| Copyright | Copyright (C) 2006-2018 Bjorn Buckwalter |
|---|---|
| License | BSD3 |
| Maintainer | bjorn@buckwalter.se |
| Stability | Stable |
| Portability | GHC only |
| Safe Haskell | None |
| 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 Unit (m :: Metricality) = Dimensional ('DUnit m)
- (-) :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a -> Quantity d a
- negate :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a
- (+) :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a -> Quantity d a
- type family (a :: Dimension) * (b :: Dimension) :: Dimension where ...
- (*) :: forall (v1 :: Variant) (v2 :: Variant) a (d1 :: Dimension) (d2 :: Dimension). (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 * d2) a
- type family (d :: Dimension) ^ (x :: TypeInt) :: Dimension where ...
- (^) :: forall a (i :: TypeInt) (v :: Variant) (d1 :: Dimension). (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a
- abs :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a
- signum :: forall a (d :: Dimension). Num a => Quantity d a -> Dimensionless a
- sum :: forall a f (d :: Dimension). (Num a, Foldable f) => f (Quantity d a) -> Quantity d a
- product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a
- type family (a :: Dimension) / (d :: Dimension) :: Dimension where ...
- (/) :: forall (v1 :: Variant) (v2 :: Variant) a (d1 :: Dimension) (d2 :: Dimension). (KnownVariant v1, KnownVariant v2, KnownVariant (v1 / v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 / v2) (d1 / d2) a
- recip :: forall a (d :: Dimension). Fractional a => Quantity d a -> Quantity (Recip d) a
- atan2 :: forall a (d :: Dimension). 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 :: forall a (d :: Dimension). 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
- type Recip (d :: Dimension) = DOne / d
- class KnownVariant (v :: Variant) where
- data Dimensional (v :: Variant) :: Dimension -> Type -> Type
- data family Dimensional (v :: Variant) :: Dimension -> Type -> Type
- type Quantity = SQuantity One
- data Metricality
- data Dimension = Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt
- type family NRoot (d :: Dimension) (x :: TypeInt) :: Dimension where ...
- type Sqrt (d :: Dimension) = NRoot d 'Pos2
- type Cbrt (d :: Dimension) = 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)
- (*~) :: forall a (m :: Metricality) (d :: Dimension). Num a => a -> Unit m d a -> Quantity d a
- (/~) :: forall a (d :: Dimension) (m :: Metricality). Fractional a => Quantity d a -> Unit m d a -> a
- (^/) :: forall (n :: TypeInt) a (d :: Dimension). (KnownTypeInt n, Floating a) => Quantity d a -> Proxy n -> Quantity (NRoot d n) a
- nroot :: forall (n :: TypeInt) a (d :: Dimension). (KnownTypeInt n, Floating a) => Proxy n -> Quantity d a -> Quantity (NRoot d n) a
- cbrt :: forall a (d :: Dimension). Floating a => Quantity d a -> Quantity (Cbrt d) a
- (*~~) :: forall f a (m :: Metricality) (d :: Dimension). (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a)
- (/~~) :: forall f (m :: Metricality) (d :: Dimension) a. (Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a
- mean :: forall a f (d :: Dimension). (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a
- dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a
- nFromTo :: forall a b (d :: Dimension). (Fractional a, Integral b) => Quantity d a -> Quantity d a -> b -> [Quantity d a]
- 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
- _0 :: forall a (d :: Dimension). 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 :: Dimension) a. (KnownDimension d, Num a) => Unit 'NonMetric d a
- one :: Num a => Unit 'NonMetric DOne a
- mkUnitR :: forall a (m :: Metricality) (m1 :: Metricality) (d :: Dimension). Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a
- mkUnitQ :: forall a (m :: Metricality) (m1 :: Metricality) (d :: Dimension). Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a
- mkUnitZ :: forall a (m :: Metricality) (m1 :: Metricality) (d :: Dimension). Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a
- name :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> UnitName m
- exactValue :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> ExactPi
- weaken :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> Unit 'NonMetric d a
- strengthen :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> Maybe (Unit 'Metric d a)
- exactify :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> Unit m d ExactPi
- showIn :: forall a (m :: Metricality) (d :: Dimension). (Show a, Fractional a) => Unit m d a -> Quantity d a -> String
- changeRep :: forall (v :: Variant) a b (d :: Dimension). (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b
- changeRepApproximate :: forall (v :: Variant) b (d :: Dimension). (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b
- asLens :: forall a (m :: Metricality) (d :: Dimension). Fractional a => Unit m d a -> forall (f :: Type -> Type). 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
- maximum :: (Foldable t, Ord a) => t a -> a
- minimum :: (Foldable t, Ord a) => t a -> a
- data Int
- data Float
- data Char
- data Maybe a
- data IO a
- data Bool
- data Double
- data Word
- data Ordering
- class a ~# b => (a :: k) ~ (b :: k)
- data Integer
- cycle :: HasCallStack => [a] -> [a]
- const :: a -> b -> a
- (++) :: [a] -> [a] -> [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
- 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
- seq :: a -> b -> b
- concat :: Foldable t => t [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- print :: Show a => a -> IO ()
- otherwise :: Bool
- map :: (a -> b) -> [a] -> [b]
- ($) :: (a -> b) -> a -> b
- class Num a where
- fromInteger :: Integer -> a
- class Num a => Fractional a where
- fromRational :: Rational -> 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
- class Eq a => Ord a where
- class Applicative m => Monad (m :: Type -> Type) where
- class Functor (f :: Type -> Type) where
- class Monad m => MonadFail (m :: Type -> Type) where
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- class (Real a, Enum a) => Integral a where
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- class Semigroup a where
- (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
- class Functor f => Applicative (f :: Type -> Type) where
- class Bounded a where
- class Fractional a => Floating a
- class Read a where
- 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
- class Show a where
- 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)
- type String = [Char]
- type Rational = Ratio Integer
- data Either a b
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- curry :: ((a, b) -> c) -> a -> b -> c
- uncurry :: (a -> b -> c) -> (a, b) -> c
- error :: HasCallStack => [Char] -> a
- errorWithoutStackTrace :: [Char] -> a
- undefined :: HasCallStack => a
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- flip :: (a -> b -> c) -> b -> a -> c
- ($!) :: (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
- head :: HasCallStack => [a] -> a
- 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)]
- zipWith :: (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])
- type ShowS = String -> String
- shows :: Show a => a -> ShowS
- showChar :: Char -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- even :: Integral a => a -> Bool
- odd :: Integral a => a -> Bool
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- type ReadS a = String -> [(a, String)]
- 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
- type IOError = IOException
- userError :: String -> IOError
- type FilePath = String
- ioError :: IOError -> IO a
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- getChar :: IO Char
- getLine :: IO String
- getContents :: IO String
- interact :: (String -> String) -> IO ()
- readFile :: FilePath -> IO String
- writeFile :: FilePath -> String -> IO ()
- appendFile :: FilePath -> String -> IO ()
- readLn :: Read a => IO a
- readIO :: Read a => String -> IO a
Documentation
type Unit (m :: Metricality) = Dimensional ('DUnit m) Source #
A unit of measurement.
(-) :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #
Subtracts one Quantity from another.
negate :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a Source #
Negates the value of a Quantity.
(+) :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #
Adds two Quantitys.
type family (a :: Dimension) * (b :: Dimension) :: Dimension where ... infixl 7 Source #
Multiplication of dimensions corresponds to addition of the base dimensions' exponents.
(*) :: forall (v1 :: Variant) (v2 :: Variant) a (d1 :: Dimension) (d2 :: Dimension). (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 #
type family (d :: Dimension) ^ (x :: TypeInt) :: Dimension 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.
(^) :: forall a (i :: TypeInt) (v :: Variant) (d1 :: Dimension). (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 :: forall a (d :: Dimension). Num a => Quantity d a -> Quantity d a Source #
Takes the absolute value of a Quantity.
sum :: forall a f (d :: Dimension). (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
type family (a :: Dimension) / (d :: Dimension) :: Dimension where ... infixl 7 Source #
Division of dimensions corresponds to subtraction of the base dimensions' exponents.
(/) :: forall (v1 :: Variant) (v2 :: Variant) a (d1 :: Dimension) (d2 :: Dimension). (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 #
recip :: forall a (d :: Dimension). Fractional a => Quantity d a -> Quantity (Recip d) a Source #
Forms the reciprocal of a Quantity, which has the reciprocal dimension.
>>>recip $ 47 *~ hertz2.127659574468085e-2 s
atan2 :: forall a (d :: Dimension). 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 _10.0
>>>atan2 _1 _01.5707963267948966
>>>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 #
(**) :: 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 _83.0
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 #
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
Instances
data family Dimensional (v :: Variant) :: Dimension -> Type -> Type Source #
A dimensional value, either a Quantity or a Unit, parameterized by its Dimension and representation.
Instances
| Generic1 (Dimensional ('DQuantity s) d :: Type -> Type) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Associated Types
Methods from1 :: Dimensional ('DQuantity s) d a -> Rep1 (Dimensional ('DQuantity s) d) a Source # to1 :: Rep1 (Dimensional ('DQuantity s) d) a -> Dimensional ('DQuantity s) d a Source # | |||||
| Generic1 (Dimensional ('DUnit m) d :: Type -> Type) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Associated Types
Methods from1 :: Dimensional ('DUnit m) d a -> Rep1 (Dimensional ('DUnit m) d) a Source # to1 :: Rep1 (Dimensional ('DUnit m) d) a -> Dimensional ('DUnit m) d a Source # | |||||
| Vector Vector a => Vector Vector (SQuantity s d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods basicUnsafeFreeze :: Mutable Vector s0 (SQuantity s d a) -> ST s0 (Vector (SQuantity s d a)) basicUnsafeThaw :: Vector (SQuantity s d a) -> ST s0 (Mutable Vector s0 (SQuantity s d a)) basicLength :: Vector (SQuantity s d a) -> Int basicUnsafeSlice :: Int -> Int -> Vector (SQuantity s d a) -> Vector (SQuantity s d a) basicUnsafeIndexM :: Vector (SQuantity s d a) -> Int -> Box (SQuantity s d a) basicUnsafeCopy :: Mutable Vector s0 (SQuantity s d a) -> Vector (SQuantity s d a) -> ST s0 () elemseq :: Vector (SQuantity s d a) -> SQuantity s d a -> b -> b | |||||
| MVector MVector a => MVector MVector (SQuantity s d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods basicLength :: MVector s0 (SQuantity s d a) -> Int basicUnsafeSlice :: Int -> Int -> MVector s0 (SQuantity s d a) -> MVector s0 (SQuantity s d a) basicOverlaps :: MVector s0 (SQuantity s d a) -> MVector s0 (SQuantity s d a) -> Bool basicUnsafeNew :: Int -> ST s0 (MVector s0 (SQuantity s d a)) basicInitialize :: MVector s0 (SQuantity s d a) -> ST s0 () basicUnsafeReplicate :: Int -> SQuantity s d a -> ST s0 (MVector s0 (SQuantity s d a)) basicUnsafeRead :: MVector s0 (SQuantity s d a) -> Int -> ST s0 (SQuantity s d a) basicUnsafeWrite :: MVector s0 (SQuantity s d a) -> Int -> SQuantity s d a -> ST s0 () basicClear :: MVector s0 (SQuantity s d a) -> ST s0 () basicSet :: MVector s0 (SQuantity s d a) -> SQuantity s d a -> ST s0 () basicUnsafeCopy :: MVector s0 (SQuantity s d a) -> MVector s0 (SQuantity s d a) -> ST s0 () basicUnsafeMove :: MVector s0 (SQuantity s d a) -> MVector s0 (SQuantity s d a) -> ST s0 () basicUnsafeGrow :: MVector s0 (SQuantity s d a) -> Int -> ST s0 (MVector s0 (SQuantity s d a)) | |||||
| KnownDimension d => Demotable (Quantity d) Source # | |||||
Defined in Numeric.Units.Dimensional.Dynamic Methods demotableOut :: Quantity d a -> AnyQuantity a | |||||
| Eq1 (SQuantity s d) Source # | |||||
| Ord1 (SQuantity s d) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal | |||||
| NFData a => NFData (Quantity d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal | |||||
| KnownVariant v => Functor (Dimensional v d) Source # | A Note that this instance is dubious, because it allows you to break the dimensional abstraction. See Note that, while this instance overlaps with that given for Note that this is an orphan instance. | ||||
Defined in Numeric.Units.Dimensional.Functor Methods fmap :: (a -> b) -> Dimensional v d a -> Dimensional v d b Source # (<$) :: a -> Dimensional v d b -> Dimensional v d a Source # | |||||
| Functor (SQuantity s DOne) Source # | |||||
| KnownDimension d => HasDimension (Dimensional v d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods dimension :: Dimensional v d a -> Dimension' Source # | |||||
| KnownDimension d => HasDynamicDimension (Dimensional v d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods dynamicDimension :: Dimensional v d a -> DynamicDimension Source # | |||||
| HasInterchangeName (Unit m d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods interchangeName :: Unit m d a -> InterchangeName Source # | |||||
| Num a => Monoid (SQuantity s d a) Source # |
| ||||
| Num a => Semigroup (SQuantity s d a) Source # |
| ||||
| (Typeable s, Typeable d, Data a) => Data (Dimensional ('DQuantity s) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods gfoldl :: (forall d0 b. Data d0 => c (d0 -> b) -> d0 -> c b) -> (forall g. g -> c g) -> Dimensional ('DQuantity s) d a -> c (Dimensional ('DQuantity s) d a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dimensional ('DQuantity s) d a) Source # toConstr :: Dimensional ('DQuantity s) d a -> Constr Source # dataTypeOf :: Dimensional ('DQuantity s) d a -> DataType Source # dataCast1 :: Typeable t => (forall d0. Data d0 => c (t d0)) -> Maybe (c (Dimensional ('DQuantity s) d a)) Source # dataCast2 :: Typeable t => (forall d0 e. (Data d0, Data e) => c (t d0 e)) -> Maybe (c (Dimensional ('DQuantity s) d a)) Source # gmapT :: (forall b. Data b => b -> b) -> Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d0. Data d0 => d0 -> r') -> Dimensional ('DQuantity s) d a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d0. Data d0 => d0 -> r') -> Dimensional ('DQuantity s) d a -> r Source # gmapQ :: (forall d0. Data d0 => d0 -> u) -> Dimensional ('DQuantity s) d a -> [u] Source # gmapQi :: Int -> (forall d0. Data d0 => d0 -> u) -> Dimensional ('DQuantity s) d a -> u Source # gmapM :: Monad m => (forall d0. Data d0 => d0 -> m d0) -> Dimensional ('DQuantity s) d a -> m (Dimensional ('DQuantity s) d a) Source # gmapMp :: MonadPlus m => (forall d0. Data d0 => d0 -> m d0) -> Dimensional ('DQuantity s) d a -> m (Dimensional ('DQuantity s) d a) Source # gmapMo :: MonadPlus m => (forall d0. Data d0 => d0 -> m d0) -> Dimensional ('DQuantity s) d a -> m (Dimensional ('DQuantity s) d a) Source # | |||||
| Bounded a => Bounded (SQuantity s d a) Source # | |||||
| Storable a => Storable (SQuantity s d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods sizeOf :: SQuantity s d a -> Int Source # alignment :: SQuantity s d a -> Int Source # peekElemOff :: Ptr (SQuantity s d a) -> Int -> IO (SQuantity s d a) Source # pokeElemOff :: Ptr (SQuantity s d a) -> Int -> SQuantity s d a -> IO () Source # peekByteOff :: Ptr b -> Int -> IO (SQuantity s d a) Source # pokeByteOff :: Ptr b -> Int -> SQuantity s d a -> IO () Source # peek :: Ptr (SQuantity s d a) -> IO (SQuantity s d a) Source # poke :: Ptr (SQuantity s d a) -> SQuantity s d a -> IO () Source # | |||||
| Generic (Dimensional ('DQuantity s) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Associated Types
Methods from :: Dimensional ('DQuantity s) d a -> Rep (Dimensional ('DQuantity s) d a) x Source # to :: Rep (Dimensional ('DQuantity s) d a) x -> Dimensional ('DQuantity s) d a Source # | |||||
| Generic (Dimensional ('DUnit m) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Associated Types
Methods from :: Dimensional ('DUnit m) d a -> Rep (Dimensional ('DUnit m) d a) x Source # to :: Rep (Dimensional ('DUnit m) d a) x -> Dimensional ('DUnit m) d a Source # | |||||
| (KnownDimension d, KnownExactPi s, Show a, Real a) => Show (SQuantity s d a) Source # | Uses non-breaking spaces between the value and the unit, and within the unit name. | ||||
| Show a => Show (Unit m d a) Source # | Unit names are shown with non-breaking spaces. | ||||
| Eq a => Eq (Dimensional ('DQuantity s) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods (==) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (/=) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # | |||||
| Ord a => Ord (Dimensional ('DQuantity s) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods compare :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Ordering Source # (<) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (<=) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (>) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (>=) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # max :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a Source # min :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a Source # | |||||
| AEq a => AEq (Dimensional ('DQuantity s) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal Methods (===) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (~==) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # | |||||
| Unbox a => Unbox (SQuantity s d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal | |||||
| type Rep1 (Dimensional ('DQuantity s) d :: Type -> Type) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal type Rep1 (Dimensional ('DQuantity s) d :: Type -> Type) = D1 ('MetaData "Dimensional" "Numeric.Units.Dimensional.Internal" "dimensional-1.6.1-DmNxHObAeML5uhkkhNUdgI" 'True) (C1 ('MetaCons "Quantity" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |||||
| type Rep1 (Dimensional ('DUnit m) d :: Type -> Type) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal type Rep1 (Dimensional ('DUnit m) d :: Type -> Type) = D1 ('MetaData "Dimensional" "Numeric.Units.Dimensional.Internal" "dimensional-1.6.1-DmNxHObAeML5uhkkhNUdgI" 'False) (C1 ('MetaCons "Unit" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (UnitName m)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 ExactPi) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))) | |||||
| newtype MVector v (SQuantity s d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal | |||||
| newtype Dimensional ('DQuantity s) d a Source # | |||||
Defined in Numeric.Units.Dimensional.Internal | |||||
| data Dimensional ('DUnit m) d a Source # | |||||
Defined in Numeric.Units.Dimensional.Internal | |||||
| type Rep (Dimensional ('DQuantity s) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal type Rep (Dimensional ('DQuantity s) d a) = D1 ('MetaData "Dimensional" "Numeric.Units.Dimensional.Internal" "dimensional-1.6.1-DmNxHObAeML5uhkkhNUdgI" 'True) (C1 ('MetaCons "Quantity" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) | |||||
| type Rep (Dimensional ('DUnit m) d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal type Rep (Dimensional ('DUnit m) d a) = D1 ('MetaData "Dimensional" "Numeric.Units.Dimensional.Internal" "dimensional-1.6.1-DmNxHObAeML5uhkkhNUdgI" 'False) (C1 ('MetaCons "Unit" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (UnitName m)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 ExactPi) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))) | |||||
| newtype Vector (SQuantity s d a) Source # | |||||
Defined in Numeric.Units.Dimensional.Internal | |||||
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
| NFData Metricality Source # | |||||
Defined in Numeric.Units.Dimensional.Variants Methods rnf :: Metricality -> () Source # | |||||
| Data Metricality Source # | |||||
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 Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Metricality Source # toConstr :: Metricality -> Constr Source # dataTypeOf :: Metricality -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Metricality) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Metricality) Source # gmapT :: (forall b. Data b => b -> b) -> Metricality -> Metricality Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Metricality -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Metricality -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality Source # | |||||
| Generic Metricality Source # | |||||
Defined in Numeric.Units.Dimensional.Variants Associated Types
Methods from :: Metricality -> Rep Metricality x Source # to :: Rep Metricality x -> Metricality Source # | |||||
| Eq Metricality Source # | |||||
Defined in Numeric.Units.Dimensional.Variants Methods (==) :: Metricality -> Metricality -> Bool Source # (/=) :: Metricality -> Metricality -> Bool Source # | |||||
| Ord Metricality Source # | |||||
Defined in Numeric.Units.Dimensional.Variants Methods compare :: Metricality -> Metricality -> Ordering Source # (<) :: Metricality -> Metricality -> Bool Source # (<=) :: Metricality -> Metricality -> Bool Source # (>) :: Metricality -> Metricality -> Bool Source # (>=) :: Metricality -> Metricality -> Bool Source # max :: Metricality -> Metricality -> Metricality Source # min :: Metricality -> Metricality -> Metricality Source # | |||||
| type Rep Metricality Source # | |||||
Defined in Numeric.Units.Dimensional.Variants | |||||
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'
Instances
| (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 # | |
| (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 # | |
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) :: Dimension where ... Source #
Roots of dimensions correspond to division of the base dimensions' exponents by the order of the root.
type Sqrt (d :: Dimension) = NRoot d 'Pos2 Source #
Square root is a special case of NRoot with order 2.
type Cbrt (d :: Dimension) = 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.
Instances
| NFData Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods rnf :: Dimension' -> () Source # | |||||
| HasDimension Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dimension :: Dimension' -> Dimension' Source # | |||||
| HasDynamicDimension Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods | |||||
| Monoid Dimension' Source # | The monoid of dimensions under multiplication. | ||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods mempty :: Dimension' Source # mappend :: Dimension' -> Dimension' -> Dimension' Source # mconcat :: [Dimension'] -> Dimension' Source # | |||||
| Semigroup Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (<>) :: Dimension' -> Dimension' -> Dimension' Source # sconcat :: NonEmpty Dimension' -> Dimension' Source # stimes :: Integral b => b -> Dimension' -> Dimension' Source # | |||||
| Data Dimension' Source # | |||||
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' Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Dimension' Source # toConstr :: Dimension' -> Constr Source # dataTypeOf :: Dimension' -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Dimension') Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Dimension') Source # gmapT :: (forall b. Data b => b -> b) -> Dimension' -> Dimension' Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Dimension' -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dimension' -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' Source # | |||||
| Generic Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Associated Types
| |||||
| Show Dimension' Source # | |||||
| Eq Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (==) :: Dimension' -> Dimension' -> Bool Source # (/=) :: Dimension' -> Dimension' -> Bool Source # | |||||
| Ord Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods compare :: Dimension' -> Dimension' -> Ordering Source # (<) :: Dimension' -> Dimension' -> Bool Source # (<=) :: Dimension' -> Dimension' -> Bool Source # (>) :: Dimension' -> Dimension' -> Bool Source # (>=) :: Dimension' -> Dimension' -> Bool Source # max :: Dimension' -> Dimension' -> Dimension' Source # min :: Dimension' -> Dimension' -> Dimension' Source # | |||||
| type Rep Dimension' Source # | |||||
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel type Rep Dimension' = D1 ('MetaData "Dimension'" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.6.1-DmNxHObAeML5uhkkhNUdgI" '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
| HasDimension Dimension' Source # | |
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods dimension :: Dimension' -> Dimension' Source # | |
| HasDimension AnyUnit Source # | |
Defined in Numeric.Units.Dimensional.Dynamic Methods dimension :: AnyUnit -> Dimension' Source # | |
| HasDimension (AnyQuantity a) Source # | |
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 # | |
| KnownDimension d => HasDimension (Dimensional v d a) Source # | |
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 ddimension :: Proxy d -> Dimension'
(*~) :: forall a (m :: Metricality) (d :: Dimension). Num a => a -> Unit m d a -> Quantity d a infixl 7 Source #
Forms a Quantity by multipliying a number and a unit.
(/~) :: forall a (d :: Dimension) (m :: Metricality). Fractional a => Quantity d a -> Unit m d a -> a infixl 7 Source #
(^/) :: forall (n :: TypeInt) a (d :: Dimension). (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 :: forall (n :: TypeInt) a (d :: Dimension). (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 ^/.
(*~~) :: forall f a (m :: Metricality) (d :: Dimension). (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 :: Metricality) (d :: Dimension) 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 :: forall a f (d :: Dimension). (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
Arguments
| :: forall a b (d :: Dimension). (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]
type DOne = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero Source #
The type-level dimension of dimensionless values.
type Dimensionless = Quantity DOne Source #
_0 :: forall a (d :: Dimension). 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 :: Dimension) 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 :: forall a (m :: Metricality) (m1 :: Metricality) (d :: Dimension). 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 :: forall a (m :: Metricality) (m1 :: Metricality) (d :: Dimension). Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a Source #
mkUnitZ :: forall a (m :: Metricality) (m1 :: Metricality) (d :: Dimension). Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a Source #
exactValue :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> ExactPi Source #
weaken :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> Unit 'NonMetric d a Source #
Discards potentially unwanted type level information about a Unit.
strengthen :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> Maybe (Unit 'Metric d a) Source #
exactify :: forall (m :: Metricality) (d :: Dimension) a. Unit m d a -> Unit m d ExactPi Source #
Forms the exact version of a Unit.
showIn :: forall a (m :: Metricality) (d :: Dimension). (Show a, Fractional a) => Unit m d a -> Quantity d a -> String Source #
changeRep :: forall (v :: Variant) a b (d :: Dimension). (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 Double16.78291769 kg
changeRepApproximate :: forall (v :: Variant) b (d :: Dimension). (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b Source #
Convenient conversion from exactly represented values while retaining dimensional information.
asLens :: forall a (m :: Metricality) (d :: Dimension). Fractional a => Unit m d a -> forall (f :: Type -> Type). Functor f => (a -> f a) -> Quantity d a -> f (Quantity d a) Source #
class Category (cat :: k -> k -> Type) where Source #
A class for categories. Instances should satisfy the laws
Methods
id :: forall (a :: k). cat a a Source #
the identity morphism
(.) :: forall (b :: k) (c :: k) (a :: k). cat b c -> cat a b -> cat a c infixr 9 Source #
morphism composition
maximum :: (Foldable t, Ord a) => t a -> a Source #
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
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 Source #
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
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
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
| PrintfArg Int | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
| NFData Int | |||||
Defined in Control.DeepSeq | |||||
| Bits Int | Since: base-2.1 | ||||
Defined in GHC.Internal.Bits Methods (.&.) :: Int -> Int -> Int Source # (.|.) :: Int -> Int -> Int Source # xor :: Int -> Int -> Int Source # complement :: Int -> Int Source # shift :: Int -> Int -> Int Source # rotate :: Int -> Int -> Int Source # setBit :: Int -> Int -> Int Source # clearBit :: Int -> Int -> Int Source # complementBit :: Int -> Int -> Int Source # testBit :: Int -> Int -> Bool Source # bitSizeMaybe :: Int -> Maybe Int Source # bitSize :: Int -> Int Source # isSigned :: Int -> Bool Source # shiftL :: Int -> Int -> Int Source # unsafeShiftL :: Int -> Int -> Int Source # shiftR :: Int -> Int -> Int Source # unsafeShiftR :: Int -> Int -> Int Source # rotateL :: Int -> Int -> Int Source # | |||||
| FiniteBits Int | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Bits Methods finiteBitSize :: Int -> Int Source # countLeadingZeros :: Int -> Int Source # countTrailingZeros :: Int -> Int Source # | |||||
| Data Int | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int Source # toConstr :: Int -> Constr Source # dataTypeOf :: Int -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) Source # gmapT :: (forall b. Data b => b -> b) -> Int -> Int Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source # | |||||
| Bounded Int | Since: base-2.1 | ||||
| Enum Int | Since: base-2.1 | ||||
Defined in GHC.Internal.Enum | |||||
| Storable Int | Since: base-2.1 | ||||
Defined in GHC.Internal.Foreign.Storable | |||||
| Num Int | Since: base-2.1 | ||||
| Read Int | Since: base-2.1 | ||||
| Integral Int | Since: base-2.0.1 | ||||
| Real Int | Since: base-2.0.1 | ||||
Defined in GHC.Internal.Real Methods toRational :: Int -> Rational Source # | |||||
| Show Int | Since: base-2.1 | ||||
| Eq Int | |||||
| Ord Int | |||||
| AEq Int | |||||
| Unbox Int | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| Lift Int | |||||
| Vector Vector Int | |||||
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 () | |||||
| MVector MVector Int | |||||
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) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # | |||||
| Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 | ||||
| Generic (URec Int p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Int p) | Since: base-4.9.0.0 | ||||
| Eq (URec Int p) | Since: base-4.9.0.0 | ||||
| Ord (URec Int p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Int p -> URec Int p -> Ordering Source # (<) :: URec Int p -> URec Int p -> Bool Source # (<=) :: URec Int p -> URec Int p -> Bool Source # (>) :: URec Int p -> URec Int p -> Bool Source # (>=) :: URec Int p -> URec Int p -> Bool Source # | |||||
| newtype Vector Int | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| data URec Int (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| newtype MVector s Int | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| type Rep1 (URec Int :: k -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Int p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
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
| PrintfArg Float | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
| NFData Float | |||||
Defined in Control.DeepSeq | |||||
| Data Float | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float Source # toConstr :: Float -> Constr Source # dataTypeOf :: Float -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) Source # gmapT :: (forall b. Data b => b -> b) -> Float -> Float Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source # | |||||
| Enum Float |
List generators have extremely peculiar behavior, mandated by Haskell Report 2010:
Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods succ :: Float -> Float Source # pred :: Float -> Float Source # toEnum :: Int -> Float Source # fromEnum :: Float -> Int Source # enumFrom :: Float -> [Float] Source # enumFromThen :: Float -> Float -> [Float] Source # enumFromTo :: Float -> Float -> [Float] Source # enumFromThenTo :: Float -> Float -> Float -> [Float] Source # | |||||
| Floating Float | Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods exp :: Float -> Float Source # log :: Float -> Float Source # sqrt :: Float -> Float Source # (**) :: Float -> Float -> Float Source # logBase :: Float -> Float -> Float Source # sin :: Float -> Float Source # cos :: Float -> Float Source # tan :: Float -> Float Source # asin :: Float -> Float Source # acos :: Float -> Float Source # atan :: Float -> Float Source # sinh :: Float -> Float Source # cosh :: Float -> Float Source # tanh :: Float -> Float Source # asinh :: Float -> Float Source # acosh :: Float -> Float Source # atanh :: Float -> Float Source # log1p :: Float -> Float Source # expm1 :: Float -> Float Source # | |||||
| RealFloat Float | Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods floatRadix :: Float -> Integer Source # floatDigits :: Float -> Int Source # floatRange :: Float -> (Int, Int) Source # decodeFloat :: Float -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Float Source # exponent :: Float -> Int Source # significand :: Float -> Float Source # scaleFloat :: Int -> Float -> Float Source # isNaN :: Float -> Bool Source # isInfinite :: Float -> Bool Source # isDenormalized :: Float -> Bool Source # isNegativeZero :: Float -> Bool Source # | |||||
| Storable Float | Since: base-2.1 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Float -> Int Source # alignment :: Float -> Int Source # peekElemOff :: Ptr Float -> Int -> IO Float Source # pokeElemOff :: Ptr Float -> Int -> Float -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Float Source # pokeByteOff :: Ptr b -> Int -> Float -> IO () Source # | |||||
| Num Float | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:
Since: base-2.1 | ||||
| Read Float | Since: base-2.1 | ||||
| Fractional Float | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.
Since: base-2.1 | ||||
| Real Float | Beware that
Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods toRational :: Float -> Rational Source # | |||||
| RealFrac Float | Beware that results for non-finite arguments are garbage:
and get even more non-sensical if you ask for Since: base-2.1 | ||||
| Show Float | Since: base-2.1 | ||||
| Eq Float | Note that due to the presence of
Also note that
| ||||
| Ord Float | See | ||||
Defined in GHC.Classes | |||||
| AEq Float | |||||
| IEEE Float | |||||
Defined in Numeric.IEEE Methods minDenormal :: Float Source # copySign :: Float -> Float -> Float Source # identicalIEEE :: Float -> Float -> Bool Source # succIEEE :: Float -> Float Source # predIEEE :: Float -> Float Source # bisectIEEE :: Float -> Float -> Float Source # sameSignificandBits :: Float -> Float -> Int Source # nanWithPayload :: Word64 -> Float Source # maxNaNPayload :: Float -> Word64 Source # nanPayload :: Float -> Word64 Source # | |||||
| Unbox Float | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| Lift Float | |||||
| Vector Vector Float | |||||
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 () | |||||
| MVector MVector Float | |||||
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) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # | |||||
| Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| AEq (Complex Float) | |||||
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 | ||||
| Generic (URec Float p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Float p) | |||||
| Eq (URec Float p) | |||||
| Ord (URec Float p) | |||||
Defined in GHC.Internal.Generics Methods compare :: URec Float p -> URec Float p -> Ordering Source # (<) :: URec Float p -> URec Float p -> Bool Source # (<=) :: URec Float p -> URec Float p -> Bool Source # (>) :: URec Float p -> URec Float p -> Bool Source # (>=) :: URec Float p -> URec Float p -> Bool Source # max :: URec Float p -> URec Float p -> URec Float p Source # min :: URec Float p -> URec Float p -> URec Float p Source # | |||||
| newtype Vector Float | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| data URec Float (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| newtype MVector s Float | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| type Rep1 (URec Float :: k -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Float p) | |||||
Defined in GHC.Internal.Generics | |||||
The character type Char represents Unicode codespace
and its elements are code points as in definitions
D9 and D10 of the Unicode Standard.
Character literals in Haskell are single-quoted: 'Q', 'Я' or 'Ω'.
To represent a single quote itself use '\'', and to represent a backslash
use '\\'. The full grammar can be found in the section 2.6 of the
Haskell 2010 Language Report.
To specify a character by its code point one can use decimal, hexadecimal
or octal notation: '\65', '\x41' and '\o101' are all alternative forms
of 'A'. The largest code point is '\x10ffff'.
