Safe Haskell	None
Language	Haskell2010

BasePrelude

Description

Reexports of most of the definitions from the "base" package, which it is a common practice to import unqualified.

For details check out the source.

Synopsis

module Control.Applicative
module Control.Category
module Control.Concurrent
module Control.Exception
module Control.Monad
module Control.Monad.Fail
module Control.Monad.Fix
module Control.Monad.IO.Class
module Control.Monad.ST
module Data.Bifunctor
module Data.Bits
module Data.Bool
module Data.Char
module Data.Coerce
module Data.Complex
module Data.Data
module Data.Dynamic
module Data.Either
module Data.Fixed
module Data.Functor.Classes
module Data.Functor.Compose
module Data.Functor.Contravariant
module Data.Functor.Identity
module Data.IORef
module Data.Int
module Data.Ix
module Data.List
module Data.Maybe
module Data.Ord
module Data.Proxy
module Data.Ratio
module Data.STRef
module Data.Semigroup
module Data.String
module Data.Traversable
module Data.Tuple
module Data.Unique
module Data.Version
module Data.Void
module Data.Word
module Debug.Trace
module Foreign.ForeignPtr
module Foreign.Ptr
module Foreign.StablePtr
module Foreign.Storable
module GHC.IO.Exception
module GHC.OverloadedLabels
module GHC.Records
module Numeric
module Numeric.Natural
module System.Environment
module System.Exit
module System.IO
module System.IO.Error
module System.IO.Unsafe
module System.Mem
module System.Mem.StableName
module System.Timeout
module Unsafe.Coerce
class Category a => Arrow (a :: Type -> Type -> Type) where
- arr :: (b -> c) -> a b c
- (***) :: a b c -> a b' c' -> a (b, b') (c, c')
- (&&&) :: a b c -> a b c' -> a b (c, c')
const :: a -> b -> a
closeFdWith :: (Fd -> IO ()) -> Fd -> IO ()
class Foldable (t :: Type -> Type) where
- fold :: Monoid m => t m -> m
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldMap' :: Monoid m => (a -> m) -> t a -> m
- foldr' :: (a -> b -> b) -> b -> t a -> b
seq :: a -> b -> b
lazy :: a -> a
inline :: a -> a
($) :: (a -> b) -> a -> b
class Num a where
- (+) :: a -> a -> a
- (-) :: a -> a -> a
- (*) :: a -> a -> a
- negate :: a -> a
- abs :: a -> a
- signum :: a -> a
- fromInteger :: Integer -> a
class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
class Eq a where
- (==) :: a -> a -> Bool
- (/=) :: a -> a -> Bool
class Arrow a => ArrowApply (a :: Type -> Type -> Type) where
- app :: a (a b c, b) c
class Arrow a => ArrowChoice (a :: Type -> Type -> Type) where
- left :: a b c -> a (Either b d) (Either c d)
- right :: a b c -> a (Either d b) (Either d c)
- (+++) :: a b c -> a b' c' -> a (Either b b') (Either c c')
- (|||) :: a b d -> a c d -> a (Either b c) d
class Arrow a => ArrowLoop (a :: Type -> Type -> Type) where
- loop :: a (b, d) (c, d) -> a b c
fromIntegral :: (Integral a, Num b) => a -> b
realToFrac :: (Real a, Fractional b) => a -> b
class (Real a, Enum a) => Integral a where
- quot :: a -> a -> a
- rem :: a -> a -> a
- div :: a -> a -> a
- mod :: a -> a -> a
- quotRem :: a -> a -> (a, a)
- divMod :: a -> a -> (a, a)
- toInteger :: a -> Integer
class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
class IsList l where
- type Item l
- fromList :: [Item l] -> l
- fromListN :: Int -> [Item l] -> l
- toList :: l -> [Item l]
class Semigroup a => Monoid a where
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
class Bounded a where
- minBound :: a
- maxBound :: a
class Read a where
- readsPrec :: Int -> ReadS a
- readList :: ReadS [a]
- readPrec :: ReadPrec a
- readListPrec :: ReadPrec [a]
class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
- atan2 :: a -> a -> a
class (Real a, Fractional a) => RealFrac a where
- properFraction :: Integral b => a -> (b, a)
- truncate :: Integral b => a -> b
- round :: Integral b => a -> b
- ceiling :: Integral b => a -> b
- floor :: Integral b => a -> b
class Show a where
- showsPrec :: Int -> a -> ShowS
- show :: a -> String
- showList :: [a] -> ShowS
class Generic a
class Generic1 (f :: k -> Type)
data Double
data Float
data Integer
class a ~# b => (a :: k) ~ (b :: k)
data NonEmpty a = a :| [a]
(^) :: (Num a, Integral b) => a -> b -> a
error :: HasCallStack => [Char] -> a
errorWithoutStackTrace :: [Char] -> a
undefined :: HasCallStack => a
flip :: (a -> b -> c) -> b -> a -> c
($!) :: (a -> b) -> a -> b
until :: (a -> Bool) -> (a -> a) -> a -> a
asTypeOf :: a -> a -> a
subtract :: Num a => a -> a -> a
type ShowS = String -> String
shows :: Show a => a -> ShowS
showChar :: Char -> ShowS
showString :: String -> ShowS
showParen :: Bool -> ShowS -> ShowS
even :: Integral a => a -> Bool
odd :: Integral a => a -> Bool
(^^) :: (Fractional a, Integral b) => a -> b -> a
gcd :: Integral a => a -> a -> a
lcm :: Integral a => a -> a -> a
(<&>) :: Functor f => f a -> (a -> b) -> f b
($>) :: Functor f => f a -> b -> f b
on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
(&) :: a -> (a -> b) -> b
applyWhen :: Bool -> (a -> a) -> a -> a
data ReadP a
type ReadS a = String -> [(a, String)]
readP_to_S :: ReadP a -> ReadS a
readS_to_P :: ReadS a -> ReadP a
lex :: ReadS String
data ReadPrec a
readPrec_to_P :: ReadPrec a -> Int -> ReadP a
readP_to_Prec :: (Int -> ReadP a) -> ReadPrec a
readPrec_to_S :: ReadPrec a -> Int -> ReadS a
readS_to_Prec :: (Int -> ReadS a) -> ReadPrec a
readParen :: Bool -> ReadS a -> ReadS a
data ThreadStatus
- = ThreadRunning
- | ThreadFinished
- | ThreadBlocked BlockReason
- | ThreadDied
data BlockReason
- = BlockedOnMVar
- | BlockedOnBlackHole
- | BlockedOnException
- | BlockedOnSTM
- | BlockedOnForeignCall
- | BlockedOnOther
data TVar a = TVar (TVar# RealWorld a)
pattern ThreadId :: ThreadId# -> ThreadId
threadStatus :: ThreadId -> IO ThreadStatus
data PrimMVar
newStablePtrPrimMVar :: MVar a -> IO (StablePtr PrimMVar)
reads :: Read a => ReadS a
readEither :: Read a => String -> Either String a
readMaybe :: Read a => String -> Maybe a
read :: Read a => String -> a
newtype Alt (f :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
}
newtype Ap (f :: k -> Type) (a :: k) = Ap {
- getAp :: f a
}
foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()
newtype STM a = STM (State# RealWorld -> (# State# RealWorld, a #))
reportHeapOverflow :: IO ()
numCapabilities :: Int
getNumProcessors :: IO Int
numSparks :: IO Int
childHandler :: SomeException -> IO ()
labelThread :: ThreadId -> String -> IO ()
pseq :: a -> b -> b
par :: a -> b -> b
runSparks :: IO ()
listThreads :: IO [ThreadId]
unsafeIOToSTM :: IO a -> STM a
atomically :: STM a -> IO a
retry :: STM a
throwSTM :: Exception e => e -> STM a
catchSTM :: Exception e => STM a -> (e -> STM a) -> STM a
newTVar :: a -> STM (TVar a)
newTVarIO :: a -> IO (TVar a)
readTVarIO :: TVar a -> IO a
readTVar :: TVar a -> STM a
writeTVar :: TVar a -> a -> STM ()
reportStackOverflow :: IO ()
reportError :: SomeException -> IO ()
setUncaughtExceptionHandler :: (SomeException -> IO ()) -> IO ()
getUncaughtExceptionHandler :: IO (SomeException -> IO ())
type HandlerFun = ForeignPtr Word8 -> IO ()
type Signal = CInt
setHandler :: Signal -> Maybe (HandlerFun, Dynamic) -> IO (Maybe (HandlerFun, Dynamic))
runHandlers :: ForeignPtr Word8 -> Signal -> IO ()
ensureIOManagerIsRunning :: IO ()
ioManagerCapabilitiesChanged :: IO ()
registerDelay :: Int -> IO (TVar Bool)
type family Item l
sortWith :: Ord b => (a -> b) -> [a] -> [a]
groupWith :: Ord b => (a -> b) -> [a] -> [[a]]
newtype ArrowMonad (a :: Type -> Type -> Type) b = ArrowMonad (a () b)
class ArrowZero a => ArrowPlus (a :: Type -> Type -> Type) where
- (<+>) :: a b c -> a b c -> a b c
class Arrow a => ArrowZero (a :: Type -> Type -> Type) where
- zeroArrow :: a b c
newtype Kleisli (m :: Type -> Type) a b = Kleisli {
- runKleisli :: a -> m b
}
returnA :: Arrow a => a b b
(^>>) :: Arrow a => (b -> c) -> a c d -> a b d
(>>^) :: Arrow a => a b c -> (c -> d) -> a b d
(<<^) :: Arrow a => a c d -> (b -> c) -> a b d
(^<<) :: Arrow a => (c -> d) -> a b c -> a b d
leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d)
printf :: PrintfType r => String -> r
hPrintf :: HPrintfType r => Handle -> String -> r

Documentation

module Control.Applicative

module Control.Category

module Control.Concurrent

module Control.Exception

module Control.Monad

module Control.Monad.Fail

module Control.Monad.Fix

module Control.Monad.IO.Class

module Control.Monad.ST

module Data.Bifunctor

module Data.Bits

module Data.Bool

module Data.Char

module Data.Coerce

module Data.Complex

module Data.Data

module Data.Dynamic

module Data.Either

module Data.Fixed

module Data.Functor.Classes

module Data.Functor.Compose

module Data.Functor.Contravariant

module Data.Functor.Identity

module Data.IORef

module Data.Int

module Data.Ix

module Data.List

module Data.Maybe

module Data.Ord

module Data.Proxy

module Data.Ratio

module Data.STRef

module Data.Semigroup

module Data.String

module Data.Traversable

module Data.Tuple

module Data.Unique

module Data.Version

module Data.Void

module Data.Word

module Debug.Trace

module Foreign.ForeignPtr

module Foreign.Ptr

module Foreign.StablePtr

module Foreign.Storable

module GHC.IO.Exception

module GHC.OverloadedLabels

module GHC.Records

module Numeric

module Numeric.Natural

module System.Environment

module System.Exit

module System.IO

module System.IO.Error

module System.IO.Unsafe

module System.Mem

module System.Mem.StableName

module System.Timeout

module Unsafe.Coerce

class Category a => Arrow (a :: Type -> Type -> Type) where Source #

The basic arrow class.

Instances should satisfy the following laws:

```
arr id = id
```
```
arr (f >>> g) = arr f >>> arr g
```
```
first (arr f) = arr (first f)
```
```
first (f >>> g) = first f >>> first g
```
```
first f >>> arr fst = arr fst >>> f
```

first f >>> arr (id *** g) = arr (id *** g) >>> first f

first (first f) >>> arr assoc = arr assoc >>> first f

where

assoc ((a,b),c) = (a,(b,c))

The other combinators have sensible default definitions, which may be overridden for efficiency.

Minimal complete definition

arr, (first | (***))

Methods

arr :: (b -> c) -> a b c Source #

Lift a function to an arrow.

(***) :: a b c -> a b' c' -> a (b, b') (c, c') infixr 3 Source #

Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

(&&&) :: a b c -> a b c' -> a b (c, c') infixr 3 Source #

Fanout: send the input to both argument arrows and combine their output.

The default definition may be overridden with a more efficient version if desired.

