> MVector s Char # basicOverlaps :: MVector s Char -> MVector s Char -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Char) # basicInitialize :: MVector s Char -> ST s () # basicUnsafeReplicate :: Int -> Char -> ST s (MVector s Char) # basicUnsafeRead :: MVector s Char -> Int -> ST s Char # basicUnsafeWrite :: MVector s Char -> Int -> Char -> ST s () # basicClear :: MVector s Char -> ST s () # basicSet :: MVector s Char -> Char -> ST s () # basicUnsafeCopy :: MVector s Char -> MVector s Char -> ST s () # basicUnsafeMove :: MVector s Char -> MVector s Char -> ST s () # basicUnsafeGrow :: MVector s Char -> Int -> ST s (MVector s Char) #
Generic1 (URec Char :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Char) :: k -> Type # Methods from1 :: forall (a :: k0). URec Char a -> Rep1 (URec Char) a # to1 :: forall (a :: k0). Rep1 (URec Char) a -> URec Char a #
Foldable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # toList :: UChar a -> [a] # null :: UChar a -> Bool # length :: UChar a -> Int # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # sum :: Num a => UChar a -> a # product :: Num a => UChar a -> a #
Traversable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b) # sequenceA :: Applicative f => UChar (f a) -> f (UChar a) # mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b) # sequence :: Monad m => UChar (m a) -> m (UChar a) #
Functor (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b # (<$) :: a -> URec Char b -> URec Char a #
Generic (URec Char p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Char p) :: Type -> Type # Methods from :: URec Char p -> Rep (URec Char p) x # to :: Rep (URec Char p) x -> URec Char p #
Show (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Char p -> ShowS # show :: URec Char p -> String # showList :: [URec Char p] -> ShowS #
Eq (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Char p -> URec Char p -> Bool # (/=) :: URec Char p -> URec Char p -> Bool #
Ord (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Char p -> URec Char p -> Ordering # (<) :: URec Char p -> URec Char p -> Bool # (<=) :: URec Char p -> URec Char p -> Bool # (>) :: URec Char p -> URec Char p -> Bool # (>=) :: URec Char p -> URec Char p -> Bool # max :: URec Char p -> URec Char p -> URec Char p # min :: URec Char p -> URec Char p -> URec Char p #
newtype Vector Char
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Char = V_Char (Vector Char)
data URec Char (p :: k)	Used for marking occurrences of `Char#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Char (p :: k) = UChar { uChar# :: Char# }
newtype MVector s Char
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Char = MV_Char (MVector s Char)
type Compare (a :: Char) (b :: Char)
Instance details Defined in Data.Type.Ord type Compare (a :: Char) (b :: Char) = CmpChar a b
type Rep1 (URec Char :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Char :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: k -> Type)))
type Rep (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Char p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: Type -> Type)))

data IO a #

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances

Instances details

MonadFail IO	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fail Methods fail :: String -> IO a #
Alternative IO	Takes the first non-throwing `IO` action's result. `empty` throws an exception. Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods empty :: IO a # (<\|>) :: IO a -> IO a -> IO a # some :: IO a -> IO [a] # many :: IO a -> IO [a] #
Applicative IO	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b # (<$) :: a -> IO b -> IO a #
Monad IO	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b # (>>) :: IO a -> IO b -> IO b # return :: a -> IO a #
MonadPlus IO	Takes the first non-throwing `IO` action's result. `mzero` throws an exception. Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mzero :: IO a # mplus :: IO a -> IO a -> IO a #
PrimBase IO
Instance details Defined in Control.Monad.Primitive Methods internal :: IO a -> State# (PrimState IO) -> (# State# (PrimState IO), a #) #
PrimMonad IO
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState IO # Methods primitive :: (State# (PrimState IO) -> (# State# (PrimState IO), a #)) -> IO a #
Quasi IO
Instance details Defined in Language.Haskell.TH.Syntax Methods qNewName :: String -> IO Name # qReport :: Bool -> String -> IO () # qRecover :: IO a -> IO a -> IO a # qLookupName :: Bool -> String -> IO (Maybe Name) # qReify :: Name -> IO Info # qReifyFixity :: Name -> IO (Maybe Fixity) # qReifyType :: Name -> IO Type # qReifyInstances :: Name -> [Type] -> IO [Dec] # qReifyRoles :: Name -> IO [Role] # qReifyAnnotations :: Data a => AnnLookup -> IO [a] # qReifyModule :: Module -> IO ModuleInfo # qReifyConStrictness :: Name -> IO [DecidedStrictness] # qLocation :: IO Loc # qRunIO :: IO a -> IO a # qGetPackageRoot :: IO FilePath # qAddDependentFile :: FilePath -> IO () # qAddTempFile :: String -> IO FilePath # qAddTopDecls :: [Dec] -> IO () # qAddForeignFilePath :: ForeignSrcLang -> String -> IO () # qAddModFinalizer :: Q () -> IO () # qAddCorePlugin :: String -> IO () # qGetQ :: Typeable a => IO (Maybe a) # qPutQ :: Typeable a => a -> IO () # qIsExtEnabled :: Extension -> IO Bool # qExtsEnabled :: IO [Extension] # qPutDoc :: DocLoc -> String -> IO () # qGetDoc :: DocLoc -> IO (Maybe String) #
Quote IO
Instance details Defined in Language.Haskell.TH.Syntax Methods newName :: String -> IO Name #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Semigroup a => Semigroup (IO a)	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
type PrimState IO
Instance details Defined in Control.Monad.Primitive type PrimState IO = RealWorld

