numeric-prelude-0.4.4: An experimental alternative hierarchy of numeric type classes
Safe HaskellNone
LanguageHaskell98

NumericPrelude

Synopsis

Documentation

data Double #

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

Instances

Instances details
Eq Double

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool #

(/=) :: Double -> Double -> Bool #

Floating Double

Since: base-2.1

Instance details

Defined in GHC.Float

Ord Double

Note that due to the presence of NaN, Double's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Double)
False

Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:

>>> (0/0 :: Double) > 1
False
>>> compare (0/0 :: Double) 1
GT
Instance details

Defined in GHC.Classes

Read Double

Since: base-2.1

Instance details

Defined in GHC.Read

RealFloat Double

Since: base-2.1

Instance details

Defined in GHC.Float

Arbitrary Double 
Instance details

Defined in Test.QuickCheck.Arbitrary

CoArbitrary Double 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Double -> Gen b -> Gen b #

Storable Double

Since: base-2.1

Instance details

Defined in Foreign.Storable

NFData Double 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Double -> () #

Random Double

Note - random produces values in the closed range [0,1].

Instance details

Defined in System.Random

Methods

randomR :: RandomGen g => (Double, Double) -> g -> (Double, g) #

random :: RandomGen g => g -> (Double, g) #

randomRs :: RandomGen g => (Double, Double) -> g -> [Double] #

randoms :: RandomGen g => g -> [Double] #

UniformRange Double

See Floating point number caveats.

Instance details

Defined in System.Random.Internal

Methods

uniformRM :: StatefulGen g m => (Double, Double) -> g -> m Double #

C Double Source # 
Instance details

Defined in Algebra.Additive

C Double Source # 
Instance details

Defined in Algebra.ZeroTestable

Methods

isZero :: Double -> Bool Source #

C Double Source # 
Instance details

Defined in Algebra.Ring

C Double Source # 
Instance details

Defined in Algebra.Absolute

C Double Source # 
Instance details

Defined in Algebra.Field

C Double Source # 
Instance details

Defined in Algebra.ToRational

C Double Source # 
Instance details

Defined in Algebra.Algebraic

C Double Source # 
Instance details

Defined in Algebra.Transcendental

C Double Source # 
Instance details

Defined in Algebra.RealRing

Methods

splitFraction :: C b => Double -> (b, Double) Source #

fraction :: Double -> Double Source #

ceiling :: C b => Double -> b Source #

floor :: C b => Double -> b Source #

truncate :: C b => Double -> b Source #

round :: C b => Double -> b Source #

C Double Source # 
Instance details

Defined in Algebra.RealField

C Double Source # 
Instance details

Defined in Algebra.RealTranscendental

Methods

atan2 :: Double -> Double -> Double Source #

C Double Source # 
Instance details

Defined in Algebra.FloatingPoint

Power Double Source # 
Instance details

Defined in Number.Complex

Methods

power :: Rational -> T Double -> T Double Source #

Lift Double 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Double -> Q Exp #

liftTyped :: Double -> Q (TExp Double) #

C Double Double Source # 
Instance details

Defined in Algebra.Module

Methods

(*>) :: Double -> Double -> Double Source #

C Double Double Source # 
Instance details

Defined in Algebra.VectorSpace

C Double Double Source # 
Instance details

Defined in Algebra.ModuleBasis

C Double Double Source # 
Instance details

Defined in Algebra.OccasionallyScalar

C Double Double Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Double -> Double Source #

C Double Double Source # 
Instance details

Defined in Algebra.NormedSpace.Maximum

Methods

norm :: Double -> Double Source #

C Double Double Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Double -> Double Source #

Sqr Double Double Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

Generic1 (URec Double :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Double) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a #

to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a #

Foldable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m #

foldMap :: Monoid m => (a -> m) -> UDouble a -> m #

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m #

foldr :: (a -> b -> b) -> b -> UDouble a -> b #

foldr' :: (a -> b -> b) -> b -> UDouble a -> b #

foldl :: (b -> a -> b) -> b -> UDouble a -> b #

foldl' :: (b -> a -> b) -> b -> UDouble a -> b #

foldr1 :: (a -> a -> a) -> UDouble a -> a #

foldl1 :: (a -> a -> a) -> UDouble a -> a #

toList :: UDouble a -> [a] #

null :: UDouble a -> Bool #

length :: UDouble a -> Int #

elem :: Eq a => a -> UDouble a -> Bool #

maximum :: Ord a => UDouble a -> a #

minimum :: Ord a => UDouble a -> a #

sum :: Num a => UDouble a -> a #

product :: Num a => UDouble a -> a #

Traversable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) #

sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) #

mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) #

sequence :: Monad m => UDouble (m a) -> m (UDouble a) #

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b #

(<$) :: a -> URec Double b -> URec Double a #

Eq (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool #

(/=) :: URec Double p -> URec Double p -> Bool #

Ord (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Double p -> URec Double p -> Ordering #

(<) :: URec Double p -> URec Double p -> Bool #

(<=) :: URec Double p -> URec Double p -> Bool #

(>) :: URec Double p -> URec Double p -> Bool #

(>=) :: URec Double p -> URec Double p -> Bool #

max :: URec Double p -> URec Double p -> URec Double p #

min :: URec Double p -> URec Double p -> URec Double p #

Show (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Double p -> ShowS #

show :: URec Double p -> String #

showList :: [URec Double p] -> ShowS #

Generic (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Double p) :: Type -> Type #

Methods

from :: URec Double p -> Rep (URec Double p) x #

to :: Rep (URec Double p) x -> URec Double p #

data URec Double (p :: k)

Used for marking occurrences of Double#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Double (p :: k) = UDouble {}
type Rep1 (URec Double :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))
type Rep (URec Double p) 
Instance details

Defined in GHC.Generics

type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Float #

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

Instances

Instances details
Eq Float

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool #

(/=) :: Float -> Float -> Bool #

Floating Float

Since: base-2.1

Instance details

Defined in GHC.Float

Ord Float

Note that due to the presence of NaN, Float's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Float)
False

Also note that, due to the same, Ord's operator interactions are not respected by Float's instance:

>>> (0/0 :: Float) > 1
False
>>> compare (0/0 :: Float) 1
GT
Instance details

Defined in GHC.Classes

Methods

compare :: Float -> Float -> Ordering #

(<) :: Float -> Float -> Bool #

(<=) :: Float -> Float -> Bool #

(>) :: Float -> Float -> Bool #

(>=) :: Float -> Float -> Bool #

max :: Float -> Float -> Float #

min :: Float -> Float -> Float #

Read Float

Since: base-2.1

Instance details

Defined in GHC.Read

RealFloat Float

Since: base-2.1

Instance details

Defined in GHC.Float

Arbitrary Float 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Float #

shrink :: Float -> [Float] #

CoArbitrary Float 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Float -> Gen b -> Gen b #

Storable Float

Since: base-2.1

Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Float -> Int #

alignment :: Float -> Int #

peekElemOff :: Ptr Float -> Int -> IO Float #

pokeElemOff :: Ptr Float -> Int -> Float -> IO () #

peekByteOff :: Ptr b -> Int -> IO Float #

pokeByteOff :: Ptr b -> Int -> Float -> IO () #

peek :: Ptr Float -> IO Float #

poke :: Ptr Float -> Float -> IO () #

NFData Float 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Float -> () #

Random Float

Note - random produces values in the closed range [0,1].

Instance details

Defined in System.Random

Methods

randomR :: RandomGen g => (Float, Float) -> g -> (Float, g) #

random :: RandomGen g => g -> (Float, g) #

randomRs :: RandomGen g => (Float, Float) -> g -> [Float] #

randoms :: RandomGen g => g -> [Float] #

UniformRange Float

See Floating point number caveats.

Instance details

Defined in System.Random.Internal

Methods

uniformRM :: StatefulGen g m => (Float, Float) -> g -> m Float #

C Float Source # 
Instance details

Defined in Algebra.Additive

C Float Source # 
Instance details

Defined in Algebra.ZeroTestable

Methods

isZero :: Float -> Bool Source #

C Float Source # 
Instance details

Defined in Algebra.Ring

C Float Source # 
Instance details

Defined in Algebra.Absolute

C Float Source # 
Instance details

Defined in Algebra.Field

C Float Source # 
Instance details

Defined in Algebra.ToRational

C Float Source # 
Instance details

Defined in Algebra.Algebraic

C Float Source # 
Instance details

Defined in Algebra.Transcendental

C Float Source # 
Instance details

Defined in Algebra.RealRing

Methods

splitFraction :: C b => Float -> (b, Float) Source #

fraction :: Float -> Float Source #

ceiling :: C b => Float -> b Source #

floor :: C b => Float -> b Source #

truncate :: C b => Float -> b Source #

round :: C b => Float -> b Source #

C Float Source # 
Instance details

Defined in Algebra.RealField

C Float Source # 
Instance details

Defined in Algebra.RealTranscendental

Methods

atan2 :: Float -> Float -> Float Source #

C Float Source # 
Instance details

Defined in Algebra.FloatingPoint

Power Float Source # 
Instance details

Defined in Number.Complex

Methods

power :: Rational -> T Float -> T Float Source #

Lift Float 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Float -> Q Exp #

liftTyped :: Float -> Q (TExp Float) #

C Float Float Source # 
Instance details

Defined in Algebra.Module

Methods

(*>) :: Float -> Float -> Float Source #

C Float Float Source # 
Instance details

Defined in Algebra.VectorSpace

C Float Float Source # 
Instance details

Defined in Algebra.ModuleBasis

C Float Float Source # 
Instance details

Defined in Algebra.OccasionallyScalar

C Float Float Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Float -> Float Source #

C Float Float Source # 
Instance details

Defined in Algebra.NormedSpace.Maximum

Methods

norm :: Float -> Float Source #

C Float Float Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Float -> Float Source #

Sqr Float Float Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: Float -> Float Source #

Generic1 (URec Float :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Float) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Float a -> Rep1 (URec Float) a #

to1 :: forall (a :: k0). Rep1 (URec Float) a -> URec Float a #

Foldable (UFloat :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m #

foldMap :: Monoid m => (a -> m) -> UFloat a -> m #

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m #

foldr :: (a -> b -> b) -> b -> UFloat a -> b #

foldr' :: (a -> b -> b) -> b -> UFloat a -> b #

foldl :: (b -> a -> b) -> b -> UFloat a -> b #

foldl' :: (b -> a -> b) -> b -> UFloat a -> b #

foldr1 :: (a -> a -> a) -> UFloat a -> a #

foldl1 :: (a -> a -> a) -> UFloat a -> a #

toList :: UFloat a -> [a] #

null :: UFloat a -> Bool #

length :: UFloat a -> Int #

elem :: Eq a => a -> UFloat a -> Bool #

maximum :: Ord a => UFloat a -> a #

minimum :: Ord a => UFloat a -> a #

sum :: Num a => UFloat a -> a #

product :: Num a => UFloat a -> a #

Traversable (UFloat :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) #

sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) #

mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) #

sequence :: Monad m => UFloat (m a) -> m (UFloat a) #

Functor (URec Float :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b #

(<$) :: a -> URec Float b -> URec Float a #

Eq (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

(==) :: URec Float p -> URec Float p -> Bool #

(/=) :: URec Float p -> URec Float p -> Bool #

Ord (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

compare :: URec Float p -> URec Float p -> Ordering #

(<) :: URec Float p -> URec Float p -> Bool #

(<=) :: URec Float p -> URec Float p -> Bool #

(>) :: URec Float p -> URec Float p -> Bool #

(>=) :: URec Float p -> URec Float p -> Bool #

max :: URec Float p -> URec Float p -> URec Float p #

min :: URec Float p -> URec Float p -> URec Float p #

Show (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Float p -> ShowS #

show :: URec Float p -> String #

showList :: [URec Float p] -> ShowS #

Generic (URec Float p) 
Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Float p) :: Type -> Type #

Methods

from :: URec Float p -> Rep (URec Float p) x #

to :: Rep (URec Float p) x -> URec Float p #

data URec Float (p :: k)

Used for marking occurrences of Float#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Float (p :: k) = UFloat {}
type Rep1 (URec Float :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))
type Rep (URec Float p) 
Instance details

Defined in GHC.Generics

type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

data Int #

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

Instances

Instances details
Bounded Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: Int #

maxBound :: Int #

Enum Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Int -> Int #

pred :: Int -> Int #

toEnum :: Int -> Int #

fromEnum :: Int -> Int #

enumFrom :: Int -> [Int] #

enumFromThen :: Int -> Int -> [Int] #

enumFromTo :: Int -> Int -> [Int] #

enumFromThenTo :: Int -> Int -> Int -> [Int] #

Eq Int 
Instance details

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool #

(/=) :: Int -> Int -> Bool #

Integral Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

quot :: Int -> Int -> Int #

rem :: Int -> Int -> Int #

div :: Int -> Int -> Int #

mod :: Int -> Int -> Int #

quotRem :: Int -> Int -> (Int, Int) #

divMod :: Int -> Int -> (Int, Int) #

toInteger :: Int -> Integer #

Num Int

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Int -> Int -> Int #

(-) :: Int -> Int -> Int #

(*) :: Int -> Int -> Int #

negate :: Int -> Int #

abs :: Int -> Int #

signum :: Int -> Int #

fromInteger :: Integer -> Int #

Ord Int 
Instance details

Defined in GHC.Classes

Methods

compare :: Int -> Int -> Ordering #

(<) :: Int -> Int -> Bool #

(<=) :: Int -> Int -> Bool #

(>) :: Int -> Int -> Bool #

(>=) :: Int -> Int -> Bool #

max :: Int -> Int -> Int #

min :: Int -> Int -> Int #

Read Int

Since: base-2.1

Instance details

Defined in GHC.Read

Real Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Int -> Rational #

Show Int

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS #

show :: Int -> String #

showList :: [Int] -> ShowS #

Ix Int

Since: base-2.1

Instance details

Defined in GHC.Ix

Methods

range :: (Int, Int) -> [Int] #

index :: (Int, Int) -> Int -> Int #

unsafeIndex :: (Int, Int) -> Int -> Int #

inRange :: (Int, Int) -> Int -> Bool #

rangeSize :: (Int, Int) -> Int #

unsafeRangeSize :: (Int, Int) -> Int #

Arbitrary Int 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Int #

shrink :: Int -> [Int] #

CoArbitrary Int 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Int -> Gen b -> Gen b #

Storable Int

Since: base-2.1

Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Int -> Int #

alignment :: Int -> Int #

peekElemOff :: Ptr Int -> Int -> IO Int #

pokeElemOff :: Ptr Int -> Int -> Int -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int #

pokeByteOff :: Ptr b -> Int -> Int -> IO () #

peek :: Ptr Int -> IO Int #

poke :: Ptr Int -> Int -> IO () #

NFData Int 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Int -> () #

Random Int 
Instance details

Defined in System.Random

Methods

randomR :: RandomGen g => (Int, Int) -> g -> (Int, g) #

random :: RandomGen g => g -> (Int, g) #

randomRs :: RandomGen g => (Int, Int) -> g -> [Int] #

randoms :: RandomGen g => g -> [Int] #

Uniform Int 
Instance details

Defined in System.Random.Internal

Methods

uniformM :: StatefulGen g m => g -> m Int #

UniformRange Int 
Instance details

Defined in System.Random.Internal

Methods

uniformRM :: StatefulGen g m => (Int, Int) -> g -> m Int #

C Int Source # 
Instance details

Defined in Algebra.Additive

Methods

zero :: Int Source #

(+) :: Int -> Int -> Int Source #

(-) :: Int -> Int -> Int Source #

negate :: Int -> Int Source #

C Int Source # 
Instance details

Defined in Algebra.ZeroTestable

Methods

isZero :: Int -> Bool Source #

C Int Source # 
Instance details

Defined in Algebra.Ring

C Int Source # 
Instance details

Defined in Algebra.IntegralDomain

Methods

div :: Int -> Int -> Int Source #

mod :: Int -> Int -> Int Source #

divMod :: Int -> Int -> (Int, Int) Source #

C Int Source # 
Instance details

Defined in Algebra.Units

C Int Source # 
Instance details

Defined in Algebra.PrincipalIdealDomain

Methods

extendedGCD :: Int -> Int -> (Int, (Int, Int)) Source #

gcd :: Int -> Int -> Int Source #

lcm :: Int -> Int -> Int Source #

C Int Source # 
Instance details

Defined in Algebra.Absolute

Methods

abs :: Int -> Int Source #

signum :: Int -> Int Source #

C Int Source # 
Instance details

Defined in Algebra.ToRational

C Int Source # 
Instance details

Defined in Algebra.RealIntegral

Methods

quot :: Int -> Int -> Int Source #

rem :: Int -> Int -> Int Source #

quotRem :: Int -> Int -> (Int, Int) Source #

C Int Source # 
Instance details

Defined in Algebra.ToInteger

C Int Source # 
Instance details

Defined in Algebra.RealRing

Methods

splitFraction :: C b => Int -> (b, Int) Source #

fraction :: Int -> Int Source #

ceiling :: C b => Int -> b Source #

floor :: C b => Int -> b Source #

truncate :: C b => Int -> b Source #

round :: C b => Int -> b Source #

Lift Int 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Int -> Q Exp #

liftTyped :: Int -> Q (TExp Int) #

C Int Int Source # 
Instance details

Defined in Algebra.Module

Methods

(*>) :: Int -> Int -> Int Source #

C Int Int Source # 
Instance details

Defined in Algebra.ModuleBasis

Methods

basis :: Int -> [Int] Source #

flatten :: Int -> [Int] Source #

dimension :: Int -> Int -> Int Source #

C Int Int Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Int -> Int Source #

C Int Int Source # 
Instance details

Defined in Algebra.NormedSpace.Maximum

Methods

norm :: Int -> Int Source #

C Int Int Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Int -> Int Source #

Sqr Int Int Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: Int -> Int Source #

Generic1 (URec Int :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Int) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Int a -> Rep1 (URec Int) a #

to1 :: forall (a :: k0). Rep1 (URec Int) a -> URec Int a #

Foldable (UInt :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UInt m -> m #

foldMap :: Monoid m => (a -> m) -> UInt a -> m #

foldMap' :: Monoid m => (a -> m) -> UInt a -> m #

foldr :: (a -> b -> b) -> b -> UInt a -> b #

foldr' :: (a -> b -> b) -> b -> UInt a -> b #

foldl :: (b -> a -> b) -> b -> UInt a -> b #

foldl' :: (b -> a -> b) -> b -> UInt a -> b #

foldr1 :: (a -> a -> a) -> UInt a -> a #

foldl1 :: (a -> a -> a) -> UInt a -> a #

toList :: UInt a -> [a] #

null :: UInt a -> Bool #

length :: UInt a -> Int #

elem :: Eq a => a -> UInt a -> Bool #

maximum :: Ord a => UInt a -> a #

minimum :: Ord a => UInt a -> a #

sum :: Num a => UInt a -> a #

product :: Num a => UInt a -> a #

Traversable (UInt :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) #

sequenceA :: Applicative f => UInt (f a) -> f (UInt a) #

mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) #

sequence :: Monad m => UInt (m a) -> m (UInt a) #

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b #

(<$) :: a -> URec Int b -> URec Int a #

Eq (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Int p -> URec Int p -> Bool #

(/=) :: URec Int p -> URec Int p -> Bool #

Ord (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Int p -> URec Int p -> Ordering #

(<) :: URec Int p -> URec Int p -> Bool #

(<=) :: URec Int p -> URec Int p -> Bool #

(>) :: URec Int p -> URec Int p -> Bool #

(>=) :: URec Int p -> URec Int p -> Bool #

max :: URec Int p -> URec Int p -> URec Int p #

min :: URec Int p -> URec Int p -> URec Int p #

Show (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Int p -> ShowS #

show :: URec Int p -> String #

showList :: [URec Int p] -> ShowS #

Generic (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Int p) :: Type -> Type #

Methods

from :: URec Int p -> Rep (URec Int p) x #

to :: Rep (URec Int p) x -> URec Int p #

data URec Int (p :: k)

Used for marking occurrences of Int#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Int (p :: k) = UInt {}
type Rep1 (URec Int :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Int :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: k -> Type)))
type Rep (URec Int p) 
Instance details

Defined in GHC.Generics

type Rep (URec Int p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: Type -> Type)))

data Integer #

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

For more information about this type's representation, see the comments in its implementation.

Instances

Instances details
Enum Integer

Since: base-2.1

Instance details

Defined in GHC.Enum

Eq Integer 
Instance details

Defined in GHC.Integer.Type

Methods

(==) :: Integer -> Integer -> Bool #

(/=) :: Integer -> Integer -> Bool #

Integral Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Num Integer

Since: base-2.1

Instance details

Defined in GHC.Num

Ord Integer 
Instance details

Defined in GHC.Integer.Type

Read Integer

Since: base-2.1

Instance details

Defined in GHC.Read

Real Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Show Integer

Since: base-2.1

Instance details

Defined in GHC.Show

Ix Integer

Since: base-2.1

Instance details

Defined in GHC.Ix

Arbitrary Integer 
Instance details

Defined in Test.QuickCheck.Arbitrary

CoArbitrary Integer 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Integer -> Gen b -> Gen b #

NFData Integer 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Integer -> () #

Random Integer

Note - random generates values in the Int range

Instance details

Defined in System.Random

Methods

randomR :: RandomGen g => (Integer, Integer) -> g -> (Integer, g) #

random :: RandomGen g => g -> (Integer, g) #

randomRs :: RandomGen g => (Integer, Integer) -> g -> [Integer] #

randoms :: RandomGen g => g -> [Integer] #

UniformRange Integer 
Instance details

Defined in System.Random.Internal

Methods

uniformRM :: StatefulGen g m => (Integer, Integer) -> g -> m Integer #

C Integer Source # 
Instance details

Defined in Algebra.Indexable

C Integer Source # 
Instance details

Defined in Algebra.Additive

C Integer Source # 
Instance details

Defined in Algebra.ZeroTestable

Methods

isZero :: Integer -> Bool Source #

C Integer Source # 
Instance details

Defined in Algebra.Ring

C Integer Source # 
Instance details

Defined in Algebra.IntegralDomain

C Integer Source # 
Instance details

Defined in Algebra.Units

C Integer Source # 
Instance details

Defined in Algebra.PrincipalIdealDomain

C Integer Source # 
Instance details

Defined in Algebra.Absolute

C Integer Source # 
Instance details

Defined in Algebra.ToRational

C Integer Source # 
Instance details

Defined in Algebra.RealIntegral

C Integer Source # 
Instance details

Defined in Algebra.ToInteger

C Integer Source # 
Instance details

Defined in Algebra.RealRing

Methods

splitFraction :: C b => Integer -> (b, Integer) Source #

fraction :: Integer -> Integer Source #

ceiling :: C b => Integer -> b Source #

floor :: C b => Integer -> b Source #

truncate :: C b => Integer -> b Source #

round :: C b => Integer -> b Source #

C Integer Source # 
Instance details

Defined in Algebra.Lattice

Lift Integer 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Integer -> Q Exp #

liftTyped :: Integer -> Q (TExp Integer) #

C Integer Integer Source # 
Instance details

Defined in Algebra.Module

C Integer Integer Source # 
Instance details

Defined in Algebra.ModuleBasis

C Integer Integer Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Integer -> Integer Source #

C Integer Integer Source # 
Instance details

Defined in Algebra.NormedSpace.Maximum

Methods

norm :: Integer -> Integer Source #

C Integer Integer Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Integer -> Integer Source #

Sqr Integer Integer Source # 
Instance details

Defined in Algebra.NormedSpace.Euclidean

C a => C Integer (T a) Source # 
Instance details

Defined in Algebra.Module

Methods

(*>) :: Integer -> T a -> T a Source #

zero :: C a => a Source #

zero element of the vector space

negate :: C a => a -> a Source #

inverse with respect to +

(+), (-) :: C a => a -> a -> a infixl 6 +, - Source #

add and subtract elements

(+), (-) :: C a => a -> a -> a infixl 6 +, - Source #

add and subtract elements

subtract :: C a => a -> a -> a Source #

subtract is (-) with swapped operand order. This is the operand order which will be needed in most cases of partial application.

sum :: C a => [a] -> a Source #

Sum up all elements of a list. An empty list yields zero.

This function is inappropriate for number types like Peano. Maybe we should make sum a method of Additive. This would also make lengthLeft and lengthRight superfluous.

sum1 :: C a => [a] -> a Source #

Sum up all elements of a non-empty list. This avoids including a zero which is useful for types where no universal zero is available. ToDo: Should have NonEmpty type.

\(QC.NonEmpty ns) -> A.sum ns == (A.sum1 ns :: Integer)

isZero :: C a => a -> Bool Source #

one :: C a => a Source #

(*) :: C a => a -> a -> a infixl 7 Source #

(^) :: C a => a -> Integer -> a infixr 8 Source #

The exponent has fixed type Integer in order to avoid an arbitrarily limitted range of exponents, but to reduce the need for the compiler to guess the type (default type). In practice the exponent is most oftenly fixed, and is most oftenly 2. Fixed exponents can be optimized away and thus the expensive computation of Integers doesn't matter. The previous solution used a C constrained type and the exponent was converted to Integer before computation. So the current solution is not less efficient.

A variant of ^ with more flexibility is provided by ringPower.

sqr :: C a => a -> a Source #

product :: C a => [a] -> a Source #

product1 :: C a => [a] -> a Source #

divMod :: C a => a -> a -> (a, a) Source #

\n (QC.NonZero m) -> let (q,r) = divMod n m in n == (q*m+r :: Integer)

div, mod :: C a => a -> a -> a infixl 7 `div`, `mod` Source #

div, mod :: C a => a -> a -> a infixl 7 `div`, `mod` Source #

divides :: (C a, C a) => a -> a -> Bool Source #

even :: (C a, C a) => a -> Bool Source #

odd :: (C a, C a) => a -> Bool Source #

isUnit :: C a => a -> Bool Source #

extendedGCD :: C a => a -> a -> (a, (a, a)) Source #

Compute the greatest common divisor and solve a respective Diophantine equation.

  (g,(a,b)) = extendedGCD x y ==>
       g==a*x+b*y   &&  g == gcd x y

TODO: This method is not appropriate for the PID class, because there are rings like the one of the multivariate polynomials, where for all x and y greatest common divisors of x and y exist, but they cannot be represented as a linear combination of x and y. TODO: The definition of extendedGCD does not return the canonical associate.

gcd :: C a => a -> a -> a Source #

The Greatest Common Divisor is defined by:

  gcd x y == gcd y x
  divides z x && divides z y ==> divides z (gcd x y)   (specification)
  divides (gcd x y) x

lcm :: C a => a -> a -> a Source #

Least common multiple

euclid :: (C a, C a) => (a -> a -> a) -> a -> a -> a Source #

extendedEuclid :: (C a, C a) => (a -> a -> (a, a)) -> a -> a -> (a, (a, a)) Source #

signum :: C a => a -> a Source #

numerator :: T a -> a Source #

denominator :: T a -> a Source #

(%) :: C a => a -> a -> T a infixl 7 Source #

(^-) :: C a => a -> Integer -> a infixr 8 Source #

(/) :: C a => a -> a -> a infixl 7 Source #

recip :: C a => a -> a Source #

fromRational :: C a => Rational -> a Source #

Needed to work around shortcomings in GHC.

toRational :: C a => a -> Rational Source #

Lossless conversion from any representation of a rational to Rational

quotRem :: C a => a -> a -> (a, a) Source #

quot, rem :: C a => a -> a -> a infixl 7 `quot`, `rem` Source #

quot, rem :: C a => a -> a -> a infixl 7 `quot`, `rem` Source #

toInteger :: C a => a -> Integer Source #

fromIntegral :: (C a, C b) => a -> b Source #

ringPower :: (C a, C b) => b -> a -> a Source #

A prefix function of (^) with a parameter order that fits the needs of partial application and function composition. It has generalised exponent.