Instances

Instances details

Monad m => Arrow (Kleisli m)	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods arr :: (b -> c) -> Kleisli m b c Source # first :: Kleisli m b c -> Kleisli m (b, d) (c, d) Source # second :: Kleisli m b c -> Kleisli m (d, b) (d, c) Source # (***) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (b, b') (c, c') Source # (&&&) :: Kleisli m b c -> Kleisli m b c' -> Kleisli m b (c, c') Source #
Arrow (->)	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods arr :: (b -> c) -> b -> c Source # first :: (b -> c) -> (b, d) -> (c, d) Source # second :: (b -> c) -> (d, b) -> (d, c) Source # (***) :: (b -> c) -> (b' -> c') -> (b, b') -> (c, c') Source # (&&&) :: (b -> c) -> (b -> c') -> b -> (c, c') Source #

const :: a -> b -> a Source #

const x y always evaluates to x, ignoring its second argument.

const x = \_ -> x

This function might seem useless at first glance, but it can be very useful in a higher order context.

Examples

Expand

>>> const 42 "hello"
42

>>> map (const 42) [0..3]
[42,42,42,42]

closeFdWith Source #

Arguments

:: (Fd -> IO ())	Low-level action that performs the real close.
-> Fd	File descriptor to close.
-> IO ()

Close a file descriptor in a concurrency-safe way (GHC only). If you are using threadWaitRead or threadWaitWrite to perform blocking I/O, you must use this function to close file descriptors, or blocked threads may not be woken.

Any threads that are blocked on the file descriptor via threadWaitRead or threadWaitWrite will be unblocked by having IO exceptions thrown.

class Foldable (t :: Type -> Type) where Source #

The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.

Instances can be derived automatically by enabling the DeriveFoldable extension. For example, a derived instance for a binary tree might be:

{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
            | Leaf a
            | Node (Tree a) a (Tree a)
    deriving Foldable

A more detailed description can be found in the Overview section of Data.Foldable.

For the class laws see the Laws section of Data.Foldable.

Minimal complete definition

foldMap | foldr

Methods

fold :: Monoid m => t m -> m Source #

Given a structure with elements whose type is a Monoid, combine them via the monoid's (<>) operator. This fold is right-associative and lazy in the accumulator. When you need a strict left-associative fold, use foldMap' instead, with id as the map.

Examples

Expand

Basic usage:

>>> fold [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

>>> fold $ Node (Leaf (Sum 1)) (Sum 3) (Leaf (Sum 5))
Sum {getSum = 9}

Folds of unbounded structures do not terminate when the monoid's (<>) operator is strict:

>>> fold (repeat Nothing)
* Hangs forever *

Lazy corecursive folds of unbounded structures are fine:

>>> take 12 $ fold $ map (\i -> [i..i+2]) [0..]
[0,1,2,1,2,3,2,3,4,3,4,5]
>>> sum $ take 4000000 $ fold $ map (\i -> [i..i+2]) [0..]
2666668666666

foldMap :: Monoid m => (a -> m) -> t a -> m Source #

Map each element of the structure into a monoid, and combine the results with (<>). This fold is right-associative and lazy in the accumulator. For strict left-associative folds consider foldMap' instead.

Examples

Expand

Basic usage:

>>> foldMap Sum [1, 3, 5]
Sum {getSum = 9}

>>> foldMap Product [1, 3, 5]
Product {getProduct = 15}

>>> foldMap (replicate 3) [1, 2, 3]
[1,1,1,2,2,2,3,3,3]

When a Monoid's (<>) is lazy in its second argument, foldMap can return a result even from an unbounded structure. For example, lazy accumulation enables Data.ByteString.Builder to efficiently serialise large data structures and produce the output incrementally:

>>> import qualified Data.ByteString.Lazy as L
>>> import qualified Data.ByteString.Builder as B
>>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
>>> let lbs = B.toLazyByteString $ foldMap bld [0..]
>>> L.take 64 lbs
"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"

foldMap' :: Monoid m => (a -> m) -> t a -> m Source #

A left-associative variant of foldMap that is strict in the accumulator. Use this method for strict reduction when partial results are merged via (<>).

Examples

Expand

Define a Monoid over finite bit strings under xor. Use it to strictly compute the xor of a list of Int values.

>>> :set -XGeneralizedNewtypeDeriving
>>> import Data.Bits (Bits, FiniteBits, xor, zeroBits)
>>> import Data.Foldable (foldMap')
>>> import Numeric (showHex)
>>> 
>>> newtype X a = X a deriving (Eq, Bounded, Enum, Bits, FiniteBits)
>>> instance Bits a => Semigroup (X a) where X a <> X b = X (a `xor` b)
>>> instance Bits a => Monoid    (X a) where mempty     = X zeroBits
>>> 
>>> let bits :: [Int]; bits = [0xcafe, 0xfeed, 0xdeaf, 0xbeef, 0x5411]
>>> (\ (X a) -> showString "0x" . showHex a $ "") $ foldMap' X bits
"0x42"

Since: base-4.13.0.0

foldr' :: (a -> b -> b) -> b -> t a -> b Source #

foldr' is a variant of foldr that performs strict reduction from right to left, i.e. starting with the right-most element. The input structure must be finite, otherwise foldr' runs out of space (diverges).

If you want a strict right fold in constant space, you need a structure that supports faster than O(n) access to the right-most element, such as Seq from the containers package.

This method does not run in constant space for structures such as lists that don't support efficient right-to-left iteration and so require O(n) space to perform right-to-left reduction. Use of this method with such a structure is a hint that the chosen structure may be a poor fit for the task at hand. If the order in which the elements are combined is not important, use foldl' instead.