data Bool #

Constructors

False
True

Instances

Instances details

Data Bool	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool # toConstr :: Bool -> Constr # dataTypeOf :: Bool -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Bool) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) # gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r # gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool #
Storable Bool	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Bool -> Int # alignment :: Bool -> Int # peekElemOff :: Ptr Bool -> Int -> IO Bool # pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () # peekByteOff :: Ptr b -> Int -> IO Bool # pokeByteOff :: Ptr b -> Int -> Bool -> IO () # peek :: Ptr Bool -> IO Bool # poke :: Ptr Bool -> Bool -> IO () #
Bits Bool	Interpret `Bool` as 1-bit bit-field Since: base-4.7.0.0
Instance details Defined in GHC.Bits Methods (.&.) :: Bool -> Bool -> Bool # (.\|.) :: Bool -> Bool -> Bool # xor :: Bool -> Bool -> Bool # complement :: Bool -> Bool # shift :: Bool -> Int -> Bool # rotate :: Bool -> Int -> Bool # zeroBits :: Bool # bit :: Int -> Bool # setBit :: Bool -> Int -> Bool # clearBit :: Bool -> Int -> Bool # complementBit :: Bool -> Int -> Bool # testBit :: Bool -> Int -> Bool # bitSizeMaybe :: Bool -> Maybe Int # bitSize :: Bool -> Int # isSigned :: Bool -> Bool # shiftL :: Bool -> Int -> Bool # unsafeShiftL :: Bool -> Int -> Bool # shiftR :: Bool -> Int -> Bool # unsafeShiftR :: Bool -> Int -> Bool # rotateL :: Bool -> Int -> Bool # rotateR :: Bool -> Int -> Bool # popCount :: Bool -> Int #
FiniteBits Bool	Since: base-4.7.0.0
Instance details Defined in GHC.Bits Methods finiteBitSize :: Bool -> Int # countLeadingZeros :: Bool -> Int # countTrailingZeros :: Bool -> Int #
Bounded Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool # maxBound :: Bool #
Enum Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool # pred :: Bool -> Bool # toEnum :: Int -> Bool # fromEnum :: Bool -> Int # enumFrom :: Bool -> [Bool] # enumFromThen :: Bool -> Bool -> [Bool] # enumFromTo :: Bool -> Bool -> [Bool] # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #
Generic Bool
Instance details Defined in GHC.Generics Associated Types type Rep Bool :: Type -> Type # Methods from :: Bool -> Rep Bool x # to :: Rep Bool x -> Bool #
SingKind Bool	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type DemoteRep Bool Methods fromSing :: forall (a :: Bool). Sing a -> DemoteRep Bool
Read Bool	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool # readList :: ReadS [Bool] # readPrec :: ReadPrec Bool # readListPrec :: ReadPrec [Bool] #
Show Bool	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Bool -> ShowS # show :: Bool -> String # showList :: [Bool] -> ShowS #
NFData Bool
Instance details Defined in Control.DeepSeq Methods rnf :: Bool -> () #
Eq Bool
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool # (/=) :: Bool -> Bool -> Bool #
Ord Bool
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering # (<) :: Bool -> Bool -> Bool # (<=) :: Bool -> Bool -> Bool # (>) :: Bool -> Bool -> Bool # (>=) :: Bool -> Bool -> Bool # max :: Bool -> Bool -> Bool # min :: Bool -> Bool -> Bool #
AEq Bool
Instance details Defined in Data.AEq Methods (===) :: Bool -> Bool -> Bool # (~==) :: Bool -> Bool -> Bool #
Unbox Bool
Instance details Defined in Data.Vector.Unboxed.Base
SingI 'False	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'False
SingI 'True	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'True
Lift Bool
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Bool -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Bool -> Code m Bool #
Vector Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s Bool -> ST s (Vector Bool) # basicUnsafeThaw :: Vector Bool -> ST s (Mutable Vector s Bool) # basicLength :: Vector Bool -> Int # basicUnsafeSlice :: Int -> Int -> Vector Bool -> Vector Bool # basicUnsafeIndexM :: Vector Bool -> Int -> Box Bool # basicUnsafeCopy :: Mutable Vector s Bool -> Vector Bool -> ST s () # elemseq :: Vector Bool -> Bool -> b -> b #
MVector MVector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Bool -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Bool -> MVector s Bool # basicOverlaps :: MVector s Bool -> MVector s Bool -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Bool) # basicInitialize :: MVector s Bool -> ST s () # basicUnsafeReplicate :: Int -> Bool -> ST s (MVector s Bool) # basicUnsafeRead :: MVector s Bool -> Int -> ST s Bool # basicUnsafeWrite :: MVector s Bool -> Int -> Bool -> ST s () # basicClear :: MVector s Bool -> ST s () # basicSet :: MVector s Bool -> Bool -> ST s () # basicUnsafeCopy :: MVector s Bool -> MVector s Bool -> ST s () # basicUnsafeMove :: MVector s Bool -> MVector s Bool -> ST s () # basicUnsafeGrow :: MVector s Bool -> Int -> ST s (MVector s Bool) #
type DemoteRep Bool
Instance details Defined in GHC.Generics type DemoteRep Bool = Bool
type Rep Bool	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep Bool = D1 ('MetaData "Bool" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "False" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "True" 'PrefixI 'False) (U1 :: Type -> Type))
data Sing (a :: Bool)
Instance details Defined in GHC.Generics data Sing (a :: Bool) where STrue :: Sing 'True SFalse :: Sing 'False
newtype Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Bool = V_Bool (Vector Word8)
newtype MVector s Bool
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Bool = MV_Bool (MVector s Word8)