See: Argument order of expNat on http://www.haskell.org/pipermail/haskell-cafe/2006-September/018022.html

fieldPower :: (C a, C b) => b -> a -> a Source #

A prefix function of (^-). It has a generalised exponent.

(*>) :: C a v => a -> v -> v infixr 7 Source #

scale a vector by a scalar

sqrt :: C a => a -> a Source #

(^/) :: C a => a -> Rational -> a infixr 8 Source #

asinh, acosh, atanh :: C a => a -> a Source #

asinh, acosh, atanh :: C a => a -> a Source #

asinh, acosh, atanh :: C a => a -> a Source #

sinh, cosh, tanh :: C a => a -> a Source #

sinh, cosh, tanh :: C a => a -> a Source #

sinh, cosh, tanh :: C a => a -> a Source #

asin, acos, atan :: C a => a -> a Source #

asin, acos, atan :: C a => a -> a Source #

asin, acos, atan :: C a => a -> a Source #

sin, cos, tan :: C a => a -> a Source #

sin, cos, tan :: C a => a -> a Source #

sin, cos, tan :: C a => a -> a Source #

logBase, (**) :: C a => a -> a -> a infixr 8 Source #

logBase, (**) :: C a => a -> a -> a infixr 8 Source #

exp, log :: C a => a -> a Source #

pi :: C a => a Source #

exp, log :: C a => a -> a Source #

(^?) :: C a => a -> a -> a infixr 8 Source #

fraction :: C a => a -> a Source #

\x -> let y = fraction (x::Double) in 0<=y && y<1
\x -> let y = fraction (x::Rational) in 0<=y && y<1

splitFraction :: (C a, C b) => a -> (b, a) Source #

\x -> (x::Rational) == (uncurry (+) $ mapFst fromInteger $ splitFraction x)
\x -> uncurry (==) $ mapFst (((x::Double)-) . fromInteger) $ splitFraction x
\x -> uncurry (==) $ mapFst (((x::Rational)-) . fromInteger) $ splitFraction x
\x -> splitFraction x == (floor (x::Double) :: Integer, fraction x)
\x -> splitFraction x == (floor (x::Rational) :: Integer, fraction x)

ceiling, floor :: (C a, C b) => a -> b Source #

\x -> ceiling (-x) == negate (floor (x::Double) :: Integer)
\x -> ceiling (-x) == negate (floor (x::Rational) :: Integer)

ceiling, floor :: (C a, C b) => a -> b Source #

\x -> ceiling (-x) == negate (floor (x::Double) :: Integer)
\x -> ceiling (-x) == negate (floor (x::Rational) :: Integer)

truncate :: (C a, C b) => a -> b Source #

round :: (C a, C b) => a -> b Source #

approxRational :: (C a, C a) => a -> a -> Rational Source #

TODO: Should be moved to a continued fraction module.

atan2 :: C a => a -> a -> a Source #

(++) :: [a] -> [a] -> [a] infixr 5 #

Append 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.

seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b infixr 0 #

The value of seq a b is bottom if a 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 b does not guarantee that a 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.

filter :: (a -> Bool) -> [a] -> [a] #

\(\mathcal{O}(n)\). 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]
>>> filter odd [1, 2, 3]
[1,3]

zip :: [a] -> [b] -> [(a, b)] #

\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of corresponding pairs.

zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]

If one input list is short, excess elements of the longer list are discarded:

zip [1] ['a', 'b'] = [(1, 'a')]
zip [1, 2] ['a'] = [(1, 'a')]

zip is right-lazy:

zip [] _|_ = []
zip _|_ [] = _|_

zip is capable of list fusion, but it is restricted to its first list argument and its resulting list.

print :: Show a => a -> IO () #

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]])

fst :: (a, b) -> a #

Extract the first component of a pair.

snd :: (a, b) -> b #

Extract the second component of a pair.

otherwise :: Bool #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

map :: (a -> b) -> [a] -> [b] #

\(\mathcal{O}(n)\). 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, ...]
>>> map (+1) [1, 2, 3]

($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.

realToFrac :: (Real a, Fractional b) => a -> b #

general coercion to fractional types

class Bounded a where #

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.

Methods

minBound :: a #

maxBound :: a #

Instances

Instances details
Bounded Bool

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Char

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: Int #

maxBound :: Int #

Bounded Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Ordering

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Word

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded VecCount

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Bounded VecElem

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Bounded ()

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: () #

maxBound :: () #

Bounded All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: All #

maxBound :: All #

Bounded Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Any #

maxBound :: Any #

Bounded Associativity

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded CChar 
Instance details

Defined in Foreign.C.Types

Bounded CSChar 
Instance details

Defined in Foreign.C.Types

Bounded CUChar 
Instance details

Defined in Foreign.C.Types

Bounded CShort 
Instance details

Defined in Foreign.C.Types

Bounded CUShort 
Instance details

Defined in Foreign.C.Types

Bounded CInt 
Instance details

Defined in Foreign.C.Types

Bounded CUInt 
Instance details

Defined in Foreign.C.Types

Bounded CLong 
Instance details

Defined in Foreign.C.Types

Bounded CULong 
Instance details

Defined in Foreign.C.Types

Bounded CLLong 
Instance details

Defined in Foreign.C.Types

Bounded CULLong 
Instance details

Defined in Foreign.C.Types

Bounded CBool 
Instance details

Defined in Foreign.C.Types

Bounded CPtrdiff 
Instance details

Defined in Foreign.C.Types

Bounded CSize 
Instance details

Defined in Foreign.C.Types

Bounded CWchar 
Instance details

Defined in Foreign.C.Types

Bounded CSigAtomic 
Instance details

Defined in Foreign.C.Types

Bounded CIntPtr 
Instance details

Defined in Foreign.C.Types

Bounded CUIntPtr 
Instance details

Defined in Foreign.C.Types

Bounded CIntMax 
Instance details

Defined in Foreign.C.Types

Bounded CUIntMax 
Instance details

Defined in Foreign.C.Types

Bounded GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Bounded Extension 
Instance details

Defined in GHC.LanguageExtensions.Type

Bounded T Source # 
Instance details

Defined in Number.Peano

Methods

minBound :: T #

maxBound :: T #

Bounded a => Bounded (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Min a #

maxBound :: Min a #

Bounded a => Bounded (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Max a #

maxBound :: Max a #

Bounded a => Bounded (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: First a #

maxBound :: First a #

Bounded a => Bounded (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Last a #

maxBound :: Last a #

Bounded m => Bounded (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Bounded a => Bounded (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a #

maxBound :: Dual a #

Bounded a => Bounded (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a #

maxBound :: Sum a #

Bounded a => Bounded (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Bounded a => Bounded (Down a)

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Methods

minBound :: Down a #

maxBound :: Down a #

(Ord a, Num a, Bounded a) => Bounded (T a) 
Instance details

Defined in Numeric.NonNegative.Wrapper

Methods

minBound :: T a #

maxBound :: T a #

Bounded a => Bounded (T a) Source # 
Instance details

Defined in MathObj.Wrapper.Haskell98

Methods

minBound :: T a #

maxBound :: T a #

Bounded a => Bounded (T a) Source # 
Instance details

Defined in MathObj.Wrapper.NumericPrelude

Methods

minBound :: T a #

maxBound :: T a #

(Bounded a, Bounded b) => Bounded (a, b)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b) #

maxBound :: (a, b) #

Bounded (Proxy t)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

minBound :: Proxy t #

maxBound :: Proxy t #

(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c) #

maxBound :: (a, b, c) #

Bounded a => Bounded (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

minBound :: Const a b #

maxBound :: Const a b #

(Applicative f, Bounded a) => Bounded (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

minBound :: Ap f a #

maxBound :: Ap f a #

a ~ b => Bounded (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

minBound :: a :~: b #

maxBound :: a :~: b #

(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d) #

maxBound :: (a, b, c, d) #

a ~~ b => Bounded (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

minBound :: a :~~: b #

maxBound :: a :~~: b #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e) #

maxBound :: (a, b, c, d, e) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f) #

maxBound :: (a, b, c, d, e, f) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g) #

maxBound :: (a, b, c, d, e, f, g) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h) #

maxBound :: (a, b, c, d, e, f, g, h) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i) #

maxBound :: (a, b, c, d, e, f, g, h, i) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j) #

maxBound :: (a, b, c, d, e, f, g, h, i, j) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

(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

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Enum a where #

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:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a #

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a #

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a #

Convert from an Int.

fromEnum :: a -> 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.

enumFrom :: a -> [a] #

Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n). For example:

  • enumFrom 4 :: [Integer] = [4,5,6,7,...]
  • enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

enumFromThen :: a -> a -> [a] #

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 For example:

  • enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
  • enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

enumFromTo :: a -> a -> [a] #

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 = []. For example:

  • enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
  • enumFromTo 42 1 :: [Integer] = []

enumFromThenTo :: a -> a -> a -> [a] #

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 = [] For example:

  • enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
  • enumFromThenTo 6 8 2 :: [Int] = []

Instances

Instances details
Enum Bool

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Bool -> Bool #

pred :: Bool -> Bool #

toEnum :: Int -> Bool #

fromEnum :: Bool -> Int #

enumFrom :: Bool -> [Bool] #

enumFromThen :: Bool -> Bool -> [Bool] #

enumFromTo :: Bool -> Bool -> [Bool] #

enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #

Enum Char

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Char -> Char #

pred :: Char -> Char #

toEnum :: Int -> Char #

fromEnum :: Char -> Int #

enumFrom :: Char -> [Char] #

enumFromThen :: Char -> Char -> [Char] #

enumFromTo :: Char -> Char -> [Char] #

enumFromThenTo :: Char -> Char -> Char -> [Char] #

Enum Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Int -> Int #

pred :: Int -> Int #

toEnum :: Int -> Int #

fromEnum :: Int -> Int #

enumFrom :: Int -> [Int] #

enumFromThen :: Int -> Int -> [Int] #

enumFromTo :: Int -> Int -> [Int] #

enumFromThenTo :: Int -> Int -> Int -> [Int] #

Enum Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

succ :: Int8 -> Int8 #

pred :: Int8 -> Int8 #

toEnum :: Int -> Int8 #

fromEnum :: Int8 -> Int #

enumFrom :: Int8 -> [Int8] #

enumFromThen :: Int8 -> Int8 -> [Int8] #

enumFromTo :: Int8 -> Int8 -> [Int8] #

enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] #

Enum Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Integer

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Enum

Enum Ordering

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Word

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Word -> Word #

pred :: Word -> Word #

toEnum :: Int -> Word #

fromEnum :: Word -> Int #

enumFrom :: Word -> [Word] #

enumFromThen :: Word -> Word -> [Word] #

enumFromTo :: Word -> Word -> [Word] #

enumFromThenTo :: Word -> Word -> Word -> [Word] #

Enum Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Enum VecCount

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Enum VecElem

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Enum ()

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: () -> () #

pred :: () -> () #

toEnum :: Int -> () #

fromEnum :: () -> Int #

enumFrom :: () -> [()] #

enumFromThen :: () -> () -> [()] #

enumFromTo :: () -> () -> [()] #

enumFromThenTo :: () -> () -> () -> [()] #

Enum Associativity

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum CChar 
Instance details

Defined in Foreign.C.Types

Enum CSChar 
Instance details

Defined in Foreign.C.Types

Enum CUChar 
Instance details

Defined in Foreign.C.Types

Enum CShort 
Instance details

Defined in Foreign.C.Types

Enum CUShort 
Instance details

Defined in Foreign.C.Types

Enum CInt 
Instance details

Defined in Foreign.C.Types

Methods

succ :: CInt -> CInt #

pred :: CInt -> CInt #

toEnum :: Int -> CInt #

fromEnum :: CInt -> Int #

enumFrom :: CInt -> [CInt] #

enumFromThen :: CInt -> CInt -> [CInt] #

enumFromTo :: CInt -> CInt -> [CInt] #

enumFromThenTo :: CInt -> CInt -> CInt -> [CInt] #

Enum CUInt 
Instance details

Defined in Foreign.C.Types

Enum CLong 
Instance details

Defined in Foreign.C.Types

Enum CULong 
Instance details

Defined in Foreign.C.Types

Enum CLLong 
Instance details

Defined in Foreign.C.Types

Enum CULLong 
Instance details

Defined in Foreign.C.Types

Enum CBool 
Instance details

Defined in Foreign.C.Types

Enum CFloat 
Instance details

Defined in Foreign.C.Types

Enum CDouble 
Instance details

Defined in Foreign.C.Types

Enum CPtrdiff 
Instance details

Defined in Foreign.C.Types

Enum CSize 
Instance details

Defined in Foreign.C.Types

Enum CWchar 
Instance details

Defined in Foreign.C.Types

Enum CSigAtomic 
Instance details

Defined in Foreign.C.Types

Enum CClock 
Instance details

Defined in Foreign.C.Types

Enum CTime 
Instance details

Defined in Foreign.C.Types

Enum CUSeconds 
Instance details

Defined in Foreign.C.Types

Enum CSUSeconds 
Instance details

Defined in Foreign.C.Types

Enum CIntPtr 
Instance details

Defined in Foreign.C.Types

Enum CUIntPtr 
Instance details

Defined in Foreign.C.Types

Enum CIntMax 
Instance details

Defined in Foreign.C.Types

Enum CUIntMax 
Instance details

Defined in Foreign.C.Types

Enum GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Enum Extension 
Instance details

Defined in GHC.LanguageExtensions.Type

Enum Message 
Instance details

Defined in Text.Parsec.Error

Enum T Source # 
Instance details

Defined in Number.Peano

Methods

succ :: T -> T #

pred :: T -> T #

toEnum :: Int -> T #

fromEnum :: T -> Int #

enumFrom :: T -> [T] #

enumFromThen :: T -> T -> [T] #

enumFromTo :: T -> T -> [T] #

enumFromThenTo :: T -> T -> T -> [T] #

Enum Dimension Source # 
Instance details

Defined in Number.SI.Unit

Integral a => Enum (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

succ :: Ratio a -> Ratio a #

pred :: Ratio a -> Ratio a #

toEnum :: Int -> Ratio a #

fromEnum :: Ratio a -> Int #

enumFrom :: Ratio a -> [Ratio a] #

enumFromThen :: Ratio a -> Ratio a -> [Ratio a] #

enumFromTo :: Ratio a -> Ratio a -> [Ratio a] #

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #

Enum a => Enum (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Min a -> Min a #

pred :: Min a -> Min a #

toEnum :: Int -> Min a #

fromEnum :: Min a -> Int #

enumFrom :: Min a -> [Min a] #

enumFromThen :: Min a -> Min a -> [Min a] #

enumFromTo :: Min a -> Min a -> [Min a] #

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] #

Enum a => Enum (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Max a -> Max a #

pred :: Max a -> Max a #

toEnum :: Int -> Max a #

fromEnum :: Max a -> Int #

enumFrom :: Max a -> [Max a] #

enumFromThen :: Max a -> Max a -> [Max a] #

enumFromTo :: Max a -> Max a -> [Max a] #

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] #

Enum a => Enum (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: First a -> First a #

pred :: First a -> First a #

toEnum :: Int -> First a #

fromEnum :: First a -> Int #

enumFrom :: First a -> [First a] #

enumFromThen :: First a -> First a -> [First a] #

enumFromTo :: First a -> First a -> [First a] #

enumFromThenTo :: First a -> First a -> First a -> [First a] #

Enum a => Enum (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Last a -> Last a #

pred :: Last a -> Last a #

toEnum :: Int -> Last a #

fromEnum :: Last a -> Int #

enumFrom :: Last a -> [Last a] #

enumFromThen :: Last a -> Last a -> [Last a] #

enumFromTo :: Last a -> Last a -> [Last a] #

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #

Enum a => Enum (WrappedMonoid a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Enum a => Enum (Down a)

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Methods

succ :: Down a -> Down a #

pred :: Down a -> Down a #

toEnum :: Int -> Down a #

fromEnum :: Down a -> Int #

enumFrom :: Down a -> [Down a] #

enumFromThen :: Down a -> Down a -> [Down a] #

enumFromTo :: Down a -> Down a -> [Down a] #

enumFromThenTo :: Down a -> Down a -> Down a -> [Down a] #

(Ord a, Num a, Enum a) => Enum (T a) 
Instance details

Defined in Numeric.NonNegative.Wrapper

Methods

succ :: T a -> T a #

pred :: T a -> T a #

toEnum :: Int -> T a #

fromEnum :: T a -> Int #

enumFrom :: T a -> [T a] #

enumFromThen :: T a -> T a -> [T a] #

enumFromTo :: T a -> T a -> [T a] #

enumFromThenTo :: T a -> T a -> T a -> [T a] #

(Enum a, C a) => Enum (T a) 
Instance details

Defined in Numeric.NonNegative.ChunkyPrivate

Methods

succ :: T a -> T a #

pred :: T a -> T a #

toEnum :: Int -> T a #

fromEnum :: T a -> Int #

enumFrom :: T a -> [T a] #

enumFromThen :: T a -> T a -> [T a] #

enumFromTo :: T a -> T a -> [T a] #

enumFromThenTo :: T a -> T a -> T a -> [T a] #

Enum a => Enum (T a) Source # 
Instance details

Defined in MathObj.Wrapper.Haskell98

Methods

succ :: T a -> T a #

pred :: T a -> T a #

toEnum :: Int -> T a #

fromEnum :: T a -> Int #

enumFrom :: T a -> [T a] #

enumFromThen :: T a -> T a -> [T a] #

enumFromTo :: T a -> T a -> [T a] #

enumFromThenTo :: T a -> T a -> T a -> [T a] #

Enum a => Enum (T a) Source # 
Instance details

Defined in MathObj.Wrapper.NumericPrelude

Methods

succ :: T a -> T a #

pred :: T a -> T a #

toEnum :: Int -> T a #

fromEnum :: T a -> Int #

enumFrom :: T a -> [T a] #

enumFromThen :: T a -> T a -> [T a] #

enumFromTo :: T a -> T a -> [T a] #

enumFromThenTo :: T a -> T a -> T a -> [T a] #

Enum (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

succ :: Fixed a -> Fixed a #

pred :: Fixed a -> Fixed a #

toEnum :: Int -> Fixed a #

fromEnum :: Fixed a -> Int #

enumFrom :: Fixed a -> [Fixed a] #

enumFromThen :: Fixed a -> Fixed a -> [Fixed a] #

enumFromTo :: Fixed a -> Fixed a -> [Fixed a] #

enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] #

Enum (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

succ :: Proxy s -> Proxy s #

pred :: Proxy s -> Proxy s #

toEnum :: Int -> Proxy s #

fromEnum :: Proxy s -> Int #

enumFrom :: Proxy s -> [Proxy s] #

enumFromThen :: Proxy s -> Proxy s -> [Proxy s] #

enumFromTo :: Proxy s -> Proxy s -> [Proxy s] #

enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] #

Enum a => Enum (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

succ :: Const a b -> Const a b #

pred :: Const a b -> Const a b #

toEnum :: Int -> Const a b #

fromEnum :: Const a b -> Int #

enumFrom :: Const a b -> [Const a b] #

enumFromThen :: Const a b -> Const a b -> [Const a b] #

enumFromTo :: Const a b -> Const a b -> [Const a b] #

enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #

Enum (f a) => Enum (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

succ :: Ap f a -> Ap f a #

pred :: Ap f a -> Ap f a #

toEnum :: Int -> Ap f a #

fromEnum :: Ap f a -> Int #

enumFrom :: Ap f a -> [Ap f a] #

enumFromThen :: Ap f a -> Ap f a -> [Ap f a] #

enumFromTo :: Ap f a -> Ap f a -> [Ap f a] #

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] #

Enum (f a) => Enum (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a #

pred :: Alt f a -> Alt f a #

toEnum :: Int -> Alt f a #

fromEnum :: Alt f a -> Int #

enumFrom :: Alt f a -> [Alt f a] #

enumFromThen :: Alt f a -> Alt f a -> [Alt f a] #

enumFromTo :: Alt f a -> Alt f a -> [Alt f a] #

enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] #

a ~ b => Enum (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

succ :: (a :~: b) -> a :~: b #

pred :: (a :~: b) -> a :~: b #

toEnum :: Int -> a :~: b #

fromEnum :: (a :~: b) -> Int #

enumFrom :: (a :~: b) -> [a :~: b] #

enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] #

enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] #

enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] #

a ~~ b => Enum (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

succ :: (a :~~: b) -> a :~~: b #

pred :: (a :~~: b) -> a :~~: b #

toEnum :: Int -> a :~~: b #

fromEnum :: (a :~~: b) -> Int #

enumFrom :: (a :~~: b) -> [a :~~: b] #

enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

class Eq a where #

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, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties:

Reflexivity
x == x = True
Symmetry
x == y = y == x
Transitivity
if x == y && y == z = True, then x == z = True
Substitutivity
if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True
Negation
x /= y = not (x == y)

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 #

(/=) :: a -> a -> Bool infix 4 #

Instances

Instances details
Eq Bool 
Instance details

Defined in GHC.Classes

Methods

(==) :: Bool -> Bool -> Bool #

(/=) :: Bool -> Bool -> Bool #

Eq Char 
Instance details

Defined in GHC.Classes

Methods

(==) :: Char -> Char -> Bool #

(/=) :: Char -> Char -> Bool #

Eq Double

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool #

(/=) :: Double -> Double -> Bool #

Eq Float

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool #

(/=) :: Float -> Float -> Bool #

Eq Int 
Instance details

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool #

(/=) :: Int -> Int -> Bool #

Eq Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int8 -> Int8 -> Bool #

(/=) :: Int8 -> Int8 -> Bool #

Eq Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int16 -> Int16 -> Bool #

(/=) :: Int16 -> Int16 -> Bool #

Eq Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int32 -> Int32 -> Bool #

(/=) :: Int32 -> Int32 -> Bool #

Eq Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int64 -> Int64 -> Bool #

(/=) :: Int64 -> Int64 -> Bool #

Eq Integer 
Instance details

Defined in GHC.Integer.Type

Methods

(==) :: Integer -> Integer -> Bool #

(/=) :: Integer -> Integer -> Bool #

Eq Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Methods

(==) :: Natural -> Natural -> Bool #

(/=) :: Natural -> Natural -> Bool #

Eq Ordering 
Instance details

Defined in GHC.Classes

Eq Word 
Instance details

Defined in GHC.Classes

Methods

(==) :: Word -> Word -> Bool #

(/=) :: Word -> Word -> Bool #

Eq Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word8 -> Word8 -> Bool #

(/=) :: Word8 -> Word8 -> Bool #

Eq Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word16 -> Word16 -> Bool #

(/=) :: Word16 -> Word16 -> Bool #

Eq Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word32 -> Word32 -> Bool #

(/=) :: Word32 -> Word32 -> Bool #

Eq Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word64 -> Word64 -> Bool #

(/=) :: Word64 -> Word64 -> Bool #

Eq SomeTypeRep 
Instance details

Defined in Data.Typeable.Internal

Eq Exp 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Exp -> Exp -> Bool #

(/=) :: Exp -> Exp -> Bool #

Eq Match 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Match -> Match -> Bool #

(/=) :: Match -> Match -> Bool #

Eq Clause 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Clause -> Clause -> Bool #

(/=) :: Clause -> Clause -> Bool #

Eq Pat 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Pat -> Pat -> Bool #

(/=) :: Pat -> Pat -> Bool #

Eq Type 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Type -> Type -> Bool #

(/=) :: Type -> Type -> Bool #

Eq Dec 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Dec -> Dec -> Bool #

(/=) :: Dec -> Dec -> Bool #

Eq Name 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Name -> Name -> Bool #

(/=) :: Name -> Name -> Bool #

Eq FunDep 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: FunDep -> FunDep -> Bool #

(/=) :: FunDep -> FunDep -> Bool #

Eq InjectivityAnn 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Overlap 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Overlap -> Overlap -> Bool #

(/=) :: Overlap -> Overlap -> Bool #

Eq () 
Instance details

Defined in GHC.Classes

Methods

(==) :: () -> () -> Bool #

(/=) :: () -> () -> Bool #

Eq TyCon 
Instance details

Defined in GHC.Classes

Methods

(==) :: TyCon -> TyCon -> Bool #

(/=) :: TyCon -> TyCon -> Bool #

Eq Module 
Instance details

Defined in GHC.Classes

Methods

(==) :: Module -> Module -> Bool #

(/=) :: Module -> Module -> Bool #

Eq TrName 
Instance details

Defined in GHC.Classes

Methods

(==) :: TrName -> TrName -> Bool #

(/=) :: TrName -> TrName -> Bool #

Eq Version

Since: base-2.1

Instance details

Defined in Data.Version

Methods

(==) :: Version -> Version -> Bool #

(/=) :: Version -> Version -> Bool #

Eq StdGen 
Instance details

Defined in System.Random.Internal

Methods

(==) :: StdGen -> StdGen -> Bool #

(/=) :: StdGen -> StdGen -> Bool #

Eq Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Methods

(==) :: Void -> Void -> Bool #

(/=) :: Void -> Void -> Bool #

Eq SpecConstrAnnotation

Since: base-4.3.0.0

Instance details

Defined in GHC.Exts

Eq Unique 
Instance details

Defined in Data.Unique

Methods

(==) :: Unique -> Unique -> Bool #

(/=) :: Unique -> Unique -> Bool #

Eq ThreadId

Since: base-4.2.0.0

Instance details

Defined in GHC.Conc.Sync

Eq BlockReason

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Eq ThreadStatus

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Eq AsyncException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Eq ArrayException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Eq ExitCode 
Instance details

Defined in GHC.IO.Exception

Eq IOErrorType

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Eq MaskingState

Since: base-4.3.0.0

Instance details

Defined in GHC.IO

Eq IOException

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Eq All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool #

(/=) :: All -> All -> Bool #

Eq Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool #

(/=) :: Any -> Any -> Bool #

Eq Fixity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: Fixity -> Fixity -> Bool #

(/=) :: Fixity -> Fixity -> Bool #

Eq Associativity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Eq SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq CChar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CChar -> CChar -> Bool #

(/=) :: CChar -> CChar -> Bool #

Eq CSChar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CSChar -> CSChar -> Bool #

(/=) :: CSChar -> CSChar -> Bool #

Eq CUChar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CUChar -> CUChar -> Bool #

(/=) :: CUChar -> CUChar -> Bool #

Eq CShort 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CShort -> CShort -> Bool #

(/=) :: CShort -> CShort -> Bool #

Eq CUShort 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CUShort -> CUShort -> Bool #

(/=) :: CUShort -> CUShort -> Bool #

Eq CInt 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CInt -> CInt -> Bool #

(/=) :: CInt -> CInt -> Bool #

Eq CUInt 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CUInt -> CUInt -> Bool #

(/=) :: CUInt -> CUInt -> Bool #

Eq CLong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CLong -> CLong -> Bool #

(/=) :: CLong -> CLong -> Bool #

Eq CULong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CULong -> CULong -> Bool #

(/=) :: CULong -> CULong -> Bool #

Eq CLLong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CLLong -> CLLong -> Bool #

(/=) :: CLLong -> CLLong -> Bool #

Eq CULLong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CULLong -> CULLong -> Bool #

(/=) :: CULLong -> CULLong -> Bool #

Eq CBool 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CBool -> CBool -> Bool #

(/=) :: CBool -> CBool -> Bool #

Eq CFloat 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CFloat -> CFloat -> Bool #

(/=) :: CFloat -> CFloat -> Bool #

Eq CDouble 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CDouble -> CDouble -> Bool #

(/=) :: CDouble -> CDouble -> Bool #

Eq CPtrdiff 
Instance details

Defined in Foreign.C.Types

Eq CSize 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CSize -> CSize -> Bool #

(/=) :: CSize -> CSize -> Bool #

Eq CWchar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CWchar -> CWchar -> Bool #