Since: base-4.6.0.0

Instances

Instances details

Foldable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m Source # foldMap :: Monoid m => (a -> m) -> Complex a -> m Source # foldMap' :: Monoid m => (a -> m) -> Complex a -> m Source # foldr :: (a -> b -> b) -> b -> Complex a -> b Source # foldr' :: (a -> b -> b) -> b -> Complex a -> b Source # foldl :: (b -> a -> b) -> b -> Complex a -> b Source # foldl' :: (b -> a -> b) -> b -> Complex a -> b Source # foldr1 :: (a -> a -> a) -> Complex a -> a Source # foldl1 :: (a -> a -> a) -> Complex a -> a Source # toList :: Complex a -> [a] Source # null :: Complex a -> Bool Source # length :: Complex a -> Int Source # elem :: Eq a => a -> Complex a -> Bool Source # maximum :: Ord a => Complex a -> a Source # minimum :: Ord a => Complex a -> a Source # sum :: Num a => Complex a -> a Source # product :: Num a => Complex a -> a Source #
Foldable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # sum :: Num a => First a -> a Source # product :: Num a => First a -> a Source #
Foldable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # sum :: Num a => Last a -> a Source # product :: Num a => Last a -> a Source #
Foldable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldMap' :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # sum :: Num a => Max a -> a Source # product :: Num a => Max a -> a Source #
Foldable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldMap' :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # sum :: Num a => Min a -> a Source # product :: Num a => Min a -> a Source #
Foldable NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # sum :: Num a => NonEmpty a -> a Source # product :: Num a => NonEmpty a -> a Source #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m Source # foldMap :: Monoid m => (a -> m) -> Identity a -> m Source # foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source # foldr :: (a -> b -> b) -> b -> Identity a -> b Source # foldr' :: (a -> b -> b) -> b -> Identity a -> b Source # foldl :: (b -> a -> b) -> b -> Identity a -> b Source # foldl' :: (b -> a -> b) -> b -> Identity a -> b Source # foldr1 :: (a -> a -> a) -> Identity a -> a Source # foldl1 :: (a -> a -> a) -> Identity a -> a Source # toList :: Identity a -> [a] Source # null :: Identity a -> Bool Source # length :: Identity a -> Int Source # elem :: Eq a => a -> Identity a -> Bool Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # sum :: Num a => Identity a -> a Source # product :: Num a => Identity a -> a Source #
Foldable First	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # sum :: Num a => First a -> a Source # product :: Num a => First a -> a Source #
Foldable Last	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # sum :: Num a => Last a -> a Source # product :: Num a => Last a -> a Source #
Foldable Down	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Down m -> m Source # foldMap :: Monoid m => (a -> m) -> Down a -> m Source # foldMap' :: Monoid m => (a -> m) -> Down a -> m Source # foldr :: (a -> b -> b) -> b -> Down a -> b Source # foldr' :: (a -> b -> b) -> b -> Down a -> b Source # foldl :: (b -> a -> b) -> b -> Down a -> b Source # foldl' :: (b -> a -> b) -> b -> Down a -> b Source # foldr1 :: (a -> a -> a) -> Down a -> a Source # foldl1 :: (a -> a -> a) -> Down a -> a Source # toList :: Down a -> [a] Source # null :: Down a -> Bool Source # length :: Down a -> Int Source # elem :: Eq a => a -> Down a -> Bool Source # maximum :: Ord a => Down a -> a Source # minimum :: Ord a => Down a -> a Source # sum :: Num a => Down a -> a Source # product :: Num a => Down a -> a Source #
Foldable Dual	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # sum :: Num a => Dual a -> a Source # product :: Num a => Dual a -> a Source #
Foldable Product	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # sum :: Num a => Product a -> a Source # product :: Num a => Product a -> a Source #
Foldable Sum	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # sum :: Num a => Sum a -> a Source # product :: Num a => Sum a -> a Source #
Foldable ZipList	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Functor.ZipList Methods fold :: Monoid m => ZipList m -> m Source # foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source # foldr :: (a -> b -> b) -> b -> ZipList a -> b Source # foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source # foldl :: (b -> a -> b) -> b -> ZipList a -> b Source # foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source # foldr1 :: (a -> a -> a) -> ZipList a -> a Source # foldl1 :: (a -> a -> a) -> ZipList a -> a Source # toList :: ZipList a -> [a] Source # null :: ZipList a -> Bool Source # length :: ZipList a -> Int Source # elem :: Eq a => a -> ZipList a -> Bool Source # maximum :: Ord a => ZipList a -> a Source # minimum :: Ord a => ZipList a -> a Source # sum :: Num a => ZipList a -> a Source # product :: Num a => ZipList a -> a Source #
Foldable Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Par1 m -> m Source # foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source # foldr :: (a -> b -> b) -> b -> Par1 a -> b Source # foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source # foldl :: (b -> a -> b) -> b -> Par1 a -> b Source # foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source # foldr1 :: (a -> a -> a) -> Par1 a -> a Source # foldl1 :: (a -> a -> a) -> Par1 a -> a Source # toList :: Par1 a -> [a] Source # null :: Par1 a -> Bool Source # length :: Par1 a -> Int Source # elem :: Eq a => a -> Par1 a -> Bool Source # maximum :: Ord a => Par1 a -> a Source # minimum :: Ord a => Par1 a -> a Source # sum :: Num a => Par1 a -> a Source # product :: Num a => Par1 a -> a Source #
Foldable Maybe	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # sum :: Num a => Maybe a -> a Source # product :: Num a => Maybe a -> a Source #
Foldable Solo	Since: base-4.15
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Solo m -> m Source # foldMap :: Monoid m => (a -> m) -> Solo a -> m Source # foldMap' :: Monoid m => (a -> m) -> Solo a -> m Source # foldr :: (a -> b -> b) -> b -> Solo a -> b Source # foldr' :: (a -> b -> b) -> b -> Solo a -> b Source # foldl :: (b -> a -> b) -> b -> Solo a -> b Source # foldl' :: (b -> a -> b) -> b -> Solo a -> b Source # foldr1 :: (a -> a -> a) -> Solo a -> a Source # foldl1 :: (a -> a -> a) -> Solo a -> a Source # toList :: Solo a -> [a] Source # null :: Solo a -> Bool Source # length :: Solo a -> Int Source # elem :: Eq a => a -> Solo a -> Bool Source # maximum :: Ord a => Solo a -> a Source # minimum :: Ord a => Solo a -> a Source # sum :: Num a => Solo a -> a Source # product :: Num a => Solo a -> a Source #
Foldable []	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => [m] -> m Source # foldMap :: Monoid m => (a -> m) -> [a] -> m Source # foldMap' :: Monoid m => (a -> m) -> [a] -> m Source # foldr :: (a -> b -> b) -> b -> [a] -> b Source # foldr' :: (a -> b -> b) -> b -> [a] -> b Source # foldl :: (b -> a -> b) -> b -> [a] -> b Source # foldl' :: (b -> a -> b) -> b -> [a] -> b Source # foldr1 :: (a -> a -> a) -> [a] -> a Source # foldl1 :: (a -> a -> a) -> [a] -> a Source # toList :: [a] -> [a] Source # null :: [a] -> Bool Source # length :: [a] -> Int Source # elem :: Eq a => a -> [a] -> Bool Source # maximum :: Ord a => [a] -> a Source # minimum :: Ord a => [a] -> a Source # sum :: Num a => [a] -> a Source # product :: Num a => [a] -> a Source #
Foldable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # sum :: Num a0 => Arg a a0 -> a0 Source # product :: Num a0 => Arg a a0 -> a0 Source #
Foldable (Array i)	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> m Source # foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source # foldr :: (a -> b -> b) -> b -> Array i a -> b Source # foldr' :: (a -> b -> b) -> b -> Array i a -> b Source # foldl :: (b -> a -> b) -> b -> Array i a -> b Source # foldl' :: (b -> a -> b) -> b -> Array i a -> b Source # foldr1 :: (a -> a -> a) -> Array i a -> a Source # foldl1 :: (a -> a -> a) -> Array i a -> a Source # toList :: Array i a -> [a] Source # null :: Array i a -> Bool Source # length :: Array i a -> Int Source # elem :: Eq a => a -> Array i a -> Bool Source # maximum :: Ord a => Array i a -> a Source # minimum :: Ord a => Array i a -> a Source # sum :: Num a => Array i a -> a Source # product :: Num a => Array i a -> a Source #
Foldable (Either a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # sum :: Num a0 => Either a a0 -> a0 Source # product :: Num a0 => Either a a0 -> a0 Source #
Foldable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Proxy m -> m Source # foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source # foldr :: (a -> b -> b) -> b -> Proxy a -> b Source # foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source # foldl :: (b -> a -> b) -> b -> Proxy a -> b Source # foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source # foldr1 :: (a -> a -> a) -> Proxy a -> a Source # foldl1 :: (a -> a -> a) -> Proxy a -> a Source # toList :: Proxy a -> [a] Source # null :: Proxy a -> Bool Source # length :: Proxy a -> Int Source # elem :: Eq a => a -> Proxy a -> Bool Source # maximum :: Ord a => Proxy a -> a Source # minimum :: Ord a => Proxy a -> a Source # sum :: Num a => Proxy a -> a Source # product :: Num a => Proxy a -> a Source #
Foldable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => U1 m -> m Source # foldMap :: Monoid m => (a -> m) -> U1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source # foldr :: (a -> b -> b) -> b -> U1 a -> b Source # foldr' :: (a -> b -> b) -> b -> U1 a -> b Source # foldl :: (b -> a -> b) -> b -> U1 a -> b Source # foldl' :: (b -> a -> b) -> b -> U1 a -> b Source # foldr1 :: (a -> a -> a) -> U1 a -> a Source # foldl1 :: (a -> a -> a) -> U1 a -> a Source # toList :: U1 a -> [a] Source # null :: U1 a -> Bool Source # length :: U1 a -> Int Source # elem :: Eq a => a -> U1 a -> Bool Source # maximum :: Ord a => U1 a -> a Source # minimum :: Ord a => U1 a -> a Source # sum :: Num a => U1 a -> a Source # product :: Num a => U1 a -> a Source #
Foldable (UAddr :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UAddr m -> m Source # foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source # foldr :: (a -> b -> b) -> b -> UAddr a -> b Source # foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source # foldl :: (b -> a -> b) -> b -> UAddr a -> b Source # foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source # foldr1 :: (a -> a -> a) -> UAddr a -> a Source # foldl1 :: (a -> a -> a) -> UAddr a -> a Source # toList :: UAddr a -> [a] Source # null :: UAddr a -> Bool Source # length :: UAddr a -> Int Source # elem :: Eq a => a -> UAddr a -> Bool Source # maximum :: Ord a => UAddr a -> a Source # minimum :: Ord a => UAddr a -> a Source # sum :: Num a => UAddr a -> a Source # product :: Num a => UAddr a -> a Source #
Foldable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # sum :: Num a => UChar a -> a Source # product :: Num a => UChar a -> a Source #
Foldable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # sum :: Num a => UDouble a -> a Source # product :: Num a => UDouble a -> a Source #
Foldable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # sum :: Num a => UFloat a -> a Source # product :: Num a => UFloat a -> a Source #
Foldable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # sum :: Num a => UInt a -> a Source # product :: Num a => UInt a -> a Source #
Foldable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # sum :: Num a => UWord a -> a Source # product :: Num a => UWord a -> a Source #
Foldable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => V1 m -> m Source # foldMap :: Monoid m => (a -> m) -> V1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source # foldr :: (a -> b -> b) -> b -> V1 a -> b Source # foldr' :: (a -> b -> b) -> b -> V1 a -> b Source # foldl :: (b -> a -> b) -> b -> V1 a -> b Source # foldl' :: (b -> a -> b) -> b -> V1 a -> b Source # foldr1 :: (a -> a -> a) -> V1 a -> a Source # foldl1 :: (a -> a -> a) -> V1 a -> a Source # toList :: V1 a -> [a] Source # null :: V1 a -> Bool Source # length :: V1 a -> Int Source # elem :: Eq a => a -> V1 a -> Bool Source # maximum :: Ord a => V1 a -> a Source # minimum :: Ord a => V1 a -> a Source # sum :: Num a => V1 a -> a Source # product :: Num a => V1 a -> a Source #
Foldable ((,) a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (a, m) -> m Source # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # toList :: (a, a0) -> [a0] Source # null :: (a, a0) -> Bool Source # length :: (a, a0) -> Int Source # elem :: Eq a0 => a0 -> (a, a0) -> Bool Source # maximum :: Ord a0 => (a, a0) -> a0 Source # minimum :: Ord a0 => (a, a0) -> a0 Source # sum :: Num a0 => (a, a0) -> a0 Source # product :: Num a0 => (a, a0) -> a0 Source #
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 Source # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldr :: (a -> b -> b) -> b -> Const m a -> b Source # foldr' :: (a -> b -> b) -> b -> Const m a -> b Source # foldl :: (b -> a -> b) -> b -> Const m a -> b Source # foldl' :: (b -> a -> b) -> b -> Const m a -> b Source # foldr1 :: (a -> a -> a) -> Const m a -> a Source # foldl1 :: (a -> a -> a) -> Const m a -> a Source # toList :: Const m a -> [a] Source # null :: Const m a -> Bool Source # length :: Const m a -> Int Source # elem :: Eq a => a -> Const m a -> Bool Source # maximum :: Ord a => Const m a -> a Source # minimum :: Ord a => Const m a -> a Source # sum :: Num a => Const m a -> a Source # product :: Num a => Const m a -> a Source #
Foldable f => Foldable (Ap f)	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source # foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source # foldr :: (a -> b -> b) -> b -> Ap f a -> b Source # foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source # foldl :: (b -> a -> b) -> b -> Ap f a -> b Source # foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source # foldr1 :: (a -> a -> a) -> Ap f a -> a Source # foldl1 :: (a -> a -> a) -> Ap f a -> a Source # toList :: Ap f a -> [a] Source # null :: Ap f a -> Bool Source # length :: Ap f a -> Int Source # elem :: Eq a => a -> Ap f a -> Bool Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # sum :: Num a => Ap f a -> a Source # product :: Num a => Ap f a -> a Source #
Foldable f => Foldable (Alt f)	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Alt f m -> m Source # foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source # foldr :: (a -> b -> b) -> b -> Alt f a -> b Source # foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source # foldl :: (b -> a -> b) -> b -> Alt f a -> b Source # foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source # foldr1 :: (a -> a -> a) -> Alt f a -> a Source # foldl1 :: (a -> a -> a) -> Alt f a -> a Source # toList :: Alt f a -> [a] Source # null :: Alt f a -> Bool Source # length :: Alt f a -> Int Source # elem :: Eq a => a -> Alt f a -> Bool Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # sum :: Num a => Alt f a -> a Source # product :: Num a => Alt f a -> a Source #
Foldable f => Foldable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m Source # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source # foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source # toList :: Rec1 f a -> [a] Source # null :: Rec1 f a -> Bool Source # length :: Rec1 f a -> Int Source # elem :: Eq a => a -> Rec1 f a -> Bool Source # maximum :: Ord a => Rec1 f a -> a Source # minimum :: Ord a => Rec1 f a -> a Source # sum :: Num a => Rec1 f a -> a Source # product :: Num a => Rec1 f a -> a Source #
(Foldable f, Foldable g) => Foldable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Product f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m Source # foldr :: (a -> b -> b) -> b -> Product f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Product f g a -> b Source # foldl :: (b -> a -> b) -> b -> Product f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Product f g a -> b Source # foldr1 :: (a -> a -> a) -> Product f g a -> a Source # foldl1 :: (a -> a -> a) -> Product f g a -> a Source # toList :: Product f g a -> [a] Source # null :: Product f g a -> Bool Source # length :: Product f g a -> Int Source # elem :: Eq a => a -> Product f g a -> Bool Source # maximum :: Ord a => Product f g a -> a Source # minimum :: Ord a => Product f g a -> a Source # sum :: Num a => Product f g a -> a Source # product :: Num a => Product f g a -> a Source #
(Foldable f, Foldable g) => Foldable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldr :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldl :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldr1 :: (a -> a -> a) -> Sum f g a -> a Source # foldl1 :: (a -> a -> a) -> Sum f g a -> a Source # toList :: Sum f g a -> [a] Source # null :: Sum f g a -> Bool Source # length :: Sum f g a -> Int Source # elem :: Eq a => a -> Sum f g a -> Bool Source # maximum :: Ord a => Sum f g a -> a Source # minimum :: Ord a => Sum f g a -> a Source # sum :: Num a => Sum f g a -> a Source # product :: Num a => Sum f g a -> a Source #
(Foldable f, Foldable g) => Foldable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :: g) a -> a Source # toList :: (f :: g) a -> [a] Source # null :: (f :: g) a -> Bool Source # length :: (f :: g) a -> Int Source # elem :: Eq a => a -> (f :: g) a -> Bool Source # maximum :: Ord a => (f :: g) a -> a Source # minimum :: Ord a => (f :: g) a -> a Source # sum :: Num a => (f :: g) a -> a Source # product :: Num a => (f :*: g) a -> a Source #
(Foldable f, Foldable g) => Foldable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source # toList :: (f :+: g) a -> [a] Source # null :: (f :+: g) a -> Bool Source # length :: (f :+: g) a -> Int Source # elem :: Eq a => a -> (f :+: g) a -> Bool Source # maximum :: Ord a => (f :+: g) a -> a Source # minimum :: Ord a => (f :+: g) a -> a Source # sum :: Num a => (f :+: g) a -> a Source # product :: Num a => (f :+: g) a -> a Source #
Foldable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => K1 i c m -> m Source # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldr1 :: (a -> a -> a) -> K1 i c a -> a Source # foldl1 :: (a -> a -> a) -> K1 i c a -> a Source # toList :: K1 i c a -> [a] Source # null :: K1 i c a -> Bool Source # length :: K1 i c a -> Int Source # elem :: Eq a => a -> K1 i c a -> Bool Source # maximum :: Ord a => K1 i c a -> a Source # minimum :: Ord a => K1 i c a -> a Source # sum :: Num a => K1 i c a -> a Source # product :: Num a => K1 i c a -> a Source #
(Foldable f, Foldable g) => Foldable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldr1 :: (a -> a -> a) -> Compose f g a -> a Source # foldl1 :: (a -> a -> a) -> Compose f g a -> a Source # toList :: Compose f g a -> [a] Source # null :: Compose f g a -> Bool Source # length :: Compose f g a -> Int Source # elem :: Eq a => a -> Compose f g a -> Bool Source # maximum :: Ord a => Compose f g a -> a Source # minimum :: Ord a => Compose f g a -> a Source # sum :: Num a => Compose f g a -> a Source # product :: Num a => Compose f g a -> a Source #
(Foldable f, Foldable g) => Foldable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source # toList :: (f :.: g) a -> [a] Source # null :: (f :.: g) a -> Bool Source # length :: (f :.: g) a -> Int Source # elem :: Eq a => a -> (f :.: g) a -> Bool Source # maximum :: Ord a => (f :.: g) a -> a Source # minimum :: Ord a => (f :.: g) a -> a Source # sum :: Num a => (f :.: g) a -> a Source # product :: Num a => (f :.: g) a -> a Source #
Foldable f => Foldable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m Source # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source # foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source # toList :: M1 i c f a -> [a] Source # null :: M1 i c f a -> Bool Source # length :: M1 i c f a -> Int Source # elem :: Eq a => a -> M1 i c f a -> Bool Source # maximum :: Ord a => M1 i c f a -> a Source # minimum :: Ord a => M1 i c f a -> a Source # sum :: Num a => M1 i c f a -> a Source # product :: Num a => M1 i c f a -> a Source #

seq :: a -> b -> b infixr 0 Source #

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.

lazy :: a -> a Source #

The lazy function restrains strictness analysis a little. The call lazy e means the same as e, but lazy has a magical property so far as strictness analysis is concerned: it is lazy in its first argument, even though its semantics is strict. After strictness analysis has run, calls to lazy are inlined to be the identity function.