data Double #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Instances details

Data Double	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double # toConstr :: Double -> Constr # dataTypeOf :: Double -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) # gmapT :: (forall b. Data b => b -> b) -> Double -> Double # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r # gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double #
Storable Double	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Double -> Int # alignment :: Double -> Int # peekElemOff :: Ptr Double -> Int -> IO Double # pokeElemOff :: Ptr Double -> Int -> Double -> IO () # peekByteOff :: Ptr b -> Int -> IO Double # pokeByteOff :: Ptr b -> Int -> Double -> IO () # peek :: Ptr Double -> IO Double # poke :: Ptr Double -> Double -> IO () #
Floating Double	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Double # exp :: Double -> Double # log :: Double -> Double # sqrt :: Double -> Double # (**) :: Double -> Double -> Double # logBase :: Double -> Double -> Double # sin :: Double -> Double # cos :: Double -> Double # tan :: Double -> Double # asin :: Double -> Double # acos :: Double -> Double # atan :: Double -> Double # sinh :: Double -> Double # cosh :: Double -> Double # tanh :: Double -> Double # asinh :: Double -> Double # acosh :: Double -> Double # atanh :: Double -> Double # log1p :: Double -> Double # expm1 :: Double -> Double # log1pexp :: Double -> Double # log1mexp :: Double -> Double #
RealFloat Double	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # exponent :: Double -> Int # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isNaN :: Double -> Bool # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # isIEEE :: Double -> Bool # atan2 :: Double -> Double -> Double #
Read Double	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double # readList :: ReadS [Double] # readPrec :: ReadPrec Double # readListPrec :: ReadPrec [Double] #
NFData Double
Instance details Defined in Control.DeepSeq Methods rnf :: Double -> () #
Eq Double	Note that due to the presence of `NaN`, `Double`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Double)`False Also note that `Double`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Double)`True `>>>` `recip 0 == recip (-0 :: Double)`False
Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool # (/=) :: Double -> Double -> Bool #
Ord Double	Note that due to the presence of `NaN`, `Double`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Double)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Double`'s instance: `>>>` `(0/0 :: Double) > 1`False `>>>` `compare (0/0 :: Double) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Double -> Double -> Ordering # (<) :: Double -> Double -> Bool # (<=) :: Double -> Double -> Bool # (>) :: Double -> Double -> Bool # (>=) :: Double -> Double -> Bool # max :: Double -> Double -> Double # min :: Double -> Double -> Double #
AEq Double
Instance details Defined in Data.AEq Methods (===) :: Double -> Double -> Bool # (~==) :: Double -> Double -> Bool #
IEEE Double
Instance details Defined in Numeric.IEEE Methods infinity :: Double # minDenormal :: Double # minNormal :: Double # maxFinite :: Double # epsilon :: Double # copySign :: Double -> Double -> Double # identicalIEEE :: Double -> Double -> Bool # succIEEE :: Double -> Double # predIEEE :: Double -> Double # bisectIEEE :: Double -> Double -> Double # sameSignificandBits :: Double -> Double -> Int # nan :: Double # nanWithPayload :: Word64 -> Double # maxNaNPayload :: Double -> Word64 # nanPayload :: Double -> Word64 #
Unbox Double
Instance details Defined in Data.Vector.Unboxed.Base
Lift Double
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Double -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Double -> Code m Double #
Vector Vector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s Double -> ST s (Vector Double) # basicUnsafeThaw :: Vector Double -> ST s (Mutable Vector s Double) # basicLength :: Vector Double -> Int # basicUnsafeSlice :: Int -> Int -> Vector Double -> Vector Double # basicUnsafeIndexM :: Vector Double -> Int -> Box Double # basicUnsafeCopy :: Mutable Vector s Double -> Vector Double -> ST s () # elemseq :: Vector Double -> Double -> b -> b #
MVector MVector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Double -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Double -> MVector s Double # basicOverlaps :: MVector s Double -> MVector s Double -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Double) # basicInitialize :: MVector s Double -> ST s () # basicUnsafeReplicate :: Int -> Double -> ST s (MVector s Double) # basicUnsafeRead :: MVector s Double -> Int -> ST s Double # basicUnsafeWrite :: MVector s Double -> Int -> Double -> ST s () # basicClear :: MVector s Double -> ST s () # basicSet :: MVector s Double -> Double -> ST s () # basicUnsafeCopy :: MVector s Double -> MVector s Double -> ST s () # basicUnsafeMove :: MVector s Double -> MVector s Double -> ST s () # basicUnsafeGrow :: MVector s Double -> Int -> ST s (MVector s Double) #
Generic1 (URec Double :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Double) :: k -> Type # Methods from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a # to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a #
Foldable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # toList :: UDouble a -> [a] # null :: UDouble a -> Bool # length :: UDouble a -> Int # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # sum :: Num a => UDouble a -> a # product :: Num a => UDouble a -> a #
Traversable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) # sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) # mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) # sequence :: Monad m => UDouble (m a) -> m (UDouble a) #
AEq (Complex Double)
Instance details Defined in Data.AEq Methods (===) :: Complex Double -> Complex Double -> Bool # (~==) :: Complex Double -> Complex Double -> Bool #
Functor (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
Generic (URec Double p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Double p) :: Type -> Type # Methods from :: URec Double p -> Rep (URec Double p) x # to :: Rep (URec Double p) x -> URec Double p #
Show (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Double p -> ShowS # show :: URec Double p -> String # showList :: [URec Double p] -> ShowS #
Eq (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Double p -> URec Double p -> Bool # (/=) :: URec Double p -> URec Double p -> Bool #
Ord (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # max :: URec Double p -> URec Double p -> URec Double p # min :: URec Double p -> URec Double p -> URec Double p #
newtype Vector Double
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Double = V_Double (Vector Double)
data URec Double (p :: k)	Used for marking occurrences of `Double#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Double (p :: k) = UDouble { uDouble# :: Double# }
newtype MVector s Double
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Double = MV_Double (MVector s Double)
type Rep1 (URec Double :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))
type Rep (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Word #

A Word is an unsigned integral type, with the same size as Int.