There is a special escape syntax for ASCII control characters:
| Escape | Alternatives | Meaning |
|---|---|---|
'\NUL' | '\0' | null character |
'\SOH' | '\1' | start of heading |
'\STX' | '\2' | start of text |
'\ETX' | '\3' | end of text |
'\EOT' | '\4' | end of transmission |
'\ENQ' | '\5' | enquiry |
'\ACK' | '\6' | acknowledge |
'\BEL' | '\7', '\a' | bell (alert) |
'\BS' | '\8', '\b' | backspace |
'\HT' | '\9', '\t' | horizontal tab |
'\LF' | '\10', '\n' | line feed (new line) |
'\VT' | '\11', '\v' | vertical tab |
'\FF' | '\12', '\f' | form feed |
'\CR' | '\13', '\r' | carriage return |
'\SO' | '\14' | shift out |
'\SI' | '\15' | shift in |
'\DLE' | '\16' | data link escape |
'\DC1' | '\17' | device control 1 |
'\DC2' | '\18' | device control 2 |
'\DC3' | '\19' | device control 3 |
'\DC4' | '\20' | device control 4 |
'\NAK' | '\21' | negative acknowledge |
'\SYN' | '\22' | synchronous idle |
'\ETB' | '\23' | end of transmission block |
'\CAN' | '\24' | cancel |
'\EM' | '\25' | end of medium |
'\SUB' | '\26' | substitute |
'\ESC' | '\27' | escape |
'\FS' | '\28' | file separator |
'\GS' | '\29' | group separator |
'\RS' | '\30' | record separator |
'\US' | '\31' | unit separator |
'\SP' | '\32', ' ' | space |
'\DEL' | '\127' | delete |
Instances
| IsChar Char | Since: base-2.1 | ||||
| PrintfArg Char | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
| NFData Char | |||||
Defined in Control.DeepSeq | |||||
| Data Char | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Char -> c Char Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Char Source # toConstr :: Char -> Constr Source # dataTypeOf :: Char -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Char) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Char) Source # gmapT :: (forall b. Data b => b -> b) -> Char -> Char Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Char -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Char -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Char -> m Char Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source # | |||||
| Bounded Char | Since: base-2.1 | ||||
| Enum Char | Since: base-2.1 | ||||
| Storable Char | Since: base-2.1 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Char -> Int Source # alignment :: Char -> Int Source # peekElemOff :: Ptr Char -> Int -> IO Char Source # pokeElemOff :: Ptr Char -> Int -> Char -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Char Source # pokeByteOff :: Ptr b -> Int -> Char -> IO () Source # | |||||
| Read Char | Since: base-2.1 | ||||
| Show Char | Since: base-2.1 | ||||
| Eq Char | |||||
| Ord Char | |||||
| AEq Char | |||||
| Unbox Char | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| Lift Char | |||||
| Vector Vector Char | |||||
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 () | |||||
| MVector MVector Char | |||||
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) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # | |||||
| Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 | ||||
| Generic (URec Char p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Char p) | Since: base-4.9.0.0 | ||||
| Eq (URec Char p) | Since: base-4.9.0.0 | ||||
| Ord (URec Char p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Char p -> URec Char p -> Ordering Source # (<) :: URec Char p -> URec Char p -> Bool Source # (<=) :: URec Char p -> URec Char p -> Bool Source # (>) :: URec Char p -> URec Char p -> Bool Source # (>=) :: URec Char p -> URec Char p -> Bool Source # | |||||
| newtype Vector Char | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| data URec Char (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| newtype MVector s Char | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| type Compare (a :: Char) (b :: Char) | |||||
Defined in GHC.Internal.Data.Type.Ord | |||||
| type Rep1 (URec Char :: k -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Char p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
The Maybe type encapsulates an optional value. A value of type
Maybe aa (represented as Just aNothing). 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.
Instances
| MonadZip Maybe | Since: base-4.8.0.0 | ||||
| Eq1 Maybe | Since: base-4.9.0.0 | ||||
| Ord1 Maybe | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Read1 Maybe | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] Source # | |||||
| Show1 Maybe | Since: base-4.9.0.0 | ||||
| NFData1 Maybe | Since: deepseq-1.4.3.0 | ||||
Defined in Control.DeepSeq | |||||
| Alternative Maybe | Picks the leftmost Since: base-2.1 | ||||
| Applicative Maybe | Since: base-2.1 | ||||
| Functor Maybe | Since: base-2.1 | ||||
| Monad Maybe | Since: base-2.1 | ||||
| MonadPlus Maybe | Picks the leftmost Since: base-2.1 | ||||
| MonadFail Maybe | Since: base-4.9.0.0 | ||||
| Foldable Maybe | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # | |||||
| Traversable Maybe | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 Maybe | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Lift a => Lift (Maybe a :: Type) | |||||
| NFData a => NFData (Maybe a) | |||||
Defined in Control.DeepSeq | |||||
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 | ||||
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 | ||||
| Data a => Data (Maybe a) | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.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) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Maybe a) Source # toConstr :: Maybe a -> Constr Source # dataTypeOf :: Maybe a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Maybe a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Maybe a)) Source # gmapT :: (forall b. Data b => b -> b) -> Maybe a -> Maybe a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Maybe a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Maybe a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # | |||||
| Generic (Maybe a) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| SingKind a => SingKind (Maybe a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Read a => Read (Maybe a) | Since: base-2.1 | ||||
| Show a => Show (Maybe a) | Since: base-2.1 | ||||
| Eq a => Eq (Maybe a) | Since: base-2.1 | ||||
| Ord a => Ord (Maybe a) | Since: base-2.1 | ||||
Defined in GHC.Internal.Maybe | |||||
| AEq a => AEq (Maybe a) | |||||
| SingI ('Nothing :: Maybe a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| SingI a2 => SingI ('Just a2 :: Maybe a1) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep1 Maybe | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type DemoteRep (Maybe a) | |||||
Defined in GHC.Internal.Generics | |||||
| type Rep (Maybe a) | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| data Sing (b :: Maybe a) | |||||
A value of type IO aa.
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
| MonadIO IO | Since: base-4.9.0.0 |
| Alternative IO | Takes the first non-throwing Since: base-4.9.0.0 |
| Applicative IO | Since: base-2.1 |
| Functor IO | Since: base-2.1 |
| Monad IO | Since: base-2.1 |
| MonadPlus IO | Takes the first non-throwing Since: base-4.9.0.0 |
| MonadFail IO | Since: base-4.9.0.0 |
| PrimBase IO | |
| PrimMonad IO | |
| Quasi IO | |
Defined in Language.Haskell.TH.Syntax Methods qNewName :: String -> IO Name Source # qReport :: Bool -> String -> IO () Source # qRecover :: IO a -> IO a -> IO a Source # qLookupName :: Bool -> String -> IO (Maybe Name) Source # qReify :: Name -> IO Info Source # qReifyFixity :: Name -> IO (Maybe Fixity) Source # qReifyType :: Name -> IO Type Source # qReifyInstances :: Name -> [Type] -> IO [Dec] Source # qReifyRoles :: Name -> IO [Role] Source # qReifyAnnotations :: Data a => AnnLookup -> IO [a] Source # qReifyModule :: Module -> IO ModuleInfo Source # qReifyConStrictness :: Name -> IO [DecidedStrictness] Source # qRunIO :: IO a -> IO a Source # qGetPackageRoot :: IO FilePath Source # qAddDependentFile :: FilePath -> IO () Source # qAddTempFile :: String -> IO FilePath Source # qAddTopDecls :: [Dec] -> IO () Source # qAddForeignFilePath :: ForeignSrcLang -> String -> IO () Source # qAddModFinalizer :: Q () -> IO () Source # qAddCorePlugin :: String -> IO () Source # qGetQ :: Typeable a => IO (Maybe a) Source # qPutQ :: Typeable a => a -> IO () Source # qIsExtEnabled :: Extension -> IO Bool Source # qExtsEnabled :: IO [Extension] Source # | |
| Quote IO | |
| a ~ () => HPrintfType (IO a) | Since: base-4.7.0.0 |
Defined in Text.Printf | |
| a ~ () => PrintfType (IO a) | Since: base-4.7.0.0 |
Defined in Text.Printf | |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
| type PrimState IO | |
Defined in Control.Monad.Primitive | |
Instances
| NFData Bool | |||||
Defined in Control.DeepSeq | |||||
| Bits Bool | Interpret Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Bits Methods (.&.) :: Bool -> Bool -> Bool Source # (.|.) :: Bool -> Bool -> Bool Source # xor :: Bool -> Bool -> Bool Source # complement :: Bool -> Bool Source # shift :: Bool -> Int -> Bool Source # rotate :: Bool -> Int -> Bool Source # setBit :: Bool -> Int -> Bool Source # clearBit :: Bool -> Int -> Bool Source # complementBit :: Bool -> Int -> Bool Source # testBit :: Bool -> Int -> Bool Source # bitSizeMaybe :: Bool -> Maybe Int Source # bitSize :: Bool -> Int Source # isSigned :: Bool -> Bool Source # shiftL :: Bool -> Int -> Bool Source # unsafeShiftL :: Bool -> Int -> Bool Source # shiftR :: Bool -> Int -> Bool Source # unsafeShiftR :: Bool -> Int -> Bool Source # rotateL :: Bool -> Int -> Bool Source # | |||||
| FiniteBits Bool | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Bits Methods finiteBitSize :: Bool -> Int Source # countLeadingZeros :: Bool -> Int Source # countTrailingZeros :: Bool -> Int Source # | |||||
| Data Bool | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool Source # toConstr :: Bool -> Constr Source # dataTypeOf :: Bool -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Bool) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) Source # gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # | |||||
| Bounded Bool | Since: base-2.1 | ||||
| Enum Bool | Since: base-2.1 | ||||
| Storable Bool | Since: base-2.1 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Bool -> Int Source # alignment :: Bool -> Int Source # peekElemOff :: Ptr Bool -> Int -> IO Bool Source # pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Bool Source # pokeByteOff :: Ptr b -> Int -> Bool -> IO () Source # | |||||
| Generic Bool | |||||
Defined in GHC.Internal.Generics | |||||
| SingKind Bool | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Read Bool | Since: base-2.1 | ||||
| Show Bool | Since: base-2.1 | ||||
| Eq Bool | |||||
| Ord Bool | |||||
| AEq Bool | |||||
| Unbox Bool | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| SingI 'False | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| SingI 'True | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| Lift Bool | |||||
| Vector Vector Bool | |||||
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 () | |||||
| MVector MVector Bool | |||||
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 | |||||
Defined in GHC.Internal.Generics | |||||
| type Rep Bool | Since: base-4.6.0.0 | ||||
| data Sing (a :: Bool) | |||||
| newtype Vector Bool | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| newtype MVector s Bool | |||||
Defined in Data.Vector.Unboxed.Base | |||||
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
| PrintfArg Double | Since: base-2.1 | ||||
Defined in Text.Printf Methods formatArg :: Double -> FieldFormatter Source # parseFormat :: Double -> ModifierParser Source # | |||||
| NFData Double | |||||
Defined in Control.DeepSeq | |||||
| Data Double | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double Source # toConstr :: Double -> Constr Source # dataTypeOf :: Double -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) Source # gmapT :: (forall b. Data b => b -> b) -> Double -> Double Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source # | |||||
| Enum Double |
List generators have extremely peculiar behavior, mandated by Haskell Report 2010:
Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods succ :: Double -> Double Source # pred :: Double -> Double Source # toEnum :: Int -> Double Source # fromEnum :: Double -> Int Source # enumFrom :: Double -> [Double] Source # enumFromThen :: Double -> Double -> [Double] Source # enumFromTo :: Double -> Double -> [Double] Source # enumFromThenTo :: Double -> Double -> Double -> [Double] Source # | |||||
| Floating Double | Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods exp :: Double -> Double Source # log :: Double -> Double Source # sqrt :: Double -> Double Source # (**) :: Double -> Double -> Double Source # logBase :: Double -> Double -> Double Source # sin :: Double -> Double Source # cos :: Double -> Double Source # tan :: Double -> Double Source # asin :: Double -> Double Source # acos :: Double -> Double Source # atan :: Double -> Double Source # sinh :: Double -> Double Source # cosh :: Double -> Double Source # tanh :: Double -> Double Source # asinh :: Double -> Double Source # acosh :: Double -> Double Source # atanh :: Double -> Double Source # log1p :: Double -> Double Source # expm1 :: Double -> Double Source # | |||||
| RealFloat Double | Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods floatRadix :: Double -> Integer Source # floatDigits :: Double -> Int Source # floatRange :: Double -> (Int, Int) Source # decodeFloat :: Double -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Double Source # exponent :: Double -> Int Source # significand :: Double -> Double Source # scaleFloat :: Int -> Double -> Double Source # isNaN :: Double -> Bool Source # isInfinite :: Double -> Bool Source # isDenormalized :: Double -> Bool Source # isNegativeZero :: Double -> Bool Source # | |||||
| Storable Double | Since: base-2.1 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Double -> Int Source # alignment :: Double -> Int Source # peekElemOff :: Ptr Double -> Int -> IO Double Source # pokeElemOff :: Ptr Double -> Int -> Double -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Double Source # pokeByteOff :: Ptr b -> Int -> Double -> IO () Source # | |||||
| Num Double | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:
Since: base-2.1 | ||||
Defined in GHC.Internal.Float | |||||
| Read Double | Since: base-2.1 | ||||
| Fractional Double | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.
Since: base-2.1 | ||||
| Real Double | Beware that
Since: base-2.1 | ||||
Defined in GHC.Internal.Float Methods toRational :: Double -> Rational Source # | |||||
| RealFrac Double | Beware that results for non-finite arguments are garbage:
and get even more non-sensical if you ask for Since: base-2.1 | ||||
| Show Double | Since: base-2.1 | ||||
| Eq Double | Note that due to the presence of
Also note that
| ||||
| Ord Double | IEEE 754 IEEE 754-2008, section 5.11 requires that if at least one of arguments of
IEEE 754-2008, section 5.10 defines Thus, users must be extremely cautious when using Moving further, the behaviour of IEEE 754-2008 compliant | ||||
| AEq Double | |||||
| IEEE Double | |||||
Defined in Numeric.IEEE Methods minDenormal :: Double Source # copySign :: Double -> Double -> Double Source # identicalIEEE :: Double -> Double -> Bool Source # succIEEE :: Double -> Double Source # predIEEE :: Double -> Double Source # bisectIEEE :: Double -> Double -> Double Source # sameSignificandBits :: Double -> Double -> Int Source # nanWithPayload :: Word64 -> Double Source # maxNaNPayload :: Double -> Word64 Source # nanPayload :: Double -> Word64 Source # | |||||
| Unbox Double | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| Lift Double | |||||
| Vector Vector Double | |||||
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 () | |||||
| MVector MVector Double | |||||
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) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # | |||||
| Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| AEq (Complex Double) | |||||
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 | ||||
| Generic (URec Double p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Double p) | Since: base-4.9.0.0 | ||||
| Eq (URec Double p) | Since: base-4.9.0.0 | ||||
| Ord (URec Double p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Double p -> URec Double p -> Ordering Source # (<) :: URec Double p -> URec Double p -> Bool Source # (<=) :: URec Double p -> URec Double p -> Bool Source # (>) :: URec Double p -> URec Double p -> Bool Source # (>=) :: URec Double p -> URec Double p -> Bool Source # max :: URec Double p -> URec Double p -> URec Double p Source # min :: URec Double p -> URec Double p -> URec Double p Source # | |||||
| newtype Vector Double | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| data URec Double (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| newtype MVector s Double | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| type Rep1 (URec Double :: k -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Double p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
Instances
| PrintfArg Word | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
| NFData Word | |||||
Defined in Control.DeepSeq | |||||
| Bits Word | Since: base-2.1 | ||||
Defined in GHC.Internal.Bits Methods (.&.) :: Word -> Word -> Word Source # (.|.) :: Word -> Word -> Word Source # xor :: Word -> Word -> Word Source # complement :: Word -> Word Source # shift :: Word -> Int -> Word Source # rotate :: Word -> Int -> Word Source # setBit :: Word -> Int -> Word Source # clearBit :: Word -> Int -> Word Source # complementBit :: Word -> Int -> Word Source # testBit :: Word -> Int -> Bool Source # bitSizeMaybe :: Word -> Maybe Int Source # bitSize :: Word -> Int Source # isSigned :: Word -> Bool Source # shiftL :: Word -> Int -> Word Source # unsafeShiftL :: Word -> Int -> Word Source # shiftR :: Word -> Int -> Word Source # unsafeShiftR :: Word -> Int -> Word Source # rotateL :: Word -> Int -> Word Source # | |||||
| FiniteBits Word | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Bits Methods finiteBitSize :: Word -> Int Source # countLeadingZeros :: Word -> Int Source # countTrailingZeros :: Word -> Int Source # | |||||
| Data Word | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word Source # toConstr :: Word -> Constr Source # dataTypeOf :: Word -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) Source # gmapT :: (forall b. Data b => b -> b) -> Word -> Word Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source # | |||||
| Bounded Word | Since: base-2.1 | ||||
| Enum Word | Since: base-2.1 | ||||
| Storable Word | Since: base-2.1 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Word -> Int Source # alignment :: Word -> Int Source # peekElemOff :: Ptr Word -> Int -> IO Word Source # pokeElemOff :: Ptr Word -> Int -> Word -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Word Source # pokeByteOff :: Ptr b -> Int -> Word -> IO () Source # | |||||
| Num Word | Since: base-2.1 | ||||
| Read Word | Since: base-4.5.0.0 | ||||
| Integral Word | Since: base-2.1 | ||||
Defined in GHC.Internal.Real | |||||
| Real Word | Since: base-2.1 | ||||
Defined in GHC.Internal.Real Methods toRational :: Word -> Rational Source # | |||||
| Show Word | Since: base-2.1 | ||||
| Eq Word | |||||
| Ord Word | |||||
| AEq Word | |||||
| Unbox Word | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| Lift Word | |||||
| Vector Vector Word | |||||
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 () | |||||
| MVector MVector Word | |||||
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) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # | |||||
| Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 | ||||
| Generic (URec Word p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Word p) | Since: base-4.9.0.0 | ||||
| Eq (URec Word p) | Since: base-4.9.0.0 | ||||
| Ord (URec Word p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Word p -> URec Word p -> Ordering Source # (<) :: URec Word p -> URec Word p -> Bool Source # (<=) :: URec Word p -> URec Word p -> Bool Source # (>) :: URec Word p -> URec Word p -> Bool Source # (>=) :: URec Word p -> URec Word p -> Bool Source # | |||||
| newtype Vector Word | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| data URec Word (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| newtype MVector s Word | |||||
Defined in Data.Vector.Unboxed.Base | |||||
| type Rep1 (URec Word :: k -> Type) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Word p) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
Instances
| NFData Ordering | |
Defined in Control.DeepSeq | |
| Monoid Ordering | Since: base-2.1 |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Data Ordering | Since: base-4.0.0.0 |
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordering -> c Ordering Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Ordering Source # toConstr :: Ordering -> Constr Source # dataTypeOf :: Ordering -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Ordering) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Ordering) Source # gmapT :: (forall b. Data b => b -> b) -> Ordering -> Ordering Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Ordering -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordering -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # | |
| Bounded Ordering | Since: base-2.1 |
| Enum Ordering | Since: base-2.1 |
Defined in GHC.Internal.Enum Methods succ :: Ordering -> Ordering Source # pred :: Ordering -> Ordering Source # toEnum :: Int -> Ordering Source # fromEnum :: Ordering -> Int Source # enumFrom :: Ordering -> [Ordering] Source # enumFromThen :: Ordering -> Ordering -> [Ordering] Source # enumFromTo :: Ordering -> Ordering -> [Ordering] Source # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] Source # | |
| Generic Ordering | |
Defined in GHC.Internal.Generics | |
| Read Ordering | Since: base-2.1 |
| Show Ordering | Since: base-2.1 |
| Eq Ordering | |
| Ord Ordering | |
Defined in GHC.Classes | |
| AEq Ordering | |
| type Rep Ordering | Since: base-4.6.0.0 |
class a ~# b => (a :: k) ~ (b :: k) infix 4 Source #
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.
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 (i.e., fits into an Int), the IS constructor is
used. Otherwise IP and IN constructors are used to store a BigNat
representing the positive or the negative value magnitude, respectively.
Invariant: IP and IN are used iff the value does not fit in IS.
Instances
| PrintfArg Integer | Since: base-2.1 |
Defined in Text.Printf Methods formatArg :: Integer -> FieldFormatter Source # parseFormat :: Integer -> ModifierParser Source # | |
| NFData Integer | |
Defined in Control.DeepSeq | |
| Bits Integer | Since: base-2.1 |
Defined in GHC.Internal.Bits Methods (.&.) :: Integer -> Integer -> Integer Source # (.|.) :: Integer -> Integer -> Integer Source # xor :: Integer -> Integer -> Integer Source # complement :: Integer -> Integer Source # shift :: Integer -> Int -> Integer Source # rotate :: Integer -> Int -> Integer Source # bit :: Int -> Integer Source # setBit :: Integer -> Int -> Integer Source # clearBit :: Integer -> Int -> Integer Source # complementBit :: Integer -> Int -> Integer Source # testBit :: Integer -> Int -> Bool Source # bitSizeMaybe :: Integer -> Maybe Int Source # bitSize :: Integer -> Int Source # isSigned :: Integer -> Bool Source # shiftL :: Integer -> Int -> Integer Source # unsafeShiftL :: Integer -> Int -> Integer Source # shiftR :: Integer -> Int -> Integer Source # unsafeShiftR :: Integer -> Int -> Integer Source # rotateL :: Integer -> Int -> Integer Source # | |
| Data Integer | Since: base-4.0.0.0 |
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer Source # toConstr :: Integer -> Constr Source # dataTypeOf :: Integer -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) Source # gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source # | |
| Enum Integer | Since: base-2.1 |
Defined in GHC.Internal.Enum Methods succ :: Integer -> Integer Source # pred :: Integer -> Integer Source # toEnum :: Int -> Integer Source # fromEnum :: Integer -> Int Source # enumFrom :: Integer -> [Integer] Source # enumFromThen :: Integer -> Integer -> [Integer] Source # enumFromTo :: Integer -> Integer -> [Integer] Source # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source # | |
| Num Integer | Since: base-2.1 |
Defined in GHC.Internal.Num | |
| Read Integer | Since: base-2.1 |
| Integral Integer | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods quot :: Integer -> Integer -> Integer Source # rem :: Integer -> Integer -> Integer Source # div :: Integer -> Integer -> Integer Source # mod :: Integer -> Integer -> Integer Source # quotRem :: Integer -> Integer -> (Integer, Integer) Source # | |
| Real Integer | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods toRational :: Integer -> Rational Source # | |
| Show Integer | Since: base-2.1 |
| Eq Integer | |
| Ord Integer | |
| AEq Integer | |
| Lift Integer | |
cycle :: HasCallStack => [a] -> [a] Source #
cycle ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.
Examples
>>>cycle []*** Exception: Prelude.cycle: empty list
>>>take 10 (cycle [42])[42,42,42,42,42,42,42,42,42,42]
>>>take 10 (cycle [2, 5, 7])[2,5,7,2,5,7,2,5,7,2]
>>>take 1 (cycle (42 : undefined))[42]
const x y always evaluates to x, ignoring its second argument.
const x = \_ -> x
This function might seem useless at first glance, but it can be very useful in a higher order context.
Examples
>>>const 42 "hello"42
>>>map (const 42) [0..3][42,42,42,42]
(++) :: [a] -> [a] -> [a] infixr 5 Source #
(++) appends two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
Performance considerations
This function takes linear time in the number of elements of the
first list. Thus it is better to associate repeated
applications of (++) to the right (which is the default behaviour):
xs ++ (ys ++ zs) or simply xs ++ ys ++ zs, but not (xs ++ ys) ++ zs.
For the same reason concat = foldr (++) []
has linear performance, while foldl (++) [] is prone
to quadratic slowdown
Examples
>>>[1, 2, 3] ++ [4, 5, 6][1,2,3,4,5,6]
>>>[] ++ [1, 2, 3][1,2,3]
>>>[3, 2, 1] ++ [][3,2,1]
class Foldable (t :: Type -> Type) where Source #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
| Leaf a
| Node (Tree a) a (Tree a)
deriving FoldableA more detailed description can be found in the Overview section of Data.Foldable.
For the class laws see the Laws section of Data.Foldable.
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m Source #
Map each element of the structure into a monoid, and combine the
results with (. This fold is right-associative and lazy in the
accumulator. For strict left-associative folds consider <>)foldMap'
instead.
Examples
Basic usage:
>>>foldMap Sum [1, 3, 5]Sum {getSum = 9}
>>>foldMap Product [1, 3, 5]Product {getProduct = 15}
>>>foldMap (replicate 3) [1, 2, 3][1,1,1,2,2,2,3,3,3]
When a Monoid's ( is lazy in its second argument, <>)foldMap can
return a result even from an unbounded structure. For example, lazy
accumulation enables Data.ByteString.Builder to efficiently serialise
large data structures and produce the output incrementally:
>>>import qualified Data.ByteString.Lazy as L>>>import qualified Data.ByteString.Builder as B>>>let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20>>>let lbs = B.toLazyByteString $ foldMap bld [0..]>>>L.take 64 lbs"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
foldr :: (a -> b -> b) -> b -> t a -> b Source #
Right-associative fold of a structure, lazy in the accumulator.
In the case of lists, foldr, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that since the head of the resulting expression is produced by an
application of the operator to the first element of the list, given an
operator lazy in its right argument, foldr can produce a terminating
expression from an unbounded list.
For a general Foldable structure this should be semantically identical
to,
foldr f z =foldrf z .toList
Examples
Basic usage:
>>>foldr (||) False [False, True, False]True
>>>foldr (||) False []False
>>>foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']"foodcba"
Infinite structures
⚠️ Applying foldr to infinite structures usually doesn't terminate.
It may still terminate under one of the following conditions:
- the folding function is short-circuiting
- the folding function is lazy on its second argument
Short-circuiting
( short-circuits on ||)True values, so the following terminates
because there is a True value finitely far from the left side:
>>>foldr (||) False (True : repeat False)True
But the following doesn't terminate:
>>>foldr (||) False (repeat False ++ [True])* Hangs forever *
Laziness in the second argument
Applying foldr to infinite structures terminates when the operator is
lazy in its second argument (the initial accumulator is never used in
this case, and so could be left undefined, but [] is more clear):
>>>take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)[1,4,7,10,13]
foldl :: (b -> a -> b) -> b -> t a -> b Source #
Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.
In the case of lists, foldl, when applied to a binary operator, a
starting value (typically the left-identity of the operator), and a
list, reduces the list using the binary operator, from left to right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. Like all left-associative folds,
foldl will diverge if given an infinite list.
If you want an efficient strict left-fold, you probably want to use
foldl' instead of foldl. The reason for this is that the latter
does not force the inner results (e.g. z `f` x1 in the above
example) before applying them to the operator (e.g. to (`f` x2)).
This results in a thunk chain O(n) elements long, which then must be
evaluated from the outside-in.
For a general Foldable structure this should be semantically identical
to:
foldl f z =foldlf z .toList
Examples
The first example is a strict fold, which in practice is best performed
with foldl'.
>>>foldl (+) 42 [1,2,3,4]52
Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.
>>>foldl (\acc c -> c : acc) "abcd" "efgh""hgfeabcd"
A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:
>>>foldl (\a _ -> a) 0 $ repeat 1* Hangs forever *
WARNING: When it comes to lists, you always want to use either foldl' or foldr instead.
foldl' :: (b -> a -> b) -> b -> t a -> b Source #
Left-associative fold of a structure but with strict application of the operator.
This ensures that each step of the fold is forced to Weak Head Normal
Form before being applied, avoiding the collection of thunks that would
otherwise occur. This is often what you want to strictly reduce a
finite structure to a single strict result (e.g. sum).
For a general Foldable structure this should be semantically identical
to,
foldl' f z =foldl'f z .toList
Since: base-4.6.0.0
foldr1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
Examples
Basic usage:
>>>foldr1 (+) [1..4]10
>>>foldr1 (+) []Exception: Prelude.foldr1: empty list
>>>foldr1 (+) Nothing*** Exception: foldr1: empty structure
>>>foldr1 (-) [1..4]-2
>>>foldr1 (&&) [True, False, True, True]False
>>>foldr1 (||) [False, False, True, True]True
>>>foldr1 (+) [1..]* Hangs forever *
foldl1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
foldl1f =foldl1f .toList
Examples
Basic usage:
>>>foldl1 (+) [1..4]10
>>>foldl1 (+) []*** Exception: Prelude.foldl1: empty list
>>>foldl1 (+) Nothing*** Exception: foldl1: empty structure
>>>foldl1 (-) [1..4]-8
>>>foldl1 (&&) [True, False, True, True]False
>>>foldl1 (||) [False, False, True, True]True
>>>foldl1 (+) [1..]* Hangs forever *
Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.
Examples
Basic usage:
>>>null []True
>>>null [1]False
null is expected to terminate even for infinite structures.
The default implementation terminates provided the structure
is bounded on the left (there is a leftmost element).
>>>null [1..]False
Since: base-4.8.0.0
Returns the size/length of a finite structure as an Int. The
default implementation just counts elements starting with the leftmost.
Instances for structures that can compute the element count faster
than via element-by-element counting, should provide a specialised
implementation.
Examples
Basic usage:
>>>length []0
>>>length ['a', 'b', 'c']3>>>length [1..]* Hangs forever *
Since: base-4.8.0.0
elem :: Eq a => a -> t a -> Bool infix 4 Source #
Does the element occur in the structure?
Note: elem is often used in infix form.