(/=) :: CWchar -> CWchar -> Bool #

Eq CSigAtomic 
Instance details

Defined in Foreign.C.Types

Eq CClock 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CClock -> CClock -> Bool #

(/=) :: CClock -> CClock -> Bool #

Eq CTime 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CTime -> CTime -> Bool #

(/=) :: CTime -> CTime -> Bool #

Eq CUSeconds 
Instance details

Defined in Foreign.C.Types

Eq CSUSeconds 
Instance details

Defined in Foreign.C.Types

Eq CIntPtr 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CIntPtr -> CIntPtr -> Bool #

(/=) :: CIntPtr -> CIntPtr -> Bool #

Eq CUIntPtr 
Instance details

Defined in Foreign.C.Types

Eq CIntMax 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CIntMax -> CIntMax -> Bool #

(/=) :: CIntMax -> CIntMax -> Bool #

Eq CUIntMax 
Instance details

Defined in Foreign.C.Types

Eq Fingerprint

Since: base-4.4.0.0

Instance details

Defined in GHC.Fingerprint.Type

Eq Lexeme

Since: base-2.1

Instance details

Defined in Text.Read.Lex

Methods

(==) :: Lexeme -> Lexeme -> Bool #

(/=) :: Lexeme -> Lexeme -> Bool #

Eq Number

Since: base-4.6.0.0

Instance details

Defined in Text.Read.Lex

Methods

(==) :: Number -> Number -> Bool #

(/=) :: Number -> Number -> Bool #

Eq GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Eq SrcLoc

Since: base-4.9.0.0

Instance details

Defined in GHC.Stack.Types

Methods

(==) :: SrcLoc -> SrcLoc -> Bool #

(/=) :: SrcLoc -> SrcLoc -> Bool #

Eq IntSet 
Instance details

Defined in Data.IntSet.Internal

Methods

(==) :: IntSet -> IntSet -> Bool #

(/=) :: IntSet -> IntSet -> Bool #

Eq Extension 
Instance details

Defined in GHC.LanguageExtensions.Type

Eq ForeignSrcLang 
Instance details

Defined in GHC.ForeignSrcLang.Type

Eq BigNat 
Instance details

Defined in GHC.Integer.Type

Methods

(==) :: BigNat -> BigNat -> Bool #

(/=) :: BigNat -> BigNat -> Bool #

Eq Message 
Instance details

Defined in Text.Parsec.Error

Methods

(==) :: Message -> Message -> Bool #

(/=) :: Message -> Message -> Bool #

Eq ParseError 
Instance details

Defined in Text.Parsec.Error

Eq SourcePos 
Instance details

Defined in Text.Parsec.Pos

Eq Doc 
Instance details

Defined in Text.PrettyPrint.HughesPJ

Methods

(==) :: Doc -> Doc -> Bool #

(/=) :: Doc -> Doc -> Bool #

Eq TextDetails 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Eq Style 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

(==) :: Style -> Style -> Bool #

(/=) :: Style -> Style -> Bool #

Eq Mode 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

(==) :: Mode -> Mode -> Bool #

(/=) :: Mode -> Mode -> Bool #

Eq ModName 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: ModName -> ModName -> Bool #

(/=) :: ModName -> ModName -> Bool #

Eq PkgName 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: PkgName -> PkgName -> Bool #

(/=) :: PkgName -> PkgName -> Bool #

Eq Module 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Module -> Module -> Bool #

(/=) :: Module -> Module -> Bool #

Eq OccName 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: OccName -> OccName -> Bool #

(/=) :: OccName -> OccName -> Bool #

Eq NameFlavour 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq NameSpace 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Loc 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Loc -> Loc -> Bool #

(/=) :: Loc -> Loc -> Bool #

Eq Info 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Info -> Info -> Bool #

(/=) :: Info -> Info -> Bool #

Eq ModuleInfo 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Fixity 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Fixity -> Fixity -> Bool #

(/=) :: Fixity -> Fixity -> Bool #

Eq FixityDirection 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Lit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Lit -> Lit -> Bool #

(/=) :: Lit -> Lit -> Bool #

Eq Bytes 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Bytes -> Bytes -> Bool #

(/=) :: Bytes -> Bytes -> Bool #

Eq Body 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Body -> Body -> Bool #

(/=) :: Body -> Body -> Bool #

Eq Guard 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Guard -> Guard -> Bool #

(/=) :: Guard -> Guard -> Bool #

Eq Stmt 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Stmt -> Stmt -> Bool #

(/=) :: Stmt -> Stmt -> Bool #

Eq Range 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Range -> Range -> Bool #

(/=) :: Range -> Range -> Bool #

Eq DerivClause 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq DerivStrategy 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq TypeFamilyHead 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq TySynEqn 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Foreign 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Foreign -> Foreign -> Bool #

(/=) :: Foreign -> Foreign -> Bool #

Eq Callconv 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Safety 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Safety -> Safety -> Bool #

(/=) :: Safety -> Safety -> Bool #

Eq Pragma 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Pragma -> Pragma -> Bool #

(/=) :: Pragma -> Pragma -> Bool #

Eq Inline 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Inline -> Inline -> Bool #

(/=) :: Inline -> Inline -> Bool #

Eq RuleMatch 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Phases 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Phases -> Phases -> Bool #

(/=) :: Phases -> Phases -> Bool #

Eq RuleBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq AnnTarget 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq SourceUnpackedness 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq SourceStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq DecidedStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Con 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Con -> Con -> Bool #

(/=) :: Con -> Con -> Bool #

Eq Bang 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Bang -> Bang -> Bool #

(/=) :: Bang -> Bang -> Bool #

Eq PatSynDir 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq PatSynArgs 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq TyVarBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq FamilyResultSig 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq TyLit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: TyLit -> TyLit -> Bool #

(/=) :: TyLit -> TyLit -> Bool #

Eq Role 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: Role -> Role -> Bool #

(/=) :: Role -> Role -> Bool #

Eq AnnLookup 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq T Source # 
Instance details

Defined in Number.Peano

Methods

(==) :: T -> T -> Bool #

(/=) :: T -> T -> Bool #

Eq T Source # 
Instance details

Defined in Number.GaloisField2p32m5

Methods

(==) :: T -> T -> Bool #

(/=) :: T -> T -> Bool #

Eq T Source # 
Instance details

Defined in Number.FixedPoint.Check

Methods

(==) :: T -> T -> Bool #

(/=) :: T -> T -> Bool #

Eq T Source # 
Instance details

Defined in Number.Positional.Check

Methods

(==) :: T -> T -> Bool #

(/=) :: T -> T -> Bool #

Eq Dimension Source # 
Instance details

Defined in Number.SI.Unit

Eq a => Eq [a] 
Instance details

Defined in GHC.Classes

Methods

(==) :: [a] -> [a] -> Bool #

(/=) :: [a] -> [a] -> Bool #

Eq a => Eq (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Maybe

Methods

(==) :: Maybe a -> Maybe a -> Bool #

(/=) :: Maybe a -> Maybe a -> Bool #

Eq a => Eq (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

(==) :: Ratio a -> Ratio a -> Bool #

(/=) :: Ratio a -> Ratio a -> Bool #

Eq (StablePtr a)

Since: base-2.1

Instance details

Defined in GHC.Stable

Methods

(==) :: StablePtr a -> StablePtr a -> Bool #

(/=) :: StablePtr a -> StablePtr a -> Bool #

Eq (Ptr a)

Since: base-2.1

Instance details

Defined in GHC.Ptr

Methods

(==) :: Ptr a -> Ptr a -> Bool #

(/=) :: Ptr a -> Ptr a -> Bool #

Eq (FunPtr a) 
Instance details

Defined in GHC.Ptr

Methods

(==) :: FunPtr a -> FunPtr a -> Bool #

(/=) :: FunPtr a -> FunPtr a -> Bool #

Eq p => Eq (Par1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: Par1 p -> Par1 p -> Bool #

(/=) :: Par1 p -> Par1 p -> Bool #

Eq a => Eq (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

(==) :: Complex a -> Complex a -> Bool #

(/=) :: Complex a -> Complex a -> Bool #

Eq a => Eq (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Min a -> Min a -> Bool #

(/=) :: Min a -> Min a -> Bool #

Eq a => Eq (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Max a -> Max a -> Bool #

(/=) :: Max a -> Max a -> Bool #

Eq a => Eq (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: First a -> First a -> Bool #

(/=) :: First a -> First a -> Bool #

Eq a => Eq (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Last a -> Last a -> Bool #

(/=) :: Last a -> Last a -> Bool #

Eq m => Eq (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Eq a => Eq (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Option a -> Option a -> Bool #

(/=) :: Option a -> Option a -> Bool #

Eq (StableName a)

Since: base-2.1

Instance details

Defined in GHC.StableName

Methods

(==) :: StableName a -> StableName a -> Bool #

(/=) :: StableName a -> StableName a -> Bool #

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

(==) :: ZipList a -> ZipList a -> Bool #

(/=) :: ZipList a -> ZipList a -> Bool #

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(==) :: Identity a -> Identity a -> Bool #

(/=) :: Identity a -> Identity a -> Bool #

Eq (TVar a)

Since: base-4.8.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

(==) :: TVar a -> TVar a -> Bool #

(/=) :: TVar a -> TVar a -> Bool #

Eq (IORef a)

Pointer equality.

Since: base-4.0.0.0

Instance details

Defined in GHC.IORef

Methods

(==) :: IORef a -> IORef a -> Bool #

(/=) :: IORef a -> IORef a -> Bool #

Eq a => Eq (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

(==) :: First a -> First a -> Bool #

(/=) :: First a -> First a -> Bool #

Eq a => Eq (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

(==) :: Last a -> Last a -> Bool #

(/=) :: Last a -> Last a -> Bool #

Eq a => Eq (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Dual a -> Dual a -> Bool #

(/=) :: Dual a -> Dual a -> Bool #

Eq a => Eq (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Sum a -> Sum a -> Bool #

(/=) :: Sum a -> Sum a -> Bool #

Eq a => Eq (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Product a -> Product a -> Bool #

(/=) :: Product a -> Product a -> Bool #

Eq a => Eq (Down a)

Since: base-4.6.0.0

Instance details

Defined in Data.Ord

Methods

(==) :: Down a -> Down a -> Bool #

(/=) :: Down a -> Down a -> Bool #

Eq (MVar a)

Since: base-4.1.0.0

Instance details

Defined in GHC.MVar

Methods

(==) :: MVar a -> MVar a -> Bool #

(/=) :: MVar a -> MVar a -> Bool #

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(==) :: NonEmpty a -> NonEmpty a -> Bool #

(/=) :: NonEmpty a -> NonEmpty a -> Bool #

Eq a => Eq (IntMap a) 
Instance details

Defined in Data.IntMap.Internal

Methods

(==) :: IntMap a -> IntMap a -> Bool #

(/=) :: IntMap a -> IntMap a -> Bool #

Eq a => Eq (Tree a) 
Instance details

Defined in Data.Tree

Methods

(==) :: Tree a -> Tree a -> Bool #

(/=) :: Tree a -> Tree a -> Bool #

Eq a => Eq (Seq a) 
Instance details

Defined in Data.Sequence.Internal

Methods

(==) :: Seq a -> Seq a -> Bool #

(/=) :: Seq a -> Seq a -> Bool #

Eq a => Eq (ViewL a) 
Instance details

Defined in Data.Sequence.Internal

Methods

(==) :: ViewL a -> ViewL a -> Bool #

(/=) :: ViewL a -> ViewL a -> Bool #

Eq a => Eq (ViewR a) 
Instance details

Defined in Data.Sequence.Internal

Methods

(==) :: ViewR a -> ViewR a -> Bool #

(/=) :: ViewR a -> ViewR a -> Bool #

Eq a => Eq (Set a) 
Instance details

Defined in Data.Set.Internal

Methods

(==) :: Set a -> Set a -> Bool #

(/=) :: Set a -> Set a -> Bool #

Eq a => Eq (T a) 
Instance details

Defined in Numeric.NonNegative.Wrapper

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

C a => Eq (T a) 
Instance details

Defined in Numeric.NonNegative.ChunkyPrivate

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq (Doc a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

(==) :: Doc a -> Doc a -> Bool #

(/=) :: Doc a -> Doc a -> Bool #

Eq a => Eq (AnnotDetails a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Eq a => Eq (Span a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

(==) :: Span a -> Span a -> Bool #

(/=) :: Span a -> Span a -> Bool #

Eq g => Eq (StateGen g) 
Instance details

Defined in System.Random.Internal

Methods

(==) :: StateGen g -> StateGen g -> Bool #

(/=) :: StateGen g -> StateGen g -> Bool #

Eq a => Eq (ToOrd a) Source # 
Instance details

Defined in Algebra.Indexable

Methods

(==) :: ToOrd a -> ToOrd a -> Bool #

(/=) :: ToOrd a -> ToOrd a -> Bool #

Eq a => Eq (Max a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

(==) :: Max a -> Max a -> Bool #

(/=) :: Max a -> Max a -> Bool #

Eq a => Eq (Min a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

(==) :: Min a -> Min a -> Bool #

(/=) :: Min a -> Min a -> Bool #

Eq a => Eq (LCM a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

(==) :: LCM a -> LCM a -> Bool #

(/=) :: LCM a -> LCM a -> Bool #

Eq a => Eq (GCD a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

(==) :: GCD a -> GCD a -> Bool #

(/=) :: GCD a -> GCD a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in Number.Ratio

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in MathObj.Wrapper.Haskell98

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

(Eq a, C a, C a) => Eq (T a) Source # 
Instance details

Defined in Number.ResidueClass.Maybe

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq (T a) Source # 
Instance details

Defined in Number.ResidueClass.Func

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in Number.ResidueClass.Check

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq a => Eq (Valuable a) Source # 
Instance details

Defined in Number.Peano

Methods

(==) :: Valuable a -> Valuable a -> Bool #

(/=) :: Valuable a -> Valuable a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in Number.PartiallyTranscendental

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

C a => Eq (T a) Source # 
Instance details

Defined in Number.NonNegativeChunky

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

(Eq a, C a) => Eq (T a) Source # 
Instance details

Defined in MathObj.PowerSeries

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

(Eq a, C a) => Eq (T a) Source # 
Instance details

Defined in MathObj.PowerSeries2

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

(Eq a, C a) => Eq (T a) Source # 
Instance details

Defined in MathObj.Polynomial

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

(Eq a, C a) => Eq (T a) Source # 
Instance details

Defined in Number.Root

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Ix i => Eq (T i) Source #

These instances may need more work They involve converting a permutation to a table.

Instance details

Defined in MathObj.Permutation.CycleList.Check

Methods

(==) :: T i -> T i -> Bool #

(/=) :: T i -> T i -> Bool #

Eq i => Eq (Cycle i) Source # 
Instance details

Defined in MathObj.Permutation.CycleList.Check

Methods

(==) :: Cycle i -> Cycle i -> Bool #

(/=) :: Cycle i -> Cycle i -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in MathObj.PartialFraction

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in MathObj.Matrix

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in Number.Complex

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in Number.Quaternion

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

(Eq a, C a) => Eq (T a) Source # 
Instance details

Defined in MathObj.LaurentPolynomial

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

Eq a => Eq (T a) Source # 
Instance details

Defined in MathObj.Wrapper.NumericPrelude

Methods

(==) :: T a -> T a -> Bool #

(/=) :: T a -> T a -> Bool #

(Eq a, Eq b) => Eq (Either a b)

Since: base-2.1

Instance details

Defined in Data.Either

Methods

(==) :: Either a b -> Either a b -> Bool #

(/=) :: Either a b -> Either a b -> Bool #

Eq (V1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: V1 p -> V1 p -> Bool #

(/=) :: V1 p -> V1 p -> Bool #

Eq (U1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: U1 p -> U1 p -> Bool #

(/=) :: U1 p -> U1 p -> Bool #

Eq (TypeRep a)

Since: base-2.1

Instance details

Defined in Data.Typeable.Internal

Methods

(==) :: TypeRep a -> TypeRep a -> Bool #

(/=) :: TypeRep a -> TypeRep a -> Bool #

(Eq a, Eq b) => Eq (a, b) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b) -> (a, b) -> Bool #

(/=) :: (a, b) -> (a, b) -> Bool #

(Ix i, Eq e) => Eq (Array i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: Array i e -> Array i e -> Bool #

(/=) :: Array i e -> Array i e -> Bool #

Eq (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

(==) :: Fixed a -> Fixed a -> Bool #

(/=) :: Fixed a -> Fixed a -> Bool #

Eq a => Eq (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool #

(/=) :: Arg a b -> Arg a b -> Bool #

Eq (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

(==) :: Proxy s -> Proxy s -> Bool #

(/=) :: Proxy s -> Proxy s -> Bool #

Eq (STRef s a)

Pointer equality.

Since: base-2.1

Instance details

Defined in GHC.STRef

Methods

(==) :: STRef s a -> STRef s a -> Bool #

(/=) :: STRef s a -> STRef s a -> Bool #

(Eq k, Eq a) => Eq (Map k a) 
Instance details

Defined in Data.Map.Internal

Methods

(==) :: Map k a -> Map k a -> Bool #

(/=) :: Map k a -> Map k a -> Bool #

(Eq a, Eq b) => Eq (T a b) Source # 
Instance details

Defined in MathObj.Algebra

Methods

(==) :: T a b -> T a b -> Bool #

(/=) :: T a b -> T a b -> Bool #

Eq v => Eq (T a v) Source # 
Instance details

Defined in Number.OccasionallyScalarExpression

Methods

(==) :: T a v -> T a v -> Bool #

(/=) :: T a v -> T a v -> Bool #

Eq a => Eq (T u a) Source # 
Instance details

Defined in Number.DimensionTerm

Methods

(==) :: T u a -> T u a -> Bool #

(/=) :: T u a -> T u a -> Bool #

(Eq i, Eq a) => Eq (T i a) Source # 
Instance details

Defined in Number.Physical

Methods

(==) :: T i a -> T i a -> Bool #

(/=) :: T i a -> T i a -> Bool #

Eq v => Eq (T a v) Source # 
Instance details

Defined in Number.SI

Methods

(==) :: T a v -> T a v -> Bool #

(/=) :: T a v -> T a v -> Bool #

Eq (f p) => Eq (Rec1 f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: Rec1 f p -> Rec1 f p -> Bool #

(/=) :: Rec1 f p -> Rec1 f p -> Bool #

Eq (URec (Ptr ()) p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

Eq (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Char p -> URec Char p -> Bool #

(/=) :: URec Char p -> URec Char p -> Bool #

Eq (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool #

(/=) :: URec Double p -> URec Double p -> Bool #

Eq (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

(==) :: URec Float p -> URec Float p -> Bool #

(/=) :: URec Float p -> URec Float p -> Bool #

Eq (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Int p -> URec Int p -> Bool #

(/=) :: URec Int p -> URec Int p -> Bool #

Eq (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Word p -> URec Word p -> Bool #

(/=) :: URec Word p -> URec Word p -> Bool #

(Eq a, Eq b, Eq c) => Eq (a, b, c) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c) -> (a, b, c) -> Bool #

(/=) :: (a, b, c) -> (a, b, c) -> Bool #

Eq (STArray s i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: STArray s i e -> STArray s i e -> Bool #

(/=) :: STArray s i e -> STArray s i e -> Bool #

Eq a => Eq (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(==) :: Const a b -> Const a b -> Bool #

(/=) :: Const a b -> Const a b -> Bool #

Eq (f a) => Eq (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(==) :: Ap f a -> Ap f a -> Bool #

(/=) :: Ap f a -> Ap f a -> Bool #

Eq (f a) => Eq (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Alt f a -> Alt f a -> Bool #

(/=) :: Alt f a -> Alt f a -> Bool #

Eq (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

(==) :: (a :~: b) -> (a :~: b) -> Bool #

(/=) :: (a :~: b) -> (a :~: b) -> Bool #

(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

(==) :: ErrorT e m a -> ErrorT e m a -> Bool #

(/=) :: ErrorT e m a -> ErrorT e m a -> Bool #

Eq a => Eq (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Methods

(==) :: Constant a b -> Constant a b -> Bool #

(/=) :: Constant a b -> Constant a b -> Bool #

Eq c => Eq (K1 i c p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: K1 i c p -> K1 i c p -> Bool #

(/=) :: K1 i c p -> K1 i c p -> Bool #

(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: (f :+: g) p -> (f :+: g) p -> Bool #

(/=) :: (f :+: g) p -> (f :+: g) p -> Bool #

(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: (f :*: g) p -> (f :*: g) p -> Bool #

(/=) :: (f :*: g) p -> (f :*: g) p -> Bool #

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

(==) :: Product f g a -> Product f g a -> Bool #

(/=) :: Product f g a -> Product f g a -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

(==) :: Sum f g a -> Sum f g a -> Bool #

(/=) :: Sum f g a -> Sum f g a -> Bool #

Eq (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

(==) :: (a :~~: b) -> (a :~~: b) -> Bool #

(/=) :: (a :~~: b) -> (a :~~: b) -> Bool #

Eq (f p) => Eq (M1 i c f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: M1 i c f p -> M1 i c f p -> Bool #

(/=) :: M1 i c f p -> M1 i c f p -> Bool #

Eq (f (g p)) => Eq ((f :.: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: (f :.: g) p -> (f :.: g) p -> Bool #

(/=) :: (f :.: g) p -> (f :.: g) p -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(==) :: Compose f g a -> Compose f g a -> Bool #

(/=) :: Compose f g a -> Compose f g a -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (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 #

(/=) :: (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 #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (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 #

(/=) :: (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 #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (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 #

(/=) :: (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 #

(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) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (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 #

(/=) :: (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 #

class Applicative m => Monad (m :: Type -> Type) where #

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
return a >>= 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 lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

'as >>= bs' can be understood as the do expression

do a <- as
   bs a

(>>) :: m a -> m b -> m b infixl 1 #

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

'as >> bs' can be understood as the do expression

do as
   bs

return :: a -> m a #

Inject a value into the monadic type.

Instances

Instances details
Monad []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: [a] -> (a -> [b]) -> [b] #

(>>) :: [a] -> [b] -> [b] #

return :: a -> [a] #

Monad Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b #

(>>) :: Maybe a -> Maybe b -> Maybe b #

return :: a -> Maybe a #

Monad IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b #

(>>) :: IO a -> IO b -> IO b #

return :: a -> IO a #

Monad Par1

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b #

(>>) :: Par1 a -> Par1 b -> Par1 b #

return :: a -> Par1 a #

Monad Q 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

(>>=) :: Q a -> (a -> Q b) -> Q b #

(>>) :: Q a -> Q b -> Q b #

return :: a -> Q a #

Monad Rose 
Instance details

Defined in Test.QuickCheck.Property

Methods

(>>=) :: Rose a -> (a -> Rose b) -> Rose b #

(>>) :: Rose a -> Rose b -> Rose b #

return :: a -> Rose a #

Monad Gen 
Instance details

Defined in Test.QuickCheck.Gen

Methods

(>>=) :: Gen a -> (a -> Gen b) -> Gen b #

(>>) :: Gen a -> Gen b -> Gen b #

return :: a -> Gen a #

Monad Complex

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b #

(>>) :: Complex a -> Complex b -> Complex b #

return :: a -> Complex a #

Monad Min

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b #

(>>) :: Min a -> Min b -> Min b #

return :: a -> Min a #

Monad Max

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b #

(>>) :: Max a -> Max b -> Max b #

return :: a -> Max a #

Monad First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: First a -> (a -> First b) -> First b #

(>>) :: First a -> First b -> First b #

return :: a -> First a #

Monad Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b #

(>>) :: Last a -> Last b -> Last b #

return :: a -> Last a #

Monad Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Option a -> (a -> Option b) -> Option b #

(>>) :: Option a -> Option b -> Option b #

return :: a -> Option a #

Monad Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b #

(>>) :: Identity a -> Identity b -> Identity b #

return :: a -> Identity a #

Monad STM

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

(>>=) :: STM a -> (a -> STM b) -> STM b #

(>>) :: STM a -> STM b -> STM b #

return :: a -> STM a #

Monad First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

(>>=) :: First a -> (a -> First b) -> First b #

(>>) :: First a -> First b -> First b #

return :: a -> First a #

Monad Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b #

(>>) :: Last a -> Last b -> Last b #

return :: a -> Last a #

Monad Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b #

(>>) :: Dual a -> Dual b -> Dual b #

return :: a -> Dual a #

Monad Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b #

(>>) :: Sum a -> Sum b -> Sum b #

return :: a -> Sum a #

Monad Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b #

(>>) :: Product a -> Product b -> Product b #

return :: a -> Product a #

Monad Down

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

(>>=) :: Down a -> (a -> Down b) -> Down b #

(>>) :: Down a -> Down b -> Down b #

return :: a -> Down a #

Monad ReadPrec

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

(>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b #

(>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b #

return :: a -> ReadPrec a #

Monad ReadP

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b #

(>>) :: ReadP a -> ReadP b -> ReadP b #

return :: a -> ReadP a #

Monad NonEmpty

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b #

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b #

return :: a -> NonEmpty a #

Monad Tree 
Instance details

Defined in Data.Tree

Methods

(>>=) :: Tree a -> (a -> Tree b) -> Tree b #

(>>) :: Tree a -> Tree b -> Tree b #

return :: a -> Tree a #

Monad Seq 
Instance details

Defined in Data.Sequence.Internal

Methods

(>>=) :: Seq a -> (a -> Seq b) -> Seq b #

(>>) :: Seq a -> Seq b -> Seq b #

return :: a -> Seq a #

Monad P

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

(>>=) :: P a -> (a -> P b) -> P b #

(>>) :: P a -> P b -> P b #

return :: a -> P a #

Monad (Either e)

Since: base-4.4.0.0

Instance details

Defined in Data.Either

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b #

(>>) :: Either e a -> Either e b -> Either e b #

return :: a -> Either e a #

Monad (U1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(>>=) :: U1 a -> (a -> U1 b) -> U1 b #

(>>) :: U1 a -> U1 b -> U1 b #

return :: a -> U1 a #

Monoid a => Monad ((,) a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) #

(>>) :: (a, a0) -> (a, b) -> (a, b) #

return :: a0 -> (a, a0) #

Monad m => Monad (WrappedMonad m)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b #

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b #

return :: a -> WrappedMonad m a #

ArrowApply a => Monad (ArrowMonad a)

Since: base-2.1

Instance details

Defined in Control.Arrow

Methods

(>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b #

(>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b #

return :: a0 -> ArrowMonad a a0 #

Monad (Proxy :: Type -> Type)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b #

(>>) :: Proxy a -> Proxy b -> Proxy b #

return :: a -> Proxy a #

Monad (T a) Source # 
Instance details

Defined in Number.ResidueClass.Reader

Methods

(>>=) :: T a a0 -> (a0 -> T a b) -> T a b #

(>>) :: T a a0 -> T a b -> T a b #

return :: a0 -> T a a0 #

Monad (T i) Source # 
Instance details

Defined in Number.Physical

Methods

(>>=) :: T i a -> (a -> T i b) -> T i b #

(>>) :: T i a -> T i b -> T i b #

return :: a -> T i a #

Monad f => Monad (Rec1 f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b #

(>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b #

return :: a -> Rec1 f a #

(Monoid a, Monoid b) => Monad ((,,) a b)

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

(>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) #

(>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) #

return :: a0 -> (a, b, a0) #

Monad m => Monad (Kleisli m a)

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Methods

(>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b #

(>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b #

return :: a0 -> Kleisli m a a0 #

Monad f => Monad (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b #

(>>) :: Ap f a -> Ap f b -> Ap f b #

return :: a -> Ap f a #

Monad f => Monad (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b #

(>>) :: Alt f a -> Alt f b -> Alt f b #

return :: a -> Alt f a #

(Applicative f, Monad f) => Monad (WhenMissing f x)

Equivalent to ReaderT k (ReaderT x (MaybeT f)).