Instances

Instances details

Data Word	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word # toConstr :: Word -> Constr # dataTypeOf :: Word -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) # gmapT :: (forall b. Data b => b -> b) -> Word -> Word # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r # gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word #
Storable Word	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word -> Int # alignment :: Word -> Int # peekElemOff :: Ptr Word -> Int -> IO Word # pokeElemOff :: Ptr Word -> Int -> Word -> IO () # peekByteOff :: Ptr b -> Int -> IO Word # pokeByteOff :: Ptr b -> Int -> Word -> IO () # peek :: Ptr Word -> IO Word # poke :: Ptr Word -> Word -> IO () #
Bits Word	Since: base-2.1
Instance details Defined in GHC.Bits Methods (.&.) :: Word -> Word -> Word # (.\|.) :: Word -> Word -> Word # xor :: Word -> Word -> Word # complement :: Word -> Word # shift :: Word -> Int -> Word # rotate :: Word -> Int -> Word # zeroBits :: Word # bit :: Int -> Word # setBit :: Word -> Int -> Word # clearBit :: Word -> Int -> Word # complementBit :: Word -> Int -> Word # testBit :: Word -> Int -> Bool # bitSizeMaybe :: Word -> Maybe Int # bitSize :: Word -> Int # isSigned :: Word -> Bool # shiftL :: Word -> Int -> Word # unsafeShiftL :: Word -> Int -> Word # shiftR :: Word -> Int -> Word # unsafeShiftR :: Word -> Int -> Word # rotateL :: Word -> Int -> Word # rotateR :: Word -> Int -> Word # popCount :: Word -> Int #
FiniteBits Word	Since: base-4.6.0.0
Instance details Defined in GHC.Bits Methods finiteBitSize :: Word -> Int # countLeadingZeros :: Word -> Int # countTrailingZeros :: Word -> Int #
Bounded Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Word # maxBound :: Word #
Enum Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Word -> Word # pred :: Word -> Word # toEnum :: Int -> Word # fromEnum :: Word -> Int # enumFrom :: Word -> [Word] # enumFromThen :: Word -> Word -> [Word] # enumFromTo :: Word -> Word -> [Word] # enumFromThenTo :: Word -> Word -> Word -> [Word] #
Num Word	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Word -> Word -> Word # (-) :: Word -> Word -> Word # (*) :: Word -> Word -> Word # negate :: Word -> Word # abs :: Word -> Word # signum :: Word -> Word # fromInteger :: Integer -> Word #
Read Word	Since: base-4.5.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word # readList :: ReadS [Word] # readPrec :: ReadPrec Word # readListPrec :: ReadPrec [Word] #
Integral Word	Since: base-2.1
Instance details Defined in GHC.Real Methods quot :: Word -> Word -> Word # rem :: Word -> Word -> Word # div :: Word -> Word -> Word # mod :: Word -> Word -> Word # quotRem :: Word -> Word -> (Word, Word) # divMod :: Word -> Word -> (Word, Word) # toInteger :: Word -> Integer #
Real Word	Since: base-2.1
Instance details Defined in GHC.Real Methods toRational :: Word -> Rational #
Show Word	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Word -> ShowS # show :: Word -> String # showList :: [Word] -> ShowS #
NFData Word
Instance details Defined in Control.DeepSeq Methods rnf :: Word -> () #
Eq Word
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool # (/=) :: Word -> Word -> Bool #
Ord Word
Instance details Defined in GHC.Classes Methods compare :: Word -> Word -> Ordering # (<) :: Word -> Word -> Bool # (<=) :: Word -> Word -> Bool # (>) :: Word -> Word -> Bool # (>=) :: Word -> Word -> Bool # max :: Word -> Word -> Word # min :: Word -> Word -> Word #
AEq Word
Instance details Defined in Data.AEq Methods (===) :: Word -> Word -> Bool # (~==) :: Word -> Word -> Bool #
Unbox Word
Instance details Defined in Data.Vector.Unboxed.Base