Examples
Basic usage:
>>>3 `elem` []False
>>>3 `elem` [1,2]False
>>>3 `elem` [1,2,3,4,5]True
For infinite structures, the default implementation of elem
terminates if the sought-after value exists at a finite distance
from the left side of the structure:
>>>3 `elem` [1..]True
>>>3 `elem` ([4..] ++ [3])* Hangs forever *
Since: base-4.8.0.0
Instances
| Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m Source # foldMap :: Monoid m => (a -> m) -> Complex a -> m Source # foldMap' :: Monoid m => (a -> m) -> Complex a -> m Source # foldr :: (a -> b -> b) -> b -> Complex a -> b Source # foldr' :: (a -> b -> b) -> b -> Complex a -> b Source # foldl :: (b -> a -> b) -> b -> Complex a -> b Source # foldl' :: (b -> a -> b) -> b -> Complex a -> b Source # foldr1 :: (a -> a -> a) -> Complex a -> a Source # foldl1 :: (a -> a -> a) -> Complex a -> a Source # toList :: Complex a -> [a] Source # null :: Complex a -> Bool Source # length :: Complex a -> Int Source # elem :: Eq a => a -> Complex a -> Bool Source # maximum :: Ord a => Complex a -> a Source # minimum :: Ord a => Complex a -> a Source # | |
| Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
| Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldMap' :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # | |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldMap' :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # | |
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # | |
| Foldable Identity | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m Source # foldMap :: Monoid m => (a -> m) -> Identity a -> m Source # foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source # foldr :: (a -> b -> b) -> b -> Identity a -> b Source # foldr' :: (a -> b -> b) -> b -> Identity a -> b Source # foldl :: (b -> a -> b) -> b -> Identity a -> b Source # foldl' :: (b -> a -> b) -> b -> Identity a -> b Source # foldr1 :: (a -> a -> a) -> Identity a -> a Source # foldl1 :: (a -> a -> a) -> Identity a -> a Source # toList :: Identity a -> [a] Source # null :: Identity a -> Bool Source # length :: Identity a -> Int Source # elem :: Eq a => a -> Identity a -> Bool Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # | |
| Foldable First | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
| Foldable Last | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
| Foldable Down | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Down m -> m Source # foldMap :: Monoid m => (a -> m) -> Down a -> m Source # foldMap' :: Monoid m => (a -> m) -> Down a -> m Source # foldr :: (a -> b -> b) -> b -> Down a -> b Source # foldr' :: (a -> b -> b) -> b -> Down a -> b Source # foldl :: (b -> a -> b) -> b -> Down a -> b Source # foldl' :: (b -> a -> b) -> b -> Down a -> b Source # foldr1 :: (a -> a -> a) -> Down a -> a Source # foldl1 :: (a -> a -> a) -> Down a -> a Source # toList :: Down a -> [a] Source # null :: Down a -> Bool Source # length :: Down a -> Int Source # elem :: Eq a => a -> Down a -> Bool Source # maximum :: Ord a => Down a -> a Source # minimum :: Ord a => Down a -> a Source # | |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # | |
| Foldable Product | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # | |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # | |
| Foldable ZipList | Since: base-4.9.0.0 |
Defined in GHC.Internal.Functor.ZipList Methods fold :: Monoid m => ZipList m -> m Source # foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source # foldr :: (a -> b -> b) -> b -> ZipList a -> b Source # foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source # foldl :: (b -> a -> b) -> b -> ZipList a -> b Source # foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source # foldr1 :: (a -> a -> a) -> ZipList a -> a Source # foldl1 :: (a -> a -> a) -> ZipList a -> a Source # toList :: ZipList a -> [a] Source # null :: ZipList a -> Bool Source # length :: ZipList a -> Int Source # elem :: Eq a => a -> ZipList a -> Bool Source # maximum :: Ord a => ZipList a -> a Source # minimum :: Ord a => ZipList a -> a Source # | |
| Foldable Par1 | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Par1 m -> m Source # foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source # foldr :: (a -> b -> b) -> b -> Par1 a -> b Source # foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source # foldl :: (b -> a -> b) -> b -> Par1 a -> b Source # foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source # foldr1 :: (a -> a -> a) -> Par1 a -> a Source # foldl1 :: (a -> a -> a) -> Par1 a -> a Source # toList :: Par1 a -> [a] Source # null :: Par1 a -> Bool Source # length :: Par1 a -> Int Source # elem :: Eq a => a -> Par1 a -> Bool Source # maximum :: Ord a => Par1 a -> a Source # minimum :: Ord a => Par1 a -> a Source # | |
| Foldable Array | |
Defined in Data.Primitive.Array Methods fold :: Monoid m => Array m -> m Source # foldMap :: Monoid m => (a -> m) -> Array a -> m Source # foldMap' :: Monoid m => (a -> m) -> Array a -> m Source # foldr :: (a -> b -> b) -> b -> Array a -> b Source # foldr' :: (a -> b -> b) -> b -> Array a -> b Source # foldl :: (b -> a -> b) -> b -> Array a -> b Source # foldl' :: (b -> a -> b) -> b -> Array a -> b Source # foldr1 :: (a -> a -> a) -> Array a -> a Source # foldl1 :: (a -> a -> a) -> Array a -> a Source # toList :: Array a -> [a] Source # null :: Array a -> Bool Source # length :: Array a -> Int Source # elem :: Eq a => a -> Array a -> Bool Source # maximum :: Ord a => Array a -> a Source # minimum :: Ord a => Array a -> a Source # | |
| Foldable SmallArray | |
Defined in Data.Primitive.SmallArray Methods fold :: Monoid m => SmallArray m -> m Source # foldMap :: Monoid m => (a -> m) -> SmallArray a -> m Source # foldMap' :: Monoid m => (a -> m) -> SmallArray a -> m Source # foldr :: (a -> b -> b) -> b -> SmallArray a -> b Source # foldr' :: (a -> b -> b) -> b -> SmallArray a -> b Source # foldl :: (b -> a -> b) -> b -> SmallArray a -> b Source # foldl' :: (b -> a -> b) -> b -> SmallArray a -> b Source # foldr1 :: (a -> a -> a) -> SmallArray a -> a Source # foldl1 :: (a -> a -> a) -> SmallArray a -> a Source # toList :: SmallArray a -> [a] Source # null :: SmallArray a -> Bool Source # length :: SmallArray a -> Int Source # elem :: Eq a => a -> SmallArray a -> Bool Source # maximum :: Ord a => SmallArray a -> a Source # minimum :: Ord a => SmallArray a -> a Source # | |
| Foldable TyVarBndr | |
Defined in Language.Haskell.TH.Syntax Methods fold :: Monoid m => TyVarBndr m -> m Source # foldMap :: Monoid m => (a -> m) -> TyVarBndr a -> m Source # foldMap' :: Monoid m => (a -> m) -> TyVarBndr a -> m Source # foldr :: (a -> b -> b) -> b -> TyVarBndr a -> b Source # foldr' :: (a -> b -> b) -> b -> TyVarBndr a -> b Source # foldl :: (b -> a -> b) -> b -> TyVarBndr a -> b Source # foldl' :: (b -> a -> b) -> b -> TyVarBndr a -> b Source # foldr1 :: (a -> a -> a) -> TyVarBndr a -> a Source # foldl1 :: (a -> a -> a) -> TyVarBndr a -> a Source # toList :: TyVarBndr a -> [a] Source # null :: TyVarBndr a -> Bool Source # length :: TyVarBndr a -> Int Source # elem :: Eq a => a -> TyVarBndr a -> Bool Source # maximum :: Ord a => TyVarBndr a -> a Source # minimum :: Ord a => TyVarBndr a -> a Source # | |
| Foldable Vector | |
Defined in Data.Vector Methods fold :: Monoid m => Vector m -> m Source # foldMap :: Monoid m => (a -> m) -> Vector a -> m Source # foldMap' :: Monoid m => (a -> m) -> Vector a -> m Source # foldr :: (a -> b -> b) -> b -> Vector a -> b Source # foldr' :: (a -> b -> b) -> b -> Vector a -> b Source # foldl :: (b -> a -> b) -> b -> Vector a -> b Source # foldl' :: (b -> a -> b) -> b -> Vector a -> b Source # foldr1 :: (a -> a -> a) -> Vector a -> a Source # foldl1 :: (a -> a -> a) -> Vector a -> a Source # toList :: Vector a -> [a] Source # null :: Vector a -> Bool Source # length :: Vector a -> Int Source # elem :: Eq a => a -> Vector a -> Bool Source # maximum :: Ord a => Vector a -> a Source # minimum :: Ord a => Vector a -> a Source # | |
| Foldable Vector | |
Defined in Data.Vector.Strict Methods fold :: Monoid m => Vector m -> m Source # foldMap :: Monoid m => (a -> m) -> Vector a -> m Source # foldMap' :: Monoid m => (a -> m) -> Vector a -> m Source # foldr :: (a -> b -> b) -> b -> Vector a -> b Source # foldr' :: (a -> b -> b) -> b -> Vector a -> b Source # foldl :: (b -> a -> b) -> b -> Vector a -> b Source # foldl' :: (b -> a -> b) -> b -> Vector a -> b Source # foldr1 :: (a -> a -> a) -> Vector a -> a Source # foldl1 :: (a -> a -> a) -> Vector a -> a Source # toList :: Vector a -> [a] Source # null :: Vector a -> Bool Source # length :: Vector a -> Int Source # elem :: Eq a => a -> Vector a -> Bool Source # maximum :: Ord a => Vector a -> a Source # minimum :: Ord a => Vector a -> a Source # | |
| Foldable Maybe | Since: base-2.1 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # | |
| Foldable Solo | Since: base-4.15 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Solo m -> m Source # foldMap :: Monoid m => (a -> m) -> Solo a -> m Source # foldMap' :: Monoid m => (a -> m) -> Solo a -> m Source # foldr :: (a -> b -> b) -> b -> Solo a -> b Source # foldr' :: (a -> b -> b) -> b -> Solo a -> b Source # foldl :: (b -> a -> b) -> b -> Solo a -> b Source # foldl' :: (b -> a -> b) -> b -> Solo a -> b Source # foldr1 :: (a -> a -> a) -> Solo a -> a Source # foldl1 :: (a -> a -> a) -> Solo a -> a Source # toList :: Solo a -> [a] Source # null :: Solo a -> Bool Source # length :: Solo a -> Int Source # elem :: Eq a => a -> Solo a -> Bool Source # maximum :: Ord a => Solo a -> a Source # minimum :: Ord a => Solo a -> a Source # | |
| Foldable [] | Since: base-2.1 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => [m] -> m Source # foldMap :: Monoid m => (a -> m) -> [a] -> m Source # foldMap' :: Monoid m => (a -> m) -> [a] -> m Source # foldr :: (a -> b -> b) -> b -> [a] -> b Source # foldr' :: (a -> b -> b) -> b -> [a] -> b Source # foldl :: (b -> a -> b) -> b -> [a] -> b Source # foldl' :: (b -> a -> b) -> b -> [a] -> b Source # foldr1 :: (a -> a -> a) -> [a] -> a Source # foldl1 :: (a -> a -> a) -> [a] -> a Source # elem :: Eq a => a -> [a] -> Bool Source # maximum :: Ord a => [a] -> a Source # minimum :: Ord a => [a] -> a Source # | |
| Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # | |
| Foldable (Array i) | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> m Source # foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source # foldr :: (a -> b -> b) -> b -> Array i a -> b Source # foldr' :: (a -> b -> b) -> b -> Array i a -> b Source # foldl :: (b -> a -> b) -> b -> Array i a -> b Source # foldl' :: (b -> a -> b) -> b -> Array i a -> b Source # foldr1 :: (a -> a -> a) -> Array i a -> a Source # foldl1 :: (a -> a -> a) -> Array i a -> a Source # toList :: Array i a -> [a] Source # null :: Array i a -> Bool Source # length :: Array i a -> Int Source # elem :: Eq a => a -> Array i a -> Bool Source # maximum :: Ord a => Array i a -> a Source # minimum :: Ord a => Array i a -> a Source # | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # | |
| Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Proxy m -> m Source # foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source # foldr :: (a -> b -> b) -> b -> Proxy a -> b Source # foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source # foldl :: (b -> a -> b) -> b -> Proxy a -> b Source # foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source # foldr1 :: (a -> a -> a) -> Proxy a -> a Source # foldl1 :: (a -> a -> a) -> Proxy a -> a Source # toList :: Proxy a -> [a] Source # null :: Proxy a -> Bool Source # length :: Proxy a -> Int Source # elem :: Eq a => a -> Proxy a -> Bool Source # maximum :: Ord a => Proxy a -> a Source # minimum :: Ord a => Proxy a -> a Source # | |
| Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => U1 m -> m Source # foldMap :: Monoid m => (a -> m) -> U1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source # foldr :: (a -> b -> b) -> b -> U1 a -> b Source # foldr' :: (a -> b -> b) -> b -> U1 a -> b Source # foldl :: (b -> a -> b) -> b -> U1 a -> b Source # foldl' :: (b -> a -> b) -> b -> U1 a -> b Source # foldr1 :: (a -> a -> a) -> U1 a -> a Source # foldl1 :: (a -> a -> a) -> U1 a -> a Source # toList :: U1 a -> [a] Source # length :: U1 a -> Int Source # elem :: Eq a => a -> U1 a -> Bool Source # maximum :: Ord a => U1 a -> a Source # minimum :: Ord a => U1 a -> a Source # | |
| Foldable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UAddr m -> m Source # foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source # foldr :: (a -> b -> b) -> b -> UAddr a -> b Source # foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source # foldl :: (b -> a -> b) -> b -> UAddr a -> b Source # foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source # foldr1 :: (a -> a -> a) -> UAddr a -> a Source # foldl1 :: (a -> a -> a) -> UAddr a -> a Source # toList :: UAddr a -> [a] Source # null :: UAddr a -> Bool Source # length :: UAddr a -> Int Source # elem :: Eq a => a -> UAddr a -> Bool Source # maximum :: Ord a => UAddr a -> a Source # minimum :: Ord a => UAddr a -> a Source # | |
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # | |
| Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # | |
| Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # | |
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # | |
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # | |
| Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => V1 m -> m Source # foldMap :: Monoid m => (a -> m) -> V1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source # foldr :: (a -> b -> b) -> b -> V1 a -> b Source # foldr' :: (a -> b -> b) -> b -> V1 a -> b Source # foldl :: (b -> a -> b) -> b -> V1 a -> b Source # foldl' :: (b -> a -> b) -> b -> V1 a -> b Source # foldr1 :: (a -> a -> a) -> V1 a -> a Source # foldl1 :: (a -> a -> a) -> V1 a -> a Source # toList :: V1 a -> [a] Source # length :: V1 a -> Int Source # elem :: Eq a => a -> V1 a -> Bool Source # maximum :: Ord a => V1 a -> a Source # minimum :: Ord a => V1 a -> a Source # | |
| Foldable f => Foldable (MaybeT f) | |
Defined in Control.Monad.Trans.Maybe Methods fold :: Monoid m => MaybeT f m -> m Source # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldr1 :: (a -> a -> a) -> MaybeT f a -> a Source # foldl1 :: (a -> a -> a) -> MaybeT f a -> a Source # toList :: MaybeT f a -> [a] Source # null :: MaybeT f a -> Bool Source # length :: MaybeT f a -> Int Source # elem :: Eq a => a -> MaybeT f a -> Bool Source # maximum :: Ord a => MaybeT f a -> a Source # minimum :: Ord a => MaybeT f a -> a Source # | |
| Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (a, m) -> m Source # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # toList :: (a, a0) -> [a0] Source # null :: (a, a0) -> Bool Source # length :: (a, a0) -> Int Source # elem :: Eq a0 => a0 -> (a, a0) -> Bool Source # maximum :: Ord a0 => (a, a0) -> a0 Source # minimum :: Ord a0 => (a, a0) -> a0 Source # | |
| Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 Source # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldr :: (a -> b -> b) -> b -> Const m a -> b Source # foldr' :: (a -> b -> b) -> b -> Const m a -> b Source # foldl :: (b -> a -> b) -> b -> Const m a -> b Source # foldl' :: (b -> a -> b) -> b -> Const m a -> b Source # foldr1 :: (a -> a -> a) -> Const m a -> a Source # foldl1 :: (a -> a -> a) -> Const m a -> a Source # toList :: Const m a -> [a] Source # null :: Const m a -> Bool Source # length :: Const m a -> Int Source # elem :: Eq a => a -> Const m a -> Bool Source # maximum :: Ord a => Const m a -> a Source # minimum :: Ord a => Const m a -> a Source # | |
| Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source # foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source # foldr :: (a -> b -> b) -> b -> Ap f a -> b Source # foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source # foldl :: (b -> a -> b) -> b -> Ap f a -> b Source # foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source # foldr1 :: (a -> a -> a) -> Ap f a -> a Source # foldl1 :: (a -> a -> a) -> Ap f a -> a Source # toList :: Ap f a -> [a] Source # null :: Ap f a -> Bool Source # length :: Ap f a -> Int Source # elem :: Eq a => a -> Ap f a -> Bool Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # | |
| Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Alt f m -> m Source # foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source # foldr :: (a -> b -> b) -> b -> Alt f a -> b Source # foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source # foldl :: (b -> a -> b) -> b -> Alt f a -> b Source # foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source # foldr1 :: (a -> a -> a) -> Alt f a -> a Source # foldl1 :: (a -> a -> a) -> Alt f a -> a Source # toList :: Alt f a -> [a] Source # null :: Alt f a -> Bool Source # length :: Alt f a -> Int Source # elem :: Eq a => a -> Alt f a -> Bool Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # | |
| Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m Source # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source # foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source # toList :: Rec1 f a -> [a] Source # null :: Rec1 f a -> Bool Source # length :: Rec1 f a -> Int Source # elem :: Eq a => a -> Rec1 f a -> Bool Source # maximum :: Ord a => Rec1 f a -> a Source # minimum :: Ord a => Rec1 f a -> a Source # | |
| Foldable f => Foldable (ExceptT e f) | |
Defined in Control.Monad.Trans.Except Methods fold :: Monoid m => ExceptT e f m -> m Source # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a Source # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a Source # toList :: ExceptT e f a -> [a] Source # null :: ExceptT e f a -> Bool Source # length :: ExceptT e f a -> Int Source # elem :: Eq a => a -> ExceptT e f a -> Bool Source # maximum :: Ord a => ExceptT e f a -> a Source # minimum :: Ord a => ExceptT e f a -> a Source # | |
| Foldable f => Foldable (IdentityT f) | |
Defined in Control.Monad.Trans.Identity Methods fold :: Monoid m => IdentityT f m -> m Source # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldr1 :: (a -> a -> a) -> IdentityT f a -> a Source # foldl1 :: (a -> a -> a) -> IdentityT f a -> a Source # toList :: IdentityT f a -> [a] Source # null :: IdentityT f a -> Bool Source # length :: IdentityT f a -> Int Source # elem :: Eq a => a -> IdentityT f a -> Bool Source # maximum :: Ord a => IdentityT f a -> a Source # minimum :: Ord a => IdentityT f a -> a Source # | |
| Foldable f => Foldable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # | |
| Foldable f => Foldable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Strict Methods fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Product f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m Source # foldr :: (a -> b -> b) -> b -> Product f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Product f g a -> b Source # foldl :: (b -> a -> b) -> b -> Product f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Product f g a -> b Source # foldr1 :: (a -> a -> a) -> Product f g a -> a Source # foldl1 :: (a -> a -> a) -> Product f g a -> a Source # toList :: Product f g a -> [a] Source # null :: Product f g a -> Bool Source # length :: Product f g a -> Int Source # elem :: Eq a => a -> Product f g a -> Bool Source # maximum :: Ord a => Product f g a -> a Source # minimum :: Ord a => Product f g a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldr :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldl :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldr1 :: (a -> a -> a) -> Sum f g a -> a Source # foldl1 :: (a -> a -> a) -> Sum f g a -> a Source # toList :: Sum f g a -> [a] Source # null :: Sum f g a -> Bool Source # length :: Sum f g a -> Int Source # elem :: Eq a => a -> Sum f g a -> Bool Source # maximum :: Ord a => Sum f g a -> a Source # minimum :: Ord a => Sum f g a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source # toList :: (f :*: g) a -> [a] Source # null :: (f :*: g) a -> Bool Source # length :: (f :*: g) a -> Int Source # elem :: Eq a => a -> (f :*: g) a -> Bool Source # maximum :: Ord a => (f :*: g) a -> a Source # minimum :: Ord a => (f :*: g) a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source # toList :: (f :+: g) a -> [a] Source # null :: (f :+: g) a -> Bool Source # length :: (f :+: g) a -> Int Source # elem :: Eq a => a -> (f :+: g) a -> Bool Source # maximum :: Ord a => (f :+: g) a -> a Source # minimum :: Ord a => (f :+: g) a -> a Source # | |
| Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => K1 i c m -> m Source # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldr1 :: (a -> a -> a) -> K1 i c a -> a Source # foldl1 :: (a -> a -> a) -> K1 i c a -> a Source # toList :: K1 i c a -> [a] Source # null :: K1 i c a -> Bool Source # length :: K1 i c a -> Int Source # elem :: Eq a => a -> K1 i c a -> Bool Source # maximum :: Ord a => K1 i c a -> a Source # minimum :: Ord a => K1 i c a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldr1 :: (a -> a -> a) -> Compose f g a -> a Source # foldl1 :: (a -> a -> a) -> Compose f g a -> a Source # toList :: Compose f g a -> [a] Source # null :: Compose f g a -> Bool Source # length :: Compose f g a -> Int Source # elem :: Eq a => a -> Compose f g a -> Bool Source # maximum :: Ord a => Compose f g a -> a Source # minimum :: Ord a => Compose f g a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source # toList :: (f :.: g) a -> [a] Source # null :: (f :.: g) a -> Bool Source # length :: (f :.: g) a -> Int Source # elem :: Eq a => a -> (f :.: g) a -> Bool Source # maximum :: Ord a => (f :.: g) a -> a Source # minimum :: Ord a => (f :.: g) a -> a Source # | |
| Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m Source # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source # foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source # toList :: M1 i c f a -> [a] Source # null :: M1 i c f a -> Bool Source # length :: M1 i c f a -> Int Source # elem :: Eq a => a -> M1 i c f a -> Bool Source # maximum :: Ord a => M1 i c f a -> a Source # minimum :: Ord a => M1 i c f a -> a Source # | |
seq :: a -> b -> b infixr 0 Source #
The value of seq a ba is bottom, and
otherwise equal to b. In other words, it evaluates the first
argument a to weak head normal form (WHNF). seq is usually
introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a ba will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
concat :: Foldable t => t [a] -> [a] Source #
The concatenation of all the elements of a container of lists.
Examples
Basic usage:
>>>concat (Just [1, 2, 3])[1,2,3]
>>>concat (Left 42)[]
>>>concat [[1, 2, 3], [4, 5], [6], []][1,2,3,4,5,6]
filter :: (a -> Bool) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). filter, applied to a predicate and a list, returns
the list of those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
Examples
>>>filter odd [1, 2, 3][1,3]
>>>filter (\l -> length l > 3) ["Hello", ", ", "World", "!"]["Hello","World"]
>>>filter (/= 3) [1, 2, 3, 4, 3, 2, 1][1,2,4,2,1]
zip :: [a] -> [b] -> [(a, b)] Source #
\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of
corresponding pairs.
zip is right-lazy:
>>>zip [] undefined[]>>>zip undefined []*** Exception: Prelude.undefined ...
zip is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
Examples
>>>zip [1, 2, 3] ['a', 'b', 'c'][(1,'a'),(2,'b'),(3,'c')]
If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:
>>>zip [1] ['a', 'b'][(1,'a')]
>>>zip [1, 2] ['a'][(1,'a')]
>>>zip [] [1..][]
>>>zip [1..] [][]
print :: Show a => a -> IO () Source #
The print function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class Show; print
converts values to strings for output using the show operation and
adds a newline.
For example, a program to print the first 20 integers and their powers of 2 could be written as:
main = print ([(n, 2^n) | n <- [0..19]])
map :: (a -> b) -> [a] -> [b] Source #
\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to
each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
this means that map id == id
Examples
>>>map (+1) [1, 2, 3][2,3,4]
>>>map id [1, 2, 3][1,2,3]
>>>map (\n -> 3 * n + 1) [1, 2, 3][4,7,10]
($) :: (a -> b) -> a -> b infixr 0 Source #
($)
Applying ($)f and an argument x gives the same result as applying f to x directly. The definition is akin to this:
($) :: (a -> b) -> a -> b ($) f x = f x
This is ida -> a to (a -> b) -> (a -> b) which by the associativity of (->)
is the same as (a -> b) -> a -> b.
On the face of it, this may appear pointless! But it's actually one of the most useful and important operators in Haskell.
The order of operations is very different between ($) and normal function application. Normal function application has precedence 10 - higher than any operator - and associates to the left. So these two definitions are equivalent:
expr = min 5 1 + 5 expr = ((min 5) 1) + 5
($) has precedence 0 (the lowest) and associates to the right, so these are equivalent:
expr = min 5 $ 1 + 5 expr = (min 5) (1 + 5)
Examples
A common use cases of ($) is to avoid parentheses in complex expressions.
For example, instead of using nested parentheses in the following Haskell function:
-- | Sum numbers in a string: strSum "100 5 -7" == 98 strSum ::String->IntstrSum s =sum(mapMaybereadMaybe(wordss))
we can deploy the function application operator:
-- | Sum numbers in a string: strSum "100 5 -7" == 98 strSum ::String->IntstrSum s =sum$mapMaybereadMaybe$wordss
($) is also used as a section (a partially applied operator), in order to indicate that we wish to apply some yet-unspecified function to a given value. For example, to apply the argument 5 to a list of functions:
applyFive :: [Int] applyFive = map ($ 5) [(+1), (2^)] >>> [6, 32]
Technical Remark (Representation Polymorphism)
($) is fully representation-polymorphic. This allows it to also be used with arguments of unlifted and even unboxed kinds, such as unboxed integers:
fastMod :: Int -> Int -> Int fastMod (I# x) (I# m) = I# $ remInt# x m
Basic numeric class.
The Haskell Report defines no laws for Num. However, ( and +)( are
customarily expected to define a ring and have the following properties:*)
- Associativity of
(+) (x + y) + z=x + (y + z)- Commutativity of
(+) x + y=y + xfromInteger0x + fromInteger 0=xnegategives the additive inversex + negate x=fromInteger 0- Associativity of
(*) (x * y) * z=x * (y * z)fromInteger1x * fromInteger 1=xandfromInteger 1 * x=x- Distributivity of
(with respect to*)(+) a * (b + c)=(a * b) + (a * c)and(b + c) * a=(b * a) + (c * a)- Coherence with
toInteger - if the type also implements
Integral, thenfromIntegeris a left inverse fortoInteger, i.e.fromInteger (toInteger i) == i
Note that it isn't customarily expected that a type instance of both Num
and Ord implement an ordered ring. Indeed, in base only Integer and
Rational do.
Methods
fromInteger :: Integer -> a Source #
Conversion from an Integer.
An integer literal represents the application of the function
fromInteger to the appropriate value of type Integer,
so such literals have type (.Num a) => a
Instances
| Num ExactPi | |
Defined in Data.ExactPi | |
| Num CBool | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CChar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CClock | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CDouble | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CFloat | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CInt | |
| Num CIntMax | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CIntPtr | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CLLong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CLong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CPtrdiff | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # (-) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # (*) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # negate :: CPtrdiff -> CPtrdiff Source # abs :: CPtrdiff -> CPtrdiff Source # signum :: CPtrdiff -> CPtrdiff Source # fromInteger :: Integer -> CPtrdiff Source # | |
| Num CSChar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # (-) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # (*) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # negate :: CSUSeconds -> CSUSeconds Source # abs :: CSUSeconds -> CSUSeconds Source # signum :: CSUSeconds -> CSUSeconds Source # fromInteger :: Integer -> CSUSeconds Source # | |
| Num CShort | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # (-) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # (*) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # negate :: CSigAtomic -> CSigAtomic Source # abs :: CSigAtomic -> CSigAtomic Source # signum :: CSigAtomic -> CSigAtomic Source # fromInteger :: Integer -> CSigAtomic Source # | |
| Num CSize | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CTime | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUChar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUInt | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUIntMax | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUIntMax -> CUIntMax -> CUIntMax Source # (-) :: CUIntMax -> CUIntMax -> CUIntMax Source # (*) :: CUIntMax -> CUIntMax -> CUIntMax Source # negate :: CUIntMax -> CUIntMax Source # abs :: CUIntMax -> CUIntMax Source # signum :: CUIntMax -> CUIntMax Source # fromInteger :: Integer -> CUIntMax Source # | |
| Num CUIntPtr | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # (-) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # (*) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # negate :: CUIntPtr -> CUIntPtr Source # abs :: CUIntPtr -> CUIntPtr Source # signum :: CUIntPtr -> CUIntPtr Source # fromInteger :: Integer -> CUIntPtr Source # | |
| Num CULLong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CULong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUSeconds -> CUSeconds -> CUSeconds Source # (-) :: CUSeconds -> CUSeconds -> CUSeconds Source # (*) :: CUSeconds -> CUSeconds -> CUSeconds Source # negate :: CUSeconds -> CUSeconds Source # abs :: CUSeconds -> CUSeconds Source # signum :: CUSeconds -> CUSeconds Source # fromInteger :: Integer -> CUSeconds Source # | |
| Num CUShort | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CWchar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num Int16 | Since: base-2.1 |
| Num Int32 | Since: base-2.1 |
| Num Int64 | Since: base-2.1 |
| Num Int8 | Since: base-2.1 |
| Num Word16 | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Num Word32 | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Num Word64 | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Num Word8 | Since: base-2.1 |
| Num Size | |
| Num Integer | Since: base-2.1 |
Defined in GHC.Internal.Num | |
| Num Natural | Note that Since: base-4.8.0.0 |
Defined in GHC.Internal.Num | |
| Num Double | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:
Since: base-2.1 |
Defined in GHC.Internal.Float | |
| Num Float | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:
Since: base-2.1 |
| Num Int | Since: base-2.1 |
| Num Word | Since: base-2.1 |
| RealFloat a => Num (Complex a) | Since: base-2.1 |
Defined in Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a Source # (-) :: Complex a -> Complex a -> Complex a Source # (*) :: Complex a -> Complex a -> Complex a Source # negate :: Complex a -> Complex a Source # abs :: Complex a -> Complex a Source # signum :: Complex a -> Complex a Source # fromInteger :: Integer -> Complex a Source # | |
| Num a => Num (Max a) | Since: base-4.9.0.0 |
| Num a => Num (Min a) | Since: base-4.9.0.0 |
| Num a => Num (DynQuantity a) Source # | |
Defined in Numeric.Units.Dimensional.Dynamic Methods (+) :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # (-) :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # (*) :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # negate :: DynQuantity a -> DynQuantity a Source # abs :: DynQuantity a -> DynQuantity a Source # signum :: DynQuantity a -> DynQuantity a Source # fromInteger :: Integer -> DynQuantity a Source # | |
| Num a => Num (Identity a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a Source # (-) :: Identity a -> Identity a -> Identity a Source # (*) :: Identity a -> Identity a -> Identity a Source # negate :: Identity a -> Identity a Source # abs :: Identity a -> Identity a Source # signum :: Identity a -> Identity a Source # fromInteger :: Integer -> Identity a Source # | |
| Num a => Num (Down a) | Since: base-4.11.0.0 |
Defined in GHC.Internal.Data.Ord | |
| Num a => Num (Product a) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source # | |
| Num a => Num (Sum a) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Integral a => Num (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Internal.Real | |
| HasResolution a => Num (Fixed a) | Multiplication is not associative or distributive:
Since: base-2.1 |
Defined in Data.Fixed | |
| Num a => Num (Op a b) | |
Defined in Data.Functor.Contravariant | |
| Num a => Num (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b Source # (-) :: Const a b -> Const a b -> Const a b Source # (*) :: Const a b -> Const a b -> Const a b Source # negate :: Const a b -> Const a b Source # abs :: Const a b -> Const a b Source # signum :: Const a b -> Const a b Source # fromInteger :: Integer -> Const a b Source # | |
| (Applicative f, Num a) => Num (Ap f a) | Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Monoid | |
| Num (f a) => Num (Alt f a) | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Num (f (g a)) => Num (Compose f g a) | Since: base-4.19.0.0 |
Defined in Data.Functor.Compose Methods (+) :: Compose f g a -> Compose f g a -> Compose f g a Source # (-) :: Compose f g a -> Compose f g a -> Compose f g a Source # (*) :: Compose f g a -> Compose f g a -> Compose f g a Source # negate :: Compose f g a -> Compose f g a Source # abs :: Compose f g a -> Compose f g a Source # signum :: Compose f g a -> Compose f g a Source # fromInteger :: Integer -> Compose f g a Source # | |
class Num a => Fractional a where Source #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, ( and
+)( are customarily expected to define a division ring and have the
following properties:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1- Totality of
toRational toRationalis total- Coherence with
toRational - if the type also implements
Real, thenfromRationalis a left inverse fortoRational, i.e.fromRational (toRational i) = i
Note that it isn't customarily expected that a type instance of
Fractional implement a field. However, all instances in base do.
Methods
fromRational :: Rational -> a Source #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional ExactPi | |
| Fractional CDouble | |
| Fractional CFloat | |
| Fractional Double | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.
Since: base-2.1 |
| Fractional Float | This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.
Since: base-2.1 |
| RealFloat a => Fractional (Complex a) | Since: base-2.1 |
| Fractional a => Fractional (DynQuantity a) Source # | |
Defined in Numeric.Units.Dimensional.Dynamic Methods (/) :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # recip :: DynQuantity a -> DynQuantity a Source # fromRational :: Rational -> DynQuantity a Source # | |
| Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
| Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
| Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
| HasResolution a => Fractional (Fixed a) | Since: base-2.1 |
| Fractional a => Fractional (Op a b) | |
| Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
| Fractional (f (g a)) => Fractional (Compose f g a) | Since: base-4.20.0.0 |
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum from 0 through n-1.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum,
the following should hold:
- The calls
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBoundMethods
Successor of a value. For numeric types, succ adds 1.
Predecessor of a value. For numeric types, pred subtracts 1.
Convert from an Int.
Convert to an Int.
It is implementation-dependent what fromEnum returns when
applied to a value that is too large to fit in an Int.
Used in Haskell's translation of [n..] with [n..] = enumFrom n,
a possible implementation being enumFrom n = n : enumFrom (succ n).