Since: containers-0.5.9

Instance details

Defined in Data.IntMap.Internal

Methods

(>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b #

(>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b #

return :: a -> WhenMissing f x a #

(Monad m, Error e) => Monad (ErrorT e m) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

(>>=) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b #

(>>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b #

return :: a -> ErrorT e m a #

Monad ((->) r :: Type -> Type)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b #

(>>) :: (r -> a) -> (r -> b) -> r -> b #

return :: a -> r -> a #

(Monad f, Monad g) => Monad (f :*: g)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b #

(>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b #

return :: a -> (f :*: g) a #

(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c)

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

(>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) #

(>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) #

return :: a0 -> (a, b, c, a0) #

(Monad f, Monad g) => Monad (Product f g)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

(>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b #

(>>) :: Product f g a -> Product f g b -> Product f g b #

return :: a -> Product f g a #

(Monad f, Applicative f) => Monad (WhenMatched f x y)

Equivalent to ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))

Since: containers-0.5.9

Instance details

Defined in Data.IntMap.Internal

Methods

(>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b #

(>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b #

return :: a -> WhenMatched f x y a #

(Applicative f, Monad f) => Monad (WhenMissing f k x)

Equivalent to ReaderT k (ReaderT x (MaybeT f)) .

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

(>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b #

(>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b #

return :: a -> WhenMissing f k x a #

Monad (ParsecT s u m) 
Instance details

Defined in Text.Parsec.Prim

Methods

(>>=) :: ParsecT s u m a -> (a -> ParsecT s u m b) -> ParsecT s u m b #

(>>) :: ParsecT s u m a -> ParsecT s u m b -> ParsecT s u m b #

return :: a -> ParsecT s u m a #

Monad f => Monad (M1 i c f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b #

(>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b #

return :: a -> M1 i c f a #

(Monad f, Applicative f) => Monad (WhenMatched f k x y)

Equivalent to ReaderT k (ReaderT x (ReaderT y (MaybeT f)))

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

(>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b #

(>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b #

return :: a -> WhenMatched f k x y a #

class Functor (f :: Type -> Type) where #

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:

Identity
fmap id == id
Composition
fmap (f . g) == fmap f . fmap g

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.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b #

Using ApplicativeDo: 'fmap f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint.

(<$) :: a -> f b -> f a infixl 4 #

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Using ApplicativeDo: 'a <$ bs' can be understood as the do expression

do bs
   pure a

with an inferred Functor constraint.

Instances

Instances details
Functor []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> [a] -> [b] #

(<$) :: a -> [b] -> [a] #

Functor Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b #

(<$) :: a -> Maybe b -> Maybe a #

Functor IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> IO a -> IO b #

(<$) :: a -> IO b -> IO a #

Functor Par1

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b #

(<$) :: a -> Par1 b -> Par1 a #

Functor Q 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

fmap :: (a -> b) -> Q a -> Q b #

(<$) :: a -> Q b -> Q a #

Functor Rose 
Instance details

Defined in Test.QuickCheck.Property

Methods

fmap :: (a -> b) -> Rose a -> Rose b #

(<$) :: a -> Rose b -> Rose a #

Functor Gen 
Instance details

Defined in Test.QuickCheck.Gen

Methods

fmap :: (a -> b) -> Gen a -> Gen b #

(<$) :: a -> Gen b -> Gen a #

Functor Complex

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b #

(<$) :: a -> Complex b -> Complex a #

Functor Min

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Min a -> Min b #

(<$) :: a -> Min b -> Min a #

Functor Max

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Max a -> Max b #

(<$) :: a -> Max b -> Max a #

Functor First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

Functor Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

Functor Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Option a -> Option b #

(<$) :: a -> Option b -> Option a #

Functor ZipList

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b #

(<$) :: a -> ZipList b -> ZipList a #

Functor Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b #

(<$) :: a -> Identity b -> Identity a #

Functor Handler

Since: base-4.6.0.0

Instance details

Defined in Control.Exception

Methods

fmap :: (a -> b) -> Handler a -> Handler b #

(<$) :: a -> Handler b -> Handler a #

Functor STM

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

fmap :: (a -> b) -> STM a -> STM b #

(<$) :: a -> STM b -> STM a #

Functor First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

Functor Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

Functor Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Dual a -> Dual b #

(<$) :: a -> Dual b -> Dual a #

Functor Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b #

(<$) :: a -> Sum b -> Sum a #

Functor Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b #

(<$) :: a -> Product b -> Product a #

Functor Down

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

fmap :: (a -> b) -> Down a -> Down b #

(<$) :: a -> Down b -> Down a #

Functor ReadPrec

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b #

(<$) :: a -> ReadPrec b -> ReadPrec a #

Functor ReadP

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b #

(<$) :: a -> ReadP b -> ReadP a #

Functor NonEmpty

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b #

(<$) :: a -> NonEmpty b -> NonEmpty a #

Functor IntMap 
Instance details

Defined in Data.IntMap.Internal

Methods

fmap :: (a -> b) -> IntMap a -> IntMap b #

(<$) :: a -> IntMap b -> IntMap a #

Functor Tree 
Instance details

Defined in Data.Tree

Methods

fmap :: (a -> b) -> Tree a -> Tree b #

(<$) :: a -> Tree b -> Tree a #

Functor Seq 
Instance details

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Seq a -> Seq b #

(<$) :: a -> Seq b -> Seq a #

Functor FingerTree 
Instance details

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> FingerTree a -> FingerTree b #

(<$) :: a -> FingerTree b -> FingerTree a #

Functor Digit 
Instance details

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Digit a -> Digit b #

(<$) :: a -> Digit b -> Digit a #

Functor Node 
Instance details

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Node a -> Node b #

(<$) :: a -> Node b -> Node a #

Functor Elem 
Instance details

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Elem a -> Elem b #

(<$) :: a -> Elem b -> Elem a #

Functor ViewL 
Instance details

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> ViewL a -> ViewL b #

(<$) :: a -> ViewL b -> ViewL a #

Functor ViewR 
Instance details

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> ViewR a -> ViewR b #

(<$) :: a -> ViewR b -> ViewR a #

Functor Consumed 
Instance details

Defined in Text.Parsec.Prim

Methods

fmap :: (a -> b) -> Consumed a -> Consumed b #

(<$) :: a -> Consumed b -> Consumed a #

Functor Doc 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

fmap :: (a -> b) -> Doc a -> Doc b #

(<$) :: a -> Doc b -> Doc a #

Functor AnnotDetails 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

fmap :: (a -> b) -> AnnotDetails a -> AnnotDetails b #

(<$) :: a -> AnnotDetails b -> AnnotDetails a #

Functor Span 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

fmap :: (a -> b) -> Span a -> Span b #

(<$) :: a -> Span b -> Span a #

Functor P

Since: base-4.8.0.0

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> P a -> P b #

(<$) :: a -> P b -> P a #

Functor T Source # 
Instance details

Defined in MathObj.Wrapper.Haskell98

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in MathObj.PowerSeries

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in MathObj.PowerSeries2

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in MathObj.Polynomial

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in MathObj.RefinementMask2

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source #

When you use fmap you must assert that forall n. fmap f (Cons d x) == fmap f (Cons (n*d) (x^n))

Instance details

Defined in Number.Root

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in MathObj.Matrix

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in Number.Complex

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in MathObj.LaurentPolynomial

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor T Source # 
Instance details

Defined in MathObj.Wrapper.NumericPrelude

Methods

fmap :: (a -> b) -> T a -> T b #

(<$) :: a -> T b -> T a #

Functor (Either a)

Since: base-3.0

Instance details

Defined in Data.Either

Methods

fmap :: (a0 -> b) -> Either a a0 -> Either a b #

(<$) :: a0 -> Either a b -> Either a a0 #

Functor (V1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> V1 a -> V1 b #

(<$) :: a -> V1 b -> V1 a #

Functor (U1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> U1 a -> U1 b #

(<$) :: a -> U1 b -> U1 a #

Functor ((,) a)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a0 -> b) -> (a, a0) -> (a, b) #

(<$) :: a0 -> (a, b) -> (a, a0) #

Functor (Array i)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b #

(<$) :: a -> Array i b -> Array i a #

Functor (Arg a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b #

(<$) :: a0 -> Arg a b -> Arg a a0 #

Monad m => Functor (WrappedMonad m)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b #

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a #

Arrow a => Functor (ArrowMonad a)

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b #

(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 #

Functor (Proxy :: Type -> Type)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

fmap :: (a -> b) -> Proxy a -> Proxy b #

(<$) :: a -> Proxy b -> Proxy a #

Functor (Map k) 
Instance details

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> Map k a -> Map k b #

(<$) :: a -> Map k b -> Map k a #

Functor (Access r) 
Instance details

Defined in Foreign.Storable.Record

Methods

fmap :: (a -> b) -> Access r a -> Access r b #

(<$) :: a -> Access r b -> Access r a #

Functor (T v) Source # 
Instance details

Defined in NumericPrelude.Elementwise

Methods

fmap :: (a -> b) -> T v a -> T v b #

(<$) :: a -> T v b -> T v a #

Functor (T a) Source # 
Instance details

Defined in MathObj.Algebra

Methods

fmap :: (a0 -> b) -> T a a0 -> T a b #

(<$) :: a0 -> T a b -> T a a0 #

Functor (Box r) 
Instance details

Defined in Foreign.Storable.Record

Methods

fmap :: (a -> b) -> Box r a -> Box r b #

(<$) :: a -> Box r b -> Box r a #

Functor (T a) Source # 
Instance details

Defined in Number.ResidueClass.Reader

Methods

fmap :: (a0 -> b) -> T a a0 -> T a b #

(<$) :: a0 -> T a b -> T a a0 #

Functor (T i) Source # 
Instance details

Defined in Number.Physical

Methods

fmap :: (a -> b) -> T i a -> T i b #

(<$) :: a -> T i b -> T i a #

Functor (T a) Source # 
Instance details

Defined in Number.SI

Methods

fmap :: (a0 -> b) -> T a a0 -> T a b #

(<$) :: a0 -> T a b -> T a a0 #

Functor f => Functor (Rec1 f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b #

(<$) :: a -> Rec1 f b -> Rec1 f a #

Functor (URec Char :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b #

(<$) :: a -> URec Char b -> URec Char a #

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b #

(<$) :: a -> URec Double b -> URec Double a #

Functor (URec Float :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b #

(<$) :: a -> URec Float b -> URec Float a #

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b #

(<$) :: a -> URec Int b -> URec Int a #

Functor (URec Word :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b #

(<$) :: a -> URec Word b -> URec Word a #

Functor (URec (Ptr ()) :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b #

(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a #

Functor ((,,) a b)

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) #

(<$) :: a0 -> (a, b, b0) -> (a, b, a0) #

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 #

(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #

Functor m => Functor (Kleisli m a)

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Methods

fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b #

(<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 #

Functor (Const m :: Type -> Type)

Since: base-2.1

Instance details

Defined in Data.Functor.Const

Methods

fmap :: (a -> b) -> Const m a -> Const m b #

(<$) :: a -> Const m b -> Const m a #

Functor f => Functor (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> Ap f a -> Ap f b #

(<$) :: a -> Ap f b -> Ap f a #

Functor f => Functor (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Alt f a -> Alt f b #

(<$) :: a -> Alt f b -> Alt f a #

(Applicative f, Monad f) => Functor (WhenMissing f x)

Since: containers-0.5.9

Instance details

Defined in Data.IntMap.Internal

Methods

fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b #

(<$) :: a -> WhenMissing f x b -> WhenMissing f x a #

Functor m => Functor (ErrorT e m) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b #

(<$) :: a -> ErrorT e m b -> ErrorT e m a #

Functor (Reply s u) 
Instance details

Defined in Text.Parsec.Prim

Methods

fmap :: (a -> b) -> Reply s u a -> Reply s u b #

(<$) :: a -> Reply s u b -> Reply s u a #

Functor (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

fmap :: (a0 -> b) -> Constant a a0 -> Constant a b #

(<$) :: a0 -> Constant a b -> Constant a a0 #

Functor ((->) r :: Type -> Type)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b #

(<$) :: a -> (r -> b) -> r -> a #

Functor (K1 i c :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> K1 i c a -> K1 i c b #

(<$) :: a -> K1 i c b -> K1 i c a #

(Functor f, Functor g) => Functor (f :+: g)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b #

(<$) :: a -> (f :+: g) b -> (f :+: g) a #

(Functor f, Functor g) => Functor (f :*: g)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b #

(<$) :: a -> (f :*: g) b -> (f :*: g) a #

Functor ((,,,) a b c)

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) #

(<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) #

(Functor f, Functor g) => Functor (Product f g)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

fmap :: (a -> b) -> Product f g a -> Product f g b #

(<$) :: a -> Product f g b -> Product f g a #

(Functor f, Functor g) => Functor (Sum f g)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

fmap :: (a -> b) -> Sum f g a -> Sum f g b #

(<$) :: a -> Sum f g b -> Sum f g a #

Functor f => Functor (WhenMatched f x y)

Since: containers-0.5.9

Instance details

Defined in Data.IntMap.Internal

Methods

fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b #

(<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a #

(Applicative f, Monad f) => Functor (WhenMissing f k x)

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b #

(<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a #

Functor (ParsecT s u m) 
Instance details

Defined in Text.Parsec.Prim

Methods

fmap :: (a -> b) -> ParsecT s u m a -> ParsecT s u m b #

(<$) :: a -> ParsecT s u m b -> ParsecT s u m a #

Functor f => Functor (M1 i c f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> M1 i c f a -> M1 i c f b #

(<$) :: a -> M1 i c f b -> M1 i c f a #

(Functor f, Functor g) => Functor (f :.: g)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b #

(<$) :: a -> (f :.: g) b -> (f :.: g) a #

(Functor f, Functor g) => Functor (Compose f g)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

fmap :: (a -> b) -> Compose f g a -> Compose f g b #

(<$) :: a -> Compose f g b -> Compose f g a #

Functor f => Functor (WhenMatched f k x y)

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b #

(<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a #

class Eq a => Ord a where #

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.

The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:

Transitivity
if x <= y && y <= z = True, then x <= z = True
Reflexivity
x <= x = True
Antisymmetry
if x <= y && y <= x = True, then x == y = True

Note that the following operator interactions are expected to hold:

  1. x >= y = y <= x
  2. x < y = x <= y && x /= y
  3. x > y = y < x
  4. x < y = compare x y == LT
  5. x > y = compare x y == GT
  6. x == y = compare x y == EQ
  7. min x y == if x <= y then x else y = True
  8. max 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.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering #

(<) :: a -> a -> Bool infix 4 #

(<=) :: a -> a -> Bool infix 4 #

(>) :: a -> a -> Bool infix 4 #

(>=) :: a -> a -> Bool infix 4 #

Instances

Instances details
Ord Bool 
Instance details

Defined in GHC.Classes

Methods

compare :: Bool -> Bool -> Ordering #

(<) :: Bool -> Bool -> Bool #

(<=) :: Bool -> Bool -> Bool #

(>) :: Bool -> Bool -> Bool #

(>=) :: Bool -> Bool -> Bool #

max :: Bool -> Bool -> Bool #

min :: Bool -> Bool -> Bool #

Ord Char 
Instance details

Defined in GHC.Classes

Methods

compare :: Char -> Char -> Ordering #

(<) :: Char -> Char -> Bool #

(<=) :: Char -> Char -> Bool #

(>) :: Char -> Char -> Bool #

(>=) :: Char -> Char -> Bool #

max :: Char -> Char -> Char #

min :: Char -> Char -> Char #

Ord Double

Note that due to the presence of NaN, Double's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Double)
False

Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:

>>> (0/0 :: Double) > 1
False
>>> compare (0/0 :: Double) 1
GT
Instance details

Defined in GHC.Classes

Ord Float

Note that due to the presence of NaN, Float's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Float)
False

Also note that, due to the same, Ord's operator interactions are not respected by Float's instance:

>>> (0/0 :: Float) > 1
False
>>> compare (0/0 :: Float) 1
GT
Instance details

Defined in GHC.Classes

Methods

compare :: Float -> Float -> Ordering #

(<) :: Float -> Float -> Bool #

(<=) :: Float -> Float -> Bool #

(>) :: Float -> Float -> Bool #

(>=) :: Float -> Float -> Bool #

max :: Float -> Float -> Float #

min :: Float -> Float -> Float #

Ord Int 
Instance details

Defined in GHC.Classes

Methods

compare :: Int -> Int -> Ordering #

(<) :: Int -> Int -> Bool #

(<=) :: Int -> Int -> Bool #

(>) :: Int -> Int -> Bool #

(>=) :: Int -> Int -> Bool #

max :: Int -> Int -> Int #

min :: Int -> Int -> Int #

Ord Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int8 -> Int8 -> Ordering #

(<) :: Int8 -> Int8 -> Bool #

(<=) :: Int8 -> Int8 -> Bool #

(>) :: Int8 -> Int8 -> Bool #

(>=) :: Int8 -> Int8 -> Bool #

max :: Int8 -> Int8 -> Int8 #

min :: Int8 -> Int8 -> Int8 #

Ord Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int16 -> Int16 -> Ordering #

(<) :: Int16 -> Int16 -> Bool #

(<=) :: Int16 -> Int16 -> Bool #

(>) :: Int16 -> Int16 -> Bool #

(>=) :: Int16 -> Int16 -> Bool #

max :: Int16 -> Int16 -> Int16 #

min :: Int16 -> Int16 -> Int16 #

Ord Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int32 -> Int32 -> Ordering #

(<) :: Int32 -> Int32 -> Bool #

(<=) :: Int32 -> Int32 -> Bool #

(>) :: Int32 -> Int32 -> Bool #

(>=) :: Int32 -> Int32 -> Bool #

max :: Int32 -> Int32 -> Int32 #

min :: Int32 -> Int32 -> Int32 #

Ord Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int64 -> Int64 -> Ordering #

(<) :: Int64 -> Int64 -> Bool #

(<=) :: Int64 -> Int64 -> Bool #

(>) :: Int64 -> Int64 -> Bool #

(>=) :: Int64 -> Int64 -> Bool #

max :: Int64 -> Int64 -> Int64 #

min :: Int64 -> Int64 -> Int64 #

Ord Integer 
Instance details

Defined in GHC.Integer.Type

Ord Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Ord Ordering 
Instance details

Defined in GHC.Classes

Ord Word 
Instance details

Defined in GHC.Classes

Methods

compare :: Word -> Word -> Ordering #

(<) :: Word -> Word -> Bool #

(<=) :: Word -> Word -> Bool #

(>) :: Word -> Word -> Bool #

(>=) :: Word -> Word -> Bool #

max :: Word -> Word -> Word #

min :: Word -> Word -> Word #

Ord Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

compare :: Word8 -> Word8 -> Ordering #

(<) :: Word8 -> Word8 -> Bool #

(<=) :: Word8 -> Word8 -> Bool #

(>) :: Word8 -> Word8 -> Bool #

(>=) :: Word8 -> Word8 -> Bool #

max :: Word8 -> Word8 -> Word8 #

min :: Word8 -> Word8 -> Word8 #

Ord Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Ord SomeTypeRep 
Instance details

Defined in Data.Typeable.Internal

Ord Exp 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Exp -> Exp -> Ordering #

(<) :: Exp -> Exp -> Bool #

(<=) :: Exp -> Exp -> Bool #

(>) :: Exp -> Exp -> Bool #

(>=) :: Exp -> Exp -> Bool #

max :: Exp -> Exp -> Exp #

min :: Exp -> Exp -> Exp #

Ord Match 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Match -> Match -> Ordering #

(<) :: Match -> Match -> Bool #

(<=) :: Match -> Match -> Bool #

(>) :: Match -> Match -> Bool #

(>=) :: Match -> Match -> Bool #

max :: Match -> Match -> Match #

min :: Match -> Match -> Match #

Ord Clause 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Pat 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Pat -> Pat -> Ordering #

(<) :: Pat -> Pat -> Bool #

(<=) :: Pat -> Pat -> Bool #

(>) :: Pat -> Pat -> Bool #

(>=) :: Pat -> Pat -> Bool #

max :: Pat -> Pat -> Pat #

min :: Pat -> Pat -> Pat #

Ord Type 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Type -> Type -> Ordering #

(<) :: Type -> Type -> Bool #

(<=) :: Type -> Type -> Bool #

(>) :: Type -> Type -> Bool #

(>=) :: Type -> Type -> Bool #

max :: Type -> Type -> Type #

min :: Type -> Type -> Type #

Ord Dec 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Dec -> Dec -> Ordering #

(<) :: Dec -> Dec -> Bool #

(<=) :: Dec -> Dec -> Bool #

(>) :: Dec -> Dec -> Bool #

(>=) :: Dec -> Dec -> Bool #

max :: Dec -> Dec -> Dec #

min :: Dec -> Dec -> Dec #

Ord Name 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Name -> Name -> Ordering #

(<) :: Name -> Name -> Bool #

(<=) :: Name -> Name -> Bool #

(>) :: Name -> Name -> Bool #

(>=) :: Name -> Name -> Bool #

max :: Name -> Name -> Name #

min :: Name -> Name -> Name #

Ord FunDep 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord InjectivityAnn 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Overlap 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord () 
Instance details

Defined in GHC.Classes

Methods

compare :: () -> () -> Ordering #

(<) :: () -> () -> Bool #

(<=) :: () -> () -> Bool #

(>) :: () -> () -> Bool #

(>=) :: () -> () -> Bool #

max :: () -> () -> () #

min :: () -> () -> () #

Ord TyCon 
Instance details

Defined in GHC.Classes

Methods

compare :: TyCon -> TyCon -> Ordering #

(<) :: TyCon -> TyCon -> Bool #

(<=) :: TyCon -> TyCon -> Bool #

(>) :: TyCon -> TyCon -> Bool #

(>=) :: TyCon -> TyCon -> Bool #

max :: TyCon -> TyCon -> TyCon #

min :: TyCon -> TyCon -> TyCon #

Ord Version

Since: base-2.1

Instance details

Defined in Data.Version

Ord Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Methods

compare :: Void -> Void -> Ordering #

(<) :: Void -> Void -> Bool #

(<=) :: Void -> Void -> Bool #

(>) :: Void -> Void -> Bool #

(>=) :: Void -> Void -> Bool #

max :: Void -> Void -> Void #

min :: Void -> Void -> Void #

Ord Unique 
Instance details

Defined in Data.Unique

Ord ThreadId

Since: base-4.2.0.0

Instance details

Defined in GHC.Conc.Sync

Ord BlockReason

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Ord ThreadStatus

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Ord AsyncException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Ord ArrayException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Ord ExitCode 
Instance details

Defined in GHC.IO.Exception

Ord All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering #

(<) :: All -> All -> Bool #

(<=) :: All -> All -> Bool #

(>) :: All -> All -> Bool #

(>=) :: All -> All -> Bool #

max :: All -> All -> All #

min :: All -> All -> All #

Ord Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering #

(<) :: Any -> Any -> Bool #

(<=) :: Any -> Any -> Bool #

(>) :: Any -> Any -> Bool #

(>=) :: Any -> Any -> Bool #

max :: Any -> Any -> Any #

min :: Any -> Any -> Any #

Ord Fixity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Ord Associativity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Ord SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Ord SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Ord DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Ord CChar 
Instance details

Defined in Foreign.C.Types

Methods

compare :: CChar -> CChar -> Ordering #

(<) :: CChar -> CChar -> Bool #

(<=) :: CChar -> CChar -> Bool #

(>) :: CChar -> CChar -> Bool #

(>=) :: CChar -> CChar -> Bool #

max :: CChar -> CChar -> CChar #

min :: CChar -> CChar -> CChar #

Ord CSChar 
Instance details

Defined in Foreign.C.Types

Ord CUChar 
Instance details

Defined in Foreign.C.Types

Ord CShort 
Instance details

Defined in Foreign.C.Types

Ord CUShort 
Instance details

Defined in Foreign.C.Types

Ord CInt 
Instance details

Defined in Foreign.C.Types

Methods

compare :: CInt -> CInt -> Ordering #

(<) :: CInt -> CInt -> Bool #

(<=) :: CInt -> CInt -> Bool #

(>) :: CInt -> CInt -> Bool #

(>=) :: CInt -> CInt -> Bool #

max :: CInt -> CInt -> CInt #

min :: CInt -> CInt -> CInt #

Ord CUInt 
Instance details

Defined in Foreign.C.Types

Methods

compare :: CUInt -> CUInt -> Ordering #

(<) :: CUInt -> CUInt -> Bool #

(<=) :: CUInt -> CUInt -> Bool #

(>) :: CUInt -> CUInt -> Bool #

(>=) :: CUInt -> CUInt -> Bool #

max :: CUInt -> CUInt -> CUInt #

min :: CUInt -> CUInt -> CUInt #

Ord CLong 
Instance details

Defined in Foreign.C.Types

Methods

compare :: CLong -> CLong -> Ordering #

(<) :: CLong -> CLong -> Bool #

(<=) :: CLong -> CLong -> Bool #

(>) :: CLong -> CLong -> Bool #

(>=) :: CLong -> CLong -> Bool #

max :: CLong -> CLong -> CLong #

min :: CLong -> CLong -> CLong #

Ord CULong 
Instance details

Defined in Foreign.C.Types

Ord CLLong 
Instance details

Defined in Foreign.C.Types

Ord CULLong 
Instance details

Defined in Foreign.C.Types

Ord CBool 
Instance details

Defined in Foreign.C.Types

Methods

compare :: CBool -> CBool -> Ordering #

(<) :: CBool -> CBool -> Bool #

(<=) :: CBool -> CBool -> Bool #

(>) :: CBool -> CBool -> Bool #

(>=) :: CBool -> CBool -> Bool #

max :: CBool -> CBool -> CBool #

min :: CBool -> CBool -> CBool #

Ord CFloat 
Instance details

Defined in Foreign.C.Types

Ord CDouble 
Instance details

Defined in Foreign.C.Types

Ord CPtrdiff 
Instance details

Defined in Foreign.C.Types

Ord CSize 
Instance details

Defined in Foreign.C.Types

Methods

compare :: CSize -> CSize -> Ordering #

(<) :: CSize -> CSize -> Bool #

(<=) :: CSize -> CSize -> Bool #

(>) :: CSize -> CSize -> Bool #

(>=) :: CSize -> CSize -> Bool #

max :: CSize -> CSize -> CSize #

min :: CSize -> CSize -> CSize #

Ord CWchar 
Instance details

Defined in Foreign.C.Types

Ord CSigAtomic 
Instance details

Defined in Foreign.C.Types

Ord CClock 
Instance details

Defined in Foreign.C.Types

Ord CTime 
Instance details

Defined in Foreign.C.Types

Methods

compare :: CTime -> CTime -> Ordering #

(<) :: CTime -> CTime -> Bool #

(<=) :: CTime -> CTime -> Bool #

(>) :: CTime -> CTime -> Bool #

(>=) :: CTime -> CTime -> Bool #

max :: CTime -> CTime -> CTime #

min :: CTime -> CTime -> CTime #

Ord CUSeconds 
Instance details

Defined in Foreign.C.Types

Ord CSUSeconds 
Instance details

Defined in Foreign.C.Types

Ord CIntPtr 
Instance details

Defined in Foreign.C.Types

Ord CUIntPtr 
Instance details

Defined in Foreign.C.Types

Ord CIntMax 
Instance details

Defined in Foreign.C.Types

Ord CUIntMax 
Instance details

Defined in Foreign.C.Types

Ord Fingerprint

Since: base-4.4.0.0

Instance details

Defined in GHC.Fingerprint.Type

Ord GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Ord IntSet 
Instance details