Lift Word
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Word -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Word -> Code m Word #
Vector Vector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s Word -> ST s (Vector Word) # basicUnsafeThaw :: Vector Word -> ST s (Mutable Vector s Word) # basicLength :: Vector Word -> Int # basicUnsafeSlice :: Int -> Int -> Vector Word -> Vector Word # basicUnsafeIndexM :: Vector Word -> Int -> Box Word # basicUnsafeCopy :: Mutable Vector s Word -> Vector Word -> ST s () # elemseq :: Vector Word -> Word -> b -> b #
MVector MVector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Word -> MVector s Word # basicOverlaps :: MVector s Word -> MVector s Word -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Word) # basicInitialize :: MVector s Word -> ST s () # basicUnsafeReplicate :: Int -> Word -> ST s (MVector s Word) # basicUnsafeRead :: MVector s Word -> Int -> ST s Word # basicUnsafeWrite :: MVector s Word -> Int -> Word -> ST s () # basicClear :: MVector s Word -> ST s () # basicSet :: MVector s Word -> Word -> ST s () # basicUnsafeCopy :: MVector s Word -> MVector s Word -> ST s () # basicUnsafeMove :: MVector s Word -> MVector s Word -> ST s () # basicUnsafeGrow :: MVector s Word -> Int -> ST s (MVector s Word) #
Generic1 (URec Word :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Word) :: k -> Type # Methods from1 :: forall (a :: k0). URec Word a -> Rep1 (URec Word) a # to1 :: forall (a :: k0). Rep1 (URec Word) a -> URec Word a #
Foldable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # toList :: UWord a -> [a] # null :: UWord a -> Bool # length :: UWord a -> Int # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # sum :: Num a => UWord a -> a # product :: Num a => UWord a -> a #
Traversable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b) # sequenceA :: Applicative f => UWord (f a) -> f (UWord a) # mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b) # sequence :: Monad m => UWord (m a) -> m (UWord a) #
Functor (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b # (<$) :: a -> URec Word b -> URec Word a #
Generic (URec Word p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Word p) :: Type -> Type # Methods from :: URec Word p -> Rep (URec Word p) x # to :: Rep (URec Word p) x -> URec Word p #
Show (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Word p -> ShowS # show :: URec Word p -> String # showList :: [URec Word p] -> ShowS #
Eq (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Word p -> URec Word p -> Bool # (/=) :: URec Word p -> URec Word p -> Bool #
Ord (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Word p -> URec Word p -> Ordering # (<) :: URec Word p -> URec Word p -> Bool # (<=) :: URec Word p -> URec Word p -> Bool # (>) :: URec Word p -> URec Word p -> Bool # (>=) :: URec Word p -> URec Word p -> Bool # max :: URec Word p -> URec Word p -> URec Word p # min :: URec Word p -> URec Word p -> URec Word p #
newtype Vector Word
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word = V_Word (Vector Word)
data URec Word (p :: k)	Used for marking occurrences of `Word#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Word (p :: k) = UWord { uWord# :: Word# }
newtype MVector s Word
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word = MV_Word (MVector s Word)
type Rep1 (URec Word :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Word :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: k -> Type)))
type Rep (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Word p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: Type -> Type)))