This behaviour is occasionally useful when controlling evaluation order. Notably, lazy is used in the library definition of par:

par :: a -> b -> b
par x y = case (par# x) of _ -> lazy y

If lazy were not lazy, par would look strict in y which would defeat the whole purpose of par.

inline :: a -> a Source #

The call inline f arranges that f is inlined, regardless of its size. More precisely, the call inline f rewrites to the right-hand side of f's definition. This allows the programmer to control inlining from a particular call site rather than the definition site of the function (c.f. INLINE pragmas).

This inlining occurs regardless of the argument to the call or the size of f's definition; it is unconditional. The main caveat is that f's definition must be visible to the compiler; it is therefore recommended to mark the function with an INLINABLE pragma at its definition so that GHC guarantees to record its unfolding regardless of size.

If no inlining takes place, the inline function expands to the identity function in Phase zero, so its use imposes no overhead.

($) :: (a -> b) -> a -> b infixr 0 Source #

($) is the function application operator.

Applying ($) to a function f and an argument x gives the same result as applying f to x directly. The definition is akin to this:

($) :: (a -> b) -> a -> b
($) f x = f x

This is id specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is the same as (a -> b) -> a -> b.

On the face of it, this may appear pointless! But it's actually one of the most useful and important operators in Haskell.

The order of operations is very different between ($) and normal function application. Normal function application has precedence 10 - higher than any operator - and associates to the left. So these two definitions are equivalent:

expr = min 5 1 + 5
expr = ((min 5) 1) + 5

($) has precedence 0 (the lowest) and associates to the right, so these are equivalent:

expr = min 5 $ 1 + 5
expr = (min 5) (1 + 5)

Examples

Expand

A common use cases of ($) is to avoid parentheses in complex expressions.

For example, instead of using nested parentheses in the following Haskell function:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum (mapMaybe readMaybe (words s))

we can deploy the function application operator:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum $ mapMaybe readMaybe $ words s

($) is also used as a section (a partially applied operator), in order to indicate that we wish to apply some yet-unspecified function to a given value. For example, to apply the argument 5 to a list of functions:

applyFive :: [Int]
applyFive = map ($ 5) [(+1), (2^)]
>>> [6, 32]

Technical Remark (Representation Polymorphism)

Expand

($) is fully representation-polymorphic. This allows it to also be used with arguments of unlifted and even unboxed kinds, such as unboxed integers:

fastMod :: Int -> Int -> Int
fastMod (I# x) (I# m) = I# $ remInt# x m

class Num a where Source #

Basic numeric class.

The Haskell Report defines no laws for Num. However, (+) and (*) are customarily expected to define a ring and have the following properties:

Associativity of (+): (x + y) + z = x + (y + z)
Commutativity of (+): x + y = y + x
fromInteger 0 is the additive identity: x + fromInteger 0 = x
negate gives the additive inverse: x + negate x = fromInteger 0
Associativity of (*): (x * y) * z = x * (y * z)
fromInteger 1 is the multiplicative identity: x * fromInteger 1 = x and fromInteger 1 * x = x
Distributivity of (*) with respect to (+): a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)
Coherence with toInteger: if the type also implements Integral, then fromInteger is a left inverse for toInteger, i.e. fromInteger (toInteger i) == i

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6 Source #

(-) :: a -> a -> a infixl 6 Source #

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

negate :: a -> a Source #

Unary negation.

abs :: a -> a Source #

Absolute value.