Examples
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] Source #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n', a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n'),
worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
Examples
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] Source #
Used in Haskell's translation of [n..m] with
[n..m] = enumFromTo n m, a possible implementation being
enumFromTo n m
| n <= m = n : enumFromTo (succ n) m
| otherwise = []
Examples
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] Source #
Used in Haskell's translation of [n,n'..m] with
[n,n'..m] = enumFromThenTo n n' m, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m,
x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
Examples
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
| Enum Extension | |
Defined in GHC.LanguageExtensions.Type Methods succ :: Extension -> Extension Source # pred :: Extension -> Extension Source # toEnum :: Int -> Extension Source # fromEnum :: Extension -> Int Source # enumFrom :: Extension -> [Extension] Source # enumFromThen :: Extension -> Extension -> [Extension] Source # enumFromTo :: Extension -> Extension -> [Extension] Source # enumFromThenTo :: Extension -> Extension -> Extension -> [Extension] Source # | |
| Enum CBool | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CBool -> CBool Source # pred :: CBool -> CBool Source # toEnum :: Int -> CBool Source # fromEnum :: CBool -> Int Source # enumFrom :: CBool -> [CBool] Source # enumFromThen :: CBool -> CBool -> [CBool] Source # enumFromTo :: CBool -> CBool -> [CBool] Source # enumFromThenTo :: CBool -> CBool -> CBool -> [CBool] Source # | |
| Enum CChar | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CChar -> CChar Source # pred :: CChar -> CChar Source # toEnum :: Int -> CChar Source # fromEnum :: CChar -> Int Source # enumFrom :: CChar -> [CChar] Source # enumFromThen :: CChar -> CChar -> [CChar] Source # enumFromTo :: CChar -> CChar -> [CChar] Source # enumFromThenTo :: CChar -> CChar -> CChar -> [CChar] Source # | |
| Enum CClock | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CClock -> CClock Source # pred :: CClock -> CClock Source # toEnum :: Int -> CClock Source # fromEnum :: CClock -> Int Source # enumFrom :: CClock -> [CClock] Source # enumFromThen :: CClock -> CClock -> [CClock] Source # enumFromTo :: CClock -> CClock -> [CClock] Source # enumFromThenTo :: CClock -> CClock -> CClock -> [CClock] Source # | |
| Enum CDouble | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CDouble -> CDouble Source # pred :: CDouble -> CDouble Source # toEnum :: Int -> CDouble Source # fromEnum :: CDouble -> Int Source # enumFrom :: CDouble -> [CDouble] Source # enumFromThen :: CDouble -> CDouble -> [CDouble] Source # enumFromTo :: CDouble -> CDouble -> [CDouble] Source # enumFromThenTo :: CDouble -> CDouble -> CDouble -> [CDouble] Source # | |
| Enum CFloat | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CFloat -> CFloat Source # pred :: CFloat -> CFloat Source # toEnum :: Int -> CFloat Source # fromEnum :: CFloat -> Int Source # enumFrom :: CFloat -> [CFloat] Source # enumFromThen :: CFloat -> CFloat -> [CFloat] Source # enumFromTo :: CFloat -> CFloat -> [CFloat] Source # enumFromThenTo :: CFloat -> CFloat -> CFloat -> [CFloat] Source # | |
| Enum CInt | |
| Enum CIntMax | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CIntMax -> CIntMax Source # pred :: CIntMax -> CIntMax Source # toEnum :: Int -> CIntMax Source # fromEnum :: CIntMax -> Int Source # enumFrom :: CIntMax -> [CIntMax] Source # enumFromThen :: CIntMax -> CIntMax -> [CIntMax] Source # enumFromTo :: CIntMax -> CIntMax -> [CIntMax] Source # enumFromThenTo :: CIntMax -> CIntMax -> CIntMax -> [CIntMax] Source # | |
| Enum CIntPtr | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CIntPtr -> CIntPtr Source # pred :: CIntPtr -> CIntPtr Source # toEnum :: Int -> CIntPtr Source # fromEnum :: CIntPtr -> Int Source # enumFrom :: CIntPtr -> [CIntPtr] Source # enumFromThen :: CIntPtr -> CIntPtr -> [CIntPtr] Source # enumFromTo :: CIntPtr -> CIntPtr -> [CIntPtr] Source # enumFromThenTo :: CIntPtr -> CIntPtr -> CIntPtr -> [CIntPtr] Source # | |
| Enum CLLong | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CLLong -> CLLong Source # pred :: CLLong -> CLLong Source # toEnum :: Int -> CLLong Source # fromEnum :: CLLong -> Int Source # enumFrom :: CLLong -> [CLLong] Source # enumFromThen :: CLLong -> CLLong -> [CLLong] Source # enumFromTo :: CLLong -> CLLong -> [CLLong] Source # enumFromThenTo :: CLLong -> CLLong -> CLLong -> [CLLong] Source # | |
| Enum CLong | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CLong -> CLong Source # pred :: CLong -> CLong Source # toEnum :: Int -> CLong Source # fromEnum :: CLong -> Int Source # enumFrom :: CLong -> [CLong] Source # enumFromThen :: CLong -> CLong -> [CLong] Source # enumFromTo :: CLong -> CLong -> [CLong] Source # enumFromThenTo :: CLong -> CLong -> CLong -> [CLong] Source # | |
| Enum CPtrdiff | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CPtrdiff -> CPtrdiff Source # pred :: CPtrdiff -> CPtrdiff Source # toEnum :: Int -> CPtrdiff Source # fromEnum :: CPtrdiff -> Int Source # enumFrom :: CPtrdiff -> [CPtrdiff] Source # enumFromThen :: CPtrdiff -> CPtrdiff -> [CPtrdiff] Source # enumFromTo :: CPtrdiff -> CPtrdiff -> [CPtrdiff] Source # enumFromThenTo :: CPtrdiff -> CPtrdiff -> CPtrdiff -> [CPtrdiff] Source # | |
| Enum CSChar | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CSChar -> CSChar Source # pred :: CSChar -> CSChar Source # toEnum :: Int -> CSChar Source # fromEnum :: CSChar -> Int Source # enumFrom :: CSChar -> [CSChar] Source # enumFromThen :: CSChar -> CSChar -> [CSChar] Source # enumFromTo :: CSChar -> CSChar -> [CSChar] Source # enumFromThenTo :: CSChar -> CSChar -> CSChar -> [CSChar] Source # | |
| Enum CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CSUSeconds -> CSUSeconds Source # pred :: CSUSeconds -> CSUSeconds Source # toEnum :: Int -> CSUSeconds Source # fromEnum :: CSUSeconds -> Int Source # enumFrom :: CSUSeconds -> [CSUSeconds] Source # enumFromThen :: CSUSeconds -> CSUSeconds -> [CSUSeconds] Source # enumFromTo :: CSUSeconds -> CSUSeconds -> [CSUSeconds] Source # enumFromThenTo :: CSUSeconds -> CSUSeconds -> CSUSeconds -> [CSUSeconds] Source # | |
| Enum CShort | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CShort -> CShort Source # pred :: CShort -> CShort Source # toEnum :: Int -> CShort Source # fromEnum :: CShort -> Int Source # enumFrom :: CShort -> [CShort] Source # enumFromThen :: CShort -> CShort -> [CShort] Source # enumFromTo :: CShort -> CShort -> [CShort] Source # enumFromThenTo :: CShort -> CShort -> CShort -> [CShort] Source # | |
| Enum CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CSigAtomic -> CSigAtomic Source # pred :: CSigAtomic -> CSigAtomic Source # toEnum :: Int -> CSigAtomic Source # fromEnum :: CSigAtomic -> Int Source # enumFrom :: CSigAtomic -> [CSigAtomic] Source # enumFromThen :: CSigAtomic -> CSigAtomic -> [CSigAtomic] Source # enumFromTo :: CSigAtomic -> CSigAtomic -> [CSigAtomic] Source # enumFromThenTo :: CSigAtomic -> CSigAtomic -> CSigAtomic -> [CSigAtomic] Source # | |
| Enum CSize | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CSize -> CSize Source # pred :: CSize -> CSize Source # toEnum :: Int -> CSize Source # fromEnum :: CSize -> Int Source # enumFrom :: CSize -> [CSize] Source # enumFromThen :: CSize -> CSize -> [CSize] Source # enumFromTo :: CSize -> CSize -> [CSize] Source # enumFromThenTo :: CSize -> CSize -> CSize -> [CSize] Source # | |
| Enum CTime | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CTime -> CTime Source # pred :: CTime -> CTime Source # toEnum :: Int -> CTime Source # fromEnum :: CTime -> Int Source # enumFrom :: CTime -> [CTime] Source # enumFromThen :: CTime -> CTime -> [CTime] Source # enumFromTo :: CTime -> CTime -> [CTime] Source # enumFromThenTo :: CTime -> CTime -> CTime -> [CTime] Source # | |
| Enum CUChar | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CUChar -> CUChar Source # pred :: CUChar -> CUChar Source # toEnum :: Int -> CUChar Source # fromEnum :: CUChar -> Int Source # enumFrom :: CUChar -> [CUChar] Source # enumFromThen :: CUChar -> CUChar -> [CUChar] Source # enumFromTo :: CUChar -> CUChar -> [CUChar] Source # enumFromThenTo :: CUChar -> CUChar -> CUChar -> [CUChar] Source # | |
| Enum CUInt | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CUInt -> CUInt Source # pred :: CUInt -> CUInt Source # toEnum :: Int -> CUInt Source # fromEnum :: CUInt -> Int Source # enumFrom :: CUInt -> [CUInt] Source # enumFromThen :: CUInt -> CUInt -> [CUInt] Source # enumFromTo :: CUInt -> CUInt -> [CUInt] Source # enumFromThenTo :: CUInt -> CUInt -> CUInt -> [CUInt] Source # | |
| Enum CUIntMax | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CUIntMax -> CUIntMax Source # pred :: CUIntMax -> CUIntMax Source # toEnum :: Int -> CUIntMax Source # fromEnum :: CUIntMax -> Int Source # enumFrom :: CUIntMax -> [CUIntMax] Source # enumFromThen :: CUIntMax -> CUIntMax -> [CUIntMax] Source # enumFromTo :: CUIntMax -> CUIntMax -> [CUIntMax] Source # enumFromThenTo :: CUIntMax -> CUIntMax -> CUIntMax -> [CUIntMax] Source # | |
| Enum CUIntPtr | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CUIntPtr -> CUIntPtr Source # pred :: CUIntPtr -> CUIntPtr Source # toEnum :: Int -> CUIntPtr Source # fromEnum :: CUIntPtr -> Int Source # enumFrom :: CUIntPtr -> [CUIntPtr] Source # enumFromThen :: CUIntPtr -> CUIntPtr -> [CUIntPtr] Source # enumFromTo :: CUIntPtr -> CUIntPtr -> [CUIntPtr] Source # enumFromThenTo :: CUIntPtr -> CUIntPtr -> CUIntPtr -> [CUIntPtr] Source # | |
| Enum CULLong | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CULLong -> CULLong Source # pred :: CULLong -> CULLong Source # toEnum :: Int -> CULLong Source # fromEnum :: CULLong -> Int Source # enumFrom :: CULLong -> [CULLong] Source # enumFromThen :: CULLong -> CULLong -> [CULLong] Source # enumFromTo :: CULLong -> CULLong -> [CULLong] Source # enumFromThenTo :: CULLong -> CULLong -> CULLong -> [CULLong] Source # | |
| Enum CULong | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CULong -> CULong Source # pred :: CULong -> CULong Source # toEnum :: Int -> CULong Source # fromEnum :: CULong -> Int Source # enumFrom :: CULong -> [CULong] Source # enumFromThen :: CULong -> CULong -> [CULong] Source # enumFromTo :: CULong -> CULong -> [CULong] Source # enumFromThenTo :: CULong -> CULong -> CULong -> [CULong] Source # | |
| Enum CUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CUSeconds -> CUSeconds Source # pred :: CUSeconds -> CUSeconds Source # toEnum :: Int -> CUSeconds Source # fromEnum :: CUSeconds -> Int Source # enumFrom :: CUSeconds -> [CUSeconds] Source # enumFromThen :: CUSeconds -> CUSeconds -> [CUSeconds] Source # enumFromTo :: CUSeconds -> CUSeconds -> [CUSeconds] Source # enumFromThenTo :: CUSeconds -> CUSeconds -> CUSeconds -> [CUSeconds] Source # | |
| Enum CUShort | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CUShort -> CUShort Source # pred :: CUShort -> CUShort Source # toEnum :: Int -> CUShort Source # fromEnum :: CUShort -> Int Source # enumFrom :: CUShort -> [CUShort] Source # enumFromThen :: CUShort -> CUShort -> [CUShort] Source # enumFromTo :: CUShort -> CUShort -> [CUShort] Source # enumFromThenTo :: CUShort -> CUShort -> CUShort -> [CUShort] Source # | |
| Enum CWchar | |
Defined in GHC.Internal.Foreign.C.Types Methods succ :: CWchar -> CWchar Source # pred :: CWchar -> CWchar Source # toEnum :: Int -> CWchar Source # fromEnum :: CWchar -> Int Source # enumFrom :: CWchar -> [CWchar] Source # enumFromThen :: CWchar -> CWchar -> [CWchar] Source # enumFromTo :: CWchar -> CWchar -> [CWchar] Source # enumFromThenTo :: CWchar -> CWchar -> CWchar -> [CWchar] Source # | |
| Enum Associativity | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods succ :: Associativity -> Associativity Source # pred :: Associativity -> Associativity Source # toEnum :: Int -> Associativity Source # fromEnum :: Associativity -> Int Source # enumFrom :: Associativity -> [Associativity] Source # enumFromThen :: Associativity -> Associativity -> [Associativity] Source # enumFromTo :: Associativity -> Associativity -> [Associativity] Source # enumFromThenTo :: Associativity -> Associativity -> Associativity -> [Associativity] Source # | |
| Enum DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods succ :: DecidedStrictness -> DecidedStrictness Source # pred :: DecidedStrictness -> DecidedStrictness Source # toEnum :: Int -> DecidedStrictness Source # fromEnum :: DecidedStrictness -> Int Source # enumFrom :: DecidedStrictness -> [DecidedStrictness] Source # enumFromThen :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] Source # enumFromTo :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] Source # enumFromThenTo :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] Source # | |
| Enum SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods succ :: SourceStrictness -> SourceStrictness Source # pred :: SourceStrictness -> SourceStrictness Source # toEnum :: Int -> SourceStrictness Source # fromEnum :: SourceStrictness -> Int Source # enumFrom :: SourceStrictness -> [SourceStrictness] Source # enumFromThen :: SourceStrictness -> SourceStrictness -> [SourceStrictness] Source # enumFromTo :: SourceStrictness -> SourceStrictness -> [SourceStrictness] Source # enumFromThenTo :: SourceStrictness -> SourceStrictness -> SourceStrictness -> [SourceStrictness] Source # | |
| Enum SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods succ :: SourceUnpackedness -> SourceUnpackedness Source # pred :: SourceUnpackedness -> SourceUnpackedness Source # toEnum :: Int -> SourceUnpackedness Source # fromEnum :: SourceUnpackedness -> Int Source # enumFrom :: SourceUnpackedness -> [SourceUnpackedness] Source # enumFromThen :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] Source # enumFromTo :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] Source # enumFromThenTo :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] Source # | |
| Enum Int16 | Since: base-2.1 |
Defined in GHC.Internal.Int Methods succ :: Int16 -> Int16 Source # pred :: Int16 -> Int16 Source # toEnum :: Int -> Int16 Source # fromEnum :: Int16 -> Int Source # enumFrom :: Int16 -> [Int16] Source # enumFromThen :: Int16 -> Int16 -> [Int16] Source # enumFromTo :: Int16 -> Int16 -> [Int16] Source # enumFromThenTo :: Int16 -> Int16 -> Int16 -> [Int16] Source # | |
| Enum Int32 | Since: base-2.1 |
Defined in GHC.Internal.Int Methods succ :: Int32 -> Int32 Source # pred :: Int32 -> Int32 Source # toEnum :: Int -> Int32 Source # fromEnum :: Int32 -> Int Source # enumFrom :: Int32 -> [Int32] Source # enumFromThen :: Int32 -> Int32 -> [Int32] Source # enumFromTo :: Int32 -> Int32 -> [Int32] Source # enumFromThenTo :: Int32 -> Int32 -> Int32 -> [Int32] Source # | |
| Enum Int64 | Since: base-2.1 |
Defined in GHC.Internal.Int Methods succ :: Int64 -> Int64 Source # pred :: Int64 -> Int64 Source # toEnum :: Int -> Int64 Source # fromEnum :: Int64 -> Int Source # enumFrom :: Int64 -> [Int64] Source # enumFromThen :: Int64 -> Int64 -> [Int64] Source # enumFromTo :: Int64 -> Int64 -> [Int64] Source # enumFromThenTo :: Int64 -> Int64 -> Int64 -> [Int64] Source # | |
| Enum Int8 | Since: base-2.1 |
| Enum DoCostCentres | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags Methods succ :: DoCostCentres -> DoCostCentres Source # pred :: DoCostCentres -> DoCostCentres Source # toEnum :: Int -> DoCostCentres Source # fromEnum :: DoCostCentres -> Int Source # enumFrom :: DoCostCentres -> [DoCostCentres] Source # enumFromThen :: DoCostCentres -> DoCostCentres -> [DoCostCentres] Source # enumFromTo :: DoCostCentres -> DoCostCentres -> [DoCostCentres] Source # enumFromThenTo :: DoCostCentres -> DoCostCentres -> DoCostCentres -> [DoCostCentres] Source # | |
| Enum DoHeapProfile | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags Methods succ :: DoHeapProfile -> DoHeapProfile Source # pred :: DoHeapProfile -> DoHeapProfile Source # toEnum :: Int -> DoHeapProfile Source # fromEnum :: DoHeapProfile -> Int Source # enumFrom :: DoHeapProfile -> [DoHeapProfile] Source # enumFromThen :: DoHeapProfile -> DoHeapProfile -> [DoHeapProfile] Source # enumFromTo :: DoHeapProfile -> DoHeapProfile -> [DoHeapProfile] Source # enumFromThenTo :: DoHeapProfile -> DoHeapProfile -> DoHeapProfile -> [DoHeapProfile] Source # | |
| Enum DoTrace | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags Methods succ :: DoTrace -> DoTrace Source # pred :: DoTrace -> DoTrace Source # toEnum :: Int -> DoTrace Source # fromEnum :: DoTrace -> Int Source # enumFrom :: DoTrace -> [DoTrace] Source # enumFromThen :: DoTrace -> DoTrace -> [DoTrace] Source # enumFromTo :: DoTrace -> DoTrace -> [DoTrace] Source # enumFromThenTo :: DoTrace -> DoTrace -> DoTrace -> [DoTrace] Source # | |
| Enum GiveGCStats | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags Methods succ :: GiveGCStats -> GiveGCStats Source # pred :: GiveGCStats -> GiveGCStats Source # toEnum :: Int -> GiveGCStats Source # fromEnum :: GiveGCStats -> Int Source # enumFrom :: GiveGCStats -> [GiveGCStats] Source # enumFromThen :: GiveGCStats -> GiveGCStats -> [GiveGCStats] Source # enumFromTo :: GiveGCStats -> GiveGCStats -> [GiveGCStats] Source # enumFromThenTo :: GiveGCStats -> GiveGCStats -> GiveGCStats -> [GiveGCStats] Source # | |
| Enum IoSubSystem | Since: base-4.9.0.0 |
Defined in GHC.Internal.RTS.Flags Methods succ :: IoSubSystem -> IoSubSystem Source # pred :: IoSubSystem -> IoSubSystem Source # toEnum :: Int -> IoSubSystem Source # fromEnum :: IoSubSystem -> Int Source # enumFrom :: IoSubSystem -> [IoSubSystem] Source # enumFromThen :: IoSubSystem -> IoSubSystem -> [IoSubSystem] Source # enumFromTo :: IoSubSystem -> IoSubSystem -> [IoSubSystem] Source # enumFromThenTo :: IoSubSystem -> IoSubSystem -> IoSubSystem -> [IoSubSystem] Source # | |
| Enum Word16 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods succ :: Word16 -> Word16 Source # pred :: Word16 -> Word16 Source # toEnum :: Int -> Word16 Source # fromEnum :: Word16 -> Int Source # enumFrom :: Word16 -> [Word16] Source # enumFromThen :: Word16 -> Word16 -> [Word16] Source # enumFromTo :: Word16 -> Word16 -> [Word16] Source # enumFromThenTo :: Word16 -> Word16 -> Word16 -> [Word16] Source # | |
| Enum Word32 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods succ :: Word32 -> Word32 Source # pred :: Word32 -> Word32 Source # toEnum :: Int -> Word32 Source # fromEnum :: Word32 -> Int Source # enumFrom :: Word32 -> [Word32] Source # enumFromThen :: Word32 -> Word32 -> [Word32] Source # enumFromTo :: Word32 -> Word32 -> [Word32] Source # enumFromThenTo :: Word32 -> Word32 -> Word32 -> [Word32] Source # | |
| Enum Word64 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods succ :: Word64 -> Word64 Source # pred :: Word64 -> Word64 Source # toEnum :: Int -> Word64 Source # fromEnum :: Word64 -> Int Source # enumFrom :: Word64 -> [Word64] Source # enumFromThen :: Word64 -> Word64 -> [Word64] Source # enumFromTo :: Word64 -> Word64 -> [Word64] Source # enumFromThenTo :: Word64 -> Word64 -> Word64 -> [Word64] Source # | |
| Enum Word8 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods succ :: Word8 -> Word8 Source # pred :: Word8 -> Word8 Source # toEnum :: Int -> Word8 Source # fromEnum :: Word8 -> Int Source # enumFrom :: Word8 -> [Word8] Source # enumFromThen :: Word8 -> Word8 -> [Word8] Source # enumFromTo :: Word8 -> Word8 -> [Word8] Source # enumFromThenTo :: Word8 -> Word8 -> Word8 -> [Word8] Source # | |
| Enum Ordering | Since: base-2.1 |
Defined in GHC.Internal.Enum Methods succ :: Ordering -> Ordering Source # pred :: Ordering -> Ordering Source # toEnum :: Int -> Ordering Source # fromEnum :: Ordering -> Int Source # enumFrom :: Ordering -> [Ordering] Source # enumFromThen :: Ordering -> Ordering -> [Ordering] Source # enumFromTo :: Ordering -> Ordering -> [Ordering] Source # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] Source # | |
| Enum Integer | Since: base-2.1 |
Defined in GHC.Internal.Enum Methods succ :: Integer -> Integer Source # pred :: Integer -> Integer Source # toEnum :: Int -> Integer Source # fromEnum :: Integer -> Int Source # enumFrom :: Integer -> [Integer] Source # enumFromThen :: Integer -> Integer -> [Integer] Source # enumFromTo :: Integer -> Integer -> [Integer] Source # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source # | |
| Enum Natural | Since: base-4.8.0.0 |
Defined in GHC.Internal.Enum Methods succ :: Natural -> Natural Source # pred :: Natural -> Natural Source # toEnum :: Int -> Natural Source # fromEnum :: Natural -> Int Source # enumFrom :: Natural -> [Natural] Source # enumFromThen :: Natural -> Natural -> [Natural] Source # enumFromTo :: Natural -> Natural -> [Natural] Source # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source # | |
| Enum () | Since: base-2.1 |
Defined in GHC.Internal.Enum | |
| Enum Bool | Since: base-2.1 |
| Enum Char | Since: base-2.1 |
| Enum Double |
List generators have extremely peculiar behavior, mandated by Haskell Report 2010:
Since: base-2.1 |
Defined in GHC.Internal.Float Methods succ :: Double -> Double Source # pred :: Double -> Double Source # toEnum :: Int -> Double Source # fromEnum :: Double -> Int Source # enumFrom :: Double -> [Double] Source # enumFromThen :: Double -> Double -> [Double] Source # enumFromTo :: Double -> Double -> [Double] Source # enumFromThenTo :: Double -> Double -> Double -> [Double] Source # | |
| Enum Float |
List generators have extremely peculiar behavior, mandated by Haskell Report 2010:
Since: base-2.1 |
Defined in GHC.Internal.Float Methods succ :: Float -> Float Source # pred :: Float -> Float Source # toEnum :: Int -> Float Source # fromEnum :: Float -> Int Source # enumFrom :: Float -> [Float] Source # enumFromThen :: Float -> Float -> [Float] Source # enumFromTo :: Float -> Float -> [Float] Source # enumFromThenTo :: Float -> Float -> Float -> [Float] Source # | |
| Enum Int | Since: base-2.1 |
Defined in GHC.Internal.Enum | |
| Enum Levity | Since: base-4.16.0.0 |
Defined in GHC.Internal.Enum Methods succ :: Levity -> Levity Source # pred :: Levity -> Levity Source # toEnum :: Int -> Levity Source # fromEnum :: Levity -> Int Source # enumFrom :: Levity -> [Levity] Source # enumFromThen :: Levity -> Levity -> [Levity] Source # enumFromTo :: Levity -> Levity -> [Levity] Source # enumFromThenTo :: Levity -> Levity -> Levity -> [Levity] Source # | |
| Enum VecCount | Since: base-4.10.0.0 |
Defined in GHC.Internal.Enum Methods succ :: VecCount -> VecCount Source # pred :: VecCount -> VecCount Source # toEnum :: Int -> VecCount Source # fromEnum :: VecCount -> Int Source # enumFrom :: VecCount -> [VecCount] Source # enumFromThen :: VecCount -> VecCount -> [VecCount] Source # enumFromTo :: VecCount -> VecCount -> [VecCount] Source # enumFromThenTo :: VecCount -> VecCount -> VecCount -> [VecCount] Source # | |
| Enum VecElem | Since: base-4.10.0.0 |
Defined in GHC.Internal.Enum Methods succ :: VecElem -> VecElem Source # pred :: VecElem -> VecElem Source # toEnum :: Int -> VecElem Source # fromEnum :: VecElem -> Int Source # enumFrom :: VecElem -> [VecElem] Source # enumFromThen :: VecElem -> VecElem -> [VecElem] Source # enumFromTo :: VecElem -> VecElem -> [VecElem] Source # enumFromThenTo :: VecElem -> VecElem -> VecElem -> [VecElem] Source # | |
| Enum Word | Since: base-2.1 |
| Enum a => Enum (First a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: First a -> First a Source # pred :: First a -> First a Source # toEnum :: Int -> First a Source # fromEnum :: First a -> Int Source # enumFrom :: First a -> [First a] Source # enumFromThen :: First a -> First a -> [First a] Source # enumFromTo :: First a -> First a -> [First a] Source # enumFromThenTo :: First a -> First a -> First a -> [First a] Source # | |
| Enum a => Enum (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: Last a -> Last a Source # pred :: Last a -> Last a Source # toEnum :: Int -> Last a Source # fromEnum :: Last a -> Int Source # enumFrom :: Last a -> [Last a] Source # enumFromThen :: Last a -> Last a -> [Last a] Source # enumFromTo :: Last a -> Last a -> [Last a] Source # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source # | |
| Enum a => Enum (Max a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: Max a -> Max a Source # pred :: Max a -> Max a Source # toEnum :: Int -> Max a Source # fromEnum :: Max a -> Int Source # enumFrom :: Max a -> [Max a] Source # enumFromThen :: Max a -> Max a -> [Max a] Source # enumFromTo :: Max a -> Max a -> [Max a] Source # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source # | |
| Enum a => Enum (Min a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: Min a -> Min a Source # pred :: Min a -> Min a Source # toEnum :: Int -> Min a Source # fromEnum :: Min a -> Int Source # enumFrom :: Min a -> [Min a] Source # enumFromThen :: Min a -> Min a -> [Min a] Source # enumFromTo :: Min a -> Min a -> [Min a] Source # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source # | |
| Enum a => Enum (WrappedMonoid a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: WrappedMonoid a -> WrappedMonoid a Source # pred :: WrappedMonoid a -> WrappedMonoid a Source # toEnum :: Int -> WrappedMonoid a Source # fromEnum :: WrappedMonoid a -> Int Source # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # | |
| Enum a => Enum (Identity a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods succ :: Identity a -> Identity a Source # pred :: Identity a -> Identity a Source # toEnum :: Int -> Identity a Source # fromEnum :: Identity a -> Int Source # enumFrom :: Identity a -> [Identity a] Source # enumFromThen :: Identity a -> Identity a -> [Identity a] Source # enumFromTo :: Identity a -> Identity a -> [Identity a] Source # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] Source # | |
| (Enum a, Bounded a, Eq a) => Enum (Down a) | Swaps Since: base-4.18.0.0 |
Defined in GHC.Internal.Data.Ord Methods succ :: Down a -> Down a Source # pred :: Down a -> Down a Source # toEnum :: Int -> Down a Source # fromEnum :: Down a -> Int Source # enumFrom :: Down a -> [Down a] Source # enumFromThen :: Down a -> Down a -> [Down a] Source # enumFromTo :: Down a -> Down a -> [Down a] Source # enumFromThenTo :: Down a -> Down a -> Down a -> [Down a] Source # | |
| Integral a => Enum (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods succ :: Ratio a -> Ratio a Source # pred :: Ratio a -> Ratio a Source # toEnum :: Int -> Ratio a Source # fromEnum :: Ratio a -> Int Source # enumFrom :: Ratio a -> [Ratio a] Source # enumFromThen :: Ratio a -> Ratio a -> [Ratio a] Source # enumFromTo :: Ratio a -> Ratio a -> [Ratio a] Source # enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] Source # | |
| Enum a => Enum (Solo a) | |
Defined in GHC.Internal.Enum Methods succ :: Solo a -> Solo a Source # pred :: Solo a -> Solo a Source # toEnum :: Int -> Solo a Source # fromEnum :: Solo a -> Int Source # enumFrom :: Solo a -> [Solo a] Source # enumFromThen :: Solo a -> Solo a -> [Solo a] Source # enumFromTo :: Solo a -> Solo a -> [Solo a] Source # enumFromThenTo :: Solo a -> Solo a -> Solo a -> [Solo a] Source # | |
| Enum (Fixed a) | Recall that, for numeric types,
and likewise
In other words,
and similarly
This is worth bearing in mind when defining [1..10] :: [Pico] evaluates to However, this is not true. On the contrary, similarly to the above
implementations of [1.000000000000, 1.00000000001, 1.00000000002, ..., 10.000000000000] and contains Since: base-2.1 |
Defined in Data.Fixed Methods succ :: Fixed a -> Fixed a Source # pred :: Fixed a -> Fixed a Source # toEnum :: Int -> Fixed a Source # fromEnum :: Fixed a -> Int Source # enumFrom :: Fixed a -> [Fixed a] Source # enumFromThen :: Fixed a -> Fixed a -> [Fixed a] Source # enumFromTo :: Fixed a -> Fixed a -> [Fixed a] Source # enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] Source # | |
| Enum (Proxy s) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Proxy Methods succ :: Proxy s -> Proxy s Source # pred :: Proxy s -> Proxy s Source # toEnum :: Int -> Proxy s Source # fromEnum :: Proxy s -> Int Source # enumFrom :: Proxy s -> [Proxy s] Source # enumFromThen :: Proxy s -> Proxy s -> [Proxy s] Source # enumFromTo :: Proxy s -> Proxy s -> [Proxy s] Source # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] Source # | |
| Enum a => Enum (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods succ :: Const a b -> Const a b Source # pred :: Const a b -> Const a b Source # toEnum :: Int -> Const a b Source # fromEnum :: Const a b -> Int Source # enumFrom :: Const a b -> [Const a b] Source # enumFromThen :: Const a b -> Const a b -> [Const a b] Source # enumFromTo :: Const a b -> Const a b -> [Const a b] Source # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] Source # | |
| Enum (f a) => Enum (Ap f a) | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Monoid Methods succ :: Ap f a -> Ap f a Source # pred :: Ap f a -> Ap f a Source # toEnum :: Int -> Ap f a Source # fromEnum :: Ap f a -> Int Source # enumFrom :: Ap f a -> [Ap f a] Source # enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source # | |
| Enum (f a) => Enum (Alt f a) | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal Methods succ :: Alt f a -> Alt f a Source # pred :: Alt f a -> Alt f a Source # toEnum :: Int -> Alt f a Source # fromEnum :: Alt f a -> Int Source # enumFrom :: Alt f a -> [Alt f a] Source # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source # | |
| Enum (f (g a)) => Enum (Compose f g a) | Since: base-4.19.0.0 |
Defined in Data.Functor.Compose Methods succ :: Compose f g a -> Compose f g a Source # pred :: Compose f g a -> Compose f g a Source # toEnum :: Int -> Compose f g a Source # fromEnum :: Compose f g a -> Int Source # enumFrom :: Compose f g a -> [Compose f g a] Source # enumFromThen :: Compose f g a -> Compose f g a -> [Compose f g a] Source # enumFromTo :: Compose f g a -> Compose f g a -> [Compose f g a] Source # enumFromThenTo :: Compose f g a -> Compose f g a -> Compose f g a -> [Compose f g a] Source # | |
The Eq class defines equality (==) and inequality (/=).
All the basic datatypes exported by the Prelude are instances of Eq,
and Eq may be derived for any datatype whose constituents are also
instances of Eq.
The Haskell Report defines no laws for Eq. However, instances are
encouraged to follow these properties:
Instances
| Eq ByteArray | Since: base-4.17.0.0 |
| Eq Timeout | |
| Eq Dimension' Source # | |
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (==) :: Dimension' -> Dimension' -> Bool Source # (/=) :: Dimension' -> Dimension' -> Bool Source # | |
| Eq DynamicDimension Source # | |
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (==) :: DynamicDimension -> DynamicDimension -> Bool Source # (/=) :: DynamicDimension -> DynamicDimension -> Bool Source # | |
| Eq InterchangeName Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods (==) :: InterchangeName -> InterchangeName -> Bool Source # (/=) :: InterchangeName -> InterchangeName -> Bool Source # | |
| Eq InterchangeNameAuthority Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods (==) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool Source # (/=) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool Source # | |
| Eq Prefix Source # | |
| Eq Metricality Source # | |
Defined in Numeric.Units.Dimensional.Variants Methods (==) :: Metricality -> Metricality -> Bool Source # (/=) :: Metricality -> Metricality -> Bool Source # | |
| Eq BigNat | |
| Eq ForeignSrcLang | |
Defined in GHC.ForeignSrcLang.Type Methods (==) :: ForeignSrcLang -> ForeignSrcLang -> Bool Source # (/=) :: ForeignSrcLang -> ForeignSrcLang -> Bool Source # | |
| Eq Extension | |
| Eq Void | Since: base-4.8.0.0 |
| Eq Constr | Equality of constructors Since: base-4.0.0.0 |
| Eq ConstrRep | Since: base-4.0.0.0 |
| Eq DataRep | Since: base-4.0.0.0 |
| Eq Fixity | Since: base-4.0.0.0 |
| Eq All | Since: base-2.1 |
| Eq Any | Since: base-2.1 |
| Eq SomeTypeRep | |
Defined in GHC.Internal.Data.Typeable.Internal Methods (==) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # | |
| Eq Version | Since: base-2.1 |
| Eq CBool | |
| Eq CChar | |
| Eq CClock | |
| Eq CDouble | |
| Eq CFloat | |
| Eq CInt | |
| Eq CIntMax | |
| Eq CIntPtr | |
| Eq CLLong | |
| Eq CLong | |
| Eq CPtrdiff | |
| Eq CSChar | |
| Eq CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods (==) :: CSUSeconds -> CSUSeconds -> Bool Source # (/=) :: CSUSeconds -> CSUSeconds -> Bool Source # | |
| Eq CShort | |
| Eq CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods (==) :: CSigAtomic -> CSigAtomic -> Bool Source # (/=) :: CSigAtomic -> CSigAtomic -> Bool Source # | |
| Eq CSize | |
| Eq CTime | |
| Eq CUChar | |
| Eq CUInt | |
| Eq CUIntMax | |
| Eq CUIntPtr | |
| Eq CULLong | |
| Eq CULong | |
| Eq CUSeconds | |
| Eq CUShort | |
| Eq CWchar | |
| Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: Associativity -> Associativity -> Bool Source # (/=) :: Associativity -> Associativity -> Bool Source # | |
| Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # | |
| Eq Fixity | Since: base-4.6.0.0 |
| Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool Source # (/=) :: SourceStrictness -> SourceStrictness -> Bool Source # | |
| Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # | |
| Eq MaskingState | Since: base-4.3.0.0 |
Defined in GHC.Internal.IO Methods (==) :: MaskingState -> MaskingState -> Bool Source # (/=) :: MaskingState -> MaskingState -> Bool Source # | |
| Eq ArrayException | Since: base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool Source # (/=) :: ArrayException -> ArrayException -> Bool Source # | |
| Eq AsyncException | Since: base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool Source # (/=) :: AsyncException -> AsyncException -> Bool Source # | |
| Eq ExitCode | |
| Eq IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool Source # (/=) :: IOErrorType -> IOErrorType -> Bool Source # | |
| Eq IOException | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: IOException -> IOException -> Bool Source # (/=) :: IOException -> IOException -> Bool Source # | |
| Eq Int16 | Since: base-2.1 |
| Eq Int32 | Since: base-2.1 |
| Eq Int64 | Since: base-2.1 |
| Eq Int8 | Since: base-2.1 |
| Eq IoSubSystem | |
Defined in GHC.Internal.RTS.Flags Methods (==) :: IoSubSystem -> IoSubSystem -> Bool Source # (/=) :: IoSubSystem -> IoSubSystem -> Bool Source # | |
| Eq SrcLoc | Since: base-4.9.0.0 |
| Eq SomeNat | Since: base-4.7.0.0 |
| Eq Word16 | Since: base-2.1 |
| Eq Word32 | Since: base-2.1 |
| Eq Word64 | Since: base-2.1 |
| Eq Word8 | Since: base-2.1 |
| Eq Module | |
| Eq Ordering | |
| Eq TrName | |
| Eq TyCon | |
| Eq AnnLookup | |
| Eq AnnTarget | |
| Eq Bang | |
| Eq BndrVis | |
| Eq Body | |
| Eq Bytes | |
| Eq Callconv | |
| Eq Clause | |
| Eq Con | |
| Eq Dec | |
| Eq DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # | |
| Eq DerivClause | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DerivClause -> DerivClause -> Bool Source # (/=) :: DerivClause -> DerivClause -> Bool Source # | |
| Eq DerivStrategy | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DerivStrategy -> DerivStrategy -> Bool Source # (/=) :: DerivStrategy -> DerivStrategy -> Bool Source # | |
| Eq DocLoc | |
| Eq Exp | |
| Eq FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FamilyResultSig -> FamilyResultSig -> Bool Source # (/=) :: FamilyResultSig -> FamilyResultSig -> Bool Source # | |
| Eq Fixity | |
| Eq FixityDirection | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FixityDirection -> FixityDirection -> Bool Source # (/=) :: FixityDirection -> FixityDirection -> Bool Source # | |
| Eq Foreign | |
| Eq FunDep | |
| Eq Guard | |
| Eq Info | |
| Eq InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: InjectivityAnn -> InjectivityAnn -> Bool Source # (/=) :: InjectivityAnn -> InjectivityAnn -> Bool Source # | |
| Eq Inline | |
| Eq Lit | |
| Eq Loc | |
| Eq Match | |
| Eq ModName | |
| Eq Module | |
| Eq ModuleInfo | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: ModuleInfo -> ModuleInfo -> Bool Source # (/=) :: ModuleInfo -> ModuleInfo -> Bool Source # | |
| Eq Name | |
| Eq NameFlavour | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: NameFlavour -> NameFlavour -> Bool Source # (/=) :: NameFlavour -> NameFlavour -> Bool Source # | |
| Eq NameSpace | |
| Eq NamespaceSpecifier | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: NamespaceSpecifier -> NamespaceSpecifier -> Bool Source # (/=) :: NamespaceSpecifier -> NamespaceSpecifier -> Bool Source # | |
| Eq OccName | |
| Eq Overlap | |
| Eq Pat | |
| Eq PatSynArgs | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: PatSynArgs -> PatSynArgs -> Bool Source # (/=) :: PatSynArgs -> PatSynArgs -> Bool Source # | |
| Eq PatSynDir | |
| Eq Phases | |
| Eq PkgName | |
| Eq Pragma | |
| Eq Range | |
| Eq Role | |
| Eq RuleBndr | |
| Eq RuleMatch | |
| Eq Safety | |
| Eq SourceStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceStrictness -> SourceStrictness -> Bool Source # (/=) :: SourceStrictness -> SourceStrictness -> Bool Source # | |
| Eq SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # | |
| Eq Specificity | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: Specificity -> Specificity -> Bool Source # (/=) :: Specificity -> Specificity -> Bool Source # | |
| Eq Stmt | |
| Eq TyLit | |
| Eq TySynEqn | |
| Eq Type | |
| Eq TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: TypeFamilyHead -> TypeFamilyHead -> Bool Source # (/=) :: TypeFamilyHead -> TypeFamilyHead -> Bool Source # | |
| Eq Size | |
| Eq Checks | |
| Eq Integer | |
| Eq Natural | |
| Eq () | |
| Eq Bool | |
| Eq Char | |
| Eq Double | Note that due to the presence of
Also note that
|
| Eq Float | Note that due to the presence of
Also note that
|
| Eq Int | |
| Eq Word | |
| Eq (Chan a) | Since: base-4.4.0.0 |
| Eq (MutableByteArray s) | Since: base-4.17.0.0 |
Defined in Data.Array.Byte Methods (==) :: MutableByteArray s -> MutableByteArray s -> Bool Source # (/=) :: MutableByteArray s -> MutableByteArray s -> Bool Source # | |
| Eq a => Eq (Complex a) | Since: base-2.1 |
| Eq a => Eq (First a) | Since: base-4.9.0.0 |
| Eq a => Eq (Last a) | Since: base-4.9.0.0 |
| Eq a => Eq (Max a) | Since: base-4.9.0.0 |
| Eq a => Eq (Min a) | Since: base-4.9.0.0 |
| Eq m => Eq (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # | |
| Eq a => Eq (AnyQuantity a) Source # | |
Defined in Numeric.Units.Dimensional.Dynamic Methods (==) :: AnyQuantity a -> AnyQuantity a -> Bool Source # (/=) :: AnyQuantity a -> AnyQuantity a -> Bool Source # | |
| Eq a => Eq (DynQuantity a) Source # | |
Defined in Numeric.Units.Dimensional.Dynamic Methods (==) :: DynQuantity a -> DynQuantity a -> Bool Source # (/=) :: DynQuantity a -> DynQuantity a -> Bool Source # | |
| Eq (NameAtom m) Source # | |
| Eq (UnitName m) Source # | |
| Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
| Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
| Eq a => Eq (First a) | Since: base-2.1 |
| Eq a => Eq (Last a) | Since: base-2.1 |
| Eq a => Eq (Down a) | Since: base-4.6.0.0 |
| Eq a => Eq (Dual a) | Since: base-2.1 |
| Eq a => Eq (Product a) | Since: base-2.1 |
| Eq a => Eq (Sum a) | Since: base-2.1 |
| Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
| Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
| Eq (FunPtr a) | |
| Eq (Ptr a) | Since: base-2.1 |
| Eq a => Eq (Ratio a) | Since: base-2.1 |
| Eq (SNat n) | Since: base-4.19.0.0 |
| Eq a => Eq (Array a) | |
| (Eq a, Prim a) => Eq (PrimArray a) | |
| Eq a => Eq (SmallArray a) | |
| Eq flag => Eq (TyVarBndr flag) | |
| Eq a => Eq (Vector a) | |
| (Prim a, Eq a) => Eq (Vector a) | |
| (Storable a, Eq a) => Eq (Vector a) | |
| Eq a => Eq (Vector a) | |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Eq a => Eq (Solo a) | |
| Eq a => Eq [a] | |
| Eq (Fixed a) | Since: base-2.1 |
| Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| Eq (Proxy s) | Since: base-4.7.0.0 |
| Eq (TypeRep a) | Since: base-2.1 |
| Eq (U1 p) | Since: base-4.9.0.0 |
| Eq (V1 p) | Since: base-4.9.0.0 |
| Eq (MutableArray s a) | |
| Eq (MutablePrimArray s a) | |
| Eq (SmallMutableArray s a) | |
| (Eq1 m, Eq a) => Eq (MaybeT m a) | |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq a => Eq (Dimensional ('DQuantity s) d a) Source # | |
Defined in Numeric.Units.Dimensional.Internal Methods (==) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (/=) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # | |
| Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
| Eq (f a) => Eq (Ap f a) | Since: base-4.12.0.0 |
| Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0 |
| Eq (OrderingI a b) | |
| (Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a) | Since: base-4.18.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: Generically1 f a -> Generically1 f a -> Bool Source # (/=) :: Generically1 f a -> Generically1 f a -> Bool Source # | |
| Eq (f p) => Eq (Rec1 f p) | Since: base-4.7.0.0 |
| Eq (URec (Ptr ()) p) | Since: base-4.9.0.0 |
| Eq (URec Char p) | Since: base-4.9.0.0 |
| Eq (URec Double p) | Since: base-4.9.0.0 |
| Eq (URec Float p) | |
| Eq (URec Int p) | Since: base-4.9.0.0 |
| Eq (URec Word p) | Since: base-4.9.0.0 |
| (Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a) | |
| (Eq1 f, Eq a) => Eq (IdentityT f a) | |
| (Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) | |
| (Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) | |
| Eq a => Eq (Bundle Id v a) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| (Eq (f a), Eq (g a)) => Eq (Product f g a) | Since: base-4.18.0.0 |
| (Eq (f a), Eq (g a)) => Eq (Sum f g a) | Since: base-4.18.0.0 |
| (Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
| (Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
| Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| Eq (f (g a)) => Eq (Compose f g a) | Since: base-4.18.0.0 |
| Eq (f (g p)) => Eq ((f :.: g) p) | Since: base-4.7.0.0 |
| Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
class Eq a => Ord a where Source #
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined datatype whose
constituent types are in Ord. The declared order of the constructors in
the data declaration determines the ordering in derived Ord instances. The
Ordering datatype allows a single comparison to determine the precise
ordering of two objects.