data Ordering #

Constructors

LT
EQ
GT

Instances

Instances details

Data Ordering	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordering -> c Ordering # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Ordering # toConstr :: Ordering -> Constr # dataTypeOf :: Ordering -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Ordering) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Ordering) # gmapT :: (forall b. Data b => b -> b) -> Ordering -> Ordering # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r # gmapQ :: (forall d. Data d => d -> u) -> Ordering -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordering -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering #
Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Bounded Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering # maxBound :: Ordering #
Enum Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Ordering -> Ordering # pred :: Ordering -> Ordering # toEnum :: Int -> Ordering # fromEnum :: Ordering -> Int # enumFrom :: Ordering -> [Ordering] # enumFromThen :: Ordering -> Ordering -> [Ordering] # enumFromTo :: Ordering -> Ordering -> [Ordering] # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] #
Generic Ordering
Instance details Defined in GHC.Generics Associated Types type Rep Ordering :: Type -> Type # Methods from :: Ordering -> Rep Ordering x # to :: Rep Ordering x -> Ordering #
Read Ordering	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering # readList :: ReadS [Ordering] # readPrec :: ReadPrec Ordering # readListPrec :: ReadPrec [Ordering] #
Show Ordering	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS # show :: Ordering -> String # showList :: [Ordering] -> ShowS #
NFData Ordering
Instance details Defined in Control.DeepSeq Methods rnf :: Ordering -> () #
Eq Ordering
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool # (/=) :: Ordering -> Ordering -> Bool #
Ord Ordering
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering # (<) :: Ordering -> Ordering -> Bool # (<=) :: Ordering -> Ordering -> Bool # (>) :: Ordering -> Ordering -> Bool # (>=) :: Ordering -> Ordering -> Bool # max :: Ordering -> Ordering -> Ordering # min :: Ordering -> Ordering -> Ordering #
AEq Ordering
Instance details Defined in Data.AEq Methods (===) :: Ordering -> Ordering -> Bool # (~==) :: Ordering -> Ordering -> Bool #
type Rep Ordering	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep Ordering = D1 ('MetaData "Ordering" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "LT" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "EQ" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "GT" 'PrefixI 'False) (U1 :: Type -> Type)))