signum :: a -> a Source #

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a Source #

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances

Instances details

Num IntPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods (+) :: IntPtr -> IntPtr -> IntPtr Source # (-) :: IntPtr -> IntPtr -> IntPtr Source # (*) :: IntPtr -> IntPtr -> IntPtr Source # negate :: IntPtr -> IntPtr Source # abs :: IntPtr -> IntPtr Source # signum :: IntPtr -> IntPtr Source # fromInteger :: Integer -> IntPtr Source #
Num WordPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods (+) :: WordPtr -> WordPtr -> WordPtr Source # (-) :: WordPtr -> WordPtr -> WordPtr Source # (*) :: WordPtr -> WordPtr -> WordPtr Source # negate :: WordPtr -> WordPtr Source # abs :: WordPtr -> WordPtr Source # signum :: WordPtr -> WordPtr Source # fromInteger :: Integer -> WordPtr Source #
Num Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int16 -> Int16 -> Int16 Source # (-) :: Int16 -> Int16 -> Int16 Source # (*) :: Int16 -> Int16 -> Int16 Source # negate :: Int16 -> Int16 Source # abs :: Int16 -> Int16 Source # signum :: Int16 -> Int16 Source # fromInteger :: Integer -> Int16 Source #
Num Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int32 -> Int32 -> Int32 Source # (-) :: Int32 -> Int32 -> Int32 Source # (*) :: Int32 -> Int32 -> Int32 Source # negate :: Int32 -> Int32 Source # abs :: Int32 -> Int32 Source # signum :: Int32 -> Int32 Source # fromInteger :: Integer -> Int32 Source #
Num Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int64 -> Int64 -> Int64 Source # (-) :: Int64 -> Int64 -> Int64 Source # (*) :: Int64 -> Int64 -> Int64 Source # negate :: Int64 -> Int64 Source # abs :: Int64 -> Int64 Source # signum :: Int64 -> Int64 Source # fromInteger :: Integer -> Int64 Source #
Num Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int8 -> Int8 -> Int8 Source # (-) :: Int8 -> Int8 -> Int8 Source # (*) :: Int8 -> Int8 -> Int8 Source # negate :: Int8 -> Int8 Source # abs :: Int8 -> Int8 Source # signum :: Int8 -> Int8 Source # fromInteger :: Integer -> Int8 Source #
Num CBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # (-) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # (*) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # negate :: CBlkCnt -> CBlkCnt Source # abs :: CBlkCnt -> CBlkCnt Source # signum :: CBlkCnt -> CBlkCnt Source # fromInteger :: Integer -> CBlkCnt Source #
Num CBlkSize
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CBlkSize -> CBlkSize -> CBlkSize Source # (-) :: CBlkSize -> CBlkSize -> CBlkSize Source # (*) :: CBlkSize -> CBlkSize -> CBlkSize Source # negate :: CBlkSize -> CBlkSize Source # abs :: CBlkSize -> CBlkSize Source # signum :: CBlkSize -> CBlkSize Source # fromInteger :: Integer -> CBlkSize Source #
Num CCc
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CCc -> CCc -> CCc Source # (-) :: CCc -> CCc -> CCc Source # (*) :: CCc -> CCc -> CCc Source # negate :: CCc -> CCc Source # abs :: CCc -> CCc Source # signum :: CCc -> CCc Source # fromInteger :: Integer -> CCc Source #
Num CClockId
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CClockId -> CClockId -> CClockId Source # (-) :: CClockId -> CClockId -> CClockId Source # (*) :: CClockId -> CClockId -> CClockId Source # negate :: CClockId -> CClockId Source # abs :: CClockId -> CClockId Source # signum :: CClockId -> CClockId Source # fromInteger :: Integer -> CClockId Source #
Num CDev
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CDev -> CDev -> CDev Source # (-) :: CDev -> CDev -> CDev Source # (*) :: CDev -> CDev -> CDev Source # negate :: CDev -> CDev Source # abs :: CDev -> CDev Source # signum :: CDev -> CDev Source # fromInteger :: Integer -> CDev Source #
Num CFsBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # (-) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # (*) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # negate :: CFsBlkCnt -> CFsBlkCnt Source # abs :: CFsBlkCnt -> CFsBlkCnt Source # signum :: CFsBlkCnt -> CFsBlkCnt Source # fromInteger :: Integer -> CFsBlkCnt Source #
Num CFsFilCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # (-) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # (*) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # negate :: CFsFilCnt -> CFsFilCnt Source # abs :: CFsFilCnt -> CFsFilCnt Source # signum :: CFsFilCnt -> CFsFilCnt Source # fromInteger :: Integer -> CFsFilCnt Source #
Num CGid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CGid -> CGid -> CGid Source # (-) :: CGid -> CGid -> CGid Source # (*) :: CGid -> CGid -> CGid Source # negate :: CGid -> CGid Source # abs :: CGid -> CGid Source # signum :: CGid -> CGid Source # fromInteger :: Integer -> CGid Source #
Num CId
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CId -> CId -> CId Source # (-) :: CId -> CId -> CId Source # (*) :: CId -> CId -> CId Source # negate :: CId -> CId Source # abs :: CId -> CId Source # signum :: CId -> CId Source # fromInteger :: Integer -> CId Source #
Num CIno
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CIno -> CIno -> CIno Source # (-) :: CIno -> CIno -> CIno Source # (*) :: CIno -> CIno -> CIno Source # negate :: CIno -> CIno Source # abs :: CIno -> CIno Source # signum :: CIno -> CIno Source # fromInteger :: Integer -> CIno Source #
Num CKey
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CKey -> CKey -> CKey Source # (-) :: CKey -> CKey -> CKey Source # (*) :: CKey -> CKey -> CKey Source # negate :: CKey -> CKey Source # abs :: CKey -> CKey Source # signum :: CKey -> CKey Source # fromInteger :: Integer -> CKey Source #
Num CMode
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CMode -> CMode -> CMode Source # (-) :: CMode -> CMode -> CMode Source # (*) :: CMode -> CMode -> CMode Source # negate :: CMode -> CMode Source # abs :: CMode -> CMode Source # signum :: CMode -> CMode Source # fromInteger :: Integer -> CMode Source #
Num CNfds
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CNfds -> CNfds -> CNfds Source # (-) :: CNfds -> CNfds -> CNfds Source # (*) :: CNfds -> CNfds -> CNfds Source # negate :: CNfds -> CNfds Source # abs :: CNfds -> CNfds Source # signum :: CNfds -> CNfds Source # fromInteger :: Integer -> CNfds Source #
Num CNlink
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CNlink -> CNlink -> CNlink Source # (-) :: CNlink -> CNlink -> CNlink Source # (*) :: CNlink -> CNlink -> CNlink Source # negate :: CNlink -> CNlink Source # abs :: CNlink -> CNlink Source # signum :: CNlink -> CNlink Source # fromInteger :: Integer -> CNlink Source #
Num COff
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: COff -> COff -> COff Source # (-) :: COff -> COff -> COff Source # (*) :: COff -> COff -> COff Source # negate :: COff -> COff Source # abs :: COff -> COff Source # signum :: COff -> COff Source # fromInteger :: Integer -> COff Source #
Num CPid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CPid -> CPid -> CPid Source # (-) :: CPid -> CPid -> CPid Source # (*) :: CPid -> CPid -> CPid Source # negate :: CPid -> CPid Source # abs :: CPid -> CPid Source # signum :: CPid -> CPid Source # fromInteger :: Integer -> CPid Source #
Num CRLim
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CRLim -> CRLim -> CRLim Source # (-) :: CRLim -> CRLim -> CRLim Source # (*) :: CRLim -> CRLim -> CRLim Source # negate :: CRLim -> CRLim Source # abs :: CRLim -> CRLim Source # signum :: CRLim -> CRLim Source # fromInteger :: Integer -> CRLim Source #
Num CSocklen
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CSocklen -> CSocklen -> CSocklen Source # (-) :: CSocklen -> CSocklen -> CSocklen Source # (*) :: CSocklen -> CSocklen -> CSocklen Source # negate :: CSocklen -> CSocklen Source # abs :: CSocklen -> CSocklen Source # signum :: CSocklen -> CSocklen Source # fromInteger :: Integer -> CSocklen Source #
Num CSpeed
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CSpeed -> CSpeed -> CSpeed Source # (-) :: CSpeed -> CSpeed -> CSpeed Source # (*) :: CSpeed -> CSpeed -> CSpeed Source # negate :: CSpeed -> CSpeed Source # abs :: CSpeed -> CSpeed Source # signum :: CSpeed -> CSpeed Source # fromInteger :: Integer -> CSpeed Source #
Num CSsize
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CSsize -> CSsize -> CSsize Source # (-) :: CSsize -> CSsize -> CSsize Source # (*) :: CSsize -> CSsize -> CSsize Source # negate :: CSsize -> CSsize Source # abs :: CSsize -> CSsize Source # signum :: CSsize -> CSsize Source # fromInteger :: Integer -> CSsize Source #
Num CTcflag
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CTcflag -> CTcflag -> CTcflag Source # (-) :: CTcflag -> CTcflag -> CTcflag Source # (*) :: CTcflag -> CTcflag -> CTcflag Source # negate :: CTcflag -> CTcflag Source # abs :: CTcflag -> CTcflag Source # signum :: CTcflag -> CTcflag Source # fromInteger :: Integer -> CTcflag Source #
Num CUid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: CUid -> CUid -> CUid Source # (-) :: CUid -> CUid -> CUid Source # (*) :: CUid -> CUid -> CUid Source # negate :: CUid -> CUid Source # abs :: CUid -> CUid Source # signum :: CUid -> CUid Source # fromInteger :: Integer -> CUid Source #
Num Fd
Instance details Defined in GHC.Internal.System.Posix.Types Methods (+) :: Fd -> Fd -> Fd Source # (-) :: Fd -> Fd -> Fd Source # (*) :: Fd -> Fd -> Fd Source # negate :: Fd -> Fd Source # abs :: Fd -> Fd Source # signum :: Fd -> Fd Source # fromInteger :: Integer -> Fd Source #
Num Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word16 -> Word16 -> Word16 Source # (-) :: Word16 -> Word16 -> Word16 Source # (*) :: Word16 -> Word16 -> Word16 Source # negate :: Word16 -> Word16 Source # abs :: Word16 -> Word16 Source # signum :: Word16 -> Word16 Source # fromInteger :: Integer -> Word16 Source #
Num Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word32 -> Word32 -> Word32 Source # (-) :: Word32 -> Word32 -> Word32 Source # (*) :: Word32 -> Word32 -> Word32 Source # negate :: Word32 -> Word32 Source # abs :: Word32 -> Word32 Source # signum :: Word32 -> Word32 Source # fromInteger :: Integer -> Word32 Source #
Num Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word64 -> Word64 -> Word64 Source # (-) :: Word64 -> Word64 -> Word64 Source # (*) :: Word64 -> Word64 -> Word64 Source # negate :: Word64 -> Word64 Source # abs :: Word64 -> Word64 Source # signum :: Word64 -> Word64 Source # fromInteger :: Integer -> Word64 Source #
Num Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word8 -> Word8 -> Word8 Source # (-) :: Word8 -> Word8 -> Word8 Source # (*) :: Word8 -> Word8 -> Word8 Source # negate :: Word8 -> Word8 Source # abs :: Word8 -> Word8 Source # signum :: Word8 -> Word8 Source # fromInteger :: Integer -> Word8 Source #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Internal.Num Methods (+) :: Integer -> Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source # (*) :: Integer -> Integer -> Integer Source # negate :: Integer -> Integer Source # abs :: Integer -> Integer Source # signum :: Integer -> Integer Source # fromInteger :: Integer -> Integer Source #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Num Methods (+) :: Natural -> Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source # (*) :: Natural -> Natural -> Natural Source # negate :: Natural -> Natural Source # abs :: Natural -> Natural Source # signum :: Natural -> Natural Source # fromInteger :: Integer -> Natural Source #
Num Double	This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive: `>>>` `(0.1 + 0.1) + 0.4 == 0.1 + (0.1 + 0.4)`False `>>>` *`(0.1 + 0.2) 0.3 == 0.1 * 0.3 + 0.2 * 0.3`False `>>>` `(0.1 * 0.1) * 0.3 == 0.1 * (0.1 * 0.3)`*False Since: base-2.1*
Instance details Defined in GHC.Internal.Float Methods (+) :: Double -> Double -> Double Source # (-) :: Double -> Double -> Double Source # (*) :: Double -> Double -> Double Source # negate :: Double -> Double Source # abs :: Double -> Double Source # signum :: Double -> Double Source # fromInteger :: Integer -> Double Source #
Num Float	This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive: `>>>` `(0.1 + 0.1 :: Float) + 0.5 == 0.1 + (0.1 + 0.5)`False `>>>` *`(0.1 + 0.2 :: Float) 0.9 == 0.1 * 0.9 + 0.2 * 0.9`False `>>>` `(0.1 * 0.1 :: Float) * 0.9 == 0.1 * (0.1 * 0.9)`*False Since: base-2.1*
Instance details Defined in GHC.Internal.Float Methods (+) :: Float -> Float -> Float Source # (-) :: Float -> Float -> Float Source # (*) :: Float -> Float -> Float Source # negate :: Float -> Float Source # abs :: Float -> Float Source # signum :: Float -> Float Source # fromInteger :: Integer -> Float Source #
Num Int	Since: base-2.1
Instance details Defined in GHC.Internal.Num Methods (+) :: Int -> Int -> Int Source # (-) :: Int -> Int -> Int Source # (*) :: Int -> Int -> Int Source # negate :: Int -> Int Source # abs :: Int -> Int Source # signum :: Int -> Int Source # fromInteger :: Integer -> Int Source #
Num Word	Since: base-2.1
Instance details Defined in GHC.Internal.Num Methods (+) :: Word -> Word -> Word Source # (-) :: Word -> Word -> Word Source # (*) :: Word -> Word -> Word Source # negate :: Word -> Word Source # abs :: Word -> Word Source # signum :: Word -> Word Source # fromInteger :: Integer -> Word Source #
RealFloat a => Num (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a Source # (-) :: Complex a -> Complex a -> Complex a Source # (*) :: Complex a -> Complex a -> Complex a Source # negate :: Complex a -> Complex a Source # abs :: Complex a -> Complex a Source # signum :: Complex a -> Complex a Source # fromInteger :: Integer -> Complex a Source #
Num a => Num (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Max a -> Max a -> Max a Source # (-) :: Max a -> Max a -> Max a Source # (*) :: Max a -> Max a -> Max a Source # negate :: Max a -> Max a Source # abs :: Max a -> Max a Source # signum :: Max a -> Max a Source # fromInteger :: Integer -> Max a Source #
Num a => Num (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Min a -> Min a -> Min a Source # (-) :: Min a -> Min a -> Min a Source # (*) :: Min a -> Min a -> Min a Source # negate :: Min a -> Min a Source # abs :: Min a -> Min a Source # signum :: Min a -> Min a Source # fromInteger :: Integer -> Min a Source #
Num a => Num (Identity a)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a Source # (-) :: Identity a -> Identity a -> Identity a Source # (*) :: Identity a -> Identity a -> Identity a Source # negate :: Identity a -> Identity a Source # abs :: Identity a -> Identity a Source # signum :: Identity a -> Identity a Source # fromInteger :: Integer -> Identity a Source #
Num a => Num (Down a)	Since: base-4.11.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods (+) :: Down a -> Down a -> Down a Source # (-) :: Down a -> Down a -> Down a Source # (*) :: Down a -> Down a -> Down a Source # negate :: Down a -> Down a Source # abs :: Down a -> Down a Source # signum :: Down a -> Down a Source # fromInteger :: Integer -> Down a Source #
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source #
Num a => Num (Sum a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a Source # (-) :: Sum a -> Sum a -> Sum a Source # (*) :: Sum a -> Sum a -> Sum a Source # negate :: Sum a -> Sum a Source # abs :: Sum a -> Sum a Source # signum :: Sum a -> Sum a Source # fromInteger :: Integer -> Sum a Source #
Integral a => Num (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Internal.Real Methods (+) :: Ratio a -> Ratio a -> Ratio a Source # (-) :: Ratio a -> Ratio a -> Ratio a Source # (*) :: Ratio a -> Ratio a -> Ratio a Source # negate :: Ratio a -> Ratio a Source # abs :: Ratio a -> Ratio a Source # signum :: Ratio a -> Ratio a Source # fromInteger :: Integer -> Ratio a Source #
HasResolution a => Num (Fixed a)	Multiplication is not associative or distributive: `>>>` *`(0.2 0.6 :: Deci) * 0.9 == 0.2 * (0.6 * 0.9)`False `>>>` `(0.1 + 0.1 :: Deci) * 0.5 == 0.1 * 0.5 + 0.1 * 0.5`*False Since: base-2.1*
Instance details Defined in Data.Fixed Methods (+) :: Fixed a -> Fixed a -> Fixed a Source # (-) :: Fixed a -> Fixed a -> Fixed a Source # (*) :: Fixed a -> Fixed a -> Fixed a Source # negate :: Fixed a -> Fixed a Source # abs :: Fixed a -> Fixed a Source # signum :: Fixed a -> Fixed a Source # fromInteger :: Integer -> Fixed a Source #
Num a => Num (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods (+) :: Op a b -> Op a b -> Op a b Source # (-) :: Op a b -> Op a b -> Op a b Source # (*) :: Op a b -> Op a b -> Op a b Source # negate :: Op a b -> Op a b Source # abs :: Op a b -> Op a b Source # signum :: Op a b -> Op a b Source # fromInteger :: Integer -> Op a b Source #
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b Source # (-) :: Const a b -> Const a b -> Const a b Source # (*) :: Const a b -> Const a b -> Const a b Source # negate :: Const a b -> Const a b Source # abs :: Const a b -> Const a b Source # signum :: Const a b -> Const a b Source # fromInteger :: Integer -> Const a b Source #
(Applicative f, Num a) => Num (Ap f a)	Note that even if the underlying `Num` and `Applicative` instances are lawful, for most `Applicative`s, this instance will not be lawful. If you use this instance with the list `Applicative`, the following customary laws will not hold: Commutativity: `>>>` `Ap [10,20] + Ap [1,2]`Ap {getAp = [11,12,21,22]} `>>>` `Ap [1,2] + Ap [10,20]`Ap {getAp = [11,21,12,22]} Additive inverse: `>>>` `Ap [] + negate (Ap [])`Ap {getAp = []} `>>>` `fromInteger 0 :: Ap [] Int`Ap {getAp = [0]} Distributivity: `>>>` *`Ap [1,2] (3 + 4)`Ap {getAp = [7,14]} `>>>` `(Ap [1,2] * 3) + (Ap [1,2] * 4)`*Ap {getAp = [7,11,10,14]} Since: base-4.12.0.0*
Instance details Defined in GHC.Internal.Data.Monoid Methods (+) :: Ap f a -> Ap f a -> Ap f a Source # (-) :: Ap f a -> Ap f a -> Ap f a Source # (*) :: Ap f a -> Ap f a -> Ap f a Source # negate :: Ap f a -> Ap f a Source # abs :: Ap f a -> Ap f a Source # signum :: Ap f a -> Ap f a Source # fromInteger :: Integer -> Ap f a Source #
Num (f a) => Num (Alt f a)	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a Source # (-) :: Alt f a -> Alt f a -> Alt f a Source # (*) :: Alt f a -> Alt f a -> Alt f a Source # negate :: Alt f a -> Alt f a Source # abs :: Alt f a -> Alt f a Source # signum :: Alt f a -> Alt f a Source # fromInteger :: Integer -> Alt f a Source #
Num (f (g a)) => Num (Compose f g a)	Since: base-4.19.0.0
Instance details Defined in Data.Functor.Compose Methods (+) :: Compose f g a -> Compose f g a -> Compose f g a Source # (-) :: Compose f g a -> Compose f g a -> Compose f g a Source # (*) :: Compose f g a -> Compose f g a -> Compose f g a Source # negate :: Compose f g a -> Compose f g a Source # abs :: Compose f g a -> Compose f g a Source # signum :: Compose f g a -> Compose f g a Source # fromInteger :: Integer -> Compose f g a Source #

class Num a => Fractional a where Source #

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, (+) and (*) are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse: x * recip x = recip x * x = fromInteger 1
Totality of toRational: toRational is total
Coherence with toRational: if the type also implements Real, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Minimal complete definition

fromRational, (recip | (/))