Defined in Data.IntSet.Internal

Ord BigNat 
Instance details

Defined in GHC.Integer.Type

Ord Message 
Instance details

Defined in Text.Parsec.Error

Ord SourcePos 
Instance details

Defined in Text.Parsec.Pos

Ord ModName 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord PkgName 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Module 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord OccName 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord NameFlavour 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord NameSpace 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Loc 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Loc -> Loc -> Ordering #

(<) :: Loc -> Loc -> Bool #

(<=) :: Loc -> Loc -> Bool #

(>) :: Loc -> Loc -> Bool #

(>=) :: Loc -> Loc -> Bool #

max :: Loc -> Loc -> Loc #

min :: Loc -> Loc -> Loc #

Ord Info 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Info -> Info -> Ordering #

(<) :: Info -> Info -> Bool #

(<=) :: Info -> Info -> Bool #

(>) :: Info -> Info -> Bool #

(>=) :: Info -> Info -> Bool #

max :: Info -> Info -> Info #

min :: Info -> Info -> Info #

Ord ModuleInfo 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Fixity 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord FixityDirection 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Lit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Lit -> Lit -> Ordering #

(<) :: Lit -> Lit -> Bool #

(<=) :: Lit -> Lit -> Bool #

(>) :: Lit -> Lit -> Bool #

(>=) :: Lit -> Lit -> Bool #

max :: Lit -> Lit -> Lit #

min :: Lit -> Lit -> Lit #

Ord Bytes 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Bytes -> Bytes -> Ordering #

(<) :: Bytes -> Bytes -> Bool #

(<=) :: Bytes -> Bytes -> Bool #

(>) :: Bytes -> Bytes -> Bool #

(>=) :: Bytes -> Bytes -> Bool #

max :: Bytes -> Bytes -> Bytes #

min :: Bytes -> Bytes -> Bytes #

Ord Body 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Body -> Body -> Ordering #

(<) :: Body -> Body -> Bool #

(<=) :: Body -> Body -> Bool #

(>) :: Body -> Body -> Bool #

(>=) :: Body -> Body -> Bool #

max :: Body -> Body -> Body #

min :: Body -> Body -> Body #

Ord Guard 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Guard -> Guard -> Ordering #

(<) :: Guard -> Guard -> Bool #

(<=) :: Guard -> Guard -> Bool #

(>) :: Guard -> Guard -> Bool #

(>=) :: Guard -> Guard -> Bool #

max :: Guard -> Guard -> Guard #

min :: Guard -> Guard -> Guard #

Ord Stmt 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Stmt -> Stmt -> Ordering #

(<) :: Stmt -> Stmt -> Bool #

(<=) :: Stmt -> Stmt -> Bool #

(>) :: Stmt -> Stmt -> Bool #

(>=) :: Stmt -> Stmt -> Bool #

max :: Stmt -> Stmt -> Stmt #

min :: Stmt -> Stmt -> Stmt #

Ord Range 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Range -> Range -> Ordering #

(<) :: Range -> Range -> Bool #

(<=) :: Range -> Range -> Bool #

(>) :: Range -> Range -> Bool #

(>=) :: Range -> Range -> Bool #

max :: Range -> Range -> Range #

min :: Range -> Range -> Range #

Ord DerivClause 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord DerivStrategy 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord TypeFamilyHead 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord TySynEqn 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Foreign 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Callconv 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Safety 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Pragma 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Inline 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord RuleMatch 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Phases 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord RuleBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord AnnTarget 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord SourceUnpackedness 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord SourceStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord DecidedStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord Con 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Con -> Con -> Ordering #

(<) :: Con -> Con -> Bool #

(<=) :: Con -> Con -> Bool #

(>) :: Con -> Con -> Bool #

(>=) :: Con -> Con -> Bool #

max :: Con -> Con -> Con #

min :: Con -> Con -> Con #

Ord Bang 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Bang -> Bang -> Ordering #

(<) :: Bang -> Bang -> Bool #

(<=) :: Bang -> Bang -> Bool #

(>) :: Bang -> Bang -> Bool #

(>=) :: Bang -> Bang -> Bool #

max :: Bang -> Bang -> Bang #

min :: Bang -> Bang -> Bang #

Ord PatSynDir 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord PatSynArgs 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord TyVarBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord FamilyResultSig 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord TyLit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: TyLit -> TyLit -> Ordering #

(<) :: TyLit -> TyLit -> Bool #

(<=) :: TyLit -> TyLit -> Bool #

(>) :: TyLit -> TyLit -> Bool #

(>=) :: TyLit -> TyLit -> Bool #

max :: TyLit -> TyLit -> TyLit #

min :: TyLit -> TyLit -> TyLit #

Ord Role 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

compare :: Role -> Role -> Ordering #

(<) :: Role -> Role -> Bool #

(<=) :: Role -> Role -> Bool #

(>) :: Role -> Role -> Bool #

(>=) :: Role -> Role -> Bool #

max :: Role -> Role -> Role #

min :: Role -> Role -> Role #

Ord AnnLookup 
Instance details

Defined in Language.Haskell.TH.Syntax

Ord T Source # 
Instance details

Defined in Number.Peano

Methods

compare :: T -> T -> Ordering #

(<) :: T -> T -> Bool #

(<=) :: T -> T -> Bool #

(>) :: T -> T -> Bool #

(>=) :: T -> T -> Bool #

max :: T -> T -> T #

min :: T -> T -> T #

Ord T Source # 
Instance details

Defined in Number.FixedPoint.Check

Methods

compare :: T -> T -> Ordering #

(<) :: T -> T -> Bool #

(<=) :: T -> T -> Bool #

(>) :: T -> T -> Bool #

(>=) :: T -> T -> Bool #

max :: T -> T -> T #

min :: T -> T -> T #

Ord T Source # 
Instance details

Defined in Number.Positional.Check

Methods

compare :: T -> T -> Ordering #

(<) :: T -> T -> Bool #

(<=) :: T -> T -> Bool #

(>) :: T -> T -> Bool #

(>=) :: T -> T -> Bool #

max :: T -> T -> T #

min :: T -> T -> T #

Ord Dimension Source # 
Instance details

Defined in Number.SI.Unit

Ord a => Ord [a] 
Instance details

Defined in GHC.Classes

Methods

compare :: [a] -> [a] -> Ordering #

(<) :: [a] -> [a] -> Bool #

(<=) :: [a] -> [a] -> Bool #

(>) :: [a] -> [a] -> Bool #

(>=) :: [a] -> [a] -> Bool #

max :: [a] -> [a] -> [a] #

min :: [a] -> [a] -> [a] #

Ord a => Ord (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Maybe

Methods

compare :: Maybe a -> Maybe a -> Ordering #

(<) :: Maybe a -> Maybe a -> Bool #

(<=) :: Maybe a -> Maybe a -> Bool #

(>) :: Maybe a -> Maybe a -> Bool #

(>=) :: Maybe a -> Maybe a -> Bool #

max :: Maybe a -> Maybe a -> Maybe a #

min :: Maybe a -> Maybe a -> Maybe a #

Integral a => Ord (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

compare :: Ratio a -> Ratio a -> Ordering #

(<) :: Ratio a -> Ratio a -> Bool #

(<=) :: Ratio a -> Ratio a -> Bool #

(>) :: Ratio a -> Ratio a -> Bool #

(>=) :: Ratio a -> Ratio a -> Bool #

max :: Ratio a -> Ratio a -> Ratio a #

min :: Ratio a -> Ratio a -> Ratio a #

Ord (Ptr a)

Since: base-2.1

Instance details

Defined in GHC.Ptr

Methods

compare :: Ptr a -> Ptr a -> Ordering #

(<) :: Ptr a -> Ptr a -> Bool #

(<=) :: Ptr a -> Ptr a -> Bool #

(>) :: Ptr a -> Ptr a -> Bool #

(>=) :: Ptr a -> Ptr a -> Bool #

max :: Ptr a -> Ptr a -> Ptr a #

min :: Ptr a -> Ptr a -> Ptr a #

Ord (FunPtr a) 
Instance details

Defined in GHC.Ptr

Methods

compare :: FunPtr a -> FunPtr a -> Ordering #

(<) :: FunPtr a -> FunPtr a -> Bool #

(<=) :: FunPtr a -> FunPtr a -> Bool #

(>) :: FunPtr a -> FunPtr a -> Bool #

(>=) :: FunPtr a -> FunPtr a -> Bool #

max :: FunPtr a -> FunPtr a -> FunPtr a #

min :: FunPtr a -> FunPtr a -> FunPtr a #

Ord p => Ord (Par1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: Par1 p -> Par1 p -> Ordering #

(<) :: Par1 p -> Par1 p -> Bool #

(<=) :: Par1 p -> Par1 p -> Bool #

(>) :: Par1 p -> Par1 p -> Bool #

(>=) :: Par1 p -> Par1 p -> Bool #

max :: Par1 p -> Par1 p -> Par1 p #

min :: Par1 p -> Par1 p -> Par1 p #

Ord a => Ord (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Min a -> Min a -> Ordering #

(<) :: Min a -> Min a -> Bool #

(<=) :: Min a -> Min a -> Bool #

(>) :: Min a -> Min a -> Bool #

(>=) :: Min a -> Min a -> Bool #

max :: Min a -> Min a -> Min a #

min :: Min a -> Min a -> Min a #

Ord a => Ord (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Max a -> Max a -> Ordering #

(<) :: Max a -> Max a -> Bool #

(<=) :: Max a -> Max a -> Bool #

(>) :: Max a -> Max a -> Bool #

(>=) :: Max a -> Max a -> Bool #

max :: Max a -> Max a -> Max a #

min :: Max a -> Max a -> Max a #

Ord a => Ord (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: First a -> First a -> Ordering #

(<) :: First a -> First a -> Bool #

(<=) :: First a -> First a -> Bool #

(>) :: First a -> First a -> Bool #

(>=) :: First a -> First a -> Bool #

max :: First a -> First a -> First a #

min :: First a -> First a -> First a #

Ord a => Ord (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Last a -> Last a -> Ordering #

(<) :: Last a -> Last a -> Bool #

(<=) :: Last a -> Last a -> Bool #

(>) :: Last a -> Last a -> Bool #

(>=) :: Last a -> Last a -> Bool #

max :: Last a -> Last a -> Last a #

min :: Last a -> Last a -> Last a #

Ord m => Ord (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Ord a => Ord (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Option a -> Option a -> Ordering #

(<) :: Option a -> Option a -> Bool #

(<=) :: Option a -> Option a -> Bool #

(>) :: Option a -> Option a -> Bool #

(>=) :: Option a -> Option a -> Bool #

max :: Option a -> Option a -> Option a #

min :: Option a -> Option a -> Option a #

Ord a => Ord (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

compare :: ZipList a -> ZipList a -> Ordering #

(<) :: ZipList a -> ZipList a -> Bool #

(<=) :: ZipList a -> ZipList a -> Bool #

(>) :: ZipList a -> ZipList a -> Bool #

(>=) :: ZipList a -> ZipList a -> Bool #

max :: ZipList a -> ZipList a -> ZipList a #

min :: ZipList a -> ZipList a -> ZipList a #

Ord a => Ord (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

compare :: Identity a -> Identity a -> Ordering #

(<) :: Identity a -> Identity a -> Bool #

(<=) :: Identity a -> Identity a -> Bool #

(>) :: Identity a -> Identity a -> Bool #

(>=) :: Identity a -> Identity a -> Bool #

max :: Identity a -> Identity a -> Identity a #

min :: Identity a -> Identity a -> Identity a #

Ord a => Ord (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

compare :: First a -> First a -> Ordering #

(<) :: First a -> First a -> Bool #

(<=) :: First a -> First a -> Bool #

(>) :: First a -> First a -> Bool #

(>=) :: First a -> First a -> Bool #

max :: First a -> First a -> First a #

min :: First a -> First a -> First a #

Ord a => Ord (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

compare :: Last a -> Last a -> Ordering #

(<) :: Last a -> Last a -> Bool #

(<=) :: Last a -> Last a -> Bool #

(>) :: Last a -> Last a -> Bool #

(>=) :: Last a -> Last a -> Bool #

max :: Last a -> Last a -> Last a #

min :: Last a -> Last a -> Last a #

Ord a => Ord (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering #

(<) :: Dual a -> Dual a -> Bool #

(<=) :: Dual a -> Dual a -> Bool #

(>) :: Dual a -> Dual a -> Bool #

(>=) :: Dual a -> Dual a -> Bool #

max :: Dual a -> Dual a -> Dual a #

min :: Dual a -> Dual a -> Dual a #

Ord a => Ord (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering #

(<) :: Sum a -> Sum a -> Bool #

(<=) :: Sum a -> Sum a -> Bool #

(>) :: Sum a -> Sum a -> Bool #

(>=) :: Sum a -> Sum a -> Bool #

max :: Sum a -> Sum a -> Sum a #

min :: Sum a -> Sum a -> Sum a #

Ord a => Ord (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering #

(<) :: Product a -> Product a -> Bool #

(<=) :: Product a -> Product a -> Bool #

(>) :: Product a -> Product a -> Bool #

(>=) :: Product a -> Product a -> Bool #

max :: Product a -> Product a -> Product a #

min :: Product a -> Product a -> Product a #

Ord a => Ord (Down a)

Since: base-4.6.0.0

Instance details

Defined in Data.Ord

Methods

compare :: Down a -> Down a -> Ordering #

(<) :: Down a -> Down a -> Bool #

(<=) :: Down a -> Down a -> Bool #

(>) :: Down a -> Down a -> Bool #

(>=) :: Down a -> Down a -> Bool #

max :: Down a -> Down a -> Down a #

min :: Down a -> Down a -> Down a #

Ord a => Ord (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

compare :: NonEmpty a -> NonEmpty a -> Ordering #

(<) :: NonEmpty a -> NonEmpty a -> Bool #

(<=) :: NonEmpty a -> NonEmpty a -> Bool #

(>) :: NonEmpty a -> NonEmpty a -> Bool #

(>=) :: NonEmpty a -> NonEmpty a -> Bool #

max :: NonEmpty a -> NonEmpty a -> NonEmpty a #

min :: NonEmpty a -> NonEmpty a -> NonEmpty a #

Ord a => Ord (IntMap a) 
Instance details

Defined in Data.IntMap.Internal

Methods

compare :: IntMap a -> IntMap a -> Ordering #

(<) :: IntMap a -> IntMap a -> Bool #

(<=) :: IntMap a -> IntMap a -> Bool #

(>) :: IntMap a -> IntMap a -> Bool #

(>=) :: IntMap a -> IntMap a -> Bool #

max :: IntMap a -> IntMap a -> IntMap a #

min :: IntMap a -> IntMap a -> IntMap a #

Ord a => Ord (Seq a) 
Instance details

Defined in Data.Sequence.Internal

Methods

compare :: Seq a -> Seq a -> Ordering #

(<) :: Seq a -> Seq a -> Bool #

(<=) :: Seq a -> Seq a -> Bool #

(>) :: Seq a -> Seq a -> Bool #

(>=) :: Seq a -> Seq a -> Bool #

max :: Seq a -> Seq a -> Seq a #

min :: Seq a -> Seq a -> Seq a #

Ord a => Ord (ViewL a) 
Instance details

Defined in Data.Sequence.Internal

Methods

compare :: ViewL a -> ViewL a -> Ordering #

(<) :: ViewL a -> ViewL a -> Bool #

(<=) :: ViewL a -> ViewL a -> Bool #

(>) :: ViewL a -> ViewL a -> Bool #

(>=) :: ViewL a -> ViewL a -> Bool #

max :: ViewL a -> ViewL a -> ViewL a #

min :: ViewL a -> ViewL a -> ViewL a #

Ord a => Ord (ViewR a) 
Instance details

Defined in Data.Sequence.Internal

Methods

compare :: ViewR a -> ViewR a -> Ordering #

(<) :: ViewR a -> ViewR a -> Bool #

(<=) :: ViewR a -> ViewR a -> Bool #

(>) :: ViewR a -> ViewR a -> Bool #

(>=) :: ViewR a -> ViewR a -> Bool #

max :: ViewR a -> ViewR a -> ViewR a #

min :: ViewR a -> ViewR a -> ViewR a #

Ord a => Ord (Set a) 
Instance details

Defined in Data.Set.Internal

Methods

compare :: Set a -> Set a -> Ordering #

(<) :: Set a -> Set a -> Bool #

(<=) :: Set a -> Set a -> Bool #

(>) :: Set a -> Set a -> Bool #

(>=) :: Set a -> Set a -> Bool #

max :: Set a -> Set a -> Set a #

min :: Set a -> Set a -> Set a #

Ord a => Ord (T a) 
Instance details

Defined in Numeric.NonNegative.Wrapper

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

C a => Ord (T a) 
Instance details

Defined in Numeric.NonNegative.ChunkyPrivate

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

Ord g => Ord (StateGen g) 
Instance details

Defined in System.Random.Internal

Methods

compare :: StateGen g -> StateGen g -> Ordering #

(<) :: StateGen g -> StateGen g -> Bool #

(<=) :: StateGen g -> StateGen g -> Bool #

(>) :: StateGen g -> StateGen g -> Bool #

(>=) :: StateGen g -> StateGen g -> Bool #

max :: StateGen g -> StateGen g -> StateGen g #

min :: StateGen g -> StateGen g -> StateGen g #

C a => Ord (ToOrd a) Source # 
Instance details

Defined in Algebra.Indexable

Methods

compare :: ToOrd a -> ToOrd a -> Ordering #

(<) :: ToOrd a -> ToOrd a -> Bool #

(<=) :: ToOrd a -> ToOrd a -> Bool #

(>) :: ToOrd a -> ToOrd a -> Bool #

(>=) :: ToOrd a -> ToOrd a -> Bool #

max :: ToOrd a -> ToOrd a -> ToOrd a #

min :: ToOrd a -> ToOrd a -> ToOrd a #

(Ord a, C a) => Ord (T a) Source # 
Instance details

Defined in Number.Ratio

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

Ord a => Ord (T a) Source # 
Instance details

Defined in MathObj.Wrapper.Haskell98

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

Ord a => Ord (Valuable a) Source # 
Instance details

Defined in Number.Peano

Methods

compare :: Valuable a -> Valuable a -> Ordering #

(<) :: Valuable a -> Valuable a -> Bool #

(<=) :: Valuable a -> Valuable a -> Bool #

(>) :: Valuable a -> Valuable a -> Bool #

(>=) :: Valuable a -> Valuable a -> Bool #

max :: Valuable a -> Valuable a -> Valuable a #

min :: Valuable a -> Valuable a -> Valuable a #

Ord a => Ord (T a) Source # 
Instance details

Defined in Number.PartiallyTranscendental

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

C a => Ord (T a) Source # 
Instance details

Defined in Number.NonNegativeChunky

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

(C a, Ord a) => Ord (T a) Source # 
Instance details

Defined in MathObj.PowerSeries

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

(C a, Ord a) => Ord (T a) Source # 
Instance details

Defined in MathObj.PowerSeries2

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

(Ord a, C a) => Ord (T a) Source # 
Instance details

Defined in Number.Root

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

Ix i => Ord (T i) Source # 
Instance details

Defined in MathObj.Permutation.CycleList.Check

Methods

compare :: T i -> T i -> Ordering #

(<) :: T i -> T i -> Bool #

(<=) :: T i -> T i -> Bool #

(>) :: T i -> T i -> Bool #

(>=) :: T i -> T i -> Bool #

max :: T i -> T i -> T i #

min :: T i -> T i -> T i #

Ord a => Ord (T a) Source # 
Instance details

Defined in MathObj.Matrix

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

Ord a => Ord (T a) Source # 
Instance details

Defined in MathObj.Wrapper.NumericPrelude

Methods

compare :: T a -> T a -> Ordering #

(<) :: T a -> T a -> Bool #

(<=) :: T a -> T a -> Bool #

(>) :: T a -> T a -> Bool #

(>=) :: T a -> T a -> Bool #

max :: T a -> T a -> T a #

min :: T a -> T a -> T a #

(Ord a, Ord b) => Ord (Either a b)

Since: base-2.1

Instance details

Defined in Data.Either

Methods

compare :: Either a b -> Either a b -> Ordering #

(<) :: Either a b -> Either a b -> Bool #

(<=) :: Either a b -> Either a b -> Bool #

(>) :: Either a b -> Either a b -> Bool #

(>=) :: Either a b -> Either a b -> Bool #

max :: Either a b -> Either a b -> Either a b #

min :: Either a b -> Either a b -> Either a b #

Ord (V1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: V1 p -> V1 p -> Ordering #

(<) :: V1 p -> V1 p -> Bool #

(<=) :: V1 p -> V1 p -> Bool #

(>) :: V1 p -> V1 p -> Bool #

(>=) :: V1 p -> V1 p -> Bool #

max :: V1 p -> V1 p -> V1 p #

min :: V1 p -> V1 p -> V1 p #

Ord (U1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: U1 p -> U1 p -> Ordering #

(<) :: U1 p -> U1 p -> Bool #

(<=) :: U1 p -> U1 p -> Bool #

(>) :: U1 p -> U1 p -> Bool #

(>=) :: U1 p -> U1 p -> Bool #

max :: U1 p -> U1 p -> U1 p #

min :: U1 p -> U1 p -> U1 p #

Ord (TypeRep a)

Since: base-4.4.0.0

Instance details

Defined in Data.Typeable.Internal

Methods

compare :: TypeRep a -> TypeRep a -> Ordering #

(<) :: TypeRep a -> TypeRep a -> Bool #

(<=) :: TypeRep a -> TypeRep a -> Bool #

(>) :: TypeRep a -> TypeRep a -> Bool #

(>=) :: TypeRep a -> TypeRep a -> Bool #

max :: TypeRep a -> TypeRep a -> TypeRep a #

min :: TypeRep a -> TypeRep a -> TypeRep a #

(Ord a, Ord b) => Ord (a, b) 
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b) -> (a, b) -> Ordering #

(<) :: (a, b) -> (a, b) -> Bool #

(<=) :: (a, b) -> (a, b) -> Bool #

(>) :: (a, b) -> (a, b) -> Bool #

(>=) :: (a, b) -> (a, b) -> Bool #

max :: (a, b) -> (a, b) -> (a, b) #

min :: (a, b) -> (a, b) -> (a, b) #

(Ix i, Ord e) => Ord (Array i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

compare :: Array i e -> Array i e -> Ordering #

(<) :: Array i e -> Array i e -> Bool #

(<=) :: Array i e -> Array i e -> Bool #

(>) :: Array i e -> Array i e -> Bool #

(>=) :: Array i e -> Array i e -> Bool #

max :: Array i e -> Array i e -> Array i e #

min :: Array i e -> Array i e -> Array i e #

Ord (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

compare :: Fixed a -> Fixed a -> Ordering #

(<) :: Fixed a -> Fixed a -> Bool #

(<=) :: Fixed a -> Fixed a -> Bool #

(>) :: Fixed a -> Fixed a -> Bool #

(>=) :: Fixed a -> Fixed a -> Bool #

max :: Fixed a -> Fixed a -> Fixed a #

min :: Fixed a -> Fixed a -> Fixed a #

Ord a => Ord (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

compare :: Arg a b -> Arg a b -> Ordering #

(<) :: Arg a b -> Arg a b -> Bool #

(<=) :: Arg a b -> Arg a b -> Bool #

(>) :: Arg a b -> Arg a b -> Bool #

(>=) :: Arg a b -> Arg a b -> Bool #

max :: Arg a b -> Arg a b -> Arg a b #

min :: Arg a b -> Arg a b -> Arg a b #

Ord (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

compare :: Proxy s -> Proxy s -> Ordering #

(<) :: Proxy s -> Proxy s -> Bool #

(<=) :: Proxy s -> Proxy s -> Bool #

(>) :: Proxy s -> Proxy s -> Bool #

(>=) :: Proxy s -> Proxy s -> Bool #

max :: Proxy s -> Proxy s -> Proxy s #

min :: Proxy s -> Proxy s -> Proxy s #

(Ord k, Ord v) => Ord (Map k v) 
Instance details

Defined in Data.Map.Internal

Methods

compare :: Map k v -> Map k v -> Ordering #

(<) :: Map k v -> Map k v -> Bool #

(<=) :: Map k v -> Map k v -> Bool #

(>) :: Map k v -> Map k v -> Bool #

(>=) :: Map k v -> Map k v -> Bool #

max :: Map k v -> Map k v -> Map k v #

min :: Map k v -> Map k v -> Map k v #

Ord v => Ord (T a v) Source # 
Instance details

Defined in Number.OccasionallyScalarExpression

Methods

compare :: T a v -> T a v -> Ordering #

(<) :: T a v -> T a v -> Bool #

(<=) :: T a v -> T a v -> Bool #

(>) :: T a v -> T a v -> Bool #

(>=) :: T a v -> T a v -> Bool #

max :: T a v -> T a v -> T a v #

min :: T a v -> T a v -> T a v #

Ord a => Ord (T u a) Source # 
Instance details

Defined in Number.DimensionTerm

Methods

compare :: T u a -> T u a -> Ordering #

(<) :: T u a -> T u a -> Bool #

(<=) :: T u a -> T u a -> Bool #

(>) :: T u a -> T u a -> Bool #

(>=) :: T u a -> T u a -> Bool #

max :: T u a -> T u a -> T u a #

min :: T u a -> T u a -> T u a #

(Ord i, Ord a) => Ord (T i a) Source # 
Instance details

Defined in Number.Physical

Methods

compare :: T i a -> T i a -> Ordering #

(<) :: T i a -> T i a -> Bool #

(<=) :: T i a -> T i a -> Bool #

(>) :: T i a -> T i a -> Bool #

(>=) :: T i a -> T i a -> Bool #

max :: T i a -> T i a -> T i a #

min :: T i a -> T i a -> T i a #

Ord v => Ord (T a v) Source # 
Instance details

Defined in Number.SI

Methods

compare :: T a v -> T a v -> Ordering #

(<) :: T a v -> T a v -> Bool #

(<=) :: T a v -> T a v -> Bool #

(>) :: T a v -> T a v -> Bool #

(>=) :: T a v -> T a v -> Bool #

max :: T a v -> T a v -> T a v #

min :: T a v -> T a v -> T a v #

Ord (f p) => Ord (Rec1 f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: Rec1 f p -> Rec1 f p -> Ordering #

(<) :: Rec1 f p -> Rec1 f p -> Bool #

(<=) :: Rec1 f p -> Rec1 f p -> Bool #

(>) :: Rec1 f p -> Rec1 f p -> Bool #

(>=) :: Rec1 f p -> Rec1 f p -> Bool #

max :: Rec1 f p -> Rec1 f p -> Rec1 f p #

min :: Rec1 f p -> Rec1 f p -> Rec1 f p #

Ord (URec (Ptr ()) p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering #

(<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #

min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #

Ord (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Char p -> URec Char p -> Ordering #

(<) :: URec Char p -> URec Char p -> Bool #

(<=) :: URec Char p -> URec Char p -> Bool #

(>) :: URec Char p -> URec Char p -> Bool #

(>=) :: URec Char p -> URec Char p -> Bool #

max :: URec Char p -> URec Char p -> URec Char p #

min :: URec Char p -> URec Char p -> URec Char p #

Ord (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Double p -> URec Double p -> Ordering #

(<) :: URec Double p -> URec Double p -> Bool #

(<=) :: URec Double p -> URec Double p -> Bool #

(>) :: URec Double p -> URec Double p -> Bool #

(>=) :: URec Double p -> URec Double p -> Bool #

max :: URec Double p -> URec Double p -> URec Double p #

min :: URec Double p -> URec Double p -> URec Double p #

Ord (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

compare :: URec Float p -> URec Float p -> Ordering #

(<) :: URec Float p -> URec Float p -> Bool #

(<=) :: URec Float p -> URec Float p -> Bool #

(>) :: URec Float p -> URec Float p -> Bool #

(>=) :: URec Float p -> URec Float p -> Bool #

max :: URec Float p -> URec Float p -> URec Float p #

min :: URec Float p -> URec Float p -> URec Float p #

Ord (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Int p -> URec Int p -> Ordering #