Ord, as defined by the Haskell report, implements a total order and has the
following properties:
- Comparability
x <= y || y <= x=True- Transitivity
- if
x <= y && y <= z=True, thenx <= z=True - Reflexivity
x <= x=True- Antisymmetry
- if
x <= y && y <= x=True, thenx == y=True
The following operator interactions are expected to hold:
x >= y=y <= xx < y=x <= y && x /= yx > y=y < xx < y=compare x y == LTx > y=compare x y == GTx == y=compare x y == EQmin x y == if x <= y then x else y=Truemax x y == if x >= y then x else y=True
Note that (7.) and (8.) do not require min and max to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==).
Minimal complete definition: either compare or <=.
Using compare can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering Source #
(<) :: a -> a -> Bool infix 4 Source #
(<=) :: a -> a -> Bool infix 4 Source #
(>) :: a -> a -> Bool infix 4 Source #
Instances
| Ord ByteArray | Non-lexicographic ordering. This compares the lengths of the byte arrays first and uses a lexicographic ordering if the lengths are equal. Subject to change between major versions. Since: base-4.17.0.0 |
Defined in Data.Array.Byte | |
| Ord Dimension' Source # | |
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods compare :: Dimension' -> Dimension' -> Ordering Source # (<) :: Dimension' -> Dimension' -> Bool Source # (<=) :: Dimension' -> Dimension' -> Bool Source # (>) :: Dimension' -> Dimension' -> Bool Source # (>=) :: Dimension' -> Dimension' -> Bool Source # max :: Dimension' -> Dimension' -> Dimension' Source # min :: Dimension' -> Dimension' -> Dimension' Source # | |
| Ord DynamicDimension Source # | |
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods compare :: DynamicDimension -> DynamicDimension -> Ordering Source # (<) :: DynamicDimension -> DynamicDimension -> Bool Source # (<=) :: DynamicDimension -> DynamicDimension -> Bool Source # (>) :: DynamicDimension -> DynamicDimension -> Bool Source # (>=) :: DynamicDimension -> DynamicDimension -> Bool Source # max :: DynamicDimension -> DynamicDimension -> DynamicDimension Source # min :: DynamicDimension -> DynamicDimension -> DynamicDimension Source # | |
| Ord InterchangeName Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods compare :: InterchangeName -> InterchangeName -> Ordering Source # (<) :: InterchangeName -> InterchangeName -> Bool Source # (<=) :: InterchangeName -> InterchangeName -> Bool Source # (>) :: InterchangeName -> InterchangeName -> Bool Source # (>=) :: InterchangeName -> InterchangeName -> Bool Source # max :: InterchangeName -> InterchangeName -> InterchangeName Source # min :: InterchangeName -> InterchangeName -> InterchangeName Source # | |
| Ord InterchangeNameAuthority Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames Methods compare :: InterchangeNameAuthority -> InterchangeNameAuthority -> Ordering Source # (<) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool Source # (<=) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool Source # (>) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool Source # (>=) :: InterchangeNameAuthority -> InterchangeNameAuthority -> Bool Source # max :: InterchangeNameAuthority -> InterchangeNameAuthority -> InterchangeNameAuthority Source # min :: InterchangeNameAuthority -> InterchangeNameAuthority -> InterchangeNameAuthority Source # | |
| Ord Prefix Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.Internal | |
| Ord Metricality Source # | |
Defined in Numeric.Units.Dimensional.Variants Methods compare :: Metricality -> Metricality -> Ordering Source # (<) :: Metricality -> Metricality -> Bool Source # (<=) :: Metricality -> Metricality -> Bool Source # (>) :: Metricality -> Metricality -> Bool Source # (>=) :: Metricality -> Metricality -> Bool Source # max :: Metricality -> Metricality -> Metricality Source # min :: Metricality -> Metricality -> Metricality Source # | |
| Ord BigNat | |
| Ord Extension | |
Defined in GHC.LanguageExtensions.Type | |
| Ord Void | Since: base-4.8.0.0 |
| Ord All | Since: base-2.1 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Ord Any | Since: base-2.1 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Ord SomeTypeRep | |
Defined in GHC.Internal.Data.Typeable.Internal Methods compare :: SomeTypeRep -> SomeTypeRep -> Ordering Source # (<) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (<=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (>) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (>=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source # min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source # | |
| Ord Version | Since: base-2.1 |
Defined in GHC.Internal.Data.Version | |
| Ord CBool | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CChar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CClock | |
| Ord CDouble | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CFloat | |
| Ord CInt | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CIntMax | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CIntPtr | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CLLong | |
| Ord CLong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CPtrdiff | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CSChar | |
| Ord CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods compare :: CSUSeconds -> CSUSeconds -> Ordering Source # (<) :: CSUSeconds -> CSUSeconds -> Bool Source # (<=) :: CSUSeconds -> CSUSeconds -> Bool Source # (>) :: CSUSeconds -> CSUSeconds -> Bool Source # (>=) :: CSUSeconds -> CSUSeconds -> Bool Source # max :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # min :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # | |
| Ord CShort | |
| Ord CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods compare :: CSigAtomic -> CSigAtomic -> Ordering Source # (<) :: CSigAtomic -> CSigAtomic -> Bool Source # (<=) :: CSigAtomic -> CSigAtomic -> Bool Source # (>) :: CSigAtomic -> CSigAtomic -> Bool Source # (>=) :: CSigAtomic -> CSigAtomic -> Bool Source # max :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # min :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # | |
| Ord CSize | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CTime | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CUChar | |
| Ord CUInt | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CUIntMax | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CUIntPtr | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CULLong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CULong | |
| Ord CUSeconds | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CUShort | |
Defined in GHC.Internal.Foreign.C.Types | |
| Ord CWchar | |
| Ord Associativity | Since: base-4.6.0.0 |
Defined in GHC.Internal.Generics Methods compare :: Associativity -> Associativity -> Ordering Source # (<) :: Associativity -> Associativity -> Bool Source # (<=) :: Associativity -> Associativity -> Bool Source # (>) :: Associativity -> Associativity -> Bool Source # (>=) :: Associativity -> Associativity -> Bool Source # max :: Associativity -> Associativity -> Associativity Source # min :: Associativity -> Associativity -> Associativity Source # | |
| Ord DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering Source # (<) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (>) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source # | |
| Ord Fixity | Since: base-4.6.0.0 |
| Ord SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: SourceStrictness -> SourceStrictness -> Ordering Source # (<) :: SourceStrictness -> SourceStrictness -> Bool Source # (<=) :: SourceStrictness -> SourceStrictness -> Bool Source # (>) :: SourceStrictness -> SourceStrictness -> Bool Source # (>=) :: SourceStrictness -> SourceStrictness -> Bool Source # max :: SourceStrictness -> SourceStrictness -> SourceStrictness Source # min :: SourceStrictness -> SourceStrictness -> SourceStrictness Source # | |
| Ord SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering Source # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source # | |
| Ord ArrayException | Since: base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods compare :: ArrayException -> ArrayException -> Ordering Source # (<) :: ArrayException -> ArrayException -> Bool Source # (<=) :: ArrayException -> ArrayException -> Bool Source # (>) :: ArrayException -> ArrayException -> Bool Source # (>=) :: ArrayException -> ArrayException -> Bool Source # max :: ArrayException -> ArrayException -> ArrayException Source # min :: ArrayException -> ArrayException -> ArrayException Source # | |
| Ord AsyncException | Since: base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods compare :: AsyncException -> AsyncException -> Ordering Source # (<) :: AsyncException -> AsyncException -> Bool Source # (<=) :: AsyncException -> AsyncException -> Bool Source # (>) :: AsyncException -> AsyncException -> Bool Source # (>=) :: AsyncException -> AsyncException -> Bool Source # max :: AsyncException -> AsyncException -> AsyncException Source # min :: AsyncException -> AsyncException -> AsyncException Source # | |
| Ord ExitCode | |
Defined in GHC.Internal.IO.Exception | |
| Ord Int16 | Since: base-2.1 |
Defined in GHC.Internal.Int | |
| Ord Int32 | Since: base-2.1 |
Defined in GHC.Internal.Int | |
| Ord Int64 | Since: base-2.1 |
Defined in GHC.Internal.Int | |
| Ord Int8 | Since: base-2.1 |
| Ord SomeNat | Since: base-4.7.0.0 |
Defined in GHC.Internal.TypeNats | |
| Ord Word16 | Since: base-2.1 |
| Ord Word32 | Since: base-2.1 |
| Ord Word64 | Since: base-2.1 |
| Ord Word8 | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Ord Ordering | |
Defined in GHC.Classes | |
| Ord TyCon | |
Defined in GHC.Classes | |
| Ord AnnLookup | |
Defined in Language.Haskell.TH.Syntax | |
| Ord AnnTarget | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Bang | |
Defined in Language.Haskell.TH.Syntax | |
| Ord BndrVis | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Body | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Bytes | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Callconv | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Clause | |
| Ord Con | |
| Ord Dec | |
| Ord DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering Source # (<) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (>) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source # | |
| Ord DerivClause | |
Defined in Language.Haskell.TH.Syntax Methods compare :: DerivClause -> DerivClause -> Ordering Source # (<) :: DerivClause -> DerivClause -> Bool Source # (<=) :: DerivClause -> DerivClause -> Bool Source # (>) :: DerivClause -> DerivClause -> Bool Source # (>=) :: DerivClause -> DerivClause -> Bool Source # max :: DerivClause -> DerivClause -> DerivClause Source # min :: DerivClause -> DerivClause -> DerivClause Source # | |
| Ord DerivStrategy | |
Defined in Language.Haskell.TH.Syntax Methods compare :: DerivStrategy -> DerivStrategy -> Ordering Source # (<) :: DerivStrategy -> DerivStrategy -> Bool Source # (<=) :: DerivStrategy -> DerivStrategy -> Bool Source # (>) :: DerivStrategy -> DerivStrategy -> Bool Source # (>=) :: DerivStrategy -> DerivStrategy -> Bool Source # max :: DerivStrategy -> DerivStrategy -> DerivStrategy Source # min :: DerivStrategy -> DerivStrategy -> DerivStrategy Source # | |
| Ord DocLoc | |
| Ord Exp | |
| Ord FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax Methods compare :: FamilyResultSig -> FamilyResultSig -> Ordering Source # (<) :: FamilyResultSig -> FamilyResultSig -> Bool Source # (<=) :: FamilyResultSig -> FamilyResultSig -> Bool Source # (>) :: FamilyResultSig -> FamilyResultSig -> Bool Source # (>=) :: FamilyResultSig -> FamilyResultSig -> Bool Source # max :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig Source # min :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig Source # | |
| Ord Fixity | |
| Ord FixityDirection | |
Defined in Language.Haskell.TH.Syntax Methods compare :: FixityDirection -> FixityDirection -> Ordering Source # (<) :: FixityDirection -> FixityDirection -> Bool Source # (<=) :: FixityDirection -> FixityDirection -> Bool Source # (>) :: FixityDirection -> FixityDirection -> Bool Source # (>=) :: FixityDirection -> FixityDirection -> Bool Source # max :: FixityDirection -> FixityDirection -> FixityDirection Source # min :: FixityDirection -> FixityDirection -> FixityDirection Source # | |
| Ord Foreign | |
Defined in Language.Haskell.TH.Syntax | |
| Ord FunDep | |
| Ord Guard | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Info | |
Defined in Language.Haskell.TH.Syntax | |
| Ord InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax Methods compare :: InjectivityAnn -> InjectivityAnn -> Ordering Source # (<) :: InjectivityAnn -> InjectivityAnn -> Bool Source # (<=) :: InjectivityAnn -> InjectivityAnn -> Bool Source # (>) :: InjectivityAnn -> InjectivityAnn -> Bool Source # (>=) :: InjectivityAnn -> InjectivityAnn -> Bool Source # max :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn Source # min :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn Source # | |
| Ord Inline | |
| Ord Lit | |
| Ord Loc | |
| Ord Match | |
Defined in Language.Haskell.TH.Syntax | |
| Ord ModName | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Module | |
| Ord ModuleInfo | |
Defined in Language.Haskell.TH.Syntax Methods compare :: ModuleInfo -> ModuleInfo -> Ordering Source # (<) :: ModuleInfo -> ModuleInfo -> Bool Source # (<=) :: ModuleInfo -> ModuleInfo -> Bool Source # (>) :: ModuleInfo -> ModuleInfo -> Bool Source # (>=) :: ModuleInfo -> ModuleInfo -> Bool Source # max :: ModuleInfo -> ModuleInfo -> ModuleInfo Source # min :: ModuleInfo -> ModuleInfo -> ModuleInfo Source # | |
| Ord Name | |
Defined in Language.Haskell.TH.Syntax | |
| Ord NameFlavour | |
Defined in Language.Haskell.TH.Syntax Methods compare :: NameFlavour -> NameFlavour -> Ordering Source # (<) :: NameFlavour -> NameFlavour -> Bool Source # (<=) :: NameFlavour -> NameFlavour -> Bool Source # (>) :: NameFlavour -> NameFlavour -> Bool Source # (>=) :: NameFlavour -> NameFlavour -> Bool Source # max :: NameFlavour -> NameFlavour -> NameFlavour Source # min :: NameFlavour -> NameFlavour -> NameFlavour Source # | |
| Ord NameSpace | |
Defined in Language.Haskell.TH.Syntax | |
| Ord NamespaceSpecifier | |
Defined in Language.Haskell.TH.Syntax Methods compare :: NamespaceSpecifier -> NamespaceSpecifier -> Ordering Source # (<) :: NamespaceSpecifier -> NamespaceSpecifier -> Bool Source # (<=) :: NamespaceSpecifier -> NamespaceSpecifier -> Bool Source # (>) :: NamespaceSpecifier -> NamespaceSpecifier -> Bool Source # (>=) :: NamespaceSpecifier -> NamespaceSpecifier -> Bool Source # max :: NamespaceSpecifier -> NamespaceSpecifier -> NamespaceSpecifier Source # min :: NamespaceSpecifier -> NamespaceSpecifier -> NamespaceSpecifier Source # | |
| Ord OccName | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Overlap | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Pat | |
| Ord PatSynArgs | |
Defined in Language.Haskell.TH.Syntax Methods compare :: PatSynArgs -> PatSynArgs -> Ordering Source # (<) :: PatSynArgs -> PatSynArgs -> Bool Source # (<=) :: PatSynArgs -> PatSynArgs -> Bool Source # (>) :: PatSynArgs -> PatSynArgs -> Bool Source # (>=) :: PatSynArgs -> PatSynArgs -> Bool Source # max :: PatSynArgs -> PatSynArgs -> PatSynArgs Source # min :: PatSynArgs -> PatSynArgs -> PatSynArgs Source # | |
| Ord PatSynDir | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Phases | |
| Ord PkgName | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Pragma | |
| Ord Range | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Role | |
Defined in Language.Haskell.TH.Syntax | |
| Ord RuleBndr | |
Defined in Language.Haskell.TH.Syntax | |
| Ord RuleMatch | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Safety | |
| Ord SourceStrictness | |
Defined in Language.Haskell.TH.Syntax Methods compare :: SourceStrictness -> SourceStrictness -> Ordering Source # (<) :: SourceStrictness -> SourceStrictness -> Bool Source # (<=) :: SourceStrictness -> SourceStrictness -> Bool Source # (>) :: SourceStrictness -> SourceStrictness -> Bool Source # (>=) :: SourceStrictness -> SourceStrictness -> Bool Source # max :: SourceStrictness -> SourceStrictness -> SourceStrictness Source # min :: SourceStrictness -> SourceStrictness -> SourceStrictness Source # | |
| Ord SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering Source # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source # | |
| Ord Specificity | |
Defined in Language.Haskell.TH.Syntax Methods compare :: Specificity -> Specificity -> Ordering Source # (<) :: Specificity -> Specificity -> Bool Source # (<=) :: Specificity -> Specificity -> Bool Source # (>) :: Specificity -> Specificity -> Bool Source # (>=) :: Specificity -> Specificity -> Bool Source # max :: Specificity -> Specificity -> Specificity Source # min :: Specificity -> Specificity -> Specificity Source # | |
| Ord Stmt | |
Defined in Language.Haskell.TH.Syntax | |
| Ord TyLit | |
Defined in Language.Haskell.TH.Syntax | |
| Ord TySynEqn | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Type | |
Defined in Language.Haskell.TH.Syntax | |
| Ord TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax Methods compare :: TypeFamilyHead -> TypeFamilyHead -> Ordering Source # (<) :: TypeFamilyHead -> TypeFamilyHead -> Bool Source # (<=) :: TypeFamilyHead -> TypeFamilyHead -> Bool Source # (>) :: TypeFamilyHead -> TypeFamilyHead -> Bool Source # (>=) :: TypeFamilyHead -> TypeFamilyHead -> Bool Source # max :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead Source # min :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead Source # | |
| Ord Integer | |
| Ord Natural | |
| Ord () | |
| Ord Bool | |
| Ord Char | |
| Ord Double | IEEE 754 IEEE 754-2008, section 5.11 requires that if at least one of arguments of
IEEE 754-2008, section 5.10 defines Thus, users must be extremely cautious when using Moving further, the behaviour of IEEE 754-2008 compliant |
| Ord Float | See |
Defined in GHC.Classes | |
| Ord Int | |
| Ord Word | |
| Ord a => Ord (First a) | Since: base-4.9.0.0 |
| Ord a => Ord (Last a) | Since: base-4.9.0.0 |
| Ord a => Ord (Max a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Ord a => Ord (Min a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Ord m => Ord (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering Source # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # | |
| Ord (NameAtom m) Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.Internal Methods compare :: NameAtom m -> NameAtom m -> Ordering Source # (<) :: NameAtom m -> NameAtom m -> Bool Source # (<=) :: NameAtom m -> NameAtom m -> Bool Source # (>) :: NameAtom m -> NameAtom m -> Bool Source # (>=) :: NameAtom m -> NameAtom m -> Bool Source # | |
| Ord a => Ord (NonEmpty a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Base Methods compare :: NonEmpty a -> NonEmpty a -> Ordering Source # (<) :: NonEmpty a -> NonEmpty a -> Bool Source # (<=) :: NonEmpty a -> NonEmpty a -> Bool Source # (>) :: NonEmpty a -> NonEmpty a -> Bool Source # (>=) :: NonEmpty a -> NonEmpty a -> Bool Source # | |
| Ord a => Ord (Identity a) | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering Source # (<) :: Identity a -> Identity a -> Bool Source # (<=) :: Identity a -> Identity a -> Bool Source # (>) :: Identity a -> Identity a -> Bool Source # (>=) :: Identity a -> Identity a -> Bool Source # | |
| Ord a => Ord (First a) | Since: base-2.1 |
Defined in GHC.Internal.Data.Monoid | |
| Ord a => Ord (Last a) | Since: base-2.1 |
| Ord a => Ord (Down a) | Since: base-4.6.0.0 |
| Ord a => Ord (Dual a) | Since: base-2.1 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Ord a => Ord (Product a) | Since: base-2.1 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Ord a => Ord (Sum a) | Since: base-2.1 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Ord a => Ord (ZipList a) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Functor.ZipList | |
| Ord p => Ord (Par1 p) | Since: base-4.7.0.0 |
| Ord (FunPtr a) | |
Defined in GHC.Internal.Ptr | |
| Ord (Ptr a) | Since: base-2.1 |
Defined in GHC.Internal.Ptr | |
| Integral a => Ord (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Internal.Real | |
| Ord (SNat n) | Since: base-4.19.0.0 |
| Ord a => Ord (Array a) | |
Defined in Data.Primitive.Array | |
| (Ord a, Prim a) => Ord (PrimArray a) | |
Defined in Data.Primitive.PrimArray Methods compare :: PrimArray a -> PrimArray a -> Ordering Source # (<) :: PrimArray a -> PrimArray a -> Bool Source # (<=) :: PrimArray a -> PrimArray a -> Bool Source # (>) :: PrimArray a -> PrimArray a -> Bool Source # (>=) :: PrimArray a -> PrimArray a -> Bool Source # | |
| Ord a => Ord (SmallArray a) | |
Defined in Data.Primitive.SmallArray Methods compare :: SmallArray a -> SmallArray a -> Ordering Source # (<) :: SmallArray a -> SmallArray a -> Bool Source # (<=) :: SmallArray a -> SmallArray a -> Bool Source # (>) :: SmallArray a -> SmallArray a -> Bool Source # (>=) :: SmallArray a -> SmallArray a -> Bool Source # max :: SmallArray a -> SmallArray a -> SmallArray a Source # min :: SmallArray a -> SmallArray a -> SmallArray a Source # | |
| Ord flag => Ord (TyVarBndr flag) | |
Defined in Language.Haskell.TH.Syntax Methods compare :: TyVarBndr flag -> TyVarBndr flag -> Ordering Source # (<) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source # (<=) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source # (>) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source # (>=) :: TyVarBndr flag -> TyVarBndr flag -> Bool Source # max :: TyVarBndr flag -> TyVarBndr flag -> TyVarBndr flag Source # min :: TyVarBndr flag -> TyVarBndr flag -> TyVarBndr flag Source # | |
| Ord a => Ord (Vector a) | |
Defined in Data.Vector | |
| (Prim a, Ord a) => Ord (Vector a) | |
Defined in Data.Vector.Primitive | |
| (Storable a, Ord a) => Ord (Vector a) | |
Defined in Data.Vector.Storable | |
| Ord a => Ord (Vector a) | |
Defined in Data.Vector.Strict | |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
Defined in GHC.Internal.Maybe | |
| Ord a => Ord (Solo a) | |
| Ord a => Ord [a] | |
| Ord (Fixed a) | Since: base-2.1 |
| Ord a => Ord (Arg a b) | Since: base-4.9.0.0 |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
Defined in GHC.Internal.Data.Either Methods compare :: Either a b -> Either a b -> Ordering Source # (<) :: Either a b -> Either a b -> Bool Source # (<=) :: Either a b -> Either a b -> Bool Source # (>) :: Either a b -> Either a b -> Bool Source # (>=) :: Either a b -> Either a b -> Bool Source # | |
| Ord (Proxy s) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Proxy | |
| Ord (TypeRep a) | Since: base-4.4.0.0 |
Defined in GHC.Internal.Data.Typeable.Internal | |
| Ord (U1 p) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Generics | |
| Ord (V1 p) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| (Ord1 m, Ord a) => Ord (MaybeT m a) | |
Defined in Control.Monad.Trans.Maybe Methods compare :: MaybeT m a -> MaybeT m a -> Ordering Source # (<) :: MaybeT m a -> MaybeT m a -> Bool Source # (<=) :: MaybeT m a -> MaybeT m a -> Bool Source # (>) :: MaybeT m a -> MaybeT m a -> Bool Source # (>=) :: MaybeT m a -> MaybeT m a -> Bool Source # | |
| (Ord a, Ord b) => Ord (a, b) | |
| Ord a => Ord (Dimensional ('DQuantity s) d a) Source # | |
Defined in Numeric.Units.Dimensional.Internal Methods compare :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Ordering Source # (<) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (<=) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (>) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # (>=) :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Bool Source # max :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a Source # min :: Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a -> Dimensional ('DQuantity s) d a Source # | |
| Ord a => Ord (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const | |
| Ord (f a) => Ord (Ap f a) | Since: base-4.12.0.0 |
| Ord (f a) => Ord (Alt f a) | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| (Generic1 f, Ord (Rep1 f a)) => Ord (Generically1 f a) | Since: base-4.18.0.0 |
Defined in GHC.Internal.Generics Methods compare :: Generically1 f a -> Generically1 f a -> Ordering Source # (<) :: Generically1 f a -> Generically1 f a -> Bool Source # (<=) :: Generically1 f a -> Generically1 f a -> Bool Source # (>) :: Generically1 f a -> Generically1 f a -> Bool Source # (>=) :: Generically1 f a -> Generically1 f a -> Bool Source # max :: Generically1 f a -> Generically1 f a -> Generically1 f a Source # min :: Generically1 f a -> Generically1 f a -> Generically1 f a Source # | |
| Ord (f p) => Ord (Rec1 f p) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Generics | |
| Ord (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering Source # (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source # min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source # | |
| Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Char p -> URec Char p -> Ordering Source # (<) :: URec Char p -> URec Char p -> Bool Source # (<=) :: URec Char p -> URec Char p -> Bool Source # (>) :: URec Char p -> URec Char p -> Bool Source # (>=) :: URec Char p -> URec Char p -> Bool Source # | |
| Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Double p -> URec Double p -> Ordering Source # (<) :: URec Double p -> URec Double p -> Bool Source # (<=) :: URec Double p -> URec Double p -> Bool Source # (>) :: URec Double p -> URec Double p -> Bool Source # (>=) :: URec Double p -> URec Double p -> Bool Source # max :: URec Double p -> URec Double p -> URec Double p Source # min :: URec Double p -> URec Double p -> URec Double p Source # | |
| Ord (URec Float p) | |
Defined in GHC.Internal.Generics Methods compare :: URec Float p -> URec Float p -> Ordering Source # (<) :: URec Float p -> URec Float p -> Bool Source # (<=) :: URec Float p -> URec Float p -> Bool Source # (>) :: URec Float p -> URec Float p -> Bool Source # (>=) :: URec Float p -> URec Float p -> Bool Source # max :: URec Float p -> URec Float p -> URec Float p Source # min :: URec Float p -> URec Float p -> URec Float p Source # | |
| Ord (URec Int p) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Int p -> URec Int p -> Ordering Source # (<) :: URec Int p -> URec Int p -> Bool Source # (<=) :: URec Int p -> URec Int p -> Bool Source # (>) :: URec Int p -> URec Int p -> Bool Source # (>=) :: URec Int p -> URec Int p -> Bool Source # | |
| Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Word p -> URec Word p -> Ordering Source # (<) :: URec Word p -> URec Word p -> Bool Source # (<=) :: URec Word p -> URec Word p -> Bool Source # (>) :: URec Word p -> URec Word p -> Bool Source # (>=) :: URec Word p -> URec Word p -> Bool Source # | |
| (Ord e, Ord1 m, Ord a) => Ord (ExceptT e m a) | |
Defined in Control.Monad.Trans.Except Methods compare :: ExceptT e m a -> ExceptT e m a -> Ordering Source # (<) :: ExceptT e m a -> ExceptT e m a -> Bool Source # (<=) :: ExceptT e m a -> ExceptT e m a -> Bool Source # (>) :: ExceptT e m a -> ExceptT e m a -> Bool Source # (>=) :: ExceptT e m a -> ExceptT e m a -> Bool Source # max :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a Source # min :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a Source # | |
| (Ord1 f, Ord a) => Ord (IdentityT f a) | |
Defined in Control.Monad.Trans.Identity Methods compare :: IdentityT f a -> IdentityT f a -> Ordering Source # (<) :: IdentityT f a -> IdentityT f a -> Bool Source # (<=) :: IdentityT f a -> IdentityT f a -> Bool Source # (>) :: IdentityT f a -> IdentityT f a -> Bool Source # (>=) :: IdentityT f a -> IdentityT f a -> Bool Source # max :: IdentityT f a -> IdentityT f a -> IdentityT f a Source # min :: IdentityT f a -> IdentityT f a -> IdentityT f a Source # | |
| (Ord w, Ord1 m, Ord a) => Ord (WriterT w m a) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods compare :: WriterT w m a -> WriterT w m a -> Ordering Source # (<) :: WriterT w m a -> WriterT w m a -> Bool Source # (<=) :: WriterT w m a -> WriterT w m a -> Bool Source # (>) :: WriterT w m a -> WriterT w m a -> Bool Source # (>=) :: WriterT w m a -> WriterT w m a -> Bool Source # max :: WriterT w m a -> WriterT w m a -> WriterT w m a Source # min :: WriterT w m a -> WriterT w m a -> WriterT w m a Source # | |
| (Ord w, Ord1 m, Ord a) => Ord (WriterT w m a) | |
Defined in Control.Monad.Trans.Writer.Strict Methods compare :: WriterT w m a -> WriterT w m a -> Ordering Source # (<) :: WriterT w m a -> WriterT w m a -> Bool Source # (<=) :: WriterT w m a -> WriterT w m a -> Bool Source # (>) :: WriterT w m a -> WriterT w m a -> Bool Source # (>=) :: WriterT w m a -> WriterT w m a -> Bool Source # max :: WriterT w m a -> WriterT w m a -> WriterT w m a Source # min :: WriterT w m a -> WriterT w m a -> WriterT w m a Source # | |
| Ord a => Ord (Bundle Id v a) | |
Defined in Data.Vector.Fusion.Bundle Methods compare :: Bundle Id v a -> Bundle Id v a -> Ordering Source # (<) :: Bundle Id v a -> Bundle Id v a -> Bool Source # (<=) :: Bundle Id v a -> Bundle Id v a -> Bool Source # (>) :: Bundle Id v a -> Bundle Id v a -> Bool Source # (>=) :: Bundle Id v a -> Bundle Id v a -> Bool Source # max :: Bundle Id v a -> Bundle Id v a -> Bundle Id v a Source # min :: Bundle Id v a -> Bundle Id v a -> Bundle Id v a Source # | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
Defined in GHC.Classes | |
| (Ord (f a), Ord (g a)) => Ord (Product f g a) | Since: base-4.18.0.0 |
Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering Source # (<) :: Product f g a -> Product f g a -> Bool Source # (<=) :: Product f g a -> Product f g a -> Bool Source # (>) :: Product f g a -> Product f g a -> Bool Source # (>=) :: Product f g a -> Product f g a -> Bool Source # max :: Product f g a -> Product f g a -> Product f g a Source # min :: Product f g a -> Product f g a -> Product f g a Source # | |
| (Ord (f a), Ord (g a)) => Ord (Sum f g a) | Since: base-4.18.0.0 |
Defined in Data.Functor.Sum | |
| (Ord (f p), Ord (g p)) => Ord ((f :*: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: (f :*: g) p -> (f :*: g) p -> Ordering Source # (<) :: (f :*: g) p -> (f :*: g) p -> Bool Source # (<=) :: (f :*: g) p -> (f :*: g) p -> Bool Source # (>) :: (f :*: g) p -> (f :*: g) p -> Bool Source # (>=) :: (f :*: g) p -> (f :*: g) p -> Bool Source # | |
| (Ord (f p), Ord (g p)) => Ord ((f :+: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: (f :+: g) p -> (f :+: g) p -> Ordering Source # (<) :: (f :+: g) p -> (f :+: g) p -> Bool Source # (<=) :: (f :+: g) p -> (f :+: g) p -> Bool Source # (>) :: (f :+: g) p -> (f :+: g) p -> Bool Source # (>=) :: (f :+: g) p -> (f :+: g) p -> Bool Source # | |
| Ord c => Ord (K1 i c p) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Generics | |
| (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering Source # (<) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # (<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # (>) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # (>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # | |
| Ord (f (g a)) => Ord (Compose f g a) | Since: base-4.18.0.0 |
Defined in Data.Functor.Compose Methods compare :: Compose f g a -> Compose f g a -> Ordering Source # (<) :: Compose f g a -> Compose f g a -> Bool Source # (<=) :: Compose f g a -> Compose f g a -> Bool Source # (>) :: Compose f g a -> Compose f g a -> Bool Source # (>=) :: Compose f g a -> Compose f g a -> Bool Source # max :: Compose f g a -> Compose f g a -> Compose f g a Source # min :: Compose f g a -> Compose f g a -> Compose f g a Source # | |
| Ord (f (g p)) => Ord ((f :.: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: (f :.: g) p -> (f :.: g) p -> Ordering Source # (<) :: (f :.: g) p -> (f :.: g) p -> Bool Source # (<=) :: (f :.: g) p -> (f :.: g) p -> Bool Source # (>) :: (f :.: g) p -> (f :.: g) p -> Bool Source # (>=) :: (f :.: g) p -> (f :.: g) p -> Bool Source # | |
| Ord (f p) => Ord (M1 i c f p) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: M1 i c f p -> M1 i c f p -> Ordering Source # (<) :: M1 i c f p -> M1 i c f p -> Bool Source # (<=) :: M1 i c f p -> M1 i c f p -> Bool Source # (>) :: M1 i c f p -> M1 i c f p -> Bool Source # (>=) :: M1 i c f p -> M1 i c f p -> Bool Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering Source # (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering Source # (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering Source # (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source # min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source # min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source # min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source # min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # | |
class Applicative m => Monad (m :: Type -> Type) where Source #
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad should satisfy the following:
- Left identity
returna>>=k = k a- Right identity
m>>=return= m- Associativity
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for List, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 Source #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
An alternative name for this function is 'bind', but some people may refer to it as 'flatMap', which results from it being equivialent to
\x f ->join(fmapf x) :: Monad m => m a -> (a -> m b) -> m b
which can be seen as mapping a value with
Monad m => m a -> m (m b) and then 'flattening' m (m b) to m b using join.