Methods

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

Fractional division.

recip :: a -> a Source #

Reciprocal fraction.

fromRational :: Rational -> a Source #

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances

Instances details

Fractional Double	This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. `>>>` `0 == (-0 :: Double)`True `>>>` `recip 0 == recip (-0 :: Double)`False `>>>` `map (/ 0) [-1, 0, 1]`[-Infinity,NaN,Infinity] `>>>` *`map ( 0) $ map (/ 0) [-1, 0, 1]`*[NaN,NaN,NaN] Since: base-2.1*
Instance details Defined in GHC.Internal.Float Methods (/) :: Double -> Double -> Double Source # recip :: Double -> Double Source # fromRational :: Rational -> Double Source #
Fractional Float	This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. `>>>` `0 == (-0 :: Float)`True `>>>` `recip 0 == recip (-0 :: Float)`False `>>>` `map (/ 0) [-1, 0, 1 :: Float]`[-Infinity,NaN,Infinity] `>>>` *`map ( 0) $ map (/ 0) [-1, 0, 1 :: Float]`*[NaN,NaN,NaN] Since: base-2.1*
Instance details Defined in GHC.Internal.Float Methods (/) :: Float -> Float -> Float Source # recip :: Float -> Float Source # fromRational :: Rational -> Float Source #
RealFloat a => Fractional (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (/) :: Complex a -> Complex a -> Complex a Source # recip :: Complex a -> Complex a Source # fromRational :: Rational -> Complex a Source #
Fractional a => Fractional (Identity a)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods (/) :: Identity a -> Identity a -> Identity a Source # recip :: Identity a -> Identity a Source # fromRational :: Rational -> Identity a Source #
Fractional a => Fractional (Down a)	Since: base-4.14.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods (/) :: Down a -> Down a -> Down a Source # recip :: Down a -> Down a Source # fromRational :: Rational -> Down a Source #
Integral a => Fractional (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Internal.Real Methods (/) :: Ratio a -> Ratio a -> Ratio a Source # recip :: Ratio a -> Ratio a Source # fromRational :: Rational -> Ratio a Source #
HasResolution a => Fractional (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (/) :: Fixed a -> Fixed a -> Fixed a Source # recip :: Fixed a -> Fixed a Source # fromRational :: Rational -> Fixed a Source #
Fractional a => Fractional (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods (/) :: Op a b -> Op a b -> Op a b Source # recip :: Op a b -> Op a b Source # fromRational :: Rational -> Op a b Source #
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b Source # recip :: Const a b -> Const a b Source # fromRational :: Rational -> Const a b Source #
Fractional (f (g a)) => Fractional (Compose f g a)	Since: base-4.20.0.0
Instance details Defined in Data.Functor.Compose Methods (/) :: Compose f g a -> Compose f g a -> Compose f g a Source # recip :: Compose f g a -> Compose f g a Source # fromRational :: Rational -> Compose f g a Source #

class Enum a where Source #

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

The calls succ maxBound and pred minBound should result in a runtime error.
fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error.
enumFrom and enumFromThen should be defined with an implicit bound, thus:

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

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a Source #

Successor of a value. For numeric types, succ adds 1.

pred :: a -> a Source #

Predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a Source #

Convert from an Int.

fromEnum :: a -> Int Source #

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] Source #

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

Examples

Expand

```
enumFrom 4 :: [Integer] = [4,5,6,7,...]
```

enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

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

Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and

  f n y
    | n > 0 = f (n - 1) (succ y)
    | n < 0 = f (n + 1) (pred y)
    | otherwise = y

Examples

Expand

enumFromThen 4 6 :: [Integer] = [4,6,8,10...]

enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

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

Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being

  enumFromTo n m
     | n <= m = n : enumFromTo (succ n) m
     | otherwise = []

Examples

Expand

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

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

Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)

  f n y
     | n > 0 = f (n - 1) (succ y)
     | n < 0 = f (n + 1) (pred y)
     | otherwise = y

and

  worker s c v m
     | c v m = v : worker s c (s v) m
     | otherwise = []

Examples

Expand

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

```
enumFromThenTo 6 8 2 :: [Int] = []
```