data Maybe a #

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing
Just a

Instances

Instances details

MonadFail Maybe	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fail Methods fail :: String -> Maybe a #
Foldable Maybe	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # toList :: Maybe a -> [a] # null :: Maybe a -> Bool # length :: Maybe a -> Int # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # sum :: Num a => Maybe a -> a # product :: Num a => Maybe a -> a #
Eq1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool #
Ord1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering #
Read1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] #
Show1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Alternative Maybe	Picks the leftmost `Just` value, or, alternatively, `Nothing`. Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: Maybe a # (<\|>) :: Maybe a -> Maybe a -> Maybe a # some :: Maybe a -> Maybe [a] # many :: Maybe a -> Maybe [a] #
Applicative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b # (<$) :: a -> Maybe b -> Maybe a #
Monad Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b # (>>) :: Maybe a -> Maybe b -> Maybe b # return :: a -> Maybe a #
MonadPlus Maybe	Picks the leftmost `Just` value, or, alternatively, `Nothing`. Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: Maybe a # mplus :: Maybe a -> Maybe a -> Maybe a #
NFData1 Maybe	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Maybe a -> () #
Generic1 Maybe
Instance details Defined in GHC.Generics Associated Types type Rep1 Maybe :: k -> Type # Methods from1 :: forall (a :: k). Maybe a -> Rep1 Maybe a # to1 :: forall (a :: k). Rep1 Maybe a -> Maybe a #
Lift a => Lift (Maybe a :: Type)
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Maybe a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Maybe a -> Code m (Maybe a) #
Data a => Data (Maybe a)	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Maybe a -> c (Maybe a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Maybe a) # toConstr :: Maybe a -> Constr # dataTypeOf :: Maybe a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Maybe a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Maybe a)) # gmapT :: (forall b. Data b => b -> b) -> Maybe a -> Maybe a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r # gmapQ :: (forall d. Data d => d -> u) -> Maybe a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Maybe a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Semigroup a => Semigroup (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Generic (Maybe a)
Instance details Defined in GHC.Generics Associated Types type Rep (Maybe a) :: Type -> Type # Methods from :: Maybe a -> Rep (Maybe a) x # to :: Rep (Maybe a) x -> Maybe a #
SingKind a => SingKind (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type DemoteRep (Maybe a) Methods fromSing :: forall (a0 :: Maybe a). Sing a0 -> DemoteRep (Maybe a)
Read a => Read (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Maybe a) # readList :: ReadS [Maybe a] # readPrec :: ReadPrec (Maybe a) # readListPrec :: ReadPrec [Maybe a] #
Show a => Show (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Maybe a -> ShowS # show :: Maybe a -> String # showList :: [Maybe a] -> ShowS #
NFData a => NFData (Maybe a)
Instance details Defined in Control.DeepSeq Methods rnf :: Maybe a -> () #
Eq a => Eq (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool # (/=) :: Maybe a -> Maybe a -> Bool #
Ord a => Ord (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods compare :: Maybe a -> Maybe a -> Ordering # (<) :: Maybe a -> Maybe a -> Bool # (<=) :: Maybe a -> Maybe a -> Bool # (>) :: Maybe a -> Maybe a -> Bool # (>=) :: Maybe a -> Maybe a -> Bool # max :: Maybe a -> Maybe a -> Maybe a # min :: Maybe a -> Maybe a -> Maybe a #
AEq a => AEq (Maybe a)
Instance details Defined in Data.AEq Methods (===) :: Maybe a -> Maybe a -> Bool # (~==) :: Maybe a -> Maybe a -> Bool #
SingI ('Nothing :: Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'Nothing
SingI a2 => SingI ('Just a2 :: Maybe a1)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing ('Just a2)
type Rep1 Maybe	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep1 Maybe = D1 ('MetaData "Maybe" "GHC.Maybe" "base" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type DemoteRep (Maybe a)
Instance details Defined in GHC.Generics type DemoteRep (Maybe a) = Maybe (DemoteRep a)
type Rep (Maybe a)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep (Maybe a) = D1 ('MetaData "Maybe" "GHC.Maybe" "base" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
data Sing (b :: Maybe a)
Instance details Defined in GHC.Generics data Sing (b :: Maybe a) where SNothing :: forall {a}. Sing ('Nothing :: Maybe a) SJust :: forall {a} (a1 :: a). Sing a1 -> Sing ('Just a1)

class a ~# b => (a :: k) ~ (b :: k) infix 4 #

Lifted, homogeneous equality. By lifted, we mean that it can be bogus (deferred type error). By homogeneous, the two types a and b must have the same kinds.

data Integer #

Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.

Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.

If the value is small (fit into an Int), IS constructor is used. Otherwise Integer and IN constructors are used to store a BigNat representing respectively the positive or the negative value magnitude.

Invariant: Integer and IN are used iff value doesn't fit in IS

Instances

Instances details

Data Integer	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer # toConstr :: Integer -> Constr # dataTypeOf :: Integer -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) # gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r # gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer #
Bits Integer	Since: base-2.1
Instance details Defined in GHC.Bits Methods (.&.) :: Integer -> Integer -> Integer # (.\|.) :: Integer -> Integer -> Integer # xor :: Integer -> Integer -> Integer # complement :: Integer -> Integer # shift :: Integer -> Int -> Integer # rotate :: Integer -> Int -> Integer # zeroBits :: Integer # bit :: Int -> Integer # setBit :: Integer -> Int -> Integer # clearBit :: Integer -> Int -> Integer # complementBit :: Integer -> Int -> Integer # testBit :: Integer -> Int -> Bool # bitSizeMaybe :: Integer -> Maybe Int # bitSize :: Integer -> Int # isSigned :: Integer -> Bool # shiftL :: Integer -> Int -> Integer # unsafeShiftL :: Integer -> Int -> Integer # shiftR :: Integer -> Int -> Integer # unsafeShiftR :: Integer -> Int -> Integer # rotateL :: Integer -> Int -> Integer # rotateR :: Integer -> Int -> Integer # popCount :: Integer -> Int #
Enum Integer	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Read Integer	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer # readList :: ReadS [Integer] # readPrec :: ReadPrec Integer # readListPrec :: ReadPrec [Integer] #
Integral Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Real Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational #
Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS # show :: Integer -> String # showList :: [Integer] -> ShowS #
NFData Integer
Instance details Defined in Control.DeepSeq Methods rnf :: Integer -> () #
Eq Integer
Instance details Defined in GHC.Num.Integer Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Ord Integer
Instance details Defined in GHC.Num.Integer Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
AEq Integer
Instance details Defined in Data.AEq Methods (===) :: Integer -> Integer -> Bool # (~==) :: Integer -> Integer -> Bool #
Lift Integer
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Integer -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Integer -> Code m Integer #

data Either a b #

The Either type represents values with two possibilities: a value of type Either a b is either Left a or Right b.