(<) :: URec Int p -> URec Int p -> Bool #

(<=) :: URec Int p -> URec Int p -> Bool #

(>) :: URec Int p -> URec Int p -> Bool #

(>=) :: URec Int p -> URec Int p -> Bool #

max :: URec Int p -> URec Int p -> URec Int p #

min :: URec Int p -> URec Int p -> URec Int p #

Ord (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Word p -> URec Word p -> Ordering #

(<) :: URec Word p -> URec Word p -> Bool #

(<=) :: URec Word p -> URec Word p -> Bool #

(>) :: URec Word p -> URec Word p -> Bool #

(>=) :: URec Word p -> URec Word p -> Bool #

max :: URec Word p -> URec Word p -> URec Word p #

min :: URec Word p -> URec Word p -> URec Word p #

(Ord a, Ord b, Ord c) => Ord (a, b, c) 
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c) -> (a, b, c) -> Ordering #

(<) :: (a, b, c) -> (a, b, c) -> Bool #

(<=) :: (a, b, c) -> (a, b, c) -> Bool #

(>) :: (a, b, c) -> (a, b, c) -> Bool #

(>=) :: (a, b, c) -> (a, b, c) -> Bool #

max :: (a, b, c) -> (a, b, c) -> (a, b, c) #

min :: (a, b, c) -> (a, b, c) -> (a, b, c) #

Ord a => Ord (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

compare :: Const a b -> Const a b -> Ordering #

(<) :: Const a b -> Const a b -> Bool #

(<=) :: Const a b -> Const a b -> Bool #

(>) :: Const a b -> Const a b -> Bool #

(>=) :: Const a b -> Const a b -> Bool #

max :: Const a b -> Const a b -> Const a b #

min :: Const a b -> Const a b -> Const a b #

Ord (f a) => Ord (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

compare :: Ap f a -> Ap f a -> Ordering #

(<) :: Ap f a -> Ap f a -> Bool #

(<=) :: Ap f a -> Ap f a -> Bool #

(>) :: Ap f a -> Ap f a -> Bool #

(>=) :: Ap f a -> Ap f a -> Bool #

max :: Ap f a -> Ap f a -> Ap f a #

min :: Ap f a -> Ap f a -> Ap f a #

Ord (f a) => Ord (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Alt f a -> Alt f a -> Ordering #

(<) :: Alt f a -> Alt f a -> Bool #

(<=) :: Alt f a -> Alt f a -> Bool #

(>) :: Alt f a -> Alt f a -> Bool #

(>=) :: Alt f a -> Alt f a -> Bool #

max :: Alt f a -> Alt f a -> Alt f a #

min :: Alt f a -> Alt f a -> Alt f a #

Ord (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

compare :: (a :~: b) -> (a :~: b) -> Ordering #

(<) :: (a :~: b) -> (a :~: b) -> Bool #

(<=) :: (a :~: b) -> (a :~: b) -> Bool #

(>) :: (a :~: b) -> (a :~: b) -> Bool #

(>=) :: (a :~: b) -> (a :~: b) -> Bool #

max :: (a :~: b) -> (a :~: b) -> a :~: b #

min :: (a :~: b) -> (a :~: b) -> a :~: b #

(Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

compare :: ErrorT e m a -> ErrorT e m a -> Ordering #

(<) :: ErrorT e m a -> ErrorT e m a -> Bool #

(<=) :: ErrorT e m a -> ErrorT e m a -> Bool #

(>) :: ErrorT e m a -> ErrorT e m a -> Bool #

(>=) :: ErrorT e m a -> ErrorT e m a -> Bool #

max :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #

min :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #

Ord a => Ord (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Methods

compare :: Constant a b -> Constant a b -> Ordering #

(<) :: Constant a b -> Constant a b -> Bool #

(<=) :: Constant a b -> Constant a b -> Bool #

(>) :: Constant a b -> Constant a b -> Bool #

(>=) :: Constant a b -> Constant a b -> Bool #

max :: Constant a b -> Constant a b -> Constant a b #

min :: Constant a b -> Constant a b -> Constant a b #

Ord c => Ord (K1 i c p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: K1 i c p -> K1 i c p -> Ordering #

(<) :: K1 i c p -> K1 i c p -> Bool #

(<=) :: K1 i c p -> K1 i c p -> Bool #

(>) :: K1 i c p -> K1 i c p -> Bool #

(>=) :: K1 i c p -> K1 i c p -> Bool #

max :: K1 i c p -> K1 i c p -> K1 i c p #

min :: K1 i c p -> K1 i c p -> K1 i c p #

(Ord (f p), Ord (g p)) => Ord ((f :+: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: (f :+: g) p -> (f :+: g) p -> Ordering #

(<) :: (f :+: g) p -> (f :+: g) p -> Bool #

(<=) :: (f :+: g) p -> (f :+: g) p -> Bool #

(>) :: (f :+: g) p -> (f :+: g) p -> Bool #

(>=) :: (f :+: g) p -> (f :+: g) p -> Bool #

max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #

min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #

(Ord (f p), Ord (g p)) => Ord ((f :*: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: (f :*: g) p -> (f :*: g) p -> Ordering #

(<) :: (f :*: g) p -> (f :*: g) p -> Bool #

(<=) :: (f :*: g) p -> (f :*: g) p -> Bool #

(>) :: (f :*: g) p -> (f :*: g) p -> Bool #

(>=) :: (f :*: g) p -> (f :*: g) p -> Bool #

max :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #

min :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #

(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) 
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering #

(<) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(>) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

(Ord1 f, Ord1 g, Ord a) => Ord (Product f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

compare :: Product f g a -> Product f g a -> Ordering #

(<) :: Product f g a -> Product f g a -> Bool #

(<=) :: Product f g a -> Product f g a -> Bool #

(>) :: Product f g a -> Product f g a -> Bool #

(>=) :: Product f g a -> Product f g a -> Bool #

max :: Product f g a -> Product f g a -> Product f g a #

min :: Product f g a -> Product f g a -> Product f g a #

(Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

compare :: Sum f g a -> Sum f g a -> Ordering #

(<) :: Sum f g a -> Sum f g a -> Bool #

(<=) :: Sum f g a -> Sum f g a -> Bool #

(>) :: Sum f g a -> Sum f g a -> Bool #

(>=) :: Sum f g a -> Sum f g a -> Bool #

max :: Sum f g a -> Sum f g a -> Sum f g a #

min :: Sum f g a -> Sum f g a -> Sum f g a #

Ord (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

compare :: (a :~~: b) -> (a :~~: b) -> Ordering #

(<) :: (a :~~: b) -> (a :~~: b) -> Bool #

(<=) :: (a :~~: b) -> (a :~~: b) -> Bool #

(>) :: (a :~~: b) -> (a :~~: b) -> Bool #

(>=) :: (a :~~: b) -> (a :~~: b) -> Bool #

max :: (a :~~: b) -> (a :~~: b) -> a :~~: b #

min :: (a :~~: b) -> (a :~~: b) -> a :~~: b #

Ord (f p) => Ord (M1 i c f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: M1 i c f p -> M1 i c f p -> Ordering #

(<) :: M1 i c f p -> M1 i c f p -> Bool #

(<=) :: M1 i c f p -> M1 i c f p -> Bool #

(>) :: M1 i c f p -> M1 i c f p -> Bool #

(>=) :: M1 i c f p -> M1 i c f p -> Bool #

max :: M1 i c f p -> M1 i c f p -> M1 i c f p #

min :: M1 i c f p -> M1 i c f p -> M1 i c f p #

Ord (f (g p)) => Ord ((f :.: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: (f :.: g) p -> (f :.: g) p -> Ordering #

(<) :: (f :.: g) p -> (f :.: g) p -> Bool #

(<=) :: (f :.: g) p -> (f :.: g) p -> Bool #

(>) :: (f :.: g) p -> (f :.: g) p -> Bool #

(>=) :: (f :.: g) p -> (f :.: g) p -> Bool #

max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #

min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #

(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) 
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering #

(<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

(Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

compare :: Compose f g a -> Compose f g a -> Ordering #

(<) :: Compose f g a -> Compose f g a -> Bool #

(<=) :: Compose f g a -> Compose f g a -> Bool #

(>) :: Compose f g a -> Compose f g a -> Bool #

(>=) :: Compose f g a -> Compose f g a -> Bool #

max :: Compose f g a -> Compose f g a -> Compose f g a #

min :: Compose f g a -> Compose f g a -> Compose f g a #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) 
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering #

(<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #

min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) 
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering #

(<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #

min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #

(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) 
Instance details

Defined in GHC.Classes

Methods

compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

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) #

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) #

(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) 
Instance details

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 #

(<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

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) #

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) #

(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) 
Instance details

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 #

(<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

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) #

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) #

(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) 
Instance details

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 #

(<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

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) #

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) #

(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) 
Instance details

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 #

(<) :: (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 #

(<=) :: (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 #

(>) :: (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 #

(>=) :: (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 #

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) #

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) #

(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) 
Instance details

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 #

(<) :: (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 #

(<=) :: (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 #

(>) :: (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 #

(>=) :: (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 #

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) #

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) #

(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) 
Instance details

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 #

(<) :: (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 #

(<=) :: (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 #

(>) :: (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 #

(>=) :: (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 #

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) #

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) #

(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) 
Instance details

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 #

(<) :: (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 #

(<=) :: (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 #

(>) :: (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 #

(>=) :: (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 #

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) #

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) #

class Read a where #

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 Read instance 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 Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
  • The derived Read instance 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 = 5

Note 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 = readListPrecDefault

Why 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:

instance Read T where
  readPrec     = ...
  readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec #

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> 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.

readList :: ReadS [a] #

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

Instances

Instances details
Read Bool

Since: base-2.1

Instance details

Defined in GHC.Read

Read Char

Since: base-2.1

Instance details

Defined in GHC.Read

Read Double

Since: base-2.1

Instance details

Defined in GHC.Read

Read Float

Since: base-2.1

Instance details

Defined in GHC.Read

Read Int

Since: base-2.1

Instance details

Defined in GHC.Read

Read Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Read Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Read Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Read Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Read Integer

Since: base-2.1

Instance details

Defined in GHC.Read

Read Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Read

Read Ordering

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word

Since: base-4.5.0.0

Instance details

Defined in GHC.Read

Read Word8

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word16

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word32

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word64

Since: base-2.1

Instance details

Defined in GHC.Read

Read ()

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS () #

readList :: ReadS [()] #

readPrec :: ReadPrec () #

readListPrec :: ReadPrec [()] #

Read Version

Since: base-2.1

Instance details

Defined in Data.Version

Read SMGen
>>> readMaybe "SMGen 1 1" :: Maybe SMGen
Just (SMGen 1 1)
>>> readMaybe "SMGen 1 2" :: Maybe SMGen
Nothing
>>> readMaybe (show (mkSMGen 42)) :: Maybe SMGen
Just (SMGen 9297814886316923340 13679457532755275413)
Instance details

Defined in System.Random.SplitMix

Read QCGen 
Instance details

Defined in Test.QuickCheck.Random

Methods

readsPrec :: Int -> ReadS QCGen #

readList :: ReadS [QCGen] #

readPrec :: ReadPrec QCGen #

readListPrec :: ReadPrec [QCGen] #

Read Void

Reading a Void value is always a parse error, considering Void as a data type with no constructors.

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Read ExitCode 
Instance details

Defined in GHC.IO.Exception

Read All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Read Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Read Fixity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Read Associativity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Read SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Read SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Read DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Read CChar 
Instance details

Defined in Foreign.C.Types

Read CSChar 
Instance details

Defined in Foreign.C.Types

Read CUChar 
Instance details

Defined in Foreign.C.Types

Read CShort 
Instance details

Defined in Foreign.C.Types

Read CUShort 
Instance details

Defined in Foreign.C.Types

Read CInt 
Instance details

Defined in Foreign.C.Types

Read CUInt 
Instance details

Defined in Foreign.C.Types

Read CLong 
Instance details

Defined in Foreign.C.Types

Read CULong 
Instance details

Defined in Foreign.C.Types

Read CLLong 
Instance details

Defined in Foreign.C.Types

Read CULLong 
Instance details

Defined in Foreign.C.Types

Read CBool 
Instance details

Defined in Foreign.C.Types

Read CFloat 
Instance details

Defined in Foreign.C.Types

Read CDouble 
Instance details

Defined in Foreign.C.Types

Read CPtrdiff 
Instance details

Defined in Foreign.C.Types

Read CSize 
Instance details

Defined in Foreign.C.Types

Read CWchar 
Instance details

Defined in Foreign.C.Types

Read CSigAtomic 
Instance details

Defined in Foreign.C.Types

Read CClock 
Instance details

Defined in Foreign.C.Types

Read CTime 
Instance details

Defined in Foreign.C.Types

Read CUSeconds 
Instance details

Defined in Foreign.C.Types

Read CSUSeconds 
Instance details

Defined in Foreign.C.Types

Read CIntPtr 
Instance details

Defined in Foreign.C.Types

Read CUIntPtr 
Instance details

Defined in Foreign.C.Types

Read CIntMax 
Instance details

Defined in Foreign.C.Types

Read CUIntMax 
Instance details

Defined in Foreign.C.Types

Read Lexeme

Since: base-2.1

Instance details

Defined in GHC.Read

Read GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Read

Read IntSet 
Instance details

Defined in Data.IntSet.Internal

Read SMGen
>>> readMaybe "SMGen 1 1" :: Maybe SMGen
Just (SMGen 1 1)
>>> readMaybe "SMGen 1 2" :: Maybe SMGen
Nothing
>>> readMaybe (show (mkSMGen 42)) :: Maybe SMGen
Just (SMGen 142593372 1604540297)
Instance details

Defined in System.Random.SplitMix32

Read T Source # 
Instance details

Defined in Number.Peano

Read a => Read [a]

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS [a] #

readList :: ReadS [[a]] #

readPrec :: ReadPrec [a] #

readListPrec :: ReadPrec [[a]] #

Read a => Read (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Read

(Integral a, Read a) => Read (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Read

Read p => Read (Par1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Read a => Read (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Read a => Read (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read m => Read (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Read a => Read (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Read a => Read (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Read a => Read (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Read a => Read (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Read a => Read (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Read a => Read (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Read a => Read (Down a)

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed

Since: base-4.7.0.0

Instance details

Defined in Data.Ord

Read a => Read (NonEmpty a)

Since: base-4.11.0.0

Instance details

Defined in GHC.Read

Read e => Read (IntMap e) 
Instance details

Defined in Data.IntMap.Internal

Read a => Read (Tree a) 
Instance details

Defined in Data.Tree

Read a => Read (Seq a) 
Instance details

Defined in Data.Sequence.Internal

Read a => Read (ViewL a) 
Instance details

Defined in Data.Sequence.Internal

Read a => Read (ViewR a) 
Instance details

Defined in Data.Sequence.Internal

(Read a, Ord a) => Read (Set a) 
Instance details

Defined in Data.Set.Internal

(Read a, C a) => Read (T a) Source # 
Instance details

Defined in Number.Ratio

Methods

readsPrec :: Int -> ReadS (T a) #

readList :: ReadS [T a] #

readPrec :: ReadPrec (T a) #

readListPrec :: ReadPrec [T a] #

Read a => Read (T a) Source # 
Instance details

Defined in Number.ResidueClass.Maybe

Methods

readsPrec :: Int -> ReadS (T a) #

readList :: ReadS [T a] #

readPrec :: ReadPrec (T a) #

readListPrec :: ReadPrec [T a] #

(Read a, C a) => Read (T a) Source # 
Instance details

Defined in Number.ResidueClass.Check

Methods

readsPrec :: Int -> ReadS (T a) #

readList :: ReadS [T a] #

readPrec :: ReadPrec (T a) #

readListPrec :: ReadPrec [T a] #

Read i => Read (Cycle i) Source # 
Instance details

Defined in MathObj.Permutation.CycleList.Check

Read a => Read (T a) Source # 
Instance details

Defined in MathObj.Matrix

Methods

readsPrec :: Int -> ReadS (T a) #

readList :: ReadS [T a] #

readPrec :: ReadPrec (T a) #

readListPrec :: ReadPrec [T a] #

Read a => Read (T a) Source # 
Instance details

Defined in Number.Complex

Methods

readsPrec :: Int -> ReadS (T a) #

readList :: ReadS [T a] #

readPrec :: ReadPrec (T a) #

readListPrec :: ReadPrec [T a] #

Read a => Read (T a) Source # 
Instance details

Defined in Number.Quaternion

Methods

readsPrec :: Int -> ReadS (T a) #

readList :: ReadS [T a] #

readPrec :: ReadPrec (T a) #

readListPrec :: ReadPrec [T a] #

(Read a, Read b) => Read (Either a b)

Since: base-3.0

Instance details

Defined in Data.Either

Read (V1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Read (U1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

(Read a, Read b) => Read (a, b)

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b) #

readList :: ReadS [(a, b)] #

readPrec :: ReadPrec (a, b) #

readListPrec :: ReadPrec [(a, b)] #

(Ix a, Read a, Read b) => Read (Array a b)

Since: base-2.1

Instance details

Defined in GHC.Read

HasResolution a => Read (Fixed a)

Since: base-4.3.0.0

Instance details

Defined in Data.Fixed

(Read a, Read b) => Read (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Arg a b) #

readList :: ReadS [Arg a b] #

readPrec :: ReadPrec (Arg a b) #

readListPrec :: ReadPrec [Arg a b] #

Read (Proxy t)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

(Ord k, Read k, Read e) => Read (Map k e) 
Instance details

Defined in Data.Map.Internal

Methods

readsPrec :: Int -> ReadS (Map k e) #

readList :: ReadS [Map k e] #

readPrec :: ReadPrec (Map k e) #

readListPrec :: ReadPrec [Map k e] #

(Read v, Ord a, C a, C a v) => Read (T a v) Source # 
Instance details

Defined in Number.SI

Methods

readsPrec :: Int -> ReadS (T a v) #

readList :: ReadS [T a v] #

readPrec :: ReadPrec (T a v) #

readListPrec :: ReadPrec [T a v] #

Read (f p) => Read (Rec1 f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS (Rec1 f p) #

readList :: ReadS [Rec1 f p] #

readPrec :: ReadPrec (Rec1 f p) #

readListPrec :: ReadPrec [Rec1 f p] #

(Read a, Read b, Read c) => Read (a, b, c)

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c) #

readList :: ReadS [(a, b, c)] #

readPrec :: ReadPrec (a, b, c) #

readListPrec :: ReadPrec [(a, b, c)] #

Read a => Read (Const a b)

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Const

Read (f a) => Read (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

readsPrec :: Int -> ReadS (Ap f a) #

readList :: ReadS [Ap f a] #

readPrec :: ReadPrec (Ap f a) #

readListPrec :: ReadPrec [Ap f a] #

Read (f a) => Read (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Alt f a) #

readList :: ReadS [Alt f a] #

readPrec :: ReadPrec (Alt f a) #

readListPrec :: ReadPrec [Alt f a] #

a ~ b => Read (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

readsPrec :: Int -> ReadS (a :~: b) #

readList :: ReadS [a :~: b] #

readPrec :: ReadPrec (a :~: b) #

readListPrec :: ReadPrec [a :~: b] #

(Read e, Read1 m, Read a) => Read (ErrorT e m a) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

readsPrec :: Int -> ReadS (ErrorT e m a) #

readList :: ReadS [ErrorT e m a] #

readPrec :: ReadPrec (ErrorT e m a) #

readListPrec :: ReadPrec [ErrorT e m a] #

Read a => Read (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Read c => Read (K1 i c p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS (K1 i c p) #

readList :: ReadS [K1 i c p] #

readPrec :: ReadPrec (K1 i c p) #

readListPrec :: ReadPrec [K1 i c p] #

(Read (f p), Read (g p)) => Read ((f :+: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS ((f :+: g) p) #

readList :: ReadS [(f :+: g) p] #

readPrec :: ReadPrec ((f :+: g) p) #

readListPrec :: ReadPrec [(f :+: g) p] #

(Read (f p), Read (g p)) => Read ((f :*: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS ((f :*: g) p) #

readList :: ReadS [(f :*: g) p] #

readPrec :: ReadPrec ((f :*: g) p) #

readListPrec :: ReadPrec [(f :*: g) p] #

(Read a, Read b, Read c, Read d) => Read (a, b, c, d)

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d) #

readList :: ReadS [(a, b, c, d)] #

readPrec :: ReadPrec (a, b, c, d) #

readListPrec :: ReadPrec [(a, b, c, d)] #

(Read1 f, Read1 g, Read a) => Read (Product f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

readsPrec :: Int -> ReadS (Product f g a) #

readList :: ReadS [Product f g a] #

readPrec :: ReadPrec (Product f g a) #

readListPrec :: ReadPrec [Product f g a] #

(Read1 f, Read1 g, Read a) => Read (Sum f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

readsPrec :: Int -> ReadS (Sum f g a) #

readList :: ReadS [Sum f g a] #

readPrec :: ReadPrec (Sum f g a) #

readListPrec :: ReadPrec [Sum f g a] #

a ~~ b => Read (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

readsPrec :: Int -> ReadS (a :~~: b) #

readList :: ReadS [a :~~: b] #

readPrec :: ReadPrec (a :~~: b) #

readListPrec :: ReadPrec [a :~~: b] #

Read (f p) => Read (M1 i c f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS (M1 i c f p) #

readList :: ReadS [M1 i c f p] #

readPrec :: ReadPrec (M1 i c f p) #

readListPrec :: ReadPrec [M1 i c f p] #

Read (f (g p)) => Read ((f :.: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS ((f :.: g) p) #

readList :: ReadS [(f :.: g) p] #

readPrec :: ReadPrec ((f :.: g) p) #

readListPrec :: ReadPrec [(f :.: g) p] #

(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e)

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e) #

readList :: ReadS [(a, b, c, d, e)] #

readPrec :: ReadPrec (a, b, c, d, e) #

readListPrec :: ReadPrec [(a, b, c, d, e)] #

(Read1 f, Read1 g, Read a) => Read (Compose f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

readsPrec :: Int -> ReadS (Compose f g a) #

readList :: ReadS [Compose f g a] #

readPrec :: ReadPrec (Compose f g a) #

readListPrec :: ReadPrec [Compose f g a] #

(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f)

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f) #

readList :: ReadS [(a, b, c, d, e, f)] #

readPrec :: ReadPrec (a, b, c, d, e, f) #

readListPrec :: ReadPrec [(a, b, c, d, e, f)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g) #

readList :: ReadS [(a, b, c, d, e, f, g)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h) #

readList :: ReadS [(a, b, c, d, e, f, g, h)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] #

(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

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] #

class Show a where #

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 show is 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 showsPrec will produce infix applications of the constructor.
  • the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
  • If the constructor is defined using record syntax, then show will 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 = 5

Note that right-associativity of :^: is ignored. For example,

  • show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Methods

showsPrec #

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> 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.

show :: a -> String #

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS #

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances

Instances details
Show Bool

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Bool -> ShowS #

show :: Bool -> String #

showList :: [Bool] -> ShowS #

Show Char

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Char -> ShowS #

show :: Char -> String #

showList :: [Char] -> ShowS #

Show Int

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS #

show :: Int -> String #

showList :: [Int] -> ShowS #

Show Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int8 -> ShowS #

show :: Int8 -> String #

showList :: [Int8] -> ShowS #

Show Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int16 -> ShowS #

show :: Int16 -> String #

showList :: [Int16] -> ShowS #

Show Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int32 -> ShowS #

show :: Int32 -> String #

showList :: [Int32] -> ShowS #

Show Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int64 -> ShowS #

show :: Int64 -> String #

showList :: [Int64] -> ShowS #

Show Integer

Since: base-2.1

Instance details

Defined in GHC.Show

Show Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Show

Show Ordering

Since: base-2.1

Instance details

Defined in GHC.Show

Show Word

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Word -> ShowS #

show :: Word -> String #

showList :: [Word] -> ShowS #

Show Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

showsPrec :: Int -> Word8 -> ShowS #

show :: Word8 -> String #

showList :: [Word8] -> ShowS #

Show Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Show Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Show Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Show RuntimeRep

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show VecCount

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show VecElem

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show CallStack

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show SomeTypeRep

Since: base-4.10.0.0

Instance details

Defined in Data.Typeable.Internal

Show Exp 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Exp -> ShowS #

show :: Exp -> String #

showList :: [Exp] -> ShowS #

Show Match 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Match -> ShowS #

show :: Match -> String #

showList :: [Match] -> ShowS #

Show Clause 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Pat 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Pat -> ShowS #

show :: Pat -> String #

showList :: [Pat] -> ShowS #

Show Type 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Type -> ShowS #

show :: Type -> String #

showList :: [Type] -> ShowS #

Show Dec 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Dec -> ShowS #

show :: Dec -> String #

showList :: [Dec] -> ShowS #

Show Name 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Name -> ShowS #

show :: Name -> String #

showList :: [Name] -> ShowS #

Show FunDep 
Instance details

Defined in Language.Haskell.TH.Syntax

Show InjectivityAnn 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Overlap 
Instance details

Defined in Language.Haskell.TH.Syntax

Show ()

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> () -> ShowS #

show :: () -> String #

showList :: [()] -> ShowS #

Show TyCon

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> TyCon -> ShowS #

show :: TyCon -> String #

showList :: [TyCon] -> ShowS #

Show Module

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show TrName

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show KindRep 
Instance details

Defined in GHC.Show

Show TypeLitSort

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show Version

Since: base-2.1

Instance details

Defined in Data.Version

Show StdGen 
Instance details

Defined in System.Random.Internal

Show SMGen 
Instance details

Defined in System.Random.SplitMix

Methods

showsPrec :: Int -> SMGen -> ShowS #

show :: SMGen -> String #

showList :: [SMGen] -> ShowS #

Show QCGen 
Instance details

Defined in Test.QuickCheck.Random

Methods

showsPrec :: Int -> QCGen -> ShowS #

show :: QCGen -> String #

showList :: [QCGen] -> ShowS #

Show Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Methods

showsPrec :: Int -> Void -> ShowS #

show :: Void -> String #

showList :: [Void] -> ShowS #

Show ThreadId

Since: base-4.2.0.0

Instance details

Defined in GHC.Conc.Sync

Show BlockReason

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Show ThreadStatus

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Show BlockedIndefinitelyOnMVar

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show BlockedIndefinitelyOnSTM

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show Deadlock

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show AllocationLimitExceeded

Since: base-4.7.1.0

Instance details

Defined in GHC.IO.Exception

Show CompactionFailed

Since: base-4.10.0.0

Instance details

Defined in GHC.IO.Exception

Show AssertionFailed

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show SomeAsyncException

Since: base-4.7.0.0

Instance details

Defined in GHC.IO.Exception

Show AsyncException

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show ArrayException

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show FixIOException

Since: base-4.11.0.0

Instance details

Defined in GHC.IO.Exception

Show ExitCode 
Instance details

Defined in GHC.IO.Exception

Show IOErrorType

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show MaskingState

Since: base-4.3.0.0

Instance details

Defined in GHC.IO

Show IOException

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Show All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS #

show :: All -> String #

showList :: [All] -> ShowS #

Show Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS #

show :: Any -> String #

showList :: [Any] -> ShowS #

Show Fixity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Show Associativity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Show SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Show SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Show DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Show CChar 
Instance details