Instances

Instances details

Enum IntPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods succ :: IntPtr -> IntPtr Source # pred :: IntPtr -> IntPtr Source # toEnum :: Int -> IntPtr Source # fromEnum :: IntPtr -> Int Source # enumFrom :: IntPtr -> [IntPtr] Source # enumFromThen :: IntPtr -> IntPtr -> [IntPtr] Source # enumFromTo :: IntPtr -> IntPtr -> [IntPtr] Source # enumFromThenTo :: IntPtr -> IntPtr -> IntPtr -> [IntPtr] Source #
Enum WordPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods succ :: WordPtr -> WordPtr Source # pred :: WordPtr -> WordPtr Source # toEnum :: Int -> WordPtr Source # fromEnum :: WordPtr -> Int Source # enumFrom :: WordPtr -> [WordPtr] Source # enumFromThen :: WordPtr -> WordPtr -> [WordPtr] Source # enumFromTo :: WordPtr -> WordPtr -> [WordPtr] Source # enumFromThenTo :: WordPtr -> WordPtr -> WordPtr -> [WordPtr] Source #
Enum Associativity	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods succ :: Associativity -> Associativity Source # pred :: Associativity -> Associativity Source # toEnum :: Int -> Associativity Source # fromEnum :: Associativity -> Int Source # enumFrom :: Associativity -> [Associativity] Source # enumFromThen :: Associativity -> Associativity -> [Associativity] Source # enumFromTo :: Associativity -> Associativity -> [Associativity] Source # enumFromThenTo :: Associativity -> Associativity -> Associativity -> [Associativity] Source #
Enum DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods succ :: DecidedStrictness -> DecidedStrictness Source # pred :: DecidedStrictness -> DecidedStrictness Source # toEnum :: Int -> DecidedStrictness Source # fromEnum :: DecidedStrictness -> Int Source # enumFrom :: DecidedStrictness -> [DecidedStrictness] Source # enumFromThen :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] Source # enumFromTo :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] Source # enumFromThenTo :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] Source #
Enum SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods succ :: SourceStrictness -> SourceStrictness Source # pred :: SourceStrictness -> SourceStrictness Source # toEnum :: Int -> SourceStrictness Source # fromEnum :: SourceStrictness -> Int Source # enumFrom :: SourceStrictness -> [SourceStrictness] Source # enumFromThen :: SourceStrictness -> SourceStrictness -> [SourceStrictness] Source # enumFromTo :: SourceStrictness -> SourceStrictness -> [SourceStrictness] Source # enumFromThenTo :: SourceStrictness -> SourceStrictness -> SourceStrictness -> [SourceStrictness] Source #
Enum SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods succ :: SourceUnpackedness -> SourceUnpackedness Source # pred :: SourceUnpackedness -> SourceUnpackedness Source # toEnum :: Int -> SourceUnpackedness Source # fromEnum :: SourceUnpackedness -> Int Source # enumFrom :: SourceUnpackedness -> [SourceUnpackedness] Source # enumFromThen :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] Source # enumFromTo :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] Source # enumFromThenTo :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] Source #
Enum SeekMode	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Device Methods succ :: SeekMode -> SeekMode Source # pred :: SeekMode -> SeekMode Source # toEnum :: Int -> SeekMode Source # fromEnum :: SeekMode -> Int Source # enumFrom :: SeekMode -> [SeekMode] Source # enumFromThen :: SeekMode -> SeekMode -> [SeekMode] Source # enumFromTo :: SeekMode -> SeekMode -> [SeekMode] Source # enumFromThenTo :: SeekMode -> SeekMode -> SeekMode -> [SeekMode] Source #
Enum IOMode	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.IOMode Methods succ :: IOMode -> IOMode Source # pred :: IOMode -> IOMode Source # toEnum :: Int -> IOMode Source # fromEnum :: IOMode -> Int Source # enumFrom :: IOMode -> [IOMode] Source # enumFromThen :: IOMode -> IOMode -> [IOMode] Source # enumFromTo :: IOMode -> IOMode -> [IOMode] Source # enumFromThenTo :: IOMode -> IOMode -> IOMode -> [IOMode] Source #
Enum Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int16 -> Int16 Source # pred :: Int16 -> Int16 Source # toEnum :: Int -> Int16 Source # fromEnum :: Int16 -> Int Source # enumFrom :: Int16 -> [Int16] Source # enumFromThen :: Int16 -> Int16 -> [Int16] Source # enumFromTo :: Int16 -> Int16 -> [Int16] Source # enumFromThenTo :: Int16 -> Int16 -> Int16 -> [Int16] Source #
Enum Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int32 -> Int32 Source # pred :: Int32 -> Int32 Source # toEnum :: Int -> Int32 Source # fromEnum :: Int32 -> Int Source # enumFrom :: Int32 -> [Int32] Source # enumFromThen :: Int32 -> Int32 -> [Int32] Source # enumFromTo :: Int32 -> Int32 -> [Int32] Source # enumFromThenTo :: Int32 -> Int32 -> Int32 -> [Int32] Source #
Enum Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int64 -> Int64 Source # pred :: Int64 -> Int64 Source # toEnum :: Int -> Int64 Source # fromEnum :: Int64 -> Int Source # enumFrom :: Int64 -> [Int64] Source # enumFromThen :: Int64 -> Int64 -> [Int64] Source # enumFromTo :: Int64 -> Int64 -> [Int64] Source # enumFromThenTo :: Int64 -> Int64 -> Int64 -> [Int64] Source #
Enum Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int8 -> Int8 Source # pred :: Int8 -> Int8 Source # toEnum :: Int -> Int8 Source # fromEnum :: Int8 -> Int Source # enumFrom :: Int8 -> [Int8] Source # enumFromThen :: Int8 -> Int8 -> [Int8] Source # enumFromTo :: Int8 -> Int8 -> [Int8] Source # enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] Source #
Enum CBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CBlkCnt -> CBlkCnt Source # pred :: CBlkCnt -> CBlkCnt Source # toEnum :: Int -> CBlkCnt Source # fromEnum :: CBlkCnt -> Int Source # enumFrom :: CBlkCnt -> [CBlkCnt] Source # enumFromThen :: CBlkCnt -> CBlkCnt -> [CBlkCnt] Source # enumFromTo :: CBlkCnt -> CBlkCnt -> [CBlkCnt] Source # enumFromThenTo :: CBlkCnt -> CBlkCnt -> CBlkCnt -> [CBlkCnt] Source #
Enum CBlkSize
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CBlkSize -> CBlkSize Source # pred :: CBlkSize -> CBlkSize Source # toEnum :: Int -> CBlkSize Source # fromEnum :: CBlkSize -> Int Source # enumFrom :: CBlkSize -> [CBlkSize] Source # enumFromThen :: CBlkSize -> CBlkSize -> [CBlkSize] Source # enumFromTo :: CBlkSize -> CBlkSize -> [CBlkSize] Source # enumFromThenTo :: CBlkSize -> CBlkSize -> CBlkSize -> [CBlkSize] Source #
Enum CCc
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CCc -> CCc Source # pred :: CCc -> CCc Source # toEnum :: Int -> CCc Source # fromEnum :: CCc -> Int Source # enumFrom :: CCc -> [CCc] Source # enumFromThen :: CCc -> CCc -> [CCc] Source # enumFromTo :: CCc -> CCc -> [CCc] Source # enumFromThenTo :: CCc -> CCc -> CCc -> [CCc] Source #
Enum CClockId
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CClockId -> CClockId Source # pred :: CClockId -> CClockId Source # toEnum :: Int -> CClockId Source # fromEnum :: CClockId -> Int Source # enumFrom :: CClockId -> [CClockId] Source # enumFromThen :: CClockId -> CClockId -> [CClockId] Source # enumFromTo :: CClockId -> CClockId -> [CClockId] Source # enumFromThenTo :: CClockId -> CClockId -> CClockId -> [CClockId] Source #
Enum CDev
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CDev -> CDev Source # pred :: CDev -> CDev Source # toEnum :: Int -> CDev Source # fromEnum :: CDev -> Int Source # enumFrom :: CDev -> [CDev] Source # enumFromThen :: CDev -> CDev -> [CDev] Source # enumFromTo :: CDev -> CDev -> [CDev] Source # enumFromThenTo :: CDev -> CDev -> CDev -> [CDev] Source #
Enum CFsBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CFsBlkCnt -> CFsBlkCnt Source # pred :: CFsBlkCnt -> CFsBlkCnt Source # toEnum :: Int -> CFsBlkCnt Source # fromEnum :: CFsBlkCnt -> Int Source # enumFrom :: CFsBlkCnt -> [CFsBlkCnt] Source # enumFromThen :: CFsBlkCnt -> CFsBlkCnt -> [CFsBlkCnt] Source # enumFromTo :: CFsBlkCnt -> CFsBlkCnt -> [CFsBlkCnt] Source # enumFromThenTo :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt -> [CFsBlkCnt] Source #
Enum CFsFilCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CFsFilCnt -> CFsFilCnt Source # pred :: CFsFilCnt -> CFsFilCnt Source # toEnum :: Int -> CFsFilCnt Source # fromEnum :: CFsFilCnt -> Int Source # enumFrom :: CFsFilCnt -> [CFsFilCnt] Source # enumFromThen :: CFsFilCnt -> CFsFilCnt -> [CFsFilCnt] Source # enumFromTo :: CFsFilCnt -> CFsFilCnt -> [CFsFilCnt] Source # enumFromThenTo :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt -> [CFsFilCnt] Source #
Enum CGid
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CGid -> CGid Source # pred :: CGid -> CGid Source # toEnum :: Int -> CGid Source # fromEnum :: CGid -> Int Source # enumFrom :: CGid -> [CGid] Source # enumFromThen :: CGid -> CGid -> [CGid] Source # enumFromTo :: CGid -> CGid -> [CGid] Source # enumFromThenTo :: CGid -> CGid -> CGid -> [CGid] Source #
Enum CId
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CId -> CId Source # pred :: CId -> CId Source # toEnum :: Int -> CId Source # fromEnum :: CId -> Int Source # enumFrom :: CId -> [CId] Source # enumFromThen :: CId -> CId -> [CId] Source # enumFromTo :: CId -> CId -> [CId] Source # enumFromThenTo :: CId -> CId -> CId -> [CId] Source #
Enum CIno
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CIno -> CIno Source # pred :: CIno -> CIno Source # toEnum :: Int -> CIno Source # fromEnum :: CIno -> Int Source # enumFrom :: CIno -> [CIno] Source # enumFromThen :: CIno -> CIno -> [CIno] Source # enumFromTo :: CIno -> CIno -> [CIno] Source # enumFromThenTo :: CIno -> CIno -> CIno -> [CIno] Source #
Enum CKey
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CKey -> CKey Source # pred :: CKey -> CKey Source # toEnum :: Int -> CKey Source # fromEnum :: CKey -> Int Source # enumFrom :: CKey -> [CKey] Source # enumFromThen :: CKey -> CKey -> [CKey] Source # enumFromTo :: CKey -> CKey -> [CKey] Source # enumFromThenTo :: CKey -> CKey -> CKey -> [CKey] Source #
Enum CMode
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CMode -> CMode Source # pred :: CMode -> CMode Source # toEnum :: Int -> CMode Source # fromEnum :: CMode -> Int Source # enumFrom :: CMode -> [CMode] Source # enumFromThen :: CMode -> CMode -> [CMode] Source # enumFromTo :: CMode -> CMode -> [CMode] Source # enumFromThenTo :: CMode -> CMode -> CMode -> [CMode] Source #
Enum CNfds
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CNfds -> CNfds Source # pred :: CNfds -> CNfds Source # toEnum :: Int -> CNfds Source # fromEnum :: CNfds -> Int Source # enumFrom :: CNfds -> [CNfds] Source # enumFromThen :: CNfds -> CNfds -> [CNfds] Source # enumFromTo :: CNfds -> CNfds -> [CNfds] Source # enumFromThenTo :: CNfds -> CNfds -> CNfds -> [CNfds] Source #
Enum CNlink
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CNlink -> CNlink Source # pred :: CNlink -> CNlink Source # toEnum :: Int -> CNlink Source # fromEnum :: CNlink -> Int Source # enumFrom :: CNlink -> [CNlink] Source # enumFromThen :: CNlink -> CNlink -> [CNlink] Source # enumFromTo :: CNlink -> CNlink -> [CNlink] Source # enumFromThenTo :: CNlink -> CNlink -> CNlink -> [CNlink] Source #
Enum COff
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: COff -> COff Source # pred :: COff -> COff Source # toEnum :: Int -> COff Source # fromEnum :: COff -> Int Source # enumFrom :: COff -> [COff] Source # enumFromThen :: COff -> COff -> [COff] Source # enumFromTo :: COff -> COff -> [COff] Source # enumFromThenTo :: COff -> COff -> COff -> [COff] Source #
Enum CPid
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CPid -> CPid Source # pred :: CPid -> CPid Source # toEnum :: Int -> CPid Source # fromEnum :: CPid -> Int Source # enumFrom :: CPid -> [CPid] Source # enumFromThen :: CPid -> CPid -> [CPid] Source # enumFromTo :: CPid -> CPid -> [CPid] Source # enumFromThenTo :: CPid -> CPid -> CPid -> [CPid] Source #
Enum CRLim
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CRLim -> CRLim Source # pred :: CRLim -> CRLim Source # toEnum :: Int -> CRLim Source # fromEnum :: CRLim -> Int Source # enumFrom :: CRLim -> [CRLim] Source # enumFromThen :: CRLim -> CRLim -> [CRLim] Source # enumFromTo :: CRLim -> CRLim -> [CRLim] Source # enumFromThenTo :: CRLim -> CRLim -> CRLim -> [CRLim] Source #
Enum CSocklen
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CSocklen -> CSocklen Source # pred :: CSocklen -> CSocklen Source # toEnum :: Int -> CSocklen Source # fromEnum :: CSocklen -> Int Source # enumFrom :: CSocklen -> [CSocklen] Source # enumFromThen :: CSocklen -> CSocklen -> [CSocklen] Source # enumFromTo :: CSocklen -> CSocklen -> [CSocklen] Source # enumFromThenTo :: CSocklen -> CSocklen -> CSocklen -> [CSocklen] Source #
Enum CSpeed
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CSpeed -> CSpeed Source # pred :: CSpeed -> CSpeed Source # toEnum :: Int -> CSpeed Source # fromEnum :: CSpeed -> Int Source # enumFrom :: CSpeed -> [CSpeed] Source # enumFromThen :: CSpeed -> CSpeed -> [CSpeed] Source # enumFromTo :: CSpeed -> CSpeed -> [CSpeed] Source # enumFromThenTo :: CSpeed -> CSpeed -> CSpeed -> [CSpeed] Source #
Enum CSsize
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CSsize -> CSsize Source # pred :: CSsize -> CSsize Source # toEnum :: Int -> CSsize Source # fromEnum :: CSsize -> Int Source # enumFrom :: CSsize -> [CSsize] Source # enumFromThen :: CSsize -> CSsize -> [CSsize] Source # enumFromTo :: CSsize -> CSsize -> [CSsize] Source # enumFromThenTo :: CSsize -> CSsize -> CSsize -> [CSsize] Source #
Enum CTcflag
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CTcflag -> CTcflag Source # pred :: CTcflag -> CTcflag Source # toEnum :: Int -> CTcflag Source # fromEnum :: CTcflag -> Int Source # enumFrom :: CTcflag -> [CTcflag] Source # enumFromThen :: CTcflag -> CTcflag -> [CTcflag] Source # enumFromTo :: CTcflag -> CTcflag -> [CTcflag] Source # enumFromThenTo :: CTcflag -> CTcflag -> CTcflag -> [CTcflag] Source #
Enum CUid
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: CUid -> CUid Source # pred :: CUid -> CUid Source # toEnum :: Int -> CUid Source # fromEnum :: CUid -> Int Source # enumFrom :: CUid -> [CUid] Source # enumFromThen :: CUid -> CUid -> [CUid] Source # enumFromTo :: CUid -> CUid -> [CUid] Source # enumFromThenTo :: CUid -> CUid -> CUid -> [CUid] Source #
Enum Fd
Instance details Defined in GHC.Internal.System.Posix.Types Methods succ :: Fd -> Fd Source # pred :: Fd -> Fd Source # toEnum :: Int -> Fd Source # fromEnum :: Fd -> Int Source # enumFrom :: Fd -> [Fd] Source # enumFromThen :: Fd -> Fd -> [Fd] Source # enumFromTo :: Fd -> Fd -> [Fd] Source # enumFromThenTo :: Fd -> Fd -> Fd -> [Fd] Source #