The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").

Examples

Expand

The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:

>>> let s = Left "foo" :: Either String Int
>>> s
Left "foo"
>>> let n = Right 3 :: Either String Int
>>> n
Right 3
>>> :type s
s :: Either String Int
>>> :type n
n :: Either String Int

The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> fmap (*2) s
Left "foo"
>>> fmap (*2) n
Right 6

The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.

>>> import Data.Char ( digitToInt, isDigit )
>>> :{
    let parseEither :: Char -> Either String Int
        parseEither c
          | isDigit c = Right (digitToInt c)
          | otherwise = Left "parse error"
>>> :}

The following should work, since both '1' and '2' can be parsed as Ints.

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Right 3

But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither 'm'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Left "parse error"

Constructors

Left a
Right b

Instances

Instances details

Eq2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Either a c -> Either b d -> Bool #
Ord2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Either a c -> Either b d -> Ordering #
Read2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] #
Show2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Either a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Either a b] -> ShowS #
NFData2 Either	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> Either a b -> () #
Generic1 (Either a :: Type -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (Either a) :: k -> Type # Methods from1 :: forall (a0 :: k). Either a a0 -> Rep1 (Either a) a0 # to1 :: forall (a0 :: k). Rep1 (Either a) a0 -> Either a a0 #
(Lift a, Lift b) => Lift (Either a b :: Type)
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Either a b -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Either a b -> Code m (Either a b) #
Foldable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # null :: Either a a0 -> Bool # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # sum :: Num a0 => Either a a0 -> a0 # product :: Num a0 => Either a a0 -> a0 #
Eq a => Eq1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a0 -> b -> Bool) -> Either a a0 -> Either a b -> Bool #
Ord a => Ord1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a0 -> b -> Ordering) -> Either a a0 -> Either a b -> Ordering #
Read a => Read1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] #
Show a => Show1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Either a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Either a a0] -> ShowS #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Applicative (Either e)	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b # (<$) :: a0 -> Either a b -> Either a a0 #
Monad (Either e)	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b # (>>) :: Either e a -> Either e b -> Either e b # return :: a -> Either e a #
NFData a => NFData1 (Either a)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a0 -> ()) -> Either a a0 -> () #
(Data a, Data b) => Data (Either a b)	Since: base-4.0.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Either a b -> c (Either a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Either a b) # toConstr :: Either a b -> Constr # dataTypeOf :: Either a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Either a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Either a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Either a b -> Either a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Either a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Either a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) #
Semigroup (Either a b)	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
Generic (Either a b)
Instance details Defined in GHC.Generics Associated Types type Rep (Either a b) :: Type -> Type # Methods from :: Either a b -> Rep (Either a b) x # to :: Rep (Either a b) x -> Either a b #
(Read a, Read b) => Read (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods readsPrec :: Int -> ReadS (Either a b) # readList :: ReadS [Either a b] # readPrec :: ReadPrec (Either a b) # readListPrec :: ReadPrec [Either a b] #
(Show a, Show b) => Show (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods showsPrec :: Int -> Either a b -> ShowS # show :: Either a b -> String # showList :: [Either a b] -> ShowS #
(NFData a, NFData b) => NFData (Either a b)
Instance details Defined in Control.DeepSeq Methods rnf :: Either a b -> () #
(Eq a, Eq b) => Eq (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods (==) :: Either a b -> Either a b -> Bool # (/=) :: Either a b -> Either a b -> Bool #
(Ord a, Ord b) => Ord (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods compare :: Either a b -> Either a b -> Ordering # (<) :: Either a b -> Either a b -> Bool # (<=) :: Either a b -> Either a b -> Bool # (>) :: Either a b -> Either a b -> Bool # (>=) :: Either a b -> Either a b -> Bool # max :: Either a b -> Either a b -> Either a b # min :: Either a b -> Either a b -> Either a b #
(AEq a, AEq b) => AEq (Either a b)
Instance details Defined in Data.AEq Methods (===) :: Either a b -> Either a b -> Bool # (~==) :: Either a b -> Either a b -> Bool #
type Rep1 (Either a :: Type -> Type)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Either a b)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep (Either a b) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

class (Real a, Enum a) => Integral a where #

Integral numbers, supporting integer division.

The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

In addition, toInteger should be total, and fromInteger should be a left inverse for it, i.e. fromInteger (toInteger i) = i.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 #

integer division truncated toward zero