(>>) :: m a -> m b -> m b infixl 1 Source #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'as ' can be understood as the >> bsdo expression
do as bs
or in terms of (>>=)
as >>= const bs
Inject a value into the monadic type.
This function should not be different from its default implementation
as pure. The justification for the existence of this function is
merely historic.
Instances
| Monad Complex | Since: base-4.9.0.0 |
| Monad First | Since: base-4.9.0.0 |
| Monad Last | Since: base-4.9.0.0 |
| Monad Max | Since: base-4.9.0.0 |
| Monad Min | Since: base-4.9.0.0 |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Monad Identity | Since: base-4.8.0.0 |
| Monad First | Since: base-4.8.0.0 |
| Monad Last | Since: base-4.8.0.0 |
| Monad Down | Since: base-4.11.0.0 |
| Monad Dual | Since: base-4.8.0.0 |
| Monad Product | Since: base-4.8.0.0 |
| Monad Sum | Since: base-4.8.0.0 |
| Monad Par1 | Since: base-4.9.0.0 |
| Monad P | Since: base-2.1 |
| Monad ReadP | Since: base-2.1 |
| Monad IO | Since: base-2.1 |
| Monad Array | |
| Monad SmallArray | |
| Monad Q | |
| Monad Vector | |
| Monad Id | |
| Monad Vector | |
| Monad Box | |
| Monad Maybe | Since: base-2.1 |
| Monad Solo | Since: base-4.15 |
| Monad [] | Since: base-2.1 |
| Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source # | |
| ArrowApply a => Monad (ArrowMonad a) | Since: base-2.1 |
Defined in GHC.Internal.Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source # | |
| Monad (Either e) | Since: base-4.4.0.0 |
| Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monad (ST s) | Since: base-2.1 |
| Monad m => Monad (MaybeT m) | |
| Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
| Monad m => Monad (Kleisli m a) | Since: base-4.14.0.0 |
| Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
| Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
| Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid w, Functor m, Monad m) => Monad (AccumT w m) | |
| Monad m => Monad (ExceptT e m) | |
| Monad m => Monad (IdentityT m) | |
| Monad m => Monad (ReaderT r m) | |
| Monad m => Monad (SelectT r m) | |
| Monad m => Monad (StateT s m) | |
| Monad m => Monad (StateT s m) | |
| Monad m => Monad (WriterT w m) | |
| (Monoid w, Monad m) => Monad (WriterT w m) | |
| (Monoid w, Monad m) => Monad (WriterT w m) | |
| (Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| Monad (ContT r m) | |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| Monad ((->) r) | Since: base-2.1 |
| Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
| Monad m => Monad (RWST r w s m) | |
| (Monoid w, Monad m) => Monad (RWST r w s m) | |
| (Monoid w, Monad m) => Monad (RWST r w s m) | |
class Functor (f :: Type -> Type) where Source #
A type f is a Functor if it provides a function fmap which, given any types a and b
lets you apply any function from (a -> b) to turn an f a into an f b, preserving the
structure of f. Furthermore f needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
See these articles by School of Haskell or
David Luposchainsky
for an explanation.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source #
fmap is used to apply a function of type (a -> b) to a value of type f a,
where f is a functor, to produce a value of type f b.
Note that for any type constructor with more than one parameter (e.g., Either),
only the last type parameter can be modified with fmap (e.g., b in `Either a b`).
Some type constructors with two parameters or more have a Bifunctor
Examples
Convert from a Maybe IntMaybe String
using show:
>>>fmap show NothingNothing>>>fmap show (Just 3)Just "3"
Convert from an Either Int IntEither Int String using show:
>>>fmap show (Left 17)Left 17>>>fmap show (Right 17)Right "17"
Double each element of a list:
>>>fmap (*2) [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>fmap even (2,2)(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance
is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over
with fmap).
It explains why fmap can be used with tuples containing values of different types as in the
following example:
>>>fmap even ("hello", 1.0, 4)("hello",1.0,True)
Instances
| Functor Complex | Since: base-4.9.0.0 |
| Functor First | Since: base-4.9.0.0 |
| Functor Last | Since: base-4.9.0.0 |
| Functor Max | Since: base-4.9.0.0 |
| Functor Min | Since: base-4.9.0.0 |
| Functor ArgDescr | Since: base-4.7.0.0 |
| Functor ArgOrder | Since: base-4.7.0.0 |
| Functor OptDescr | Since: base-4.7.0.0 |
| Functor NonEmpty | Since: base-4.9.0.0 |
| Functor Identity | Since: base-4.8.0.0 |
| Functor First | Since: base-4.8.0.0 |
| Functor Last | Since: base-4.8.0.0 |
| Functor Down | Since: base-4.11.0.0 |
| Functor Dual | Since: base-4.8.0.0 |
| Functor Product | Since: base-4.8.0.0 |
| Functor Sum | Since: base-4.8.0.0 |
| Functor ZipList | Since: base-2.1 |
| Functor Par1 | Since: base-4.9.0.0 |
| Functor P | Since: base-4.8.0.0 |
| Functor ReadP | Since: base-2.1 |
| Functor IO | Since: base-2.1 |
| Functor Array | |
| Functor SmallArray | |
| Functor Q | |
| Functor TyVarBndr | |
| Functor Vector | |
| Functor Id | |
| Functor Vector | |
| Functor Box | |
| Functor Maybe | Since: base-2.1 |
| Functor Solo | Since: base-4.15 |
| Functor [] | Since: base-2.1 |
| Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Functor (Arg a) | Since: base-4.9.0.0 |
| Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Functor (Either a) | Since: base-3.0 |
| Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (ST s) | Since: base-2.1 |
| Functor m => Functor (MaybeT m) | |
| Functor (Step s) | |
| Monad m => Functor (Stream m) | |
| Functor ((,) a) | Since: base-2.1 |
| Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| KnownVariant v => Functor (Dimensional v d) Source # | A Note that this instance is dubious, because it allows you to break the dimensional abstraction. See Note that, while this instance overlaps with that given for Note that this is an orphan instance. |
Defined in Numeric.Units.Dimensional.Functor Methods fmap :: (a -> b) -> Dimensional v d a -> Dimensional v d b Source # (<$) :: a -> Dimensional v d b -> Dimensional v d a Source # | |
| Functor (SQuantity s DOne) Source # | |
| Functor m => Functor (Kleisli m a) | Since: base-4.14.0.0 |
| Functor (Const m :: Type -> Type) | Since: base-2.1 |
| Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
| Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
| (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
| Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| Functor m => Functor (AccumT w m) | |
| Functor m => Functor (ExceptT e m) | |
| Functor m => Functor (IdentityT m) | |
| Functor m => Functor (ReaderT r m) | |
| Functor m => Functor (SelectT r m) | |
| Functor m => Functor (StateT s m) | |
| Functor m => Functor (StateT s m) | |
| Functor m => Functor (WriterT w m) | |
| Functor m => Functor (WriterT w m) | |
| Functor m => Functor (WriterT w m) | |
| Monad m => Functor (Bundle m v) | |
| Functor ((,,) a b) | Since: base-4.14.0.0 |
| (Functor f, Functor g) => Functor (Product f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
| Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (ContT r m) | |
| Functor ((,,,) a b c) | Since: base-4.14.0.0 |
| Functor ((->) r) | Since: base-2.1 |
| (Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
| Functor m => Functor (RWST r w s m) | |
| Functor m => Functor (RWST r w s m) | |
| Functor m => Functor (RWST r w s m) | |
| Functor ((,,,,) a b c d) | Since: base-4.18.0.0 |
| Functor ((,,,,,) a b c d e) | Since: base-4.18.0.0 |
| Functor ((,,,,,,) a b c d e f) | Since: base-4.18.0.0 |
class Monad m => MonadFail (m :: Type -> Type) where Source #
When a value is bound in do-notation, the pattern on the left
hand side of <- might not match. In this case, this class
provides a function to recover.
A Monad without a MonadFail instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat).
Instances of MonadFail should satisfy the following law: fail s should
be a left zero for >>=,
fail s >>= f = fail s
If your Monad is also MonadPlus, a popular definition is
fail _ = mzero
fail s should be an action that runs in the monad itself, not an
exception (except in instances of MonadIO). In particular,
fail should not be implemented in terms of error.
Since: base-4.9.0.0
Instances
| MonadFail P | Since: base-4.9.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadP | |
| MonadFail ReadP | Since: base-4.9.0.0 |
| MonadFail IO | Since: base-4.9.0.0 |
| MonadFail Array | |
Defined in Data.Primitive.Array | |
| MonadFail SmallArray | |
Defined in Data.Primitive.SmallArray | |
| MonadFail Q | |
| MonadFail Vector | |
Defined in Data.Vector | |
| MonadFail Vector | |
Defined in Data.Vector.Strict | |
| MonadFail Maybe | Since: base-4.9.0.0 |
| MonadFail [] | Since: base-4.9.0.0 |
Defined in GHC.Internal.Control.Monad.Fail | |
| Monad m => MonadFail (MaybeT m) | |
| MonadFail f => MonadFail (Ap f) | Since: base-4.12.0.0 |
| (Monoid w, MonadFail m) => MonadFail (AccumT w m) | |
| MonadFail m => MonadFail (ExceptT e m) | |
| MonadFail m => MonadFail (IdentityT m) | |
| MonadFail m => MonadFail (ReaderT r m) | |
| MonadFail m => MonadFail (SelectT r m) | |
| MonadFail m => MonadFail (StateT s m) | |
| MonadFail m => MonadFail (StateT s m) | |
| MonadFail m => MonadFail (WriterT w m) | |
| (Monoid w, MonadFail m) => MonadFail (WriterT w m) | |
| (Monoid w, MonadFail m) => MonadFail (WriterT w m) | |
| MonadFail m => MonadFail (ContT r m) | |
| MonadFail m => MonadFail (RWST r w s m) | |
| (Monoid w, MonadFail m) => MonadFail (RWST r w s m) | |
| (Monoid w, MonadFail m) => MonadFail (RWST r w s m) | |
fromIntegral :: (Integral a, Num b) => a -> b Source #
General coercion from Integral types.
WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.
realToFrac :: (Real a, Fractional b) => a -> b Source #
General coercion to Fractional types.
WARNING: This function goes through the Rational type, which does not have values for NaN for example.
This means it does not round-trip.
For Double it also behaves differently with or without -O0:
Prelude> realToFrac nan -- With -O0 -Infinity Prelude> realToFrac nan NaN
class (Real a, Enum a) => Integral a where Source #
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 ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (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.
Methods
quot :: a -> a -> a infixl 7 Source #
Integer division truncated toward zero.
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
rem :: a -> a -> a infixl 7 Source #
Integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
div :: a -> a -> a infixl 7 Source #
Integer division truncated toward negative infinity.
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
mod :: a -> a -> a infixl 7 Source #
Integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
quotRem :: a -> a -> (a, a) Source #
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
divMod :: a -> a -> (a, a) Source #
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base.
toInteger :: a -> Integer Source #
Conversion to Integer.
Instances
| Integral CBool | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CChar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CInt | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CIntMax | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CIntMax -> CIntMax -> CIntMax Source # rem :: CIntMax -> CIntMax -> CIntMax Source # div :: CIntMax -> CIntMax -> CIntMax Source # mod :: CIntMax -> CIntMax -> CIntMax Source # quotRem :: CIntMax -> CIntMax -> (CIntMax, CIntMax) Source # | |
| Integral CIntPtr | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CIntPtr -> CIntPtr -> CIntPtr Source # rem :: CIntPtr -> CIntPtr -> CIntPtr Source # div :: CIntPtr -> CIntPtr -> CIntPtr Source # mod :: CIntPtr -> CIntPtr -> CIntPtr Source # quotRem :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr) Source # | |
| Integral CLLong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CLong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CPtrdiff | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # rem :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # div :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # mod :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # quotRem :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) Source # divMod :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) Source # | |
| Integral CSChar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CShort | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # rem :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # div :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # mod :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # quotRem :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) Source # divMod :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) Source # toInteger :: CSigAtomic -> Integer Source # | |
| Integral CSize | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUChar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUInt | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUIntMax | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CUIntMax -> CUIntMax -> CUIntMax Source # rem :: CUIntMax -> CUIntMax -> CUIntMax Source # div :: CUIntMax -> CUIntMax -> CUIntMax Source # mod :: CUIntMax -> CUIntMax -> CUIntMax Source # quotRem :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) Source # divMod :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) Source # | |
| Integral CUIntPtr | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # rem :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # div :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # mod :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # quotRem :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) Source # divMod :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) Source # | |
| Integral CULLong | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CULLong -> CULLong -> CULLong Source # rem :: CULLong -> CULLong -> CULLong Source # div :: CULLong -> CULLong -> CULLong Source # mod :: CULLong -> CULLong -> CULLong Source # quotRem :: CULLong -> CULLong -> (CULLong, CULLong) Source # | |
| Integral CULong | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUShort | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CUShort -> CUShort -> CUShort Source # rem :: CUShort -> CUShort -> CUShort Source # div :: CUShort -> CUShort -> CUShort Source # mod :: CUShort -> CUShort -> CUShort Source # quotRem :: CUShort -> CUShort -> (CUShort, CUShort) Source # | |
| Integral CWchar | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral Int16 | Since: base-2.1 |
| Integral Int32 | Since: base-2.1 |
| Integral Int64 | Since: base-2.1 |
| Integral Int8 | Since: base-2.1 |
Defined in GHC.Internal.Int | |
| Integral Word16 | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Integral Word32 | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Integral Word64 | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Integral Word8 | Since: base-2.1 |
| Integral Integer | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods quot :: Integer -> Integer -> Integer Source # rem :: Integer -> Integer -> Integer Source # div :: Integer -> Integer -> Integer Source # mod :: Integer -> Integer -> Integer Source # quotRem :: Integer -> Integer -> (Integer, Integer) Source # | |
| Integral Natural | Since: base-4.8.0.0 |
Defined in GHC.Internal.Real Methods quot :: Natural -> Natural -> Natural Source # rem :: Natural -> Natural -> Natural Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # quotRem :: Natural -> Natural -> (Natural, Natural) Source # | |
| Integral Int | Since: base-2.0.1 |
| Integral Word | Since: base-2.1 |
Defined in GHC.Internal.Real | |
| Integral a => Integral (Identity a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a Source # rem :: Identity a -> Identity a -> Identity a Source # div :: Identity a -> Identity a -> Identity a Source # mod :: Identity a -> Identity a -> Identity a Source # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) Source # divMod :: Identity a -> Identity a -> (Identity a, Identity a) Source # | |
| Integral a => Integral (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b Source # rem :: Const a b -> Const a b -> Const a b Source # div :: Const a b -> Const a b -> Const a b Source # mod :: Const a b -> Const a b -> Const a b Source # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) Source # divMod :: Const a b -> Const a b -> (Const a b, Const a b) Source # | |
| Integral (f (g a)) => Integral (Compose f g a) | Since: base-4.19.0.0 |
Defined in Data.Functor.Compose Methods quot :: Compose f g a -> Compose f g a -> Compose f g a Source # rem :: Compose f g a -> Compose f g a -> Compose f g a Source # div :: Compose f g a -> Compose f g a -> Compose f g a Source # mod :: Compose f g a -> Compose f g a -> Compose f g a Source # quotRem :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source # divMod :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source # | |
class (Num a, Ord a) => Real a where Source #
Real numbers.
The Haskell report defines no laws for Real, however Real instances
are customarily expected to adhere to the following law:
- Coherence with
fromRational - if the type also implements
Fractional, thenfromRationalis a left inverse fortoRational, i.e.fromRational (toRational i) = i
The law does not hold for Float, Double, CFloat,
CDouble, etc., because these types contain non-finite values,
which cannot be roundtripped through Rational.
Methods
toRational :: a -> Rational Source #
Rational equivalent of its real argument with full precision.
Instances
| Real CBool | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CBool -> Rational Source # | |
| Real CChar | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CChar -> Rational Source # | |
| Real CClock | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CClock -> Rational Source # | |
| Real CDouble | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CDouble -> Rational Source # | |
| Real CFloat | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CFloat -> Rational Source # | |
| Real CInt | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CInt -> Rational Source # | |
| Real CIntMax | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CIntMax -> Rational Source # | |
| Real CIntPtr | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CIntPtr -> Rational Source # | |
| Real CLLong | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CLLong -> Rational Source # | |
| Real CLong | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CLong -> Rational Source # | |
| Real CPtrdiff | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CPtrdiff -> Rational Source # | |
| Real CSChar | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSChar -> Rational Source # | |
| Real CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSUSeconds -> Rational Source # | |
| Real CShort | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CShort -> Rational Source # | |
| Real CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSigAtomic -> Rational Source # | |
| Real CSize | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSize -> Rational Source # | |
| Real CTime | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CTime -> Rational Source # | |
| Real CUChar | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUChar -> Rational Source # | |
| Real CUInt | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUInt -> Rational Source # | |
| Real CUIntMax | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUIntMax -> Rational Source # | |
| Real CUIntPtr | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUIntPtr -> Rational Source # | |
| Real CULLong | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CULLong -> Rational Source # | |
| Real CULong | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CULong -> Rational Source # | |
| Real CUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUSeconds -> Rational Source # | |
| Real CUShort | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUShort -> Rational Source # | |
| Real CWchar | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CWchar -> Rational Source # | |
| Real Int16 | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int16 -> Rational Source # | |
| Real Int32 | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int32 -> Rational Source # | |
| Real Int64 | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int64 -> Rational Source # | |
| Real Int8 | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int8 -> Rational Source # | |
| Real Word16 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word16 -> Rational Source # | |
| Real Word32 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word32 -> Rational Source # | |
| Real Word64 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word64 -> Rational Source # | |
| Real Word8 | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word8 -> Rational Source # | |
| Real Integer | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods toRational :: Integer -> Rational Source # | |
| Real Natural | Since: base-4.8.0.0 |
Defined in GHC.Internal.Real Methods toRational :: Natural -> Rational Source # | |
| Real Double | Beware that
Since: base-2.1 |
Defined in GHC.Internal.Float Methods toRational :: Double -> Rational Source # | |
| Real Float | Beware that
Since: base-2.1 |
Defined in GHC.Internal.Float Methods toRational :: Float -> Rational Source # | |
| Real Int | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods toRational :: Int -> Rational Source # | |
| Real Word | Since: base-2.1 |
Defined in GHC.Internal.Real Methods toRational :: Word -> Rational Source # | |
| Real a => Real (Identity a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods toRational :: Identity a -> Rational Source # | |
| Real a => Real (Down a) | Since: base-4.14.0.0 |
Defined in GHC.Internal.Data.Ord Methods toRational :: Down a -> Rational Source # | |
| Integral a => Real (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods toRational :: Ratio a -> Rational Source # | |
| HasResolution a => Real (Fixed a) | Since: base-2.1 |
Defined in Data.Fixed Methods toRational :: Fixed a -> Rational Source # | |
| Real a => Real (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods toRational :: Const a b -> Rational Source # | |
| Real (f (g a)) => Real (Compose f g a) | Since: base-4.19.0.0 |
Defined in Data.Functor.Compose Methods toRational :: Compose f g a -> Rational Source # | |
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
You can alternatively define sconcat instead of (<>), in which case the
laws are:
Since: base-4.9.0.0
Methods
(<>) :: a -> a -> a infixr 6 Source #
An associative operation.
Examples
>>>[1,2,3] <> [4,5,6][1,2,3,4,5,6]
>>>Just [1, 2, 3] <> Just [4, 5, 6]Just [1,2,3,4,5,6]
>>>putStr "Hello, " <> putStrLn "World!"Hello, World!
Instances
| Semigroup ByteArray | Since: base-4.17.0.0 |
| Semigroup Dimension' Source # | |
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods (<>) :: Dimension' -> Dimension' -> Dimension' Source # sconcat :: NonEmpty Dimension' -> Dimension' Source # stimes :: Integral b => b -> Dimension' -> Dimension' Source # | |
| Semigroup AnyUnit Source # | |
| Semigroup ExactPi | The multiplicative semigroup over |
| Semigroup Void | Since: base-4.9.0.0 |
| Semigroup All | Since: base-4.9.0.0 |
| Semigroup Any | Since: base-4.9.0.0 |
| Semigroup ExceptionContext | |
Defined in GHC.Internal.Exception.Context Methods (<>) :: ExceptionContext -> ExceptionContext -> ExceptionContext Source # sconcat :: NonEmpty ExceptionContext -> ExceptionContext Source # stimes :: Integral b => b -> ExceptionContext -> ExceptionContext Source # | |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Semigroup () | Since: base-4.9.0.0 |
| Semigroup (FromMaybe b) | |
| Semigroup a => Semigroup (JoinWith a) | |
| Semigroup (NonEmptyDList a) | |
| Semigroup (Comparison a) |
(<>) :: Comparison a -> Comparison a -> Comparison a Comparison cmp <> Comparison cmp' = Comparison a a' -> cmp a a' <> cmp a a' |
Defined in Data.Functor.Contravariant Methods (<>) :: Comparison a -> Comparison a -> Comparison a Source # sconcat :: NonEmpty (Comparison a) -> Comparison a Source # stimes :: Integral b => b -> Comparison a -> Comparison a Source # | |
| Semigroup (Equivalence a) |
(<>) :: Equivalence a -> Equivalence a -> Equivalence a Equivalence equiv <> Equivalence equiv' = Equivalence a b -> equiv a b && equiv' a b |
Defined in Data.Functor.Contravariant Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a Source # sconcat :: NonEmpty (Equivalence a) -> Equivalence a Source # stimes :: Integral b => b -> Equivalence a -> Equivalence a Source # | |
| Semigroup (Predicate a) |
(<>) :: Predicate a -> Predicate a -> Predicate a Predicate pred <> Predicate pred' = Predicate a -> pred a && pred' a |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
| Monoid m => Semigroup (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source # | |
| Num a => Semigroup (AnyQuantity a) Source # |
|
Defined in Numeric.Units.Dimensional.Dynamic Methods (<>) :: AnyQuantity a -> AnyQuantity a -> AnyQuantity a Source # sconcat :: NonEmpty (AnyQuantity a) -> AnyQuantity a Source # stimes :: Integral b => b -> AnyQuantity a -> AnyQuantity a Source # | |
| Num a => Semigroup (DynQuantity a) Source # |
|
Defined in Numeric.Units.Dimensional.Dynamic Methods (<>) :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # sconcat :: NonEmpty (DynQuantity a) -> DynQuantity a Source # stimes :: Integral b => b -> DynQuantity a -> DynQuantity a Source # | |
| Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Down a) | Since: base-4.11.0.0 |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Semigroup (Endo a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| (Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods (<>) :: Generically a -> Generically a -> Generically a Source # sconcat :: NonEmpty (Generically a) -> Generically a Source # stimes :: Integral b => b -> Generically a -> Generically a Source # | |
| Semigroup p => Semigroup (Par1 p) | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
| Semigroup (Array a) | |
| Semigroup (PrimArray a) | |
| Semigroup (SmallArray a) | |
| Semigroup a => Semigroup (Q a) | Since: template-haskell-2.17.0.0 |
| Semigroup (Vector a) | |
| Prim a => Semigroup (Vector a) | |
| Storable a => Semigroup (Vector a) | |
| Semigroup (Vector a) | |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Solo a) | Since: base-4.15 |
| Semigroup [a] | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Op a b) |
(<>) :: Op a b -> Op a b -> Op a b Op f <> Op g = Op a -> f a <> g a |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Semigroup (Proxy s) | Since: base-4.9.0.0 |
| Semigroup (U1 p) | Since: base-4.12.0.0 |
| Semigroup (V1 p) | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (ST s a) | Since: base-4.11.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
| Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
| Num a => Semigroup (SQuantity s d a) Source # |
|
| Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 |
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (Rec1 f p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
| (Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) | Since: base-4.16.0.0 |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
| Semigroup c => Semigroup (K1 i c p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
| Semigroup (f (g a)) => Semigroup (Compose f g a) | Since: base-4.16.0.0 |
| Semigroup (f (g p)) => Semigroup ((f :.: g) p) | Since: base-4.12.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |
class Semigroup a => Monoid a where Source #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x<>mempty= x- Left identity
mempty<>x = x- Associativity
x(<>(y<>z) = (x<>y)<>zSemigrouplaw)- Concatenation
mconcat=foldr(<>)mempty
You can alternatively define mconcat instead of mempty, in which case the
laws are:
- Unit
mconcat(purex) = x- Multiplication
mconcat(joinxss) =mconcat(fmapmconcatxss)- Subclass
mconcat(toListxs) =sconcatxs
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtypes and make those instances
of Monoid, e.g. Sum and Product.
NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.
Methods
Identity of mappend
Examples
>>>"Hello world" <> mempty"Hello world"
>>>mempty <> [1, 2, 3][1,2,3]
mappend :: a -> a -> a Source #
An associative operation
NOTE: This method is redundant and has the default
implementation mappend = (<>)mappend is a synonym for
(<>), it is expected that the two functions are defined the same
way. In a future GHC release mappend will be removed from Monoid.
Fold a list using the monoid.
For most types, the default definition for mconcat will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
>>>mconcat ["Hello", " ", "Haskell", "!"]"Hello Haskell!"
Instances
| Monoid ByteArray | Since: base-4.17.0.0 |
| Monoid Dimension' Source # | The monoid of dimensions under multiplication. |
Defined in Numeric.Units.Dimensional.Dimensions.TermLevel Methods mempty :: Dimension' Source # mappend :: Dimension' -> Dimension' -> Dimension' Source # mconcat :: [Dimension'] -> Dimension' Source # | |
| Monoid AnyUnit Source # | |
| Monoid ExactPi | The multiplicative monoid over |
| Monoid All | Since: base-2.1 |
| Monoid Any | Since: base-2.1 |
| Monoid ExceptionContext | |
Defined in GHC.Internal.Exception.Context Methods mempty :: ExceptionContext Source # mappend :: ExceptionContext -> ExceptionContext -> ExceptionContext Source # mconcat :: [ExceptionContext] -> ExceptionContext Source # | |
| Monoid Ordering | Since: base-2.1 |
| Monoid () | Since: base-2.1 |
| Monoid (Comparison a) |
mempty :: Comparison a mempty = Comparison _ _ -> EQ |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source # mappend :: Comparison a -> Comparison a -> Comparison a Source # mconcat :: [Comparison a] -> Comparison a Source # | |
| Monoid (Equivalence a) |
mempty :: Equivalence a mempty = Equivalence _ _ -> True |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source # mappend :: Equivalence a -> Equivalence a -> Equivalence a Source # mconcat :: [Equivalence a] -> Equivalence a Source # | |
| Monoid (Predicate a) |
mempty :: Predicate a mempty = _ -> True |
| (Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source # | |
| Num a => Monoid (AnyQuantity a) Source # |
|
Defined in Numeric.Units.Dimensional.Dynamic Methods mempty :: AnyQuantity a Source # mappend :: AnyQuantity a -> AnyQuantity a -> AnyQuantity a Source # mconcat :: [AnyQuantity a] -> AnyQuantity a Source # | |
| Num a => Monoid (DynQuantity a) Source # |
|
Defined in Numeric.Units.Dimensional.Dynamic Methods mempty :: DynQuantity a Source # mappend :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # mconcat :: [DynQuantity a] -> DynQuantity a Source # | |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| Monoid (First a) | Since: base-2.1 |
| Monoid (Last a) | Since: base-2.1 |
| Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Monoid (Endo a) | Since: base-2.1 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| (Generic a, Monoid (Rep a ())) => Monoid (Generically a) | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods mempty :: Generically a Source # mappend :: Generically a -> Generically a -> Generically a Source # mconcat :: [Generically a] -> Generically a Source # | |
| Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Monoid (Array a) | |
| Monoid (PrimArray a) | |
| Monoid (SmallArray a) | |
| Monoid a => Monoid (Q a) | Since: template-haskell-2.17.0.0 |
| Monoid (Vector a) | |
| Prim a => Monoid (Vector a) | |
| Storable a => Monoid (Vector a) | |
| Monoid (Vector a) | |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (Solo a) | Since: base-4.15 |
| Monoid [a] | Since: base-2.1 |
| Monoid a => Monoid (Op a b) |
mempty :: Op a b mempty = Op _ -> mempty |
| Monoid (Proxy s) | Since: base-4.7.0.0 |
| Monoid (U1 p) | Since: base-4.12.0.0 |
| Monoid a => Monoid (ST s a) | Since: base-4.11.0.0 |
| (Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| Monoid b => Monoid (a -> b) | Since: base-2.1 |
| Num a => Monoid (SQuantity s d a) Source # |
|
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 |
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
| Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
| (Monoid (f a), Monoid (g a)) => Monoid (Product f g a) | Since: base-4.16.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
| Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
| Monoid (f (g a)) => Monoid (Compose f g a) | Since: base-4.16.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
| Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
class Functor f => Applicative (f :: Type -> Type) where Source #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
pureid<*>v = v- Composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- Homomorphism
puref<*>purex =pure(f x)- Interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value into the Structure.
Examples
>>>pure 1 :: Maybe IntJust 1
>>>pure 'z' :: [Char]"z"
>>>pure (pure ":D") :: Maybe [String]Just [":D"]
(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
Example
Used in combination with (<$>)(<*>)
>>>data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>>produceFoo :: Applicative f => f Foo>>>produceBar :: Applicative f => f Bar>>>produceBaz :: Applicative f => f Baz
>>>mkState :: Applicative f => f MyState>>>mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
liftA2 :: (a -> b -> c) -> f a -> f b -> f c Source #
Lift a binary function to actions.
Some functors support an implementation of liftA2 that is more
efficient than the default one. In particular, if fmap is an
expensive operation, it is likely better to use liftA2 than to
fmap over the structure and then use <*>.
This became a typeclass method in 4.10.0.0. Prior to that, it was
a function defined in terms of <*> and fmap.
Example
>>>liftA2 (,) (Just 3) (Just 5)Just (3,5)
>>>liftA2 (+) [1, 2, 3] [4, 5, 6][5,6,7,6,7,8,7,8,9]
(*>) :: f a -> f b -> f b infixl 4 Source #
Sequence actions, discarding the value of the first argument.
Examples
If used in conjunction with the Applicative instance for Maybe,
you can chain Maybe computations, with a possible "early return"
in case of Nothing.
>>>Just 2 *> Just 3Just 3
>>>Nothing *> Just 3Nothing
Of course a more interesting use case would be to have effectful computations instead of just returning pure values.
>>>import Data.Char>>>import GHC.Internal.Text.ParserCombinators.ReadP>>>let p = string "my name is " *> munch1 isAlpha <* eof>>>readP_to_S p "my name is Simon"[("Simon","")]
(<*) :: f a -> f b -> f a infixl 4 Source #
Sequence actions, discarding the value of the second argument.