Enum GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Internal.Unicode Methods succ :: GeneralCategory -> GeneralCategory Source # pred :: GeneralCategory -> GeneralCategory Source # toEnum :: Int -> GeneralCategory Source # fromEnum :: GeneralCategory -> Int Source # enumFrom :: GeneralCategory -> [GeneralCategory] Source # enumFromThen :: GeneralCategory -> GeneralCategory -> [GeneralCategory] Source # enumFromTo :: GeneralCategory -> GeneralCategory -> [GeneralCategory] Source # enumFromThenTo :: GeneralCategory -> GeneralCategory -> GeneralCategory -> [GeneralCategory] Source #
Enum Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word16 -> Word16 Source # pred :: Word16 -> Word16 Source # toEnum :: Int -> Word16 Source # fromEnum :: Word16 -> Int Source # enumFrom :: Word16 -> [Word16] Source # enumFromThen :: Word16 -> Word16 -> [Word16] Source # enumFromTo :: Word16 -> Word16 -> [Word16] Source # enumFromThenTo :: Word16 -> Word16 -> Word16 -> [Word16] Source #
Enum Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word32 -> Word32 Source # pred :: Word32 -> Word32 Source # toEnum :: Int -> Word32 Source # fromEnum :: Word32 -> Int Source # enumFrom :: Word32 -> [Word32] Source # enumFromThen :: Word32 -> Word32 -> [Word32] Source # enumFromTo :: Word32 -> Word32 -> [Word32] Source # enumFromThenTo :: Word32 -> Word32 -> Word32 -> [Word32] Source #
Enum Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word64 -> Word64 Source # pred :: Word64 -> Word64 Source # toEnum :: Int -> Word64 Source # fromEnum :: Word64 -> Int Source # enumFrom :: Word64 -> [Word64] Source # enumFromThen :: Word64 -> Word64 -> [Word64] Source # enumFromTo :: Word64 -> Word64 -> [Word64] Source # enumFromThenTo :: Word64 -> Word64 -> Word64 -> [Word64] Source #
Enum Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word8 -> Word8 Source # pred :: Word8 -> Word8 Source # toEnum :: Int -> Word8 Source # fromEnum :: Word8 -> Int Source # enumFrom :: Word8 -> [Word8] Source # enumFromThen :: Word8 -> Word8 -> [Word8] Source # enumFromTo :: Word8 -> Word8 -> [Word8] Source # enumFromThenTo :: Word8 -> Word8 -> Word8 -> [Word8] Source #
Enum Ordering	Since: base-2.1
Instance details Defined in GHC.Internal.Enum Methods succ :: Ordering -> Ordering Source # pred :: Ordering -> Ordering Source # toEnum :: Int -> Ordering Source # fromEnum :: Ordering -> Int Source # enumFrom :: Ordering -> [Ordering] Source # enumFromThen :: Ordering -> Ordering -> [Ordering] Source # enumFromTo :: Ordering -> Ordering -> [Ordering] Source # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] Source #
Enum Integer	Since: base-2.1
Instance details Defined in GHC.Internal.Enum Methods succ :: Integer -> Integer Source # pred :: Integer -> Integer Source # toEnum :: Int -> Integer Source # fromEnum :: Integer -> Int Source # enumFrom :: Integer -> [Integer] Source # enumFromThen :: Integer -> Integer -> [Integer] Source # enumFromTo :: Integer -> Integer -> [Integer] Source # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source #
Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Enum Methods succ :: Natural -> Natural Source # pred :: Natural -> Natural Source # toEnum :: Int -> Natural Source # fromEnum :: Natural -> Int Source # enumFrom :: Natural -> [Natural] Source # enumFromThen :: Natural -> Natural -> [Natural] Source # enumFromTo :: Natural -> Natural -> [Natural] Source # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source #
Enum ()	Since: base-2.1
Instance details Defined in GHC.Internal.Enum Methods succ :: () -> () Source # pred :: () -> () Source # toEnum :: Int -> () Source # fromEnum :: () -> Int Source # enumFrom :: () -> [()] Source # enumFromThen :: () -> () -> [()] Source # enumFromTo :: () -> () -> [()] Source # enumFromThenTo :: () -> () -> () -> [()] Source #
Enum Bool	Since: base-2.1
Instance details Defined in GHC.Internal.Enum Methods succ :: Bool -> Bool Source # pred :: Bool -> Bool Source # toEnum :: Int -> Bool Source # fromEnum :: Bool -> Int Source # enumFrom :: Bool -> [Bool] Source # enumFromThen :: Bool -> Bool -> [Bool] Source # enumFromTo :: Bool -> Bool -> [Bool] Source # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] Source #
Enum Char	Since: base-2.1
Instance details Defined in GHC.Internal.Enum Methods succ :: Char -> Char Source # pred :: Char -> Char Source # toEnum :: Int -> Char Source # fromEnum :: Char -> Int Source # enumFrom :: Char -> [Char] Source # enumFromThen :: Char -> Char -> [Char] Source # enumFromTo :: Char -> Char -> [Char] Source # enumFromThenTo :: Char -> Char -> Char -> [Char] Source #
Enum Double	`fromEnum` just truncates its argument, beware of all sorts of overflows. List generators have extremely peculiar behavior, mandated by Haskell Report 2010: `>>>` `[0..1.5]`[0.0,1.0,2.0] Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods succ :: Double -> Double Source # pred :: Double -> Double Source # toEnum :: Int -> Double Source # fromEnum :: Double -> Int Source # enumFrom :: Double -> [Double] Source # enumFromThen :: Double -> Double -> [Double] Source # enumFromTo :: Double -> Double -> [Double] Source # enumFromThenTo :: Double -> Double -> Double -> [Double] Source #
Enum Float	`fromEnum` just truncates its argument, beware of all sorts of overflows. List generators have extremely peculiar behavior, mandated by Haskell Report 2010: `>>>` `[0..1.5 :: Float]`[0.0,1.0,2.0] Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods succ :: Float -> Float Source # pred :: Float -> Float Source # toEnum :: Int -> Float Source # fromEnum :: Float -> Int Source # enumFrom :: Float -> [Float] Source # enumFromThen :: Float -> Float -> [Float] Source # enumFromTo :: Float -> Float -> [Float] Source # enumFromThenTo :: Float -> Float -> Float -> [Float] Source #
Enum Int	Since: base-2.1
Instance details Defined in GHC.Internal.Enum Methods succ :: Int -> Int Source # pred :: Int -> Int Source # toEnum :: Int -> Int Source # fromEnum :: Int -> Int Source # enumFrom :: Int -> [Int] Source # enumFromThen :: Int -> Int -> [Int] Source # enumFromTo :: Int -> Int -> [Int] Source # enumFromThenTo :: Int -> Int -> Int -> [Int] Source #
Enum Levity	Since: base-4.16.0.0
Instance details Defined in GHC.Internal.Enum Methods succ :: Levity -> Levity Source # pred :: Levity -> Levity Source # toEnum :: Int -> Levity Source # fromEnum :: Levity -> Int Source # enumFrom :: Levity -> [Levity] Source # enumFromThen :: Levity -> Levity -> [Levity] Source # enumFromTo :: Levity -> Levity -> [Levity] Source # enumFromThenTo :: Levity -> Levity -> Levity -> [Levity] Source #
Enum VecCount	Since: base-4.10.0.0
Instance details Defined in GHC.Internal.Enum Methods succ :: VecCount -> VecCount Source # pred :: VecCount -> VecCount Source # toEnum :: Int -> VecCount Source # fromEnum :: VecCount -> Int Source # enumFrom :: VecCount -> [VecCount] Source # enumFromThen :: VecCount -> VecCount -> [VecCount] Source # enumFromTo :: VecCount -> VecCount -> [VecCount] Source # enumFromThenTo :: VecCount -> VecCount -> VecCount -> [VecCount] Source #
Enum VecElem	Since: base-4.10.0.0
Instance details Defined in GHC.Internal.Enum Methods succ :: VecElem -> VecElem Source # pred :: VecElem -> VecElem Source # toEnum :: Int -> VecElem Source # fromEnum :: VecElem -> Int Source # enumFrom :: VecElem -> [VecElem] Source # enumFromThen :: VecElem -> VecElem -> [VecElem] Source # enumFromTo :: VecElem -> VecElem -> [VecElem] Source # enumFromThenTo :: VecElem -> VecElem -> VecElem -> [VecElem] Source #
Enum Word	Since: base-2.1
Instance details Defined in GHC.Internal.Enum Methods succ :: Word -> Word Source # pred :: Word -> Word Source # toEnum :: Int -> Word Source # fromEnum :: Word -> Int Source # enumFrom :: Word -> [Word] Source # enumFromThen :: Word -> Word -> [Word] Source # enumFromTo :: Word -> Word -> [Word] Source # enumFromThenTo :: Word -> Word -> Word -> [Word] Source #
Enum a => Enum (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: First a -> First a Source # pred :: First a -> First a Source # toEnum :: Int -> First a Source # fromEnum :: First a -> Int Source # enumFrom :: First a -> [First a] Source # enumFromThen :: First a -> First a -> [First a] Source # enumFromTo :: First a -> First a -> [First a] Source # enumFromThenTo :: First a -> First a -> First a -> [First a] Source #
Enum a => Enum (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Last a -> Last a Source # pred :: Last a -> Last a Source # toEnum :: Int -> Last a Source # fromEnum :: Last a -> Int Source # enumFrom :: Last a -> [Last a] Source # enumFromThen :: Last a -> Last a -> [Last a] Source # enumFromTo :: Last a -> Last a -> [Last a] Source # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source #
Enum a => Enum (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Max a -> Max a Source # pred :: Max a -> Max a Source # toEnum :: Int -> Max a Source # fromEnum :: Max a -> Int Source # enumFrom :: Max a -> [Max a] Source # enumFromThen :: Max a -> Max a -> [Max a] Source # enumFromTo :: Max a -> Max a -> [Max a] Source # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source #
Enum a => Enum (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Min a -> Min a Source # pred :: Min a -> Min a Source # toEnum :: Int -> Min a Source # fromEnum :: Min a -> Int Source # enumFrom :: Min a -> [Min a] Source # enumFromThen :: Min a -> Min a -> [Min a] Source # enumFromTo :: Min a -> Min a -> [Min a] Source # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source #
Enum a => Enum (WrappedMonoid a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: WrappedMonoid a -> WrappedMonoid a Source # pred :: WrappedMonoid a -> WrappedMonoid a Source # toEnum :: Int -> WrappedMonoid a Source # fromEnum :: WrappedMonoid a -> Int Source # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source #
Enum a => Enum (And a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: And a -> And a Source # pred :: And a -> And a Source # toEnum :: Int -> And a Source # fromEnum :: And a -> Int Source # enumFrom :: And a -> [And a] Source # enumFromThen :: And a -> And a -> [And a] Source # enumFromTo :: And a -> And a -> [And a] Source # enumFromThenTo :: And a -> And a -> And a -> [And a] Source #
Enum a => Enum (Iff a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: Iff a -> Iff a Source # pred :: Iff a -> Iff a Source # toEnum :: Int -> Iff a Source # fromEnum :: Iff a -> Int Source # enumFrom :: Iff a -> [Iff a] Source # enumFromThen :: Iff a -> Iff a -> [Iff a] Source # enumFromTo :: Iff a -> Iff a -> [Iff a] Source # enumFromThenTo :: Iff a -> Iff a -> Iff a -> [Iff a] Source #
Enum a => Enum (Ior a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: Ior a -> Ior a Source # pred :: Ior a -> Ior a Source # toEnum :: Int -> Ior a Source # fromEnum :: Ior a -> Int Source # enumFrom :: Ior a -> [Ior a] Source # enumFromThen :: Ior a -> Ior a -> [Ior a] Source # enumFromTo :: Ior a -> Ior a -> [Ior a] Source # enumFromThenTo :: Ior a -> Ior a -> Ior a -> [Ior a] Source #
Enum a => Enum (Xor a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: Xor a -> Xor a Source # pred :: Xor a -> Xor a Source # toEnum :: Int -> Xor a Source # fromEnum :: Xor a -> Int Source # enumFrom :: Xor a -> [Xor a] Source # enumFromThen :: Xor a -> Xor a -> [Xor a] Source # enumFromTo :: Xor a -> Xor a -> [Xor a] Source # enumFromThenTo :: Xor a -> Xor a -> Xor a -> [Xor a] Source #
Enum a => Enum (Identity a)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods succ :: Identity a -> Identity a Source # pred :: Identity a -> Identity a Source # toEnum :: Int -> Identity a Source # fromEnum :: Identity a -> Int Source # enumFrom :: Identity a -> [Identity a] Source # enumFromThen :: Identity a -> Identity a -> [Identity a] Source # enumFromTo :: Identity a -> Identity a -> [Identity a] Source # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] Source #
(Enum a, Bounded a, Eq a) => Enum (Down a)	Swaps `succ` and `pred` of the underlying type. Since: base-4.18.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods succ :: Down a -> Down a Source # pred :: Down a -> Down a Source # toEnum :: Int -> Down a Source # fromEnum :: Down a -> Int Source # enumFrom :: Down a -> [Down a] Source # enumFromThen :: Down a -> Down a -> [Down a] Source # enumFromTo :: Down a -> Down a -> [Down a] Source # enumFromThenTo :: Down a -> Down a -> Down a -> [Down a] Source #
Integral a => Enum (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Internal.Real Methods succ :: Ratio a -> Ratio a Source # pred :: Ratio a -> Ratio a Source # toEnum :: Int -> Ratio a Source # fromEnum :: Ratio a -> Int Source # enumFrom :: Ratio a -> [Ratio a] Source # enumFromThen :: Ratio a -> Ratio a -> [Ratio a] Source # enumFromTo :: Ratio a -> Ratio a -> [Ratio a] Source # enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] Source #
Enum a => Enum (Solo a)
Instance details Defined in GHC.Internal.Enum Methods succ :: Solo a -> Solo a Source # pred :: Solo a -> Solo a Source # toEnum :: Int -> Solo a Source # fromEnum :: Solo a -> Int Source # enumFrom :: Solo a -> [Solo a] Source # enumFromThen :: Solo a -> Solo a -> [Solo a] Source # enumFromTo :: Solo a -> Solo a -> [Solo a] Source # enumFromThenTo :: Solo a -> Solo a -> Solo a -> [Solo a] Source #
Enum (Fixed a)	Recall that, for numeric types, `succ` and `pred` typically add and subtract `1`, respectively. This is not true in the case of `Fixed`, whose successor and predecessor functions intuitively return the "next" and "previous" values in the enumeration. The results of these functions thus depend on the resolution of the `Fixed` value. For example, when enumerating values of resolution `10^-3` of `type Milli = Fixed E3`, `>>>` `succ (0.000 :: Milli)`0.001 and likewise `>>>` `pred (0.000 :: Milli)`-0.001 In other words, `succ` and `pred` increment and decrement a fixed-precision value by the least amount such that the value's resolution is unchanged. For example, `10^-12` is the smallest (positive) amount that can be added to a value of `type Pico = Fixed E12` without changing its resolution, and so `>>>` `succ (0.000000000000 :: Pico)`0.000000000001 and similarly `>>>` `pred (0.000000000000 :: Pico)`-0.000000000001 This is worth bearing in mind when defining `Fixed` arithmetic sequences. In particular, you may be forgiven for thinking the sequence [1..10] :: [Pico] evaluates to `[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] :: [Pico]`. However, this is not true. On the contrary, similarly to the above implementations of `succ` and `pred`, `enumFromTo :: Pico