Defined in Foreign.C.Types

Methods

showsPrec :: Int -> CChar -> ShowS #

show :: CChar -> String #

showList :: [CChar] -> ShowS #

Show CSChar 
Instance details

Defined in Foreign.C.Types

Show CUChar 
Instance details

Defined in Foreign.C.Types

Show CShort 
Instance details

Defined in Foreign.C.Types

Show CUShort 
Instance details

Defined in Foreign.C.Types

Show CInt 
Instance details

Defined in Foreign.C.Types

Methods

showsPrec :: Int -> CInt -> ShowS #

show :: CInt -> String #

showList :: [CInt] -> ShowS #

Show CUInt 
Instance details

Defined in Foreign.C.Types

Methods

showsPrec :: Int -> CUInt -> ShowS #

show :: CUInt -> String #

showList :: [CUInt] -> ShowS #

Show CLong 
Instance details

Defined in Foreign.C.Types

Methods

showsPrec :: Int -> CLong -> ShowS #

show :: CLong -> String #

showList :: [CLong] -> ShowS #

Show CULong 
Instance details

Defined in Foreign.C.Types

Show CLLong 
Instance details

Defined in Foreign.C.Types

Show CULLong 
Instance details

Defined in Foreign.C.Types

Show CBool 
Instance details

Defined in Foreign.C.Types

Methods

showsPrec :: Int -> CBool -> ShowS #

show :: CBool -> String #

showList :: [CBool] -> ShowS #

Show CFloat 
Instance details

Defined in Foreign.C.Types

Show CDouble 
Instance details

Defined in Foreign.C.Types

Show CPtrdiff 
Instance details

Defined in Foreign.C.Types

Show CSize 
Instance details

Defined in Foreign.C.Types

Methods

showsPrec :: Int -> CSize -> ShowS #

show :: CSize -> String #

showList :: [CSize] -> ShowS #

Show CWchar 
Instance details

Defined in Foreign.C.Types

Show CSigAtomic 
Instance details

Defined in Foreign.C.Types

Show CClock 
Instance details

Defined in Foreign.C.Types

Show CTime 
Instance details

Defined in Foreign.C.Types

Methods

showsPrec :: Int -> CTime -> ShowS #

show :: CTime -> String #

showList :: [CTime] -> ShowS #

Show CUSeconds 
Instance details

Defined in Foreign.C.Types

Show CSUSeconds 
Instance details

Defined in Foreign.C.Types

Show CIntPtr 
Instance details

Defined in Foreign.C.Types

Show CUIntPtr 
Instance details

Defined in Foreign.C.Types

Show CIntMax 
Instance details

Defined in Foreign.C.Types

Show CUIntMax 
Instance details

Defined in Foreign.C.Types

Show Fingerprint

Since: base-4.7.0.0

Instance details

Defined in GHC.Fingerprint.Type

Show Lexeme

Since: base-2.1

Instance details

Defined in Text.Read.Lex

Show Number

Since: base-4.6.0.0

Instance details

Defined in Text.Read.Lex

Show GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Show SrcLoc

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show IntSet 
Instance details

Defined in Data.IntSet.Internal

Show Extension 
Instance details

Defined in GHC.LanguageExtensions.Type

Show ForeignSrcLang 
Instance details

Defined in GHC.ForeignSrcLang.Type

Show ParseError 
Instance details

Defined in Text.Parsec.Error

Show SourcePos 
Instance details

Defined in Text.Parsec.Pos

Show Doc 
Instance details

Defined in Text.PrettyPrint.HughesPJ

Methods

showsPrec :: Int -> Doc -> ShowS #

show :: Doc -> String #

showList :: [Doc] -> ShowS #

Show TextDetails 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Show Style 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

showsPrec :: Int -> Style -> ShowS #

show :: Style -> String #

showList :: [Style] -> ShowS #

Show Mode 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

showsPrec :: Int -> Mode -> ShowS #

show :: Mode -> String #

showList :: [Mode] -> ShowS #

Show SMGen 
Instance details

Defined in System.Random.SplitMix32

Methods

showsPrec :: Int -> SMGen -> ShowS #

show :: SMGen -> String #

showList :: [SMGen] -> ShowS #

Show ModName 
Instance details

Defined in Language.Haskell.TH.Syntax

Show PkgName 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Module 
Instance details

Defined in Language.Haskell.TH.Syntax

Show OccName 
Instance details

Defined in Language.Haskell.TH.Syntax

Show NameFlavour 
Instance details

Defined in Language.Haskell.TH.Syntax

Show NameSpace 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Loc 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Loc -> ShowS #

show :: Loc -> String #

showList :: [Loc] -> ShowS #

Show Info 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Info -> ShowS #

show :: Info -> String #

showList :: [Info] -> ShowS #

Show ModuleInfo 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Fixity 
Instance details

Defined in Language.Haskell.TH.Syntax

Show FixityDirection 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Lit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Lit -> ShowS #

show :: Lit -> String #

showList :: [Lit] -> ShowS #

Show Bytes 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Bytes -> ShowS #

show :: Bytes -> String #

showList :: [Bytes] -> ShowS #

Show Body 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Body -> ShowS #

show :: Body -> String #

showList :: [Body] -> ShowS #

Show Guard 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Guard -> ShowS #

show :: Guard -> String #

showList :: [Guard] -> ShowS #

Show Stmt 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Stmt -> ShowS #

show :: Stmt -> String #

showList :: [Stmt] -> ShowS #

Show Range 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Range -> ShowS #

show :: Range -> String #

showList :: [Range] -> ShowS #

Show DerivClause 
Instance details

Defined in Language.Haskell.TH.Syntax

Show DerivStrategy 
Instance details

Defined in Language.Haskell.TH.Syntax

Show TypeFamilyHead 
Instance details

Defined in Language.Haskell.TH.Syntax

Show TySynEqn 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Foreign 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Callconv 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Safety 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Pragma 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Inline 
Instance details

Defined in Language.Haskell.TH.Syntax

Show RuleMatch 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Phases 
Instance details

Defined in Language.Haskell.TH.Syntax

Show RuleBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Show AnnTarget 
Instance details

Defined in Language.Haskell.TH.Syntax

Show SourceUnpackedness 
Instance details

Defined in Language.Haskell.TH.Syntax

Show SourceStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Show DecidedStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Con 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Con -> ShowS #

show :: Con -> String #

showList :: [Con] -> ShowS #

Show Bang 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Bang -> ShowS #

show :: Bang -> String #

showList :: [Bang] -> ShowS #

Show PatSynDir 
Instance details

Defined in Language.Haskell.TH.Syntax

Show PatSynArgs 
Instance details

Defined in Language.Haskell.TH.Syntax

Show TyVarBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Show FamilyResultSig 
Instance details

Defined in Language.Haskell.TH.Syntax

Show TyLit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> TyLit -> ShowS #

show :: TyLit -> String #

showList :: [TyLit] -> ShowS #

Show Role 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

showsPrec :: Int -> Role -> ShowS #

show :: Role -> String #

showList :: [Role] -> ShowS #

Show AnnLookup 
Instance details

Defined in Language.Haskell.TH.Syntax

Show Voltage Source # 
Instance details

Defined in Algebra.DimensionTerm

Show Information Source # 
Instance details

Defined in Algebra.DimensionTerm

Show Temperature Source # 
Instance details

Defined in Algebra.DimensionTerm

Show Angle Source # 
Instance details

Defined in Algebra.DimensionTerm

Methods

showsPrec :: Int -> Angle -> ShowS #

show :: Angle -> String #

showList :: [Angle] -> ShowS #

Show Charge Source # 
Instance details

Defined in Algebra.DimensionTerm

Show Mass Source # 
Instance details

Defined in Algebra.DimensionTerm

Methods

showsPrec :: Int -> Mass -> ShowS #

show :: Mass -> String #

showList :: [Mass] -> ShowS #

Show Time Source # 
Instance details

Defined in Algebra.DimensionTerm

Methods

showsPrec :: Int -> Time -> ShowS #

show :: Time -> String #

showList :: [Time] -> ShowS #

Show Length Source # 
Instance details

Defined in Algebra.DimensionTerm

Show Scalar Source # 
Instance details

Defined in Algebra.DimensionTerm

Show T Source # 
Instance details

Defined in Number.Peano

Methods

showsPrec :: Int -> T -> ShowS #

show :: T -> String #

showList :: [T] -> ShowS #

Show T Source # 
Instance details

Defined in Number.GaloisField2p32m5

Methods

showsPrec :: Int -> T -> ShowS #

show :: T -> String #

showList :: [T] -> ShowS #

Show T Source # 
Instance details

Defined in Number.FixedPoint.Check

Methods

showsPrec :: Int -> T -> ShowS #

show :: T -> String #

showList :: [T] -> ShowS #

Show T Source # 
Instance details

Defined in Number.Positional.Check

Methods

showsPrec :: Int -> T -> ShowS #

show :: T -> String #

showList :: [T] -> ShowS #

Show Dimension Source # 
Instance details

Defined in Number.SI.Unit

Show a => Show [a]

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> [a] -> ShowS #

show :: [a] -> String #

showList :: [[a]] -> ShowS #

Show a => Show (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Maybe a -> ShowS #

show :: Maybe a -> String #

showList :: [Maybe a] -> ShowS #

Show a => Show (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS #

show :: Ratio a -> String #

showList :: [Ratio a] -> ShowS #

Show (Ptr a)

Since: base-2.1

Instance details

Defined in GHC.Ptr

Methods

showsPrec :: Int -> Ptr a -> ShowS #

show :: Ptr a -> String #

showList :: [Ptr a] -> ShowS #

Show (FunPtr a)

Since: base-2.1

Instance details

Defined in GHC.Ptr

Methods

showsPrec :: Int -> FunPtr a -> ShowS #

show :: FunPtr a -> String #

showList :: [FunPtr a] -> ShowS #

Show p => Show (Par1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> Par1 p -> ShowS #

show :: Par1 p -> String #

showList :: [Par1 p] -> ShowS #

Show a => Show (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS #

show :: Complex a -> String #

showList :: [Complex a] -> ShowS #

Show a => Show (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Min a -> ShowS #

show :: Min a -> String #

showList :: [Min a] -> ShowS #

Show a => Show (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Max a -> ShowS #

show :: Max a -> String #

showList :: [Max a] -> ShowS #

Show a => Show (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Show a => Show (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Last a -> ShowS #

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Show m => Show (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Option a -> ShowS #

show :: Option a -> String #

showList :: [Option a] -> ShowS #

Show a => Show (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

showsPrec :: Int -> ZipList a -> ShowS #

show :: ZipList a -> String #

showList :: [ZipList a] -> ShowS #

Show a => Show (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

showsPrec :: Int -> Identity a -> ShowS #

show :: Identity a -> String #

showList :: [Identity a] -> ShowS #

Show a => Show (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Show a => Show (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS #

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Show a => Show (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS #

show :: Dual a -> String #

showList :: [Dual a] -> ShowS #

Show a => Show (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS #

show :: Sum a -> String #

showList :: [Sum a] -> ShowS #

Show a => Show (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS #

show :: Product a -> String #

showList :: [Product a] -> ShowS #

Show a => Show (Down a)

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed

Since: base-4.7.0.0

Instance details

Defined in Data.Ord

Methods

showsPrec :: Int -> Down a -> ShowS #

show :: Down a -> String #

showList :: [Down a] -> ShowS #

Show a => Show (NonEmpty a)

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> NonEmpty a -> ShowS #

show :: NonEmpty a -> String #

showList :: [NonEmpty a] -> ShowS #

Show a => Show (IntMap a) 
Instance details

Defined in Data.IntMap.Internal

Methods

showsPrec :: Int -> IntMap a -> ShowS #

show :: IntMap a -> String #

showList :: [IntMap a] -> ShowS #

Show a => Show (Tree a) 
Instance details

Defined in Data.Tree

Methods

showsPrec :: Int -> Tree a -> ShowS #

show :: Tree a -> String #

showList :: [Tree a] -> ShowS #

Show a => Show (Seq a) 
Instance details

Defined in Data.Sequence.Internal

Methods

showsPrec :: Int -> Seq a -> ShowS #

show :: Seq a -> String #

showList :: [Seq a] -> ShowS #

Show a => Show (ViewL a) 
Instance details

Defined in Data.Sequence.Internal

Methods

showsPrec :: Int -> ViewL a -> ShowS #

show :: ViewL a -> String #

showList :: [ViewL a] -> ShowS #

Show a => Show (ViewR a) 
Instance details

Defined in Data.Sequence.Internal

Methods

showsPrec :: Int -> ViewR a -> ShowS #

show :: ViewR a -> String #

showList :: [ViewR a] -> ShowS #

Show a => Show (Set a) 
Instance details

Defined in Data.Set.Internal

Methods

showsPrec :: Int -> Set a -> ShowS #

show :: Set a -> String #

showList :: [Set a] -> ShowS #

Show a => Show (T a) 
Instance details

Defined in Numeric.NonNegative.Wrapper

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) 
Instance details

Defined in Numeric.NonNegative.ChunkyPrivate

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show (Doc a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

showsPrec :: Int -> Doc a -> ShowS #

show :: Doc a -> String #

showList :: [Doc a] -> ShowS #

Show a => Show (AnnotDetails a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Show a => Show (Span a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

showsPrec :: Int -> Span a -> ShowS #

show :: Span a -> String #

showList :: [Span a] -> ShowS #

Show g => Show (StateGen g) 
Instance details

Defined in System.Random.Internal

Methods

showsPrec :: Int -> StateGen g -> ShowS #

show :: StateGen g -> String #

showList :: [StateGen g] -> ShowS #

Show a => Show (Recip a) Source # 
Instance details

Defined in Algebra.DimensionTerm

Methods

showsPrec :: Int -> Recip a -> ShowS #

show :: Recip a -> String #

showList :: [Recip a] -> ShowS #

Show a => Show (ToOrd a) Source # 
Instance details

Defined in Algebra.Indexable

Methods

showsPrec :: Int -> ToOrd a -> ShowS #

show :: ToOrd a -> String #

showList :: [ToOrd a] -> ShowS #

Show a => Show (Max a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

showsPrec :: Int -> Max a -> ShowS #

show :: Max a -> String #

showList :: [Max a] -> ShowS #

Show a => Show (Min a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

showsPrec :: Int -> Min a -> ShowS #

show :: Min a -> String #

showList :: [Min a] -> ShowS #

Show a => Show (LCM a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

showsPrec :: Int -> LCM a -> ShowS #

show :: LCM a -> String #

showList :: [LCM a] -> ShowS #

Show a => Show (GCD a) Source # 
Instance details

Defined in MathObj.Monoid

Methods

showsPrec :: Int -> GCD a -> ShowS #

show :: GCD a -> String #

showList :: [GCD a] -> ShowS #

(Show a, C a) => Show (T a) Source # 
Instance details

Defined in Number.Ratio

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.Wrapper.Haskell98

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in Number.ResidueClass.Maybe

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show (T a) Source # 
Instance details

Defined in Number.ResidueClass.Func

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in Number.ResidueClass.Check

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (Valuable a) Source # 
Instance details

Defined in Number.Peano

Methods

showsPrec :: Int -> Valuable a -> ShowS #

show :: Valuable a -> String #

showList :: [Valuable a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in Number.PartiallyTranscendental

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in Number.NonNegativeChunky

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.PowerSeries

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.PowerSeries2

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.Polynomial

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.RefinementMask2

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.PowerSum

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.RootSet

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in Number.Root

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show i => Show (T i) Source # 
Instance details

Defined in MathObj.Permutation.CycleList.Check

Methods

showsPrec :: Int -> T i -> ShowS #

show :: T i -> String #

showList :: [T i] -> ShowS #

Show i => Show (Cycle i) Source # 
Instance details

Defined in MathObj.Permutation.CycleList.Check

Methods

showsPrec :: Int -> Cycle i -> ShowS #

show :: Cycle i -> String #

showList :: [Cycle i] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.PartialFraction

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.Matrix

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in Number.Complex

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in Number.Quaternion

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.LaurentPolynomial

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.Wrapper.NumericPrelude

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

Show a => Show (Scale a) Source # 
Instance details

Defined in Number.Physical.UnitDatabase

Methods

showsPrec :: Int -> Scale a -> ShowS #

show :: Scale a -> String #

showList :: [Scale a] -> ShowS #

(Show a, Show b) => Show (Either a b)

Since: base-3.0

Instance details

Defined in Data.Either

Methods

showsPrec :: Int -> Either a b -> ShowS #

show :: Either a b -> String #

showList :: [Either a b] -> ShowS #

Show (V1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> V1 p -> ShowS #

show :: V1 p -> String #

showList :: [V1 p] -> ShowS #

Show (U1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> U1 p -> ShowS #

show :: U1 p -> String #

showList :: [U1 p] -> ShowS #

Show (TypeRep a) 
Instance details

Defined in Data.Typeable.Internal

Methods

showsPrec :: Int -> TypeRep a -> ShowS #

show :: TypeRep a -> String #

showList :: [TypeRep a] -> ShowS #

(Show a, Show b) => Show (a, b)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b) -> ShowS #

show :: (a, b) -> String #

showList :: [(a, b)] -> ShowS #

(Ix a, Show a, Show b) => Show (Array a b)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

showsPrec :: Int -> Array a b -> ShowS #

show :: Array a b -> String #

showList :: [Array a b] -> ShowS #

HasResolution a => Show (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

showsPrec :: Int -> Fixed a -> ShowS #

show :: Fixed a -> String #

showList :: [Fixed a] -> ShowS #

(Show a, Show b) => Show (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS #

show :: Arg a b -> String #

showList :: [Arg a b] -> ShowS #

Show (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

showsPrec :: Int -> Proxy s -> ShowS #

show :: Proxy s -> String #

showList :: [Proxy s] -> ShowS #

(Show k, Show a) => Show (Map k a) 
Instance details

Defined in Data.Map.Internal

Methods

showsPrec :: Int -> Map k a -> ShowS #

show :: Map k a -> String #

showList :: [Map k a] -> ShowS #

(Show a, Show b) => Show (Mul a b) Source # 
Instance details

Defined in Algebra.DimensionTerm

Methods

showsPrec :: Int -> Mul a b -> ShowS #

show :: Mul a b -> String #

showList :: [Mul a b] -> ShowS #

(Show a, Show b) => Show (T a b) Source # 
Instance details

Defined in MathObj.Algebra

Methods

showsPrec :: Int -> T a b -> ShowS #

show :: T a b -> String #

showList :: [T a b] -> ShowS #

Show v => Show (T a v) Source # 
Instance details

Defined in Number.OccasionallyScalarExpression

Methods

showsPrec :: Int -> T a v -> ShowS #

show :: T a v -> String #

showList :: [T a v] -> ShowS #

(C u, Show a) => Show (T u a) Source # 
Instance details

Defined in Number.DimensionTerm

Methods

showsPrec :: Int -> T u a -> ShowS #

show :: T u a -> String #

showList :: [T u a] -> ShowS #

(Show i, Show a) => Show (UnitSet i a) Source # 
Instance details

Defined in Number.Physical.UnitDatabase

Methods

showsPrec :: Int -> UnitSet i a -> ShowS #

show :: UnitSet i a -> String #

showList :: [UnitSet i a] -> ShowS #

(Ord i, Enum i, Show a) => Show (T i a) Source # 
Instance details

Defined in Number.Physical

Methods

showsPrec :: Int -> T i a -> ShowS #

show :: T i a -> String #

showList :: [T i a] -> ShowS #

(Show v, Ord a, C a, C a v) => Show (T a v) Source # 
Instance details

Defined in Number.SI

Methods

showsPrec :: Int -> T a v -> ShowS #

show :: T a v -> String #

showList :: [T a v] -> ShowS #

Show (f p) => Show (Rec1 f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> Rec1 f p -> ShowS #

show :: Rec1 f p -> String #

showList :: [Rec1 f p] -> ShowS #

Show (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Char p -> ShowS #

show :: URec Char p -> String #

showList :: [URec Char p] -> ShowS #

Show (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Double p -> ShowS #

show :: URec Double p -> String #

showList :: [URec Double p] -> ShowS #

Show (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Float p -> ShowS #

show :: URec Float p -> String #

showList :: [URec Float p] -> ShowS #

Show (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Int p -> ShowS #

show :: URec Int p -> String #

showList :: [URec Int p] -> ShowS #

Show (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Word p -> ShowS #

show :: URec Word p -> String #

showList :: [URec Word p] -> ShowS #

(Show a, Show b, Show c) => Show (a, b, c)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c) -> ShowS #

show :: (a, b, c) -> String #

showList :: [(a, b, c)] -> ShowS #

Show a => Show (Const a b)

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Const

Methods

showsPrec :: Int -> Const a b -> ShowS #

show :: Const a b -> String #

showList :: [Const a b] -> ShowS #

Show (f a) => Show (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> Ap f a -> ShowS #

show :: Ap f a -> String #

showList :: [Ap f a] -> ShowS #

Show (f a) => Show (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Alt f a -> ShowS #

show :: Alt f a -> String #

showList :: [Alt f a] -> ShowS #

Show (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

showsPrec :: Int -> (a :~: b) -> ShowS #

show :: (a :~: b) -> String #

showList :: [a :~: b] -> ShowS #

(Show e, Show1 m, Show a) => Show (ErrorT e m a) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

showsPrec :: Int -> ErrorT e m a -> ShowS #

show :: ErrorT e m a -> String #

showList :: [ErrorT e m a] -> ShowS #

Show a => Show (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Methods

showsPrec :: Int -> Constant a b -> ShowS #

show :: Constant a b -> String #

showList :: [Constant a b] -> ShowS #

Show c => Show (K1 i c p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> K1 i c p -> ShowS #

show :: K1 i c p -> String #

showList :: [K1 i c p] -> ShowS #

(Show (f p), Show (g p)) => Show ((f :+: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> (f :+: g) p -> ShowS #

show :: (f :+: g) p -> String #

showList :: [(f :+: g) p] -> ShowS #

(Show (f p), Show (g p)) => Show ((f :*: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> (f :*: g) p -> ShowS #

show :: (f :*: g) p -> String #

showList :: [(f :*: g) p] -> ShowS #

(Show a, Show b, Show c, Show d) => Show (a, b, c, d)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d) -> ShowS #

show :: (a, b, c, d) -> String #

showList :: [(a, b, c, d)] -> ShowS #

(Show1 f, Show1 g, Show a) => Show (Product f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

showsPrec :: Int -> Product f g a -> ShowS #

show :: Product f g a -> String #

showList :: [Product f g a] -> ShowS #

(Show1 f, Show1 g, Show a) => Show (Sum f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

showsPrec :: Int -> Sum f g a -> ShowS #

show :: Sum f g a -> String #

showList :: [Sum f g a] -> ShowS #

Show (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

showsPrec :: Int -> (a :~~: b) -> ShowS #

show :: (a :~~: b) -> String #

showList :: [a :~~: b] -> ShowS #

Show (f p) => Show (M1 i c f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> M1 i c f p -> ShowS #

show :: M1 i c f p -> String #

showList :: [M1 i c f p] -> ShowS #

Show (f (g p)) => Show ((f :.: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> (f :.: g) p -> ShowS #

show :: (f :.: g) p -> String #

showList :: [(f :.: g) p] -> ShowS #

(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e) -> ShowS #

show :: (a, b, c, d, e) -> String #

showList :: [(a, b, c, d, e)] -> ShowS #

(Show1 f, Show1 g, Show a) => Show (Compose f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

showsPrec :: Int -> Compose f g a -> ShowS #

show :: Compose f g a -> String #

showList :: [Compose f g a] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f) -> ShowS #

show :: (a, b, c, d, e, f) -> String #

showList :: [(a, b, c, d, e, f)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS #

show :: (a, b, c, d, e, f, g) -> String #

showList :: [(a, b, c, d, e, f, g)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS #

show :: (a, b, c, d, e, f, g, h) -> String #

showList :: [(a, b, c, d, e, f, g, h)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i) -> String #

showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS #

(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

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS #

fail :: MonadFail m => String -> m a #

elem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #

Does the element occur in the structure?

Since: base-4.8.0.0

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

The least element of a non-empty structure.

Since: base-4.8.0.0

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

The largest element of a non-empty structure.

Since: base-4.8.0.0

foldr1 :: Foldable t => (a -> a -> a) -> t a -> a #

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

foldr1 f = foldr1 f . toList

foldl1 :: Foldable t => (a -> a -> a) -> t a -> a #

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

null :: Foldable t => t a -> Bool #

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure.

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. This means that foldl' will diverge if given an infinite list.

Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that 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 \(\mathcal{O}(n)\) 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 = foldl f z . toList

foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b #

Right-associative fold of a structure.