Instances
| Applicative Complex | Since: base-4.9.0.0 |
| Applicative First | Since: base-4.9.0.0 |
| Applicative Last | Since: base-4.9.0.0 |
| Applicative Max | Since: base-4.9.0.0 |
| Applicative Min | Since: base-4.9.0.0 |
| Applicative NonEmpty | Since: base-4.9.0.0 |
Defined in GHC.Internal.Base | |
| Applicative Identity | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Functor.Identity | |
| Applicative First | Since: base-4.8.0.0 |
| Applicative Last | Since: base-4.8.0.0 |
| Applicative Down | Since: base-4.11.0.0 |
| Applicative Dual | Since: base-4.8.0.0 |
| Applicative Product | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Applicative Sum | Since: base-4.8.0.0 |
| Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN
= ZipList (zipWithN f xs1 ... xsN)where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}Since: base-2.1 |
Defined in GHC.Internal.Functor.ZipList | |
| Applicative Par1 | Since: base-4.9.0.0 |
| Applicative P | Since: base-4.5.0.0 |
| Applicative ReadP | Since: base-4.6.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadP | |
| Applicative IO | Since: base-2.1 |
| Applicative Array | |
| Applicative SmallArray | |
Defined in Data.Primitive.SmallArray Methods pure :: a -> SmallArray a Source # (<*>) :: SmallArray (a -> b) -> SmallArray a -> SmallArray b Source # liftA2 :: (a -> b -> c) -> SmallArray a -> SmallArray b -> SmallArray c Source # (*>) :: SmallArray a -> SmallArray b -> SmallArray b Source # (<*) :: SmallArray a -> SmallArray b -> SmallArray a Source # | |
| Applicative Q | |
| Applicative Vector | |
| Applicative Id | |
| Applicative Vector | |
| Applicative Box | |
| Applicative Maybe | Since: base-2.1 |
| Applicative Solo | Since: base-4.15 |
| Applicative [] | Since: base-2.1 |
| Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 Source # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Applicative (Either e) | Since: base-3.0 |
Defined in GHC.Internal.Data.Either | |
| Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Applicative (ST s) | Since: base-4.4.0.0 |
| (Functor m, Monad m) => Applicative (MaybeT m) | |
Defined in Control.Monad.Trans.Maybe | |
| Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: base-2.1 |
| Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in GHC.Internal.Control.Arrow Methods pure :: a0 -> Kleisli m a a0 Source # (<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source # (*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source # | |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
Defined in GHC.Internal.Data.Functor.Const | |
| Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
| Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
| (Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods pure :: a -> Generically1 f a Source # (<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b Source # liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c Source # (*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b Source # (<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a Source # | |
| Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid w, Functor m, Monad m) => Applicative (AccumT w m) | |
Defined in Control.Monad.Trans.Accum Methods pure :: a -> AccumT w m a Source # (<*>) :: AccumT w m (a -> b) -> AccumT w m a -> AccumT w m b Source # liftA2 :: (a -> b -> c) -> AccumT w m a -> AccumT w m b -> AccumT w m c Source # (*>) :: AccumT w m a -> AccumT w m b -> AccumT w m b Source # (<*) :: AccumT w m a -> AccumT w m b -> AccumT w m a Source # | |
| (Functor m, Monad m) => Applicative (ExceptT e m) | |
Defined in Control.Monad.Trans.Except Methods pure :: a -> ExceptT e m a Source # (<*>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b Source # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c Source # (*>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b Source # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a Source # | |
| Applicative m => Applicative (IdentityT m) | |
Defined in Control.Monad.Trans.Identity Methods pure :: a -> IdentityT m a Source # (<*>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b Source # liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c Source # (*>) :: IdentityT m a -> IdentityT m b -> IdentityT m b Source # (<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a Source # | |
| Applicative m => Applicative (ReaderT r m) | |
Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a Source # (<*>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b Source # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c Source # (*>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b Source # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a Source # | |
| (Functor m, Monad m) => Applicative (SelectT r m) | |
Defined in Control.Monad.Trans.Select Methods pure :: a -> SelectT r m a Source # (<*>) :: SelectT r m (a -> b) -> SelectT r m a -> SelectT r m b Source # liftA2 :: (a -> b -> c) -> SelectT r m a -> SelectT r m b -> SelectT r m c Source # (*>) :: SelectT r m a -> SelectT r m b -> SelectT r m b Source # (<*) :: SelectT r m a -> SelectT r m b -> SelectT r m a Source # | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Lazy Methods pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # | |
| (Functor m, Monad m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.CPS Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # | |
| (Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # | |
| (Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Strict Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # | |
| (Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
Defined in GHC.Internal.Base | |
| (Applicative f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods pure :: a -> Product f g a Source # (<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source # (*>) :: Product f g a -> Product f g b -> Product f g b Source # (<*) :: Product f g a -> Product f g b -> Product f g a Source # | |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
| Applicative (ContT r m) | |
Defined in Control.Monad.Trans.Cont | |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Internal.Base Methods pure :: a0 -> (a, b, c, a0) Source # (<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source # (*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source # | |
| Applicative ((->) r) | Since: base-2.1 |
| (Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a Source # (<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source # (*>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source # | |
| (Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| (Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.CPS Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # | |
| (Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Lazy Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # | |
| (Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Strict Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # | |
class Bounded a where Source #
The Bounded class is used to name the upper and lower limits of a
type. Ord is not a superclass of Bounded since types that are not
totally ordered may also have upper and lower bounds.
The Bounded class may be derived for any enumeration type;
minBound is the first constructor listed in the data declaration
and maxBound is the last.
Bounded may also be derived for single-constructor datatypes whose
constituent types are in Bounded.
Instances
| Bounded Extension | |
| Bounded All | Since: base-2.1 |
| Bounded Any | Since: base-2.1 |
| Bounded CBool | |
| Bounded CChar | |
| Bounded CInt | |
| Bounded CIntMax | |
| Bounded CIntPtr | |
| Bounded CLLong | |
| Bounded CLong | |
| Bounded CPtrdiff | |
| Bounded CSChar | |
| Bounded CShort | |
| Bounded CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types | |
| Bounded CSize | |
| Bounded CUChar | |
| Bounded CUInt | |
| Bounded CUIntMax | |
| Bounded CUIntPtr | |
| Bounded CULLong | |
| Bounded CULong | |
| Bounded CUShort | |
| Bounded CWchar | |
| Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Bounded Int16 | Since: base-2.1 |
| Bounded Int32 | Since: base-2.1 |
| Bounded Int64 | Since: base-2.1 |
| Bounded Int8 | Since: base-2.1 |
| Bounded Word16 | Since: base-2.1 |
| Bounded Word32 | Since: base-2.1 |
| Bounded Word64 | Since: base-2.1 |
| Bounded Word8 | Since: base-2.1 |
| Bounded Ordering | Since: base-2.1 |
| Bounded () | Since: base-2.1 |
| Bounded Bool | Since: base-2.1 |
| Bounded Char | Since: base-2.1 |
| Bounded Int | Since: base-2.1 |
| Bounded Levity | Since: base-4.16.0.0 |
| Bounded VecCount | Since: base-4.10.0.0 |
| Bounded VecElem | Since: base-4.10.0.0 |
| Bounded Word | Since: base-2.1 |
| Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Last a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Max a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Min a) | Since: base-4.9.0.0 |
| Bounded m => Bounded (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Down a) | Swaps Since: base-4.14.0.0 |
| Bounded a => Bounded (Dual a) | Since: base-2.1 |
| Bounded a => Bounded (Product a) | Since: base-2.1 |
| Bounded a => Bounded (Sum a) | Since: base-2.1 |
| Bounded a => Bounded (Solo a) | |
| Bounded (Proxy t) | Since: base-4.7.0.0 |
| (Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
| Bounded a => Bounded (SQuantity s d a) Source # | |
| Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
| (Applicative f, Bounded a) => Bounded (Ap f a) | Since: base-4.12.0.0 |
| (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1 |
| Bounded (f (g a)) => Bounded (Compose f g a) | Since: base-4.19.0.0 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
class Fractional a => Floating a Source #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (, +)(
and *)exp are customarily expected to define an exponential field and have
the following properties:
exp (a + b)=exp a * exp bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
| Floating ExactPi | |
Defined in Data.ExactPi Methods exp :: ExactPi -> ExactPi Source # log :: ExactPi -> ExactPi Source # sqrt :: ExactPi -> ExactPi Source # (**) :: ExactPi -> ExactPi -> ExactPi Source # logBase :: ExactPi -> ExactPi -> ExactPi Source # sin :: ExactPi -> ExactPi Source # cos :: ExactPi -> ExactPi Source # tan :: ExactPi -> ExactPi Source # asin :: ExactPi -> ExactPi Source # acos :: ExactPi -> ExactPi Source # atan :: ExactPi -> ExactPi Source # sinh :: ExactPi -> ExactPi Source # cosh :: ExactPi -> ExactPi Source # tanh :: ExactPi -> ExactPi Source # asinh :: ExactPi -> ExactPi Source # acosh :: ExactPi -> ExactPi Source # atanh :: ExactPi -> ExactPi Source # log1p :: ExactPi -> ExactPi Source # expm1 :: ExactPi -> ExactPi Source # | |
| Floating CDouble | |
Defined in GHC.Internal.Foreign.C.Types Methods exp :: CDouble -> CDouble Source # log :: CDouble -> CDouble Source # sqrt :: CDouble -> CDouble Source # (**) :: CDouble -> CDouble -> CDouble Source # logBase :: CDouble -> CDouble -> CDouble Source # sin :: CDouble -> CDouble Source # cos :: CDouble -> CDouble Source # tan :: CDouble -> CDouble Source # asin :: CDouble -> CDouble Source # acos :: CDouble -> CDouble Source # atan :: CDouble -> CDouble Source # sinh :: CDouble -> CDouble Source # cosh :: CDouble -> CDouble Source # tanh :: CDouble -> CDouble Source # asinh :: CDouble -> CDouble Source # acosh :: CDouble -> CDouble Source # atanh :: CDouble -> CDouble Source # log1p :: CDouble -> CDouble Source # expm1 :: CDouble -> CDouble Source # | |
| Floating CFloat | |
Defined in GHC.Internal.Foreign.C.Types Methods exp :: CFloat -> CFloat Source # log :: CFloat -> CFloat Source # sqrt :: CFloat -> CFloat Source # (**) :: CFloat -> CFloat -> CFloat Source # logBase :: CFloat -> CFloat -> CFloat Source # sin :: CFloat -> CFloat Source # cos :: CFloat -> CFloat Source # tan :: CFloat -> CFloat Source # asin :: CFloat -> CFloat Source # acos :: CFloat -> CFloat Source # atan :: CFloat -> CFloat Source # sinh :: CFloat -> CFloat Source # cosh :: CFloat -> CFloat Source # tanh :: CFloat -> CFloat Source # asinh :: CFloat -> CFloat Source # acosh :: CFloat -> CFloat Source # atanh :: CFloat -> CFloat Source # log1p :: CFloat -> CFloat Source # expm1 :: CFloat -> CFloat Source # | |
| Floating Double | Since: base-2.1 |
Defined in GHC.Internal.Float Methods exp :: Double -> Double Source # log :: Double -> Double Source # sqrt :: Double -> Double Source # (**) :: Double -> Double -> Double Source # logBase :: Double -> Double -> Double Source # sin :: Double -> Double Source # cos :: Double -> Double Source # tan :: Double -> Double Source # asin :: Double -> Double Source # acos :: Double -> Double Source # atan :: Double -> Double Source # sinh :: Double -> Double Source # cosh :: Double -> Double Source # tanh :: Double -> Double Source # asinh :: Double -> Double Source # acosh :: Double -> Double Source # atanh :: Double -> Double Source # log1p :: Double -> Double Source # expm1 :: Double -> Double Source # | |
| Floating Float | Since: base-2.1 |
Defined in GHC.Internal.Float Methods exp :: Float -> Float Source # log :: Float -> Float Source # sqrt :: Float -> Float Source # (**) :: Float -> Float -> Float Source # logBase :: Float -> Float -> Float Source # sin :: Float -> Float Source # cos :: Float -> Float Source # tan :: Float -> Float Source # asin :: Float -> Float Source # acos :: Float -> Float Source # atan :: Float -> Float Source # sinh :: Float -> Float Source # cosh :: Float -> Float Source # tanh :: Float -> Float Source # asinh :: Float -> Float Source # acosh :: Float -> Float Source # atanh :: Float -> Float Source # log1p :: Float -> Float Source # expm1 :: Float -> Float Source # | |
| RealFloat a => Floating (Complex a) | Since: base-2.1 |
Defined in Data.Complex Methods exp :: Complex a -> Complex a Source # log :: Complex a -> Complex a Source # sqrt :: Complex a -> Complex a Source # (**) :: Complex a -> Complex a -> Complex a Source # logBase :: Complex a -> Complex a -> Complex a Source # sin :: Complex a -> Complex a Source # cos :: Complex a -> Complex a Source # tan :: Complex a -> Complex a Source # asin :: Complex a -> Complex a Source # acos :: Complex a -> Complex a Source # atan :: Complex a -> Complex a Source # sinh :: Complex a -> Complex a Source # cosh :: Complex a -> Complex a Source # tanh :: Complex a -> Complex a Source # asinh :: Complex a -> Complex a Source # acosh :: Complex a -> Complex a Source # atanh :: Complex a -> Complex a Source # log1p :: Complex a -> Complex a Source # expm1 :: Complex a -> Complex a Source # | |
| Floating a => Floating (DynQuantity a) Source # | |
Defined in Numeric.Units.Dimensional.Dynamic Methods pi :: DynQuantity a Source # exp :: DynQuantity a -> DynQuantity a Source # log :: DynQuantity a -> DynQuantity a Source # sqrt :: DynQuantity a -> DynQuantity a Source # (**) :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # logBase :: DynQuantity a -> DynQuantity a -> DynQuantity a Source # sin :: DynQuantity a -> DynQuantity a Source # cos :: DynQuantity a -> DynQuantity a Source # tan :: DynQuantity a -> DynQuantity a Source # asin :: DynQuantity a -> DynQuantity a Source # acos :: DynQuantity a -> DynQuantity a Source # atan :: DynQuantity a -> DynQuantity a Source # sinh :: DynQuantity a -> DynQuantity a Source # cosh :: DynQuantity a -> DynQuantity a Source # tanh :: DynQuantity a -> DynQuantity a Source # asinh :: DynQuantity a -> DynQuantity a Source # acosh :: DynQuantity a -> DynQuantity a Source # atanh :: DynQuantity a -> DynQuantity a Source # log1p :: DynQuantity a -> DynQuantity a Source # expm1 :: DynQuantity a -> DynQuantity a Source # log1pexp :: DynQuantity a -> DynQuantity a Source # log1mexp :: DynQuantity a -> DynQuantity a Source # | |
| Floating a => Floating (Identity a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods exp :: Identity a -> Identity a Source # log :: Identity a -> Identity a Source # sqrt :: Identity a -> Identity a Source # (**) :: Identity a -> Identity a -> Identity a Source # logBase :: Identity a -> Identity a -> Identity a Source # sin :: Identity a -> Identity a Source # cos :: Identity a -> Identity a Source # tan :: Identity a -> Identity a Source # asin :: Identity a -> Identity a Source # acos :: Identity a -> Identity a Source # atan :: Identity a -> Identity a Source # sinh :: Identity a -> Identity a Source # cosh :: Identity a -> Identity a Source # tanh :: Identity a -> Identity a Source # asinh :: Identity a -> Identity a Source # acosh :: Identity a -> Identity a Source # atanh :: Identity a -> Identity a Source # log1p :: Identity a -> Identity a Source # expm1 :: Identity a -> Identity a Source # | |
| Floating a => Floating (Down a) | Since: base-4.14.0.0 |
Defined in GHC.Internal.Data.Ord Methods exp :: Down a -> Down a Source # log :: Down a -> Down a Source # sqrt :: Down a -> Down a Source # (**) :: Down a -> Down a -> Down a Source # logBase :: Down a -> Down a -> Down a Source # sin :: Down a -> Down a Source # cos :: Down a -> Down a Source # tan :: Down a -> Down a Source # asin :: Down a -> Down a Source # acos :: Down a -> Down a Source # atan :: Down a -> Down a Source # sinh :: Down a -> Down a Source # cosh :: Down a -> Down a Source # tanh :: Down a -> Down a Source # asinh :: Down a -> Down a Source # acosh :: Down a -> Down a Source # atanh :: Down a -> Down a Source # log1p :: Down a -> Down a Source # expm1 :: Down a -> Down a Source # | |
| Floating a => Floating (Op a b) | |
Defined in Data.Functor.Contravariant Methods exp :: Op a b -> Op a b Source # log :: Op a b -> Op a b Source # sqrt :: Op a b -> Op a b Source # (**) :: Op a b -> Op a b -> Op a b Source # logBase :: Op a b -> Op a b -> Op a b Source # sin :: Op a b -> Op a b Source # cos :: Op a b -> Op a b Source # tan :: Op a b -> Op a b Source # asin :: Op a b -> Op a b Source # acos :: Op a b -> Op a b Source # atan :: Op a b -> Op a b Source # sinh :: Op a b -> Op a b Source # cosh :: Op a b -> Op a b Source # tanh :: Op a b -> Op a b Source # asinh :: Op a b -> Op a b Source # acosh :: Op a b -> Op a b Source # atanh :: Op a b -> Op a b Source # log1p :: Op a b -> Op a b Source # expm1 :: Op a b -> Op a b Source # | |
| Floating a => Floating (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods exp :: Const a b -> Const a b Source # log :: Const a b -> Const a b Source # sqrt :: Const a b -> Const a b Source # (**) :: Const a b -> Const a b -> Const a b Source # logBase :: Const a b -> Const a b -> Const a b Source # sin :: Const a b -> Const a b Source # cos :: Const a b -> Const a b Source # tan :: Const a b -> Const a b Source # asin :: Const a b -> Const a b Source # acos :: Const a b -> Const a b Source # atan :: Const a b -> Const a b Source # sinh :: Const a b -> Const a b Source # cosh :: Const a b -> Const a b Source # tanh :: Const a b -> Const a b Source # asinh :: Const a b -> Const a b Source # acosh :: Const a b -> Const a b Source # atanh :: Const a b -> Const a b Source # log1p :: Const a b -> Const a b Source # expm1 :: Const a b -> Const a b Source # | |
| Floating (f (g a)) => Floating (Compose f g a) | Since: base-4.20.0.0 |
Defined in Data.Functor.Compose Methods exp :: Compose f g a -> Compose f g a Source # log :: Compose f g a -> Compose f g a Source # sqrt :: Compose f g a -> Compose f g a Source # (**) :: Compose f g a -> Compose f g a -> Compose f g a Source # logBase :: Compose f g a -> Compose f g a -> Compose f g a Source # sin :: Compose f g a -> Compose f g a Source # cos :: Compose f g a -> Compose f g a Source # tan :: Compose f g a -> Compose f g a Source # asin :: Compose f g a -> Compose f g a Source # acos :: Compose f g a -> Compose f g a Source # atan :: Compose f g a -> Compose f g a Source # sinh :: Compose f g a -> Compose f g a Source # cosh :: Compose f g a -> Compose f g a Source # tanh :: Compose f g a -> Compose f g a Source # asinh :: Compose f g a -> Compose f g a Source # acosh :: Compose f g a -> Compose f g a Source # atanh :: Compose f g a -> Compose f g a Source # log1p :: Compose f g a -> Compose f g a Source # expm1 :: Compose f g a -> Compose f g a Source # | |
Parsing of Strings, producing values.
Derived instances of Read make the following assumptions, which
derived instances of Show obey:
- If the constructor is defined to be an infix operator, then the
derived
Readinstance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Readinstance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where
readsPrec d r = readParen (d > app_prec)
(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r
++ readParen (d > up_prec)
(\r -> [(u:^:v,w) |
(u,s) <- readsPrec (up_prec+1) r,
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r
where app_prec = 10
up_prec = 5Note that right-associativity of :^: is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefaultWhy do both readsPrec and readPrec exist, and why does GHC opt to
implement readPrec in derived Read instances instead of readsPrec?
The reason is that readsPrec is based on the ReadS type, and although
ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient
parser data structure.
readPrec, on the other hand, is based on a much more efficient ReadPrec
datatype (a.k.a "new-style parsers"), but its definition relies on the use
of the RankNTypes language extension. Therefore, readPrec (and its
cousin, readListPrec) are marked as GHC-only. Nevertheless, it is
recommended to use readPrec instead of readsPrec whenever possible
for the efficiency improvements it brings.
As mentioned above, derived Read instances in GHC will implement
readPrec instead of readsPrec. The default implementations of
readsPrec (and its cousin, readList) will simply use readPrec under
the hood. If you are writing a Read instance by hand, it is recommended
to write it like so:
instanceReadT wherereadPrec= ...readListPrec=readListPrecDefault
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> ReadS a |
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that
showsPrec started with.
Instances
| Read Void | Reading a Since: base-4.8.0.0 |
| Read All | Since: base-2.1 |
| Read Any | Since: base-2.1 |
| Read Version | Since: base-2.1 |
| Read CBool | |
| Read CChar | |
| Read CClock | |
| Read CDouble | |
| Read CFloat | |
| Read CInt | |
| Read CIntMax | |
| Read CIntPtr | |
| Read CLLong | |
| Read CLong | |
| Read CPtrdiff | |
| Read CSChar | |
| Read CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types | |
| Read CShort | |
| Read CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types | |
| Read CSize | |
| Read CTime | |
| Read CUChar | |
| Read CUInt | |
| Read CUIntMax | |
| Read CUIntPtr | |
| Read CULLong | |
| Read CULong | |
| Read CUSeconds | |
| Read CUShort | |
| Read CWchar | |
| Read Associativity | Since: base-4.6.0.0 |
Defined in GHC.Internal.Generics | |
| Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Read Fixity | Since: base-4.6.0.0 |
| Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Read ExitCode | |
| Read Int16 | Since: base-2.1 |
| Read Int32 | Since: base-2.1 |
| Read Int64 | Since: base-2.1 |
| Read Int8 | Since: base-2.1 |
| Read Lexeme | Since: base-2.1 |
| Read SomeNat | Since: base-4.7.0.0 |
| Read GeneralCategory | Since: base-2.1 |
Defined in GHC.Internal.Read | |
| Read Word16 | Since: base-2.1 |
| Read Word32 | Since: base-2.1 |
| Read Word64 | Since: base-2.1 |
| Read Word8 | Since: base-2.1 |
| Read Ordering | Since: base-2.1 |
| Read Integer | Since: base-2.1 |
| Read Natural | Since: base-4.8.0.0 |
| Read () | Since: base-2.1 |
| Read Bool | Since: base-2.1 |
| Read Char | Since: base-2.1 |
| Read Double | Since: base-2.1 |
| Read Float | Since: base-2.1 |
| Read Int | Since: base-2.1 |
| Read Word | Since: base-4.5.0.0 |
| Read a => Read (Complex a) | Since: base-2.1 |
| Read a => Read (First a) | Since: base-4.9.0.0 |
| Read a => Read (Last a) | Since: base-4.9.0.0 |
| Read a => Read (Max a) | Since: base-4.9.0.0 |
| Read a => Read (Min a) | Since: base-4.9.0.0 |
| Read m => Read (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) Source # readList :: ReadS [WrappedMonoid m] Source # readPrec :: ReadPrec (WrappedMonoid m) Source # readListPrec :: ReadPrec [WrappedMonoid m] Source # | |
| Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
| Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read a => Read (First a) | Since: base-2.1 |
| Read a => Read (Last a) | Since: base-2.1 |
| Read a => Read (Down a) | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
| Read a => Read (Dual a) | Since: base-2.1 |
| Read a => Read (Product a) | Since: base-2.1 |
| Read a => Read (Sum a) | Since: base-2.1 |
| Read a => Read (ZipList a) | Since: base-4.7.0.0 |
| Read p => Read (Par1 p) | Since: base-4.7.0.0 |
| (Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
| Read a => Read (Array a) | |
| Read a => Read (SmallArray a) | |
| Read a => Read (Vector a) | |
| (Read a, Prim a) => Read (Vector a) | |
| (Read a, Storable a) => Read (Vector a) | |
| Read a => Read (Vector a) | |
| Read a => Read (Maybe a) | Since: base-2.1 |
| Read a => Read (Solo a) | Since: base-4.15 |
| Read a => Read [a] | Since: base-2.1 |
| HasResolution a => Read (Fixed a) | Since: base-4.3.0.0 |
| (Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0 |
| (Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| Read (Proxy t) | Since: base-4.7.0.0 |
| Read (U1 p) | Since: base-4.9.0.0 |
| Read (V1 p) | Since: base-4.9.0.0 |
| (Read1 m, Read a) => Read (MaybeT m a) | |
| (Read a, Read b) => Read (a, b) | Since: base-2.1 |
| Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read (f a) => Read (Ap f a) | Since: base-4.12.0.0 |
| Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 |
| Read (f p) => Read (Rec1 f p) | Since: base-4.7.0.0 |
| (Read e, Read1 m, Read a) => Read (ExceptT e m a) | |
| (Read1 f, Read a) => Read (IdentityT f a) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read a, Read b, Read c) => Read (a, b, c) | Since: base-2.1 |
| (Read (f a), Read (g a)) => Read (Product f g a) | Since: base-4.18.0.0 |
| (Read (f a), Read (g a)) => Read (Sum f g a) | Since: base-4.18.0.0 |
| (Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
| Read c => Read (K1 i c p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | Since: base-2.1 |
| Read (f (g a)) => Read (Compose f g a) | Since: base-4.18.0.0 |
| Read (f (g p)) => Read ((f :.: g) p) | Since: base-4.7.0.0 |
| Read (f p) => Read (M1 i c f p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
Defined in GHC.Internal.Read | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
Defined in GHC.Internal.Read | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # | |
class (RealFrac a, Floating a) => RealFloat a where Source #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer Source #
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> Int Source #
a constant function, returning the number of digits of
floatRadix in the significand
floatRange :: a -> (Int, Int) Source #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) Source #
The function decodeFloat applied to a real floating-point
number returns the significand expressed as an Integer and an
appropriately scaled exponent (an Int). If decodeFloat x(m,n), then x is equal in value to m*b^^n, where b
is the floating-point radix, and furthermore, either m and n
are both zero or else b^(d-1) <= , where abs m < b^dd is
the value of floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite xTrue.
encodeFloat :: Integer -> Int -> a Source #
encodeFloat performs the inverse of decodeFloat in the
sense that for finite x with the exception of -0.0,
uncurry encodeFloat (decodeFloat x) = xencodeFloat m nm*b^^n (or ±Infinity if overflow
occurs); usually the closer, but if m contains too many bits,
the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
significand x * b ^^ exponent xb is the
floating-point radix.
The behaviour is unspecified on infinite or NaN values.
significand :: a -> a Source #
The first component of decodeFloat, scaled to lie in the open
interval (-1,1), either 0.0 or of absolute value >= 1/b,
where b is the floating-point radix.
The behaviour is unspecified on infinite or NaN values.
scaleFloat :: Int -> a -> a Source #
multiplies a floating-point number by an integer power of the radix
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool Source #
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool Source #
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool Source #
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
Instances
| RealFloat CDouble | |
Defined in GHC.Internal.Foreign.C.Types Methods floatRadix :: CDouble -> Integer Source # floatDigits :: CDouble -> Int Source # floatRange :: CDouble -> (Int, Int) Source # decodeFloat :: CDouble -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> CDouble Source # exponent :: CDouble -> Int Source # significand :: CDouble -> CDouble Source # scaleFloat :: Int -> CDouble -> CDouble Source # isNaN :: CDouble -> Bool Source # isInfinite :: CDouble -> Bool Source # isDenormalized :: CDouble -> Bool Source # isNegativeZero :: CDouble -> Bool Source # | |
| RealFloat CFloat | |
Defined in GHC.Internal.Foreign.C.Types Methods floatRadix :: CFloat -> Integer Source # floatDigits :: CFloat -> Int Source # floatRange :: CFloat -> (Int, Int) Source # decodeFloat :: CFloat -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> CFloat Source # exponent :: CFloat -> Int Source # significand :: CFloat -> CFloat Source # scaleFloat :: Int -> CFloat -> CFloat Source # isNaN :: CFloat -> Bool Source # isInfinite :: CFloat -> Bool Source # isDenormalized :: CFloat -> Bool Source # isNegativeZero :: CFloat -> Bool Source # | |
| RealFloat Double | Since: base-2.1 |
Defined in GHC.Internal.Float Methods floatRadix :: Double -> Integer Source # floatDigits :: Double -> Int Source # floatRange :: Double -> (Int, Int) Source # decodeFloat :: Double -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Double Source # exponent :: Double -> Int Source # significand :: Double -> Double Source # scaleFloat :: Int -> Double -> Double Source # isNaN :: Double -> Bool Source # isInfinite :: Double -> Bool Source # isDenormalized :: Double -> Bool Source # isNegativeZero :: Double -> Bool Source # | |
| RealFloat Float | Since: base-2.1 |
Defined in GHC.Internal.Float Methods floatRadix :: Float -> Integer Source # floatDigits :: Float -> Int Source # floatRange :: Float -> (Int, Int) Source # decodeFloat :: Float -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Float Source # exponent :: Float -> Int Source # significand :: Float -> Float Source # scaleFloat :: Int -> Float -> Float Source # isNaN :: Float -> Bool Source # isInfinite :: Float -> Bool Source # isDenormalized :: Float -> Bool Source # isNegativeZero :: Float -> Bool Source # | |
| RealFloat a => RealFloat (Identity a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods floatRadix :: Identity a -> Integer Source # floatDigits :: Identity a -> Int Source # floatRange :: Identity a -> (Int, Int) Source # decodeFloat :: Identity a -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Identity a Source # exponent :: Identity a -> Int Source # significand :: Identity a -> Identity a Source # scaleFloat :: Int -> Identity a -> Identity a Source # isNaN :: Identity a -> Bool Source # isInfinite :: Identity a -> Bool Source # isDenormalized :: Identity a -> Bool Source # isNegativeZero :: Identity a -> Bool Source # | |
| RealFloat a => RealFloat (Down a) | Since: base-4.14.0.0 |
Defined in GHC.Internal.Data.Ord Methods floatRadix :: Down a -> Integer Source # floatDigits :: Down a -> Int Source # floatRange :: Down a -> (Int, Int) Source # decodeFloat :: Down a -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Down a Source # exponent :: Down a -> Int Source # significand :: Down a -> Down a Source # scaleFloat :: Int -> Down a -> Down a Source # isNaN :: Down a -> Bool Source # isInfinite :: Down a -> Bool Source # isDenormalized :: Down a -> Bool Source # isNegativeZero :: Down a -> Bool Source # | |
| RealFloat a => RealFloat (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods floatRadix :: Const a b -> Integer Source # floatDigits :: Const a b -> Int Source # floatRange :: Const a b -> (Int, Int) Source # decodeFloat :: Const a b -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Const a b Source # exponent :: Const a b -> Int Source # significand :: Const a b -> Const a b Source # scaleFloat :: Int -> Const a b -> Const a b Source # isNaN :: Const a b -> Bool Source # isInfinite :: Const a b -> Bool Source # isDenormalized :: Const a b -> Bool Source # isNegativeZero :: Const a b -> Bool Source # | |
| RealFloat (f (g a)) => RealFloat (Compose f g a) | Since: base-4.20.0.0 |
Defined in Data.Functor.Compose Methods floatRadix :: Compose f g a -> Integer Source # floatDigits :: Compose f g a -> Int Source # floatRange :: Compose f g a -> (Int, Int) Source # decodeFloat :: Compose f g a -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Compose f g a Source # exponent :: Compose f g a -> Int Source # significand :: Compose f g a -> Compose f g a Source # scaleFloat :: Int -> Compose f g a -> Compose f g a Source # isNaN :: Compose f g a -> Bool Source # isInfinite :: Compose f g a -> Bool Source # isDenormalized :: Compose f g a -> Bool Source # isNegativeZero :: Compose f g a -> Bool Source # isIEEE :: Compose f g a -> Bool Source # atan2 :: Compose f g a -> Compose f g a -> Compose f g a Source # | |
class (Real a, Fractional a) => RealFrac a where Source #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) Source #
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> b Source #
truncate xx between zero and x
round :: Integral b => a -> b Source #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b Source #
ceiling xx
floor :: Integral b => a -> b Source #
floor xx
Instances
| RealFrac CDouble | |
| RealFrac CFloat | |
| RealFrac Double | Beware that results for non-finite arguments are garbage:
and get even more non-sensical if you ask for Since: base-2.1 |
| RealFrac Float | Beware that results for non-finite arguments are garbage:
and get even more non-sensical if you ask for Since: base-2.1 |
| RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity | |
| RealFrac a => RealFrac (Down a) | Since: base-4.14.0.0 |
| Integral a => RealFrac (Ratio a) | Since: base-2.0.1 |
| HasResolution a => RealFrac (Fixed a) | Since: base-2.1 |
| RealFrac a => RealFrac (Const a b) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const | |
| RealFrac (f (g a)) => RealFrac (Compose f g a) | Since: base-4.20.0.0 |
Defined in Data.Functor.Compose | |
Conversion of values to readable Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show is equivalent to
instance (Show a) => Show (Tree a) where
showsPrec d (Leaf m) = showParen (d > app_prec) $
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10
showsPrec d (u :^: v) = showParen (d > up_prec) $
showsPrec (up_prec+1) u .
showString " :^: " .
showsPrec (up_prec+1) v
where up_prec = 5Note that right-associativity of :^: is ignored. For example,
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> a | the value to be converted to a |
| -> ShowS |
Convert a value to a readable String.
showsPrec should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that showsPrec started with.