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, foldr can produce a terminating expression from an infinite list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

length :: Foldable t => t a -> Int #

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b) #

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_.

sequence :: (Traversable t, Monad m) => t (m a) -> m (t a) #

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

data Bool #

Constructors

False 
True 

Instances

Instances details
Bounded Bool

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Bool

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Bool -> Bool #

pred :: Bool -> Bool #

toEnum :: Int -> Bool #

fromEnum :: Bool -> Int #

enumFrom :: Bool -> [Bool] #

enumFromThen :: Bool -> Bool -> [Bool] #

enumFromTo :: Bool -> Bool -> [Bool] #

enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #

Eq Bool 
Instance details

Defined in GHC.Classes

Methods

(==) :: Bool -> Bool -> Bool #

(/=) :: Bool -> Bool -> Bool #

Ord Bool 
Instance details

Defined in GHC.Classes

Methods

compare :: Bool -> Bool -> Ordering #

(<) :: Bool -> Bool -> Bool #

(<=) :: Bool -> Bool -> Bool #

(>) :: Bool -> Bool -> Bool #

(>=) :: Bool -> Bool -> Bool #

max :: Bool -> Bool -> Bool #

min :: Bool -> Bool -> Bool #

Read Bool

Since: base-2.1

Instance details

Defined in GHC.Read

Show Bool

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Bool -> ShowS #

show :: Bool -> String #

showList :: [Bool] -> ShowS #

Ix Bool

Since: base-2.1

Instance details

Defined in GHC.Ix

Methods

range :: (Bool, Bool) -> [Bool] #

index :: (Bool, Bool) -> Bool -> Int #

unsafeIndex :: (Bool, Bool) -> Bool -> Int #

inRange :: (Bool, Bool) -> Bool -> Bool #

rangeSize :: (Bool, Bool) -> Int #

unsafeRangeSize :: (Bool, Bool) -> Int #

Generic Bool

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep Bool :: Type -> Type #

Methods

from :: Bool -> Rep Bool x #

to :: Rep Bool x -> Bool #

Testable Bool 
Instance details

Defined in Test.QuickCheck.Property

Methods

property :: Bool -> Property #

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> Bool) -> Property #

Arbitrary Bool 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Bool #

shrink :: Bool -> [Bool] #

CoArbitrary Bool 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Bool -> Gen b -> Gen b #

Storable Bool

Since: base-2.1

Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Bool -> Int #

alignment :: Bool -> Int #

peekElemOff :: Ptr Bool -> Int -> IO Bool #

pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () #

peekByteOff :: Ptr b -> Int -> IO Bool #

pokeByteOff :: Ptr b -> Int -> Bool -> IO () #

peek :: Ptr Bool -> IO Bool #

poke :: Ptr Bool -> Bool -> IO () #

NFData Bool 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Bool -> () #

Random Bool 
Instance details

Defined in System.Random

Methods

randomR :: RandomGen g => (Bool, Bool) -> g -> (Bool, g) #

random :: RandomGen g => g -> (Bool, g) #

randomRs :: RandomGen g => (Bool, Bool) -> g -> [Bool] #

randoms :: RandomGen g => g -> [Bool] #

Uniform Bool 
Instance details

Defined in System.Random.Internal

Methods

uniformM :: StatefulGen g m => g -> m Bool #

UniformRange Bool 
Instance details

Defined in System.Random.Internal

Methods

uniformRM :: StatefulGen g m => (Bool, Bool) -> g -> m Bool #

SingKind Bool

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type DemoteRep Bool

Methods

fromSing :: forall (a :: Bool). Sing a -> DemoteRep Bool

C Bool Source # 
Instance details

Defined in Algebra.Lattice

Methods

up :: Bool -> Bool -> Bool Source #

dn :: Bool -> Bool -> Bool Source #

Lift Bool 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Bool -> Q Exp #

liftTyped :: Bool -> Q (TExp Bool) #

SingI 'False

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

sing :: Sing 'False

SingI 'True

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

sing :: Sing 'True

type Rep Bool 
Instance details

Defined in GHC.Generics

type Rep Bool = D1 ('MetaData "Bool" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "False" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "True" 'PrefixI 'False) (U1 :: Type -> Type))
type DemoteRep Bool 
Instance details

Defined in GHC.Generics

type DemoteRep Bool = Bool
data Sing (a :: Bool) 
Instance details

Defined in GHC.Generics

data Sing (a :: Bool) where

data Char #

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

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

Instances

Instances details
Bounded Char

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Char

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Char -> Char #

pred :: Char -> Char #

toEnum :: Int -> Char #

fromEnum :: Char -> Int #

enumFrom :: Char -> [Char] #

enumFromThen :: Char -> Char -> [Char] #

enumFromTo :: Char -> Char -> [Char] #

enumFromThenTo :: Char -> Char -> Char -> [Char] #

Eq Char 
Instance details

Defined in GHC.Classes

Methods

(==) :: Char -> Char -> Bool #

(/=) :: Char -> Char -> Bool #

Ord Char 
Instance details

Defined in GHC.Classes

Methods

compare :: Char -> Char -> Ordering #

(<) :: Char -> Char -> Bool #

(<=) :: Char -> Char -> Bool #

(>) :: Char -> Char -> Bool #

(>=) :: Char -> Char -> Bool #

max :: Char -> Char -> Char #

min :: Char -> Char -> Char #

Read Char

Since: base-2.1

Instance details

Defined in GHC.Read

Show Char

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Char -> ShowS #

show :: Char -> String #

showList :: [Char] -> ShowS #

Ix Char

Since: base-2.1

Instance details

Defined in GHC.Ix

Methods

range :: (Char, Char) -> [Char] #

index :: (Char, Char) -> Char -> Int #

unsafeIndex :: (Char, Char) -> Char -> Int #

inRange :: (Char, Char) -> Char -> Bool #

rangeSize :: (Char, Char) -> Int #

unsafeRangeSize :: (Char, Char) -> Int #

Arbitrary Char 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen Char #

shrink :: Char -> [Char] #

CoArbitrary Char 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Char -> Gen b -> Gen b #

Storable Char

Since: base-2.1

Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Char -> Int #

alignment :: Char -> Int #

peekElemOff :: Ptr Char -> Int -> IO Char #

pokeElemOff :: Ptr Char -> Int -> Char -> IO () #

peekByteOff :: Ptr b -> Int -> IO Char #

pokeByteOff :: Ptr b -> Int -> Char -> IO () #

peek :: Ptr Char -> IO Char #

poke :: Ptr Char -> Char -> IO () #

NFData Char 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Char -> () #

Random Char 
Instance details

Defined in System.Random

Methods

randomR :: RandomGen g => (Char, Char) -> g -> (Char, g) #

random :: RandomGen g => g -> (Char, g) #

randomRs :: RandomGen g => (Char, Char) -> g -> [Char] #

randoms :: RandomGen g => g -> [Char] #

Uniform Char 
Instance details

Defined in System.Random.Internal

Methods

uniformM :: StatefulGen g m => g -> m Char #

UniformRange Char 
Instance details

Defined in System.Random.Internal

Methods

uniformRM :: StatefulGen g m => (Char, Char) -> g -> m Char #

ErrorList Char 
Instance details

Defined in Control.Monad.Trans.Error

Methods

listMsg :: String -> [Char] #

Lift Char 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Char -> Q Exp #

liftTyped :: Char -> Q (TExp Char) #

Monad m => Stream ByteString m Char 
Instance details

Defined in Text.Parsec.Prim

Methods

uncons :: ByteString -> m (Maybe (Char, ByteString)) #

Monad m => Stream ByteString m Char 
Instance details

Defined in Text.Parsec.Prim

Methods

uncons :: ByteString -> m (Maybe (Char, ByteString)) #

Monad m => Stream Text m Char 
Instance details

Defined in Text.Parsec.Prim

Methods

uncons :: Text -> m (Maybe (Char, Text)) #

Monad m => Stream Text m Char 
Instance details

Defined in Text.Parsec.Prim

Methods

uncons :: Text -> m (Maybe (Char, Text)) #

Generic1 (URec Char :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Char) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Char a -> Rep1 (URec Char) a #

to1 :: forall (a :: k0). Rep1 (URec Char) a -> URec Char a #

Foldable (UChar :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UChar m -> m #

foldMap :: Monoid m => (a -> m) -> UChar a -> m #

foldMap' :: Monoid m => (a -> m) -> UChar a -> m #

foldr :: (a -> b -> b) -> b -> UChar a -> b #

foldr' :: (a -> b -> b) -> b -> UChar a -> b #

foldl :: (b -> a -> b) -> b -> UChar a -> b #

foldl' :: (b -> a -> b) -> b -> UChar a -> b #

foldr1 :: (a -> a -> a) -> UChar a -> a #

foldl1 :: (a -> a -> a) -> UChar a -> a #

toList :: UChar a -> [a] #

null :: UChar a -> Bool #

length :: UChar a -> Int #

elem :: Eq a => a -> UChar a -> Bool #

maximum :: Ord a => UChar a -> a #

minimum :: Ord a => UChar a -> a #

sum :: Num a => UChar a -> a #

product :: Num a => UChar a -> a #

Traversable (UChar :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b) #

sequenceA :: Applicative f => UChar (f a) -> f (UChar a) #

mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b) #

sequence :: Monad m => UChar (m a) -> m (UChar a) #

Functor (URec Char :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b #

(<$) :: a -> URec Char b -> URec Char a #

Eq (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Char p -> URec Char p -> Bool #

(/=) :: URec Char p -> URec Char p -> Bool #

Ord (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Char p -> URec Char p -> Ordering #

(<) :: URec Char p -> URec Char p -> Bool #

(<=) :: URec Char p -> URec Char p -> Bool #

(>) :: URec Char p -> URec Char p -> Bool #

(>=) :: URec Char p -> URec Char p -> Bool #

max :: URec Char p -> URec Char p -> URec Char p #

min :: URec Char p -> URec Char p -> URec Char p #

Show (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Char p -> ShowS #

show :: URec Char p -> String #

showList :: [URec Char p] -> ShowS #

Generic (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Char p) :: Type -> Type #

Methods

from :: URec Char p -> Rep (URec Char p) x #

to :: Rep (URec Char p) x -> URec Char p #

data URec Char (p :: k)

Used for marking occurrences of Char#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Char (p :: k) = UChar {}
type Rep1 (URec Char :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Char :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: k -> Type)))
type Rep (URec Char p) 
Instance details

Defined in GHC.Generics

type Rep (URec Char p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: Type -> Type)))

data Maybe a #

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

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

Constructors

Nothing 
Just a 

Instances

Instances details
Monad Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b #

(>>) :: Maybe a -> Maybe b -> Maybe b #

return :: a -> Maybe a #

Functor Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b #

(<$) :: a -> Maybe b -> Maybe a #

MonadFail Maybe

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Fail

Methods

fail :: String -> Maybe a #

Applicative Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> Maybe a #

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b #

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c #

(*>) :: Maybe a -> Maybe b -> Maybe b #

(<*) :: Maybe a -> Maybe b -> Maybe a #

Foldable Maybe

Since: base-2.1

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Maybe m -> m #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m #

foldMap' :: Monoid m => (a -> m) -> Maybe a -> m #

foldr :: (a -> b -> b) -> b -> Maybe a -> b #

foldr' :: (a -> b -> b) -> b -> Maybe a -> b #

foldl :: (b -> a -> b) -> b -> Maybe a -> b #

foldl' :: (b -> a -> b) -> b -> Maybe a -> b #

foldr1 :: (a -> a -> a) -> Maybe a -> a #

foldl1 :: (a -> a -> a) -> Maybe a -> a #

toList :: Maybe a -> [a] #

null :: Maybe a -> Bool #

length :: Maybe a -> Int #

elem :: Eq a => a -> Maybe a -> Bool #

maximum :: Ord a => Maybe a -> a #

minimum :: Ord a => Maybe a -> a #

sum :: Num a => Maybe a -> a #

product :: Num a => Maybe a -> a #

Traversable Maybe

Since: base-2.1

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) #

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) #

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) #

sequence :: Monad m => Maybe (m a) -> m (Maybe a) #

Arbitrary1 Maybe 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

liftArbitrary :: Gen a -> Gen (Maybe a) #

liftShrink :: (a -> [a]) -> Maybe a -> [Maybe a] #

Eq1 Maybe

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool #

Ord1 Maybe

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering #

Read1 Maybe

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] #

Show1 Maybe

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS #

Alternative Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

empty :: Maybe a #

(<|>) :: Maybe a -> Maybe a -> Maybe a #

some :: Maybe a -> Maybe [a] #

many :: Maybe a -> Maybe [a] #

MonadPlus Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mzero :: Maybe a #

mplus :: Maybe a -> Maybe a -> Maybe a #

NFData1 Maybe

Since: deepseq-1.4.3.0

Instance details

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Maybe a -> () #

Lift a => Lift (Maybe a :: Type) 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Maybe a -> Q Exp #

liftTyped :: Maybe a -> Q (TExp (Maybe a)) #

Eq a => Eq (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Maybe

Methods

(==) :: Maybe a -> Maybe a -> Bool #

(/=) :: Maybe a -> Maybe a -> Bool #

Ord a => Ord (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Maybe

Methods

compare :: Maybe a -> Maybe a -> Ordering #

(<) :: Maybe a -> Maybe a -> Bool #

(<=) :: Maybe a -> Maybe a -> Bool #

(>) :: Maybe a -> Maybe a -> Bool #

(>=) :: Maybe a -> Maybe a -> Bool #

max :: Maybe a -> Maybe a -> Maybe a #

min :: Maybe a -> Maybe a -> Maybe a #

Read a => Read (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Read

Show a => Show (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Maybe a -> ShowS #

show :: Maybe a -> String #

showList :: [Maybe a] -> ShowS #

Generic (Maybe a)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Maybe a) :: Type -> Type #

Methods

from :: Maybe a -> Rep (Maybe a) x #

to :: Rep (Maybe a) x -> Maybe a #

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a #

sconcat :: NonEmpty (Maybe a) -> Maybe a #

stimes :: Integral b => b -> Maybe a -> Maybe a #

Semigroup a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S."

Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: Maybe a #

mappend :: Maybe a -> Maybe a -> Maybe a #

mconcat :: [Maybe a] -> Maybe a #

Testable prop => Testable (Maybe prop) 
Instance details

Defined in Test.QuickCheck.Property

Methods

property :: Maybe prop -> Property #

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> Maybe prop) -> Property #

Arbitrary a => Arbitrary (Maybe a) 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Maybe a) #

shrink :: Maybe a -> [Maybe a] #

CoArbitrary a => CoArbitrary (Maybe a) 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Maybe a -> Gen b -> Gen b #

NFData a => NFData (Maybe a) 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Maybe a -> () #

SingKind a => SingKind (Maybe a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type DemoteRep (Maybe a)

Methods

fromSing :: forall (a0 :: Maybe a). Sing a0 -> DemoteRep (Maybe a)

Generic1 Maybe

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 Maybe :: k -> Type #

Methods

from1 :: forall (a :: k). Maybe a -> Rep1 Maybe a #

to1 :: forall (a :: k). Rep1 Maybe a -> Maybe a #

SingI ('Nothing :: Maybe a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

sing :: Sing 'Nothing

SingI a2 => SingI ('Just a2 :: Maybe a1)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

sing :: Sing ('Just a2)

type Rep (Maybe a) 
Instance details

Defined in GHC.Generics

type Rep (Maybe a) = D1 ('MetaData "Maybe" "GHC.Maybe" "base" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type DemoteRep (Maybe a) 
Instance details

Defined in GHC.Generics

type DemoteRep (Maybe a) = Maybe (DemoteRep a)
data Sing (b :: Maybe a) 
Instance details

Defined in GHC.Generics

data Sing (b :: Maybe a) where
type Rep1 Maybe 
Instance details

Defined in GHC.Generics

type Rep1 Maybe = D1 ('MetaData "Maybe" "GHC.Maybe" "base" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

data Ordering #

Constructors

LT 
EQ 
GT 

Instances

Instances details
Bounded Ordering

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Ordering

Since: base-2.1

Instance details

Defined in GHC.Enum

Eq Ordering 
Instance details

Defined in GHC.Classes

Ord Ordering 
Instance details

Defined in GHC.Classes

Read Ordering

Since: base-2.1

Instance details

Defined in GHC.Read

Show Ordering

Since: base-2.1

Instance details

Defined in GHC.Show

Ix Ordering

Since: base-2.1

Instance details

Defined in GHC.Ix

Generic Ordering

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep Ordering :: Type -> Type #

Methods

from :: Ordering -> Rep Ordering x #

to :: Rep Ordering x -> Ordering #

Semigroup Ordering

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Monoid Ordering

Since: base-2.1

Instance details

Defined in GHC.Base

Arbitrary Ordering 
Instance details

Defined in Test.QuickCheck.Arbitrary

CoArbitrary Ordering 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Ordering -> Gen b -> Gen b #

NFData Ordering 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Ordering -> () #

type Rep Ordering 
Instance details

Defined in GHC.Generics

type Rep Ordering = D1 ('MetaData "Ordering" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "LT" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "EQ" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "GT" 'PrefixI 'False) (U1 :: Type -> Type)))

data IO a #

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

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

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

Instances

Instances details
Monad IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b #

(>>) :: IO a -> IO b -> IO b #

return :: a -> IO a #

Functor IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> IO a -> IO b #

(<$) :: a -> IO b -> IO a #

MonadFail IO

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Fail

Methods

fail :: String -> IO a #

Applicative IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> IO a #

(<*>) :: IO (a -> b) -> IO a -> IO b #

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c #

(*>) :: IO a -> IO b -> IO b #

(<*) :: IO a -> IO b -> IO a #

Alternative IO

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

empty :: IO a #

(<|>) :: IO a -> IO a -> IO a #

some :: IO a -> IO [a] #

many :: IO a -> IO [a] #

MonadPlus IO

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

mzero :: IO a #

mplus :: IO a -> IO a -> IO a #

Quasi IO 
Instance details

Defined in Language.Haskell.TH.Syntax

Semigroup a => Semigroup (IO a)

Since: base-4.10.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a #

sconcat :: NonEmpty (IO a) -> IO a #

stimes :: Integral b => b -> IO a -> IO a #

Monoid a => Monoid (IO a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

mempty :: IO a #

mappend :: IO a -> IO a -> IO a #

mconcat :: [IO a] -> IO a #

data Either a b #

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

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

Examples

Expand

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

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

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

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

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

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

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

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}
>>> parseMultiple
Right 3

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

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

Constructors

Left a 
Right b 

Instances

Instances details
Arbitrary2 Either 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

liftArbitrary2 :: Gen a -> Gen b -> Gen (Either a b) #

liftShrink2 :: (a -> [a]) -> (b -> [b]) -> Either a b -> [Either a b] #

Eq2 Either

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Either a c -> Either b d -> Bool #

Ord2 Either

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Either a c -> Either b d -> Ordering #

Read2 Either

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) #

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] #

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) #

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] #

Show2 Either

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Either a b -> ShowS #

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Either a b] -> ShowS #

NFData2 Either

Since: deepseq-1.4.3.0

Instance details

Defined in Control.DeepSeq

Methods

liftRnf2 :: (a -> ()) -> (b -> ()) -> Either a b -> () #

(Lift a, Lift b) => Lift (Either a b :: Type) 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Either a b -> Q Exp #

liftTyped :: Either a b -> Q (TExp (Either a b)) #

Monad (Either e)

Since: base-4.4.0.0

Instance details

Defined in Data.Either

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b #

(>>) :: Either e a -> Either e b -> Either e b #

return :: a -> Either e a #

Functor (Either a)

Since: base-3.0

Instance details

Defined in Data.Either

Methods

fmap :: (a0 -> b) -> Either a a0 -> Either a b #

(<$) :: a0 -> Either a b -> Either a a0 #

Applicative (Either e)

Since: base-3.0

Instance details

Defined in Data.Either

Methods

pure :: a -> Either e a #

(<*>) :: Either e (a -> b) -> Either e a -> Either e b #

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c #

(*>) :: Either e a -> Either e b -> Either e b #

(<*) :: Either e a -> Either e b -> Either e a #

Foldable (Either a)

Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Either a m -> m #

foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m #

foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #

toList :: Either a a0 -> [a0] #

null :: Either a a0 -> Bool #

length :: Either a a0 -> Int #

elem :: Eq a0 => a0 -> Either a a0 -> Bool #

maximum :: Ord a0 => Either a a0 -> a0 #

minimum :: Ord a0 => Either a a0 -> a0 #

sum :: Num a0 => Either a a0 -> a0 #

product :: Num a0 => Either a a0 -> a0 #

Traversable (Either a)

Since: base-4.7.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) #

sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) #

mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) #

sequence :: Monad m => Either a (m a0) -> m (Either a a0) #

Arbitrary a => Arbitrary1 (Either a) 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

liftArbitrary :: Gen a0 -> Gen (Either a a0) #

liftShrink :: (a0 -> [a0]) -> Either a a0 -> [Either a a0] #

Eq a => Eq1 (Either a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a0 -> b -> Bool) -> Either a a0 -> Either a b -> Bool #

Ord a => Ord1 (Either a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a0 -> b -> Ordering) -> Either a a0 -> Either a b -> Ordering #

Read a => Read1 (Either a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) #

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] #

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) #

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] #

Show a => Show1 (Either a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Either a a0 -> ShowS #

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Either a a0] -> ShowS #

NFData a => NFData1 (Either a)

Since: deepseq-1.4.3.0

Instance details

Defined in Control.DeepSeq

Methods

liftRnf :: (a0 -> ()) -> Either a a0 -> () #

Generic1 (Either a :: Type -> Type)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (Either a) :: k -> Type #

Methods

from1 :: forall (a0 :: k). Either a a0 -> Rep1 (Either a) a0 #

to1 :: forall (a0 :: k). Rep1 (Either a) a0 -> Either a a0 #

(Eq a, Eq b) => Eq (Either a b)

Since: base-2.1

Instance details

Defined in Data.Either

Methods

(==) :: Either a b -> Either a b -> Bool #

(/=) :: Either a b -> Either a b -> Bool #

(Ord a, Ord b) => Ord (Either a b)

Since: base-2.1

Instance details

Defined in Data.Either

Methods

compare :: Either a b -> Either a b -> Ordering #

(<) :: Either a b -> Either a b -> Bool #

(<=) :: Either a b -> Either a b -> Bool #

(>) :: Either a b -> Either a b -> Bool #

(>=) :: Either a b -> Either a b -> Bool #

max :: Either a b -> Either a b -> Either a b #

min :: Either a b -> Either a b -> Either a b #

(Read a, Read b) => Read (Either a b)

Since: base-3.0

Instance details

Defined in Data.Either

(Show a, Show b) => Show (Either a b)

Since: base-3.0

Instance details

Defined in Data.Either

Methods

showsPrec :: Int -> Either a b -> ShowS #

show :: Either a b -> String #

showList :: [Either a b] -> ShowS #

Generic (Either a b)

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (Either a b) :: Type -> Type #

Methods

from :: Either a b -> Rep (Either a b) x #

to :: Rep (Either a b) x -> Either a b #

Semigroup (Either a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Either

Methods

(<>) :: Either a b -> Either a b -> Either a b #

sconcat :: NonEmpty (Either a b) -> Either a b #

stimes :: Integral b0 => b0 -> Either a b -> Either a b #

(Arbitrary a, Arbitrary b) => Arbitrary (Either a b) 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

arbitrary :: Gen (Either a b) #

shrink :: Either a b -> [Either a b] #

(CoArbitrary a, CoArbitrary b) => CoArbitrary (Either a b) 
Instance details

Defined in Test.QuickCheck.Arbitrary

Methods

coarbitrary :: Either a b -> Gen b0 -> Gen b0 #

(NFData a, NFData b) => NFData (Either a b) 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Either a b -> () #

type Rep1 (Either a :: Type -> Type) 
Instance details

Defined in GHC.Generics

type Rep (Either a b) 
Instance details

Defined in GHC.Generics

type String = [Char] #

A String is a list of characters. String constants in Haskell are values of type String.

See Data.List for operations on lists.

readIO :: Read a => String -> IO a #

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

readLn :: Read a => IO a #

The readLn function combines getLine and readIO.

appendFile :: FilePath -> String -> IO () #

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]])

writeFile :: FilePath -> String -> IO () #

The computation writeFile file str function writes the string str, to the file file.

readFile :: FilePath -> IO String #

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.

interact :: (String -> String) -> IO () #

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.

getContents :: IO String #

The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).

getLine :: IO String #

Read a line from the standard input device (same as hGetLine stdin).

getChar :: IO Char #

Read a character from the standard input device (same as hGetChar stdin).

putStrLn :: String -> IO () #

The same as putStr, but adds a newline character.

putStr :: String -> IO () #

Write a string to the standard output device (same as hPutStr stdout).

putChar :: Char -> IO () #

Write a character to the standard output device (same as hPutChar stdout).

ioError :: IOError -> IO a #

Raise an IOError in the IO monad.

type FilePath = String #

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.

userError :: String -> IOError #

Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

instance Monad IO where
  ...
  fail s = ioError (userError s)

type IOError = IOException #

The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.

In Haskell 2010, this is an opaque type.

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #

notElem is the negation of elem.

all :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether all elements of the structure satisfy the predicate.

any :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether any element of the structure satisfies the predicate.

or :: Foldable t => t Bool -> Bool #

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.

and :: Foldable t => t Bool -> Bool #

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.

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #

Map a function over all the elements of a container and concatenate the resulting lists.

concat :: Foldable t => t [a] -> [a] #

The concatenation of all the elements of a container of lists.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #

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.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

unwords :: [String] -> String #

unwords is an inverse operation to words. It joins words with separating spaces.

>>> unwords ["Lorem", "ipsum", "dolor"]
"Lorem ipsum dolor"

words :: String -> [String] #

words breaks a string up into a list of words, which were delimited by white space.

>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]

unlines :: [String] -> String #

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"

lines :: String -> [String] #

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

>>> lines ""
[]
>>> lines "\n"
[""]
>>> lines "one"
["one"]
>>> lines "one\n"
["one"]
>>> lines "one\n\n"
["one",""]
>>> lines "one\ntwo"
["one","two"]
>>> lines "one\ntwo\n"
["one","two"]

Thus lines s contains at least as many elements as newlines in s.

read :: Read a => String -> a #

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" :: Int
123
>>> read "hello" :: Int
*** Exception: Prelude.read: no parse

reads :: Read a => ReadS a #

equivalent to readsPrec with a precedence of 0.

either :: (a -> c) -> (b -> c) -> Either a b -> c #

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples

Expand

We create two values of type Either String Int, one using the Left 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) s
3
>>> either length (*2) n
6

lex :: ReadS String #

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 "" = [("","")].) If there is no legal lexeme at the beginning of the input string, 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

readParen :: Bool -> ReadS a -> ReadS a #

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

type ReadS a = String -> [(a, String)] #

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

showParen :: Bool -> ShowS -> ShowS #

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

showString :: String -> ShowS #

utility function converting a String to a show function that simply prepends the string unchanged.

showChar :: Char -> ShowS #

utility function converting a Char to a show function that simply prepends the character unchanged.

shows :: Show a => a -> ShowS #

equivalent to showsPrec with a precedence of 0.

type ShowS = String -> String #

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) #

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

unzip :: [(a, b)] -> ([a], [b]) #

unzip transforms a list of pairs into a list of first components and a list of second components.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] #

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] #

\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums:

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]

zipWith is right-lazy:

zipWith f [] _|_ = []

zipWith is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] #

zip3 takes three lists and returns a list of triples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

(!!) :: [a] -> Int -> a infixl 9 #

List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.

lookup :: Eq a => a -> [(a, b)] -> Maybe b #

\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list.

>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"

reverse :: [a] -> [a] #

reverse xs returns the elements of xs in reverse order. xs must be finite.

break :: (a -> Bool) -> [a] -> ([a], [a]) #

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 (> 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],[])

break p is equivalent to span (not . p).

span :: (a -> Bool) -> [a] -> ([a], [a]) #

span, 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 satisfy p and second element is the remainder of the list:

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])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

splitAt :: Int -> [a] -> ([a], [a]) #

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 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])

It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

drop :: Int -> [a] -> [a] #

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

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]

It is an instance of the more general genericDrop, in which n may be of any integral type.

take :: Int -> [a] -> [a] #

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

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] == []

It is an instance of the more general genericTake, in which n may be of any integral type.

dropWhile :: (a -> Bool) -> [a] -> [a] #

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

takeWhile :: (a -> Bool) -> [a] -> [a] #

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

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] == []

cycle :: [a] -> [a] #

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.

replicate :: Int -> a -> [a] #

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.

repeat :: a -> [a] #

repeat x is an infinite list, with x the value of every element.

iterate :: (a -> a) -> a -> [a] #

iterate f x returns an infinite list of repeated applications of f to x:

iterate f x == [x, f x, f (f x), ...]

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.

scanr1 :: (a -> a -> a) -> [a] -> [a] #

\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting value argument.

scanr :: (a -> b -> b) -> b -> [a] -> [b] #

\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that

head (scanr f z xs) == foldr f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a] #

\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanl :: (b -> a -> b) -> b -> [a] -> [b] #

\(\mathcal{O}(n)\). 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.

init :: [a] -> [a] #

\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.

last :: [a] -> a #

\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a] #

\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.

head :: [a] -> a #

\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.

maybe :: b -> (a -> b) -> Maybe a -> b #

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

Expand

Basic usage:

>>> maybe False odd (Just 3)
True
>>> maybe False odd Nothing
False

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 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
""

uncurry :: (a -> b -> c) -> (a, b) -> c #

uncurry converts a curried function to a function on pairs.

Examples

Expand
>>> uncurry (+) (1,2)
3
>>> uncurry ($) (show, 1)
"1"
>>> map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]

curry :: ((a, b) -> c) -> a -> b -> c #

curry converts an uncurried function to a curried function.

Examples

Expand
>>> curry fst 1 2
1

asTypeOf :: a -> a -> a #

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

until :: (a -> Bool) -> (a -> a) -> a -> a #

until p f yields the result of applying f until p holds.

($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #

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.

flip :: (a -> b -> c) -> b -> a -> c #

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

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

Function composition.

const :: a -> b -> a #

const x is a unary function which evaluates to x for all inputs.

>>> const 42 "hello"
42
>>> map (const 42) [0..3]
[42,42,42,42]

id :: a -> a #

Identity function.

id x = x

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as >>=, but with the arguments interchanged.

undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a #

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a #

error stops execution and displays an error message.

(&&) :: Bool -> Bool -> Bool infixr 3 #

Boolean "and", lazy in the second argument

(||) :: Bool -> Bool -> Bool infixr 2 #

Boolean "or", lazy in the second argument

not :: Bool -> Bool #

Boolean "not"

ifThenElse :: Bool -> a -> a -> a #

The same as if', but the name is chosen such that it can be used for GHC-7.0's rebindable if-then-else syntax.

catch :: IO a -> (IOError -> IO a) -> IO a Source #

max :: C a => a -> a -> a Source #

min :: C a => a -> a -> a Source #

abs :: (C a, C a) => a -> a Source #