Instances
| Show ByteArray | Since: base-4.17.0.0 |
| Show Timeout | Since: base-4.0 |
| Show Dimension' Source # | |
| Show DynamicDimension Source # | |
| Show AnyUnit Source # | |
| Show InterchangeName Source # | |
| Show InterchangeNameAuthority Source # | |
| Show ExactPi | |
| Show ForeignSrcLang | |
Defined in GHC.ForeignSrcLang.Type | |
| Show Extension | |
| Show Void | Since: base-4.8.0.0 |
| Show Constr | Since: base-4.0.0.0 |
| Show ConstrRep | Since: base-4.0.0.0 |
| Show DataRep | Since: base-4.0.0.0 |
| Show DataType | Since: base-4.0.0.0 |
| Show Fixity | Since: base-4.0.0.0 |
| Show All | Since: base-2.1 |
| Show Any | Since: base-2.1 |
| Show SomeTypeRep | Since: base-4.10.0.0 |
Defined in GHC.Internal.Data.Typeable.Internal | |
| Show Version | Since: base-2.1 |
| Show CBool | |
| Show CChar | |
| Show CClock | |
| Show CDouble | |
| Show CFloat | |
| Show CInt | |
| Show CIntMax | |
| Show CIntPtr | |
| Show CLLong | |
| Show CLong | |
| Show CPtrdiff | |
| Show CSChar | |
| Show CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types | |
| Show CShort | |
| Show CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types | |
| Show CSize | |
| Show CTime | |
| Show CUChar | |
| Show CUInt | |
| Show CUIntMax | |
| Show CUIntPtr | |
| Show CULLong | |
| Show CULong | |
| Show CUSeconds | |
| Show CUShort | |
| Show CWchar | |
| Show Associativity | Since: base-4.6.0.0 |
Defined in GHC.Internal.Generics | |
| Show DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Show Fixity | Since: base-4.6.0.0 |
| Show SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Show SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Show MaskingState | Since: base-4.3.0.0 |
Defined in GHC.Internal.IO | |
| Show AllocationLimitExceeded | Since: base-4.7.1.0 |
Defined in GHC.Internal.IO.Exception | |
| Show ArrayException | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show AssertionFailed | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show AsyncException | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show BlockedIndefinitelyOnMVar | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show BlockedIndefinitelyOnSTM | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show CompactionFailed | Since: base-4.10.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show Deadlock | Since: base-4.1.0.0 |
| Show ExitCode | |
| Show FixIOException | Since: base-4.11.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show IOException | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show SomeAsyncException | Since: base-4.7.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show Int16 | Since: base-2.1 |
| Show Int32 | Since: base-2.1 |
| Show Int64 | Since: base-2.1 |
| Show Int8 | Since: base-2.1 |
| Show CCFlags | Since: base-4.8.0.0 |
| Show ConcFlags | Since: base-4.8.0.0 |
| Show DebugFlags | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show DoCostCentres | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show DoHeapProfile | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show DoTrace | Since: base-4.8.0.0 |
| Show GCFlags | Since: base-4.8.0.0 |
| Show GiveGCStats | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show HpcFlags | Since: base-4.20.0.0 |
| Show IoSubSystem | |
Defined in GHC.Internal.RTS.Flags | |
| Show MiscFlags | Since: base-4.8.0.0 |
| Show ParFlags | Since: base-4.8.0.0 |
| Show ProfFlags | Since: base-4.8.0.0 |
| Show RTSFlags | Since: base-4.8.0.0 |
| Show TickyFlags | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show TraceFlags | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show FractionalExponentBase | |
Defined in GHC.Internal.Real | |
| Show CallStack | Since: base-4.9.0.0 |
| Show SrcLoc | Since: base-4.9.0.0 |
| Show SomeNat | Since: base-4.7.0.0 |
| Show Word16 | Since: base-2.1 |
| Show Word32 | Since: base-2.1 |
| Show Word64 | Since: base-2.1 |
| Show Word8 | Since: base-2.1 |
| Show KindRep | |
| Show Module | Since: base-4.9.0.0 |
| Show Ordering | Since: base-2.1 |
| Show TrName | Since: base-4.9.0.0 |
| Show TyCon | Since: base-2.1 |
| Show TypeLitSort | Since: base-4.11.0.0 |
Defined in GHC.Internal.Show | |
| Show AnnLookup | |
| Show AnnTarget | |
| Show Bang | |
| Show BndrVis | |
| Show Body | |
| Show Bytes | |
| Show Callconv | |
| Show Clause | |
| Show Con | |
| Show Dec | |
| Show DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax | |
| Show DerivClause | |
Defined in Language.Haskell.TH.Syntax | |
| Show DerivStrategy | |
Defined in Language.Haskell.TH.Syntax | |
| Show DocLoc | |
| Show Exp | |
| Show FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax | |
| Show Fixity | |
| Show FixityDirection | |
Defined in Language.Haskell.TH.Syntax | |
| Show Foreign | |
| Show FunDep | |
| Show Guard | |
| Show Info | |
| Show InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax | |
| Show Inline | |
| Show Lit | |
| Show Loc | |
| Show Match | |
| Show ModName | |
| Show Module | |
| Show ModuleInfo | |
Defined in Language.Haskell.TH.Syntax | |
| Show Name | |
| Show NameFlavour | |
Defined in Language.Haskell.TH.Syntax | |
| Show NameSpace | |
| Show NamespaceSpecifier | |
Defined in Language.Haskell.TH.Syntax | |
| Show OccName | |
| Show Overlap | |
| Show Pat | |
| Show PatSynArgs | |
Defined in Language.Haskell.TH.Syntax | |
| Show PatSynDir | |
| Show Phases | |
| Show PkgName | |
| Show Pragma | |
| Show Range | |
| Show Role | |
| Show RuleBndr | |
| Show RuleMatch | |
| Show Safety | |
| Show SourceStrictness | |
Defined in Language.Haskell.TH.Syntax | |
| Show SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax | |
| Show Specificity | |
Defined in Language.Haskell.TH.Syntax | |
| Show Stmt | |
| Show TyLit | |
| Show TySynEqn | |
| Show Type | |
| Show TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax | |
| Show Size | |
| Show Integer | Since: base-2.1 |
| Show Natural | Since: base-4.8.0.0 |
| Show () | Since: base-2.1 |
| Show Bool | Since: base-2.1 |
| Show Char | Since: base-2.1 |
| Show Double | Since: base-2.1 |
| Show Float | Since: base-2.1 |
| Show Int | Since: base-2.1 |
| Show Levity | Since: base-4.15.0.0 |
| Show RuntimeRep | Since: base-4.11.0.0 |
Defined in GHC.Internal.Show | |
| Show VecCount | Since: base-4.11.0.0 |
| Show VecElem | Since: base-4.11.0.0 |
| Show Word | Since: base-2.1 |
| Show a => Show (Complex a) | Since: base-2.1 |
| Show a => Show (First a) | Since: base-4.9.0.0 |
| Show a => Show (Last a) | Since: base-4.9.0.0 |
| Show a => Show (Max a) | Since: base-4.9.0.0 |
| Show a => Show (Min a) | Since: base-4.9.0.0 |
| Show m => Show (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Show a => Show (AnyQuantity a) Source # | |
Defined in Numeric.Units.Dimensional.Dynamic | |
| Show a => Show (DynQuantity a) Source # | |
Defined in Numeric.Units.Dimensional.Dynamic | |
| Show (UnitName m) Source # |
|
| Show a => Show (NonEmpty a) | Since: base-4.11.0.0 |
| Show a => Show (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Show a => Show (First a) | Since: base-2.1 |
| Show a => Show (Last a) | Since: base-2.1 |
| Show a => Show (Down a) | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
| Show a => Show (Dual a) | Since: base-2.1 |
| Show a => Show (Product a) | Since: base-2.1 |
| Show a => Show (Sum a) | Since: base-2.1 |
| Show a => Show (ZipList a) | Since: base-4.7.0.0 |
| Show p => Show (Par1 p) | Since: base-4.7.0.0 |
| Show (FunPtr a) | Since: base-2.1 |
| Show (Ptr a) | Since: base-2.1 |
| Show a => Show (Ratio a) | Since: base-2.0.1 |
| Show (SNat n) | Since: base-4.18.0.0 |
| Show a => Show (Array a) | |
| (Show a, Prim a) => Show (PrimArray a) | |
| Show a => Show (SmallArray a) | |
| Show flag => Show (TyVarBndr flag) | |
| Show a => Show (Vector a) | |
| (Show a, Prim a) => Show (Vector a) | |
| (Show a, Storable a) => Show (Vector a) | |
| Show a => Show (Vector a) | |
| Show a => Show (Maybe a) | Since: base-2.1 |
| Show a => Show (Solo a) | Since: base-4.15 |
| Show a => Show [a] | Since: base-2.1 |
| HasResolution a => Show (Fixed a) | Since: base-2.1 |
| (Show a, Show b) => Show (Arg a b) | Since: base-4.9.0.0 |
| (Show a, Show b) => Show (Either a b) | Since: base-3.0 |
| Show (Proxy s) | Since: base-4.7.0.0 |
| Show (TypeRep a) | |
| Show (U1 p) | Since: base-4.9.0.0 |
| Show (V1 p) | Since: base-4.9.0.0 |
| Show (ST s a) | Since: base-2.1 |
| (Show1 m, Show a) => Show (MaybeT m a) | |
| (Show a, Show b) => Show (a, b) | Since: base-2.1 |
| (KnownDimension d, KnownExactPi s, Show a, Real a) => Show (SQuantity s d a) Source # | Uses non-breaking spaces between the value and the unit, and within the unit name. |
| Show a => Show (Unit m d a) Source # | Unit names are shown with non-breaking spaces. |
| Show a => Show (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Show (f a) => Show (Ap f a) | Since: base-4.12.0.0 |
| Show (f a) => Show (Alt f a) | Since: base-4.8.0.0 |
| Show (OrderingI a b) | |
| Show (f p) => Show (Rec1 f p) | Since: base-4.7.0.0 |
| Show (URec Char p) | Since: base-4.9.0.0 |
| Show (URec Double p) | Since: base-4.9.0.0 |
| Show (URec Float p) | |
| Show (URec Int p) | Since: base-4.9.0.0 |
| Show (URec Word p) | Since: base-4.9.0.0 |
| (Show e, Show1 m, Show a) => Show (ExceptT e m a) | |
| (Show1 f, Show a) => Show (IdentityT f a) | |
| (Show w, Show1 m, Show a) => Show (WriterT w m a) | |
| (Show w, Show1 m, Show a) => Show (WriterT w m a) | |
| (Show a, Show b, Show c) => Show (a, b, c) | Since: base-2.1 |
| (Show (f a), Show (g a)) => Show (Product f g a) | Since: base-4.18.0.0 |
| (Show (f a), Show (g a)) => Show (Sum f g a) | Since: base-4.18.0.0 |
| (Show (f p), Show (g p)) => Show ((f :*: g) p) | Since: base-4.7.0.0 |
| (Show (f p), Show (g p)) => Show ((f :+: g) p) | Since: base-4.7.0.0 |
| Show c => Show (K1 i c p) | Since: base-4.7.0.0 |
| (Show a, Show b, Show c, Show d) => Show (a, b, c, d) | Since: base-2.1 |
| Show (f (g a)) => Show (Compose f g a) | Since: base-4.18.0.0 |
| Show (f (g p)) => Show ((f :.: g) p) | Since: base-4.7.0.0 |
| Show (f p) => Show (M1 i c f p) | Since: base-4.7.0.0 |
| (Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where Source #
Functors representing data structures that can be transformed to
structures of the same shape by performing an Applicative (or,
therefore, Monad) action on each element from left to right.
A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.
For the class laws see the Laws section of Data.Traversable.
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_.
Examples
Basic usage:
In the first two examples we show each evaluated action mapping to the output structure.
>>>traverse Just [1,2,3,4]Just [1,2,3,4]
>>>traverse id [Right 1, Right 2, Right 3, Right 4]Right [1,2,3,4]
In the next examples, we show that Nothing and Left values short
circuit the created structure.
>>>traverse (const Nothing) [1,2,3,4]Nothing
>>>traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]Nothing
>>>traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]Left 0
sequenceA :: Applicative f => t (f a) -> f (t a) Source #
Evaluate each action in the structure from left to right, and
collect the results. For a version that ignores the results
see sequenceA_.
Examples
Basic usage:
For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.
>>>sequenceA [Just 1, Just 2, Just 3]Just [1,2,3]
>>>sequenceA [Right 1, Right 2, Right 3]Right [1,2,3]
The next two example show Nothing and Just will short circuit
the resulting structure if present in the input. For more context,
check the Traversable instances for Either and Maybe.
>>>sequenceA [Just 1, Just 2, Just 3, Nothing]Nothing
>>>sequenceA [Right 1, Right 2, Right 3, Left 4]Left 4
mapM :: Monad m => (a -> m b) -> t a -> m (t b) Source #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_.
Examples
sequence :: Monad m => t (m a) -> m (t a) Source #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_.
Examples
Basic usage:
The first two examples are instances where the input and
and output of sequence are isomorphic.
>>>sequence $ Right [1,2,3,4][Right 1,Right 2,Right 3,Right 4]
>>>sequence $ [Right 1,Right 2,Right 3,Right 4]Right [1,2,3,4]
The following examples demonstrate short circuit behavior
for sequence.
>>>sequence $ Left [1,2,3,4]Left [1,2,3,4]
>>>sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]Left 0
Instances
| Traversable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex | |
| Traversable First | Since: base-4.9.0.0 |
| Traversable Last | Since: base-4.9.0.0 |
| Traversable Max | Since: base-4.9.0.0 |
| Traversable Min | Since: base-4.9.0.0 |
| Traversable NonEmpty | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Identity | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable First | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Last | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Down | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Dual | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Product | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Sum | Since: base-4.8.0.0 |
| Traversable ZipList | Since: base-4.9.0.0 |
Defined in GHC.Internal.Functor.ZipList | |
| Traversable Par1 | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Array | |
Defined in Data.Primitive.Array | |
| Traversable SmallArray | |
Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) Source # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) Source # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) Source # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) Source # | |
| Traversable TyVarBndr | |
Defined in Language.Haskell.TH.Syntax Methods traverse :: Applicative f => (a -> f b) -> TyVarBndr a -> f (TyVarBndr b) Source # sequenceA :: Applicative f => TyVarBndr (f a) -> f (TyVarBndr a) Source # mapM :: Monad m => (a -> m b) -> TyVarBndr a -> m (TyVarBndr b) Source # sequence :: Monad m => TyVarBndr (m a) -> m (TyVarBndr a) Source # | |
| Traversable Vector | |
| Traversable Vector | |
Defined in Data.Vector.Strict | |
| Traversable Maybe | Since: base-2.1 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Solo | Since: base-4.15 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable [] | Since: base-2.1 |
| Traversable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Ix i => Traversable (Array i) | Since: base-2.1 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (Either a) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source # sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source # | |
| Traversable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable f => Traversable (MaybeT f) | |
Defined in Control.Monad.Trans.Maybe | |
| Traversable ((,) a) | Since: base-4.7.0.0 |
| Traversable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable f => Traversable (Ap f) | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable f => Traversable (Alt f) | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable f => Traversable (Rec1 f) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable f => Traversable (ExceptT e f) | |
Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) Source # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) Source # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) Source # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) Source # | |
| Traversable f => Traversable (IdentityT f) | |
Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) Source # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) Source # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) Source # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) Source # | |
| Traversable f => Traversable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) Source # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) Source # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) Source # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) Source # | |
| Traversable f => Traversable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) Source # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) Source # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) Source # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) Source # | |
| (Traversable f, Traversable g) => Traversable (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) Source # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) Source # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) Source # sequence :: Monad m => Product f g (m a) -> m (Product f g a) Source # | |
| (Traversable f, Traversable g) => Traversable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum | |
| (Traversable f, Traversable g) => Traversable (f :*: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b) Source # sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((f :*: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b) Source # sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a) Source # | |
| (Traversable f, Traversable g) => Traversable (f :+: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) Source # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) Source # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) Source # | |
| Traversable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| (Traversable f, Traversable g) => Traversable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) Source # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) Source # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) Source # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) Source # | |
| (Traversable f, Traversable g) => Traversable (f :.: g) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) Source # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) Source # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) Source # | |
| Traversable f => Traversable (M1 i c f) | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
String is an alias for a list of characters.
String constants in Haskell are values of type String.
That means if you write a string literal like "hello world",
it will have the type [Char], which is the same as String.
Note: You can ask the compiler to automatically infer different types
with the -XOverloadedStrings language extension, for example
"hello world" :: Text. See IsString for more information.
Because String is just a list of characters, you can use normal list functions
to do basic string manipulation. See Data.List for operations on lists.
Performance considerations
[Char] is a relatively memory-inefficient type.
It is a linked list of boxed word-size characters, internally it looks something like:
╭─────┬───┬──╮ ╭─────┬───┬──╮ ╭─────┬───┬──╮ ╭────╮
│ (:) │ │ ─┼─>│ (:) │ │ ─┼─>│ (:) │ │ ─┼─>│ [] │
╰─────┴─┼─┴──╯ ╰─────┴─┼─┴──╯ ╰─────┴─┼─┴──╯ ╰────╯
v v v
'a' 'b' 'c'The String "abc" will use 5*3+1 = 16 (in general 5n+1)
words of space in memory.
Furthermore, operations like (++) (string concatenation) are O(n)
(in the left argument).
For historical reasons, the base library uses String in a lot of places
for the conceptual simplicity, but library code dealing with user-data
should use the text
package for Unicode text, or the the
bytestring package
for binary data.
The Either type represents values with two possibilities: a value of
type Either a bLeft aRight 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
The type Either String IntString 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>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: 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) sLeft "foo">>>fmap (*2) nRight 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)>>>:}
>>>parseMultipleRight 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)>>>:}
>>>parseMultipleLeft "parse error"
Instances
| Bifoldable Either | Since: base-4.10.0.0 | ||||
Defined in Data.Bifoldable | |||||
| Bifoldable1 Either | |||||
| Bifunctor Either | Since: base-4.8.0.0 | ||||
| Bitraversable Either | Since: base-4.10.0.0 | ||||
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) Source # | |||||
| Eq2 Either | Since: base-4.9.0.0 | ||||
| Ord2 Either | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Read2 Either | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) Source # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] Source # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) Source # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] Source # | |||||
| Show2 Either | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| NFData2 Either | Since: deepseq-1.4.3.0 | ||||
Defined in Control.DeepSeq | |||||
| Generic1 (Either a :: Type -> Type) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| (Lift a, Lift b) => Lift (Either a b :: Type) | |||||
| Eq a => Eq1 (Either a) | Since: base-4.9.0.0 | ||||
| Ord a => Ord1 (Either a) | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Read a => Read1 (Either a) | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) Source # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] Source # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) Source # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] Source # | |||||
| Show a => Show1 (Either a) | Since: base-4.9.0.0 | ||||
| NFData a => NFData1 (Either a) | Since: deepseq-1.4.3.0 | ||||
Defined in Control.DeepSeq | |||||
| Applicative (Either e) | Since: base-3.0 | ||||
Defined in GHC.Internal.Data.Either | |||||
| Functor (Either a) | Since: base-3.0 | ||||
| Monad (Either e) | Since: base-4.4.0.0 | ||||
| Foldable (Either a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # | |||||
| Traversable (Either a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source # sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source # | |||||
| (NFData a, NFData b) => NFData (Either a b) | |||||
Defined in Control.DeepSeq | |||||
| Semigroup (Either a b) | Since: base-4.9.0.0 | ||||
| (Data a, Data b) => Data (Either a b) | Since: base-4.0.0.0 | ||||
Defined in GHC.Internal.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) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Either a b) Source # toConstr :: Either a b -> Constr Source # dataTypeOf :: Either a b -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Either a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Either a b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Either a b -> Either a b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Either a b -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Either a b -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # | |||||
| Generic (Either a b) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 | ||||
| (Show a, Show b) => Show (Either a b) | Since: base-3.0 | ||||
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 | ||||
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Either Methods compare :: Either a b -> Either a b -> Ordering Source # (<) :: Either a b -> Either a b -> Bool Source # (<=) :: Either a b -> Either a b -> Bool Source # (>) :: Either a b -> Either a b -> Bool Source # (>=) :: Either a b -> Either a b -> Bool Source # | |||||
| (AEq a, AEq b) => AEq (Either a b) | |||||
| type Rep1 (Either a :: Type -> Type) | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" '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 | ||||
Defined in GHC.Internal.Generics type Rep (Either a b) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" '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))) | |||||
curry :: ((a, b) -> c) -> a -> b -> c Source #
Convert an uncurried function to a curried function.
Examples
>>>curry fst 1 21
uncurry :: (a -> b -> c) -> (a, b) -> c Source #
uncurry converts a curried function to a function on pairs.
Examples
>>>uncurry (+) (1,2)3
>>>uncurry ($) (show, 1)"1"
>>>map (uncurry max) [(1,2), (3,4), (6,8)][2,4,8]
errorWithoutStackTrace :: [Char] -> a Source #
A variant of error that does not produce a stack trace.
Since: base-4.9.0.0
undefined :: HasCallStack => a Source #
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #
Same as >>=, but with the arguments interchanged.
as >>= f == f =<< as
flip :: (a -> b -> c) -> b -> a -> c Source #
flip ff.
flip f x y = f y x
flip . flip = id
Examples
>>>flip (++) "hello" "world""worldhello"
>>>let (.>) = flip (.) in (+1) .> show $ 5"6"
($!) :: (a -> b) -> a -> b infixr 0 Source #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
until :: (a -> Bool) -> (a -> a) -> a -> a Source #
until p ff until p holds.
maybe :: b -> (a -> b) -> Maybe a -> b Source #
The maybe function takes a default value, a function, and a Maybe
value. If the Maybe value is Nothing, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just and returns the result.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed,
return twice the integer; that is, apply (*2) to it. If instead
we fail to parse an integer, return 0 by default:
>>>import GHC.Internal.Text.Read ( readMaybe )>>>maybe 0 (*2) (readMaybe "5")10>>>maybe 0 (*2) (readMaybe "")0
Apply show to a Maybe Int. If we have Just n, we want to show
the underlying Int n. But if we have Nothing, we return the
empty string instead of (for example) "Nothing":
>>>maybe "" show (Just 5)"5">>>maybe "" show Nothing""
head :: HasCallStack => [a] -> a Source #
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-}
at the top of the file. To disable it throughout a package put the same
options into ghc-options section of Cabal file. To disable it in GHCi
put :set -Wno-x-partial -Wno-unrecognised-warning-flags into ~/.ghci config file.
See also the migration guide.
Examples
>>>head [1, 2, 3]1
>>>head [1..]1
>>>head []*** Exception: Prelude.head: empty list
tail :: HasCallStack => [a] -> [a] Source #
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-}
at the top of the file. To disable it throughout a package put the same
options into ghc-options section of Cabal file. To disable it in GHCi
put :set -Wno-x-partial -Wno-unrecognised-warning-flags into ~/.ghci config file.
See also the migration guide.
Examples
>>>tail [1, 2, 3][2,3]
>>>tail [1][]
>>>tail []*** Exception: Prelude.tail: empty list
last :: HasCallStack => [a] -> a Source #
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
WARNING: This function is partial. Consider using unsnoc instead.
Examples
>>>last [1, 2, 3]3
>>>last [1..]* Hangs forever *
>>>last []*** Exception: Prelude.last: empty list
init :: HasCallStack => [a] -> [a] Source #
\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.
WARNING: This function is partial. Consider using unsnoc instead.
Examples
>>>init [1, 2, 3][1,2]
>>>init [1][]
>>>init []*** Exception: Prelude.init: empty list
scanl :: (b -> a -> b) -> b -> [a] -> [b] Source #
\(\mathcal{O}(n)\). scanl is similar to foldl, but returns a list of
successive reduced values from the left:
scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
Note that
last (scanl f z xs) == foldl f z xs
Examples
>>>scanl (+) 0 [1..4][0,1,3,6,10]
>>>scanl (+) 42 [][42]
>>>scanl (-) 100 [1..4][100,99,97,94,90]
>>>scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["foo","afoo","bafoo","cbafoo","dcbafoo"]
>>>take 10 (scanl (+) 0 [1..])[0,1,3,6,10,15,21,28,36,45]
>>>take 1 (scanl undefined 'a' undefined)"a"
scanl1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
Examples
>>>scanl1 (+) [1..4][1,3,6,10]
>>>scanl1 (+) [][]
>>>scanl1 (-) [1..4][1,-1,-4,-8]
>>>scanl1 (&&) [True, False, True, True][True,False,False,False]
>>>scanl1 (||) [False, False, True, True][False,False,True,True]
>>>take 10 (scanl1 (+) [1..])[1,3,6,10,15,21,28,36,45,55]
>>>take 1 (scanl1 undefined ('a' : undefined))"a"
scanr :: (a -> b -> b) -> b -> [a] -> [b] Source #
\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that the order of parameters on the accumulating function are reversed compared to scanl.
Also note that
head (scanr f z xs) == foldr f z xs.
Examples
>>>scanr (+) 0 [1..4][10,9,7,4,0]
>>>scanr (+) 42 [][42]
>>>scanr (-) 100 [1..4][98,-97,99,-96,100]
>>>scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]
>>>force $ scanr (+) 0 [1..]*** Exception: stack overflow
scanr1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting
value argument.
Examples
>>>scanr1 (+) [1..4][10,9,7,4]
>>>scanr1 (+) [][]
>>>scanr1 (-) [1..4][-2,3,-1,4]
>>>scanr1 (&&) [True, False, True, True][False,False,True,True]
>>>scanr1 (||) [True, True, False, False][True,True,False,False]
>>>force $ scanr1 (+) [1..]*** Exception: stack overflow
iterate :: (a -> a) -> a -> [a] Source #
iterate f x returns an infinite list of repeated applications
of f to x:
iterate f x == [x, f x, f (f x), ...]
Laziness
Note that iterate is lazy, potentially leading to thunk build-up if
the consumer doesn't force each iterate. See iterate' for a strict
variant of this function.
>>>take 1 $ iterate undefined 42[42]
Examples
>>>take 10 $ iterate not True[True,False,True,False,True,False,True,False,True,False]
>>>take 10 $ iterate (+3) 42[42,45,48,51,54,57,60,63,66,69]
iterate id == :repeat
>>>take 10 $ iterate id 1[1,1,1,1,1,1,1,1,1,1]
repeat x is an infinite list, with x the value of every element.
Examples
>>>take 10 $ repeat 17[17,17,17,17,17,17,17,17,17, 17]
>>>repeat undefined[*** Exception: Prelude.undefined
replicate :: Int -> a -> [a] Source #
replicate n x is a list of length n with x the value of
every element.
It is an instance of the more general genericReplicate,
in which n may be of any integral type.
Examples
>>>replicate 0 True[]
>>>replicate (-1) True[]
>>>replicate 4 True[True,True,True,True]
takeWhile :: (a -> Bool) -> [a] -> [a] Source #
takeWhile, applied to a predicate p and a list xs, returns the
longest prefix (possibly empty) of xs of elements that satisfy p.
Laziness
>>>takeWhile (const False) undefined*** Exception: Prelude.undefined
>>>takeWhile (const False) (undefined : undefined)[]
>>>take 1 (takeWhile (const True) (1 : undefined))[1]
Examples
>>>takeWhile (< 3) [1,2,3,4,1,2,3,4][1,2]
>>>takeWhile (< 9) [1,2,3][1,2,3]
>>>takeWhile (< 0) [1,2,3][]
take :: Int -> [a] -> [a] Source #
take n, applied to a list xs, returns the prefix of xs
of length n, or xs itself if n >= .length xs
It is an instance of the more general genericTake,
in which n may be of any integral type.
Laziness
>>>take 0 undefined[]>>>take 2 (1 : 2 : undefined)[1,2]
Examples
>>>take 5 "Hello World!""Hello"
>>>take 3 [1,2,3,4,5][1,2,3]
>>>take 3 [1,2][1,2]
>>>take 3 [][]
>>>take (-1) [1,2][]
>>>take 0 [1,2][]
drop :: Int -> [a] -> [a] Source #
drop n xs returns the suffix of xs
after the first n elements, or [] if n >= .length xs
It is an instance of the more general genericDrop,
in which n may be of any integral type.
Examples
>>>drop 6 "Hello World!""World!"
>>>drop 3 [1,2,3,4,5][4,5]
>>>drop 3 [1,2][]
>>>drop 3 [][]
>>>drop (-1) [1,2][1,2]
>>>drop 0 [1,2][1,2]
splitAt :: Int -> [a] -> ([a], [a]) Source #
splitAt n xs returns a tuple where first element is xs prefix of
length n and second element is the remainder of the list:
splitAt is an instance of the more general genericSplitAt,
in which n may be of any integral type.
Laziness
It is equivalent to (
unless take n xs, drop n xs)n is _|_:
splitAt _|_ xs = _|_, not (_|_, _|_)).
The first component of the tuple is produced lazily:
>>>fst (splitAt 0 undefined)[]
>>>take 1 (fst (splitAt 10 (1 : undefined)))[1]
Examples
>>>splitAt 6 "Hello World!"("Hello ","World!")
>>>splitAt 3 [1,2,3,4,5]([1,2,3],[4,5])
>>>splitAt 1 [1,2,3]([1],[2,3])
>>>splitAt 3 [1,2,3]([1,2,3],[])
>>>splitAt 4 [1,2,3]([1,2,3],[])
>>>splitAt 0 [1,2,3]([],[1,2,3])
>>>splitAt (-1) [1,2,3]([],[1,2,3])
span :: (a -> Bool) -> [a] -> ([a], [a]) Source #
span, applied to a predicate p and a list xs, returns a tuple where
first element is the longest prefix (possibly empty) of xs of elements that
satisfy p and second element is the remainder of the list:
span p xs is equivalent to (, even if takeWhile p xs, dropWhile p xs)p is _|_.
Laziness
>>>span undefined []([],[])>>>fst (span (const False) undefined)*** Exception: Prelude.undefined>>>fst (span (const False) (undefined : undefined))[]>>>take 1 (fst (span (const True) (1 : undefined)))[1]
span produces the first component of the tuple lazily:
>>>take 10 (fst (span (const True) [1..]))[1,2,3,4,5,6,7,8,9,10]
Examples
>>>span (< 3) [1,2,3,4,1,2,3,4]([1,2],[3,4,1,2,3,4])
>>>span (< 9) [1,2,3]([1,2,3],[])
>>>span (< 0) [1,2,3]([],[1,2,3])
break :: (a -> Bool) -> [a] -> ([a], [a]) Source #
break, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
do not satisfy p and second element is the remainder of the list:
break p is equivalent to span (not . p)(,
even if takeWhile (not . p) xs, dropWhile (not . p) xs)p is _|_.
Laziness
>>>break undefined []([],[])
>>>fst (break (const True) undefined)*** Exception: Prelude.undefined
>>>fst (break (const True) (undefined : undefined))[]
>>>take 1 (fst (break (const False) (1 : undefined)))[1]
break produces the first component of the tuple lazily:
>>>take 10 (fst (break (const False) [1..]))[1,2,3,4,5,6,7,8,9,10]
Examples
>>>break (> 3) [1,2,3,4,1,2,3,4]([1,2,3],[4,1,2,3,4])
>>>break (< 9) [1,2,3]([],[1,2,3])
>>>break (> 9) [1,2,3]([1,2,3],[])
reverse :: [a] -> [a] Source #
\(\mathcal{O}(n)\). reverse xs returns the elements of xs in reverse order.
xs must be finite.
Laziness
reverse is lazy in its elements.
>>>head (reverse [undefined, 1])1
>>>reverse (1 : 2 : undefined)*** Exception: Prelude.undefined
Examples
>>>reverse [][]
>>>reverse [42][42]
>>>reverse [2,5,7][7,5,2]
>>>reverse [1..]* Hangs forever *
and :: Foldable t => t Bool -> Bool Source #
and returns the conjunction of a container of Bools. For the
result to be True, the container must be finite; False, however,
results from a False value finitely far from the left end.
Examples
Basic usage:
>>>and []True
>>>and [True]True
>>>and [False]False
>>>and [True, True, False]False
>>>and (False : repeat True) -- Infinite list [False,True,True,True,...False
>>>and (repeat True)* Hangs forever *
or :: Foldable t => t Bool -> Bool Source #
or returns the disjunction of a container of Bools. For the
result to be False, the container must be finite; True, however,
results from a True value finitely far from the left end.
Examples
Basic usage:
>>>or []False
>>>or [True]True
>>>or [False]False
>>>or [True, True, False]True
>>>or (True : repeat False) -- Infinite list [True,False,False,False,...True
>>>or (repeat False)* Hangs forever *
any :: Foldable t => (a -> Bool) -> t a -> Bool Source #
Determines whether any element of the structure satisfies the predicate.
Examples
Basic usage:
>>>any (> 3) []False
>>>any (> 3) [1,2]False
>>>any (> 3) [1,2,3,4,5]True
>>>any (> 3) [1..]True
>>>any (> 3) [0, -1..]* Hangs forever *
all :: Foldable t => (a -> Bool) -> t a -> Bool Source #
Determines whether all elements of the structure satisfy the predicate.
Examples
Basic usage:
>>>all (> 3) []True
>>>all (> 3) [1,2]False
>>>all (> 3) [1,2,3,4,5]False
>>>all (> 3) [1..]False
>>>all (> 3) [4..]* Hangs forever *
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source #
notElem is the negation of elem.
Examples
Basic usage:
>>>3 `notElem` []True
>>>3 `notElem` [1,2]True
>>>3 `notElem` [1,2,3,4,5]False
For infinite structures, notElem terminates if the value exists at a
finite distance from the left side of the structure:
>>>3 `notElem` [1..]False
>>>3 `notElem` ([4..] ++ [3])* Hangs forever *
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source #
Map a function over all the elements of a container and concatenate the resulting lists.
Examples
Basic usage:
>>>concatMap (take 3) [[1..], [10..], [100..], [1000..]][1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>>concatMap (take 3) (Just [1..])[1,2,3]
(!!) :: HasCallStack => [a] -> Int -> a infixl 9 Source #
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex,
which takes an index of any integral type.
WARNING: This function is partial, and should only be used if you are
sure that the indexing will not fail. Otherwise, use !?.
WARNING: This function takes linear time in the index.
Examples
>>>['a', 'b', 'c'] !! 0'a'
>>>['a', 'b', 'c'] !! 2'c'
>>>['a', 'b', 'c'] !! 3*** Exception: Prelude.!!: index too large
>>>['a', 'b', 'c'] !! (-1)*** Exception: Prelude.!!: negative index
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source #
\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the
function given as the first argument, instead of a tupling function.
zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
zipWith is right-lazy:
>>>let f = undefined>>>zipWith f [] undefined[]
zipWith is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
Examples
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #
\(\mathcal{O}(\min(l,m,n))\). The zipWith3 function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to zipWith.
It is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
Examples
>>>zipWith3 (\x y z -> [x, y, z]) "123" "abc" "xyz"["1ax","2by","3cz"]
>>>zipWith3 (\x y z -> (x * y) + z) [1, 2, 3] [4, 5, 6] [7, 8, 9][11,18,27]
unzip :: [(a, b)] -> ([a], [b]) Source #
unzip transforms a list of pairs into a list of first components
and a list of second components.
Examples
>>>unzip []([],[])
>>>unzip [(1, 'a'), (2, 'b')]([1,2],"ab")
showChar :: Char -> ShowS Source #
utility function converting a Char to a show function that
simply prepends the character unchanged.
showString :: String -> ShowS Source #
utility function converting a String to a show function that
simply prepends the string unchanged.
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to an integral power
gcd :: Integral a => a -> a -> a Source #
gcd x yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 0 44. gcd 0 00.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0minBound0 or minBound
lcm :: Integral a => a -> a -> a Source #
lcm x yx and y divide.
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #
An infix synonym for fmap.
The name of this operator is an allusion to $.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing
>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17
>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
The lex function reads a single lexeme from the input, discarding
initial white space, and returning the characters that constitute the
lexeme. If the input string contains only white space, lex returns a
single successful `lexeme' consisting of the empty string. (Thus
lex "" = [("","")]lex fails (i.e. returns []).
This lexer is not completely faithful to the Haskell lexical syntax in the following respects:
- Qualified names are not handled properly
- Octal and hexadecimal numerics are not recognized as a single token
- Comments are not treated properly
either :: (a -> c) -> (b -> c) -> Either a b -> c Source #
Case analysis for the Either type.
If the value is Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft constructor and another using the Right constructor. Then
we apply "either" the length function (if we have a String)
or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
read :: Read a => String -> a Source #
The read function reads input from a string, which must be
completely consumed by the input process. read fails with an error if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use readMaybe or readEither for safe alternatives.
>>>read "123" :: Int123
>>>read "hello" :: Int*** Exception: Prelude.read: no parse
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence.
sequence_ is just like sequenceA_, but specialised to monadic
actions.
lines :: String -> [String] Source #
Splits the argument into a list of lines stripped of their terminating
\n characters. The \n terminator is optional in a final non-empty
line of the argument string.
When the argument string is empty, or ends in a \n character, it can be
recovered by passing the result of lines to the unlines function.
Otherwise, unlines appends the missing terminating \n. This makes
unlines . lines idempotent:
(unlines . lines) . (unlines . lines) = (unlines . lines)
Examples
>>>lines "" -- empty input contains no lines[]
>>>lines "\n" -- single empty line[""]
>>>lines "one" -- single unterminated line["one"]
>>>lines "one\n" -- single non-empty line["one"]
>>>lines "one\n\n" -- second line is empty["one",""]
>>>lines "one\ntwo" -- second line is unterminated["one","two"]
>>>lines "one\ntwo\n" -- two non-empty lines["one","two"]
type IOError = IOException Source #
type FilePath = String Source #
File and directory names are values of type String, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.
getContents :: IO String Source #
The getContents operation returns all user input as a single string,
which is read lazily as it is needed
(same as hGetContents stdin).
interact :: (String -> String) -> IO () Source #
The interact function takes a function of type String->String
as its argument. The entire input from the standard input device is
passed to this function as its argument, and the resulting string is
output on the standard output device.
readFile :: FilePath -> IO String Source #
The readFile function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with getContents.
writeFile :: FilePath -> String -> IO () Source #
The computation writeFile file str function writes the string str,
to the file file.
appendFile :: FilePath -> String -> IO () Source #
The computation appendFile file str function appends the string str,
to the file file.
Note that writeFile and appendFile write a literal string
to a file. To write a value of any printable type, as with print,
use the show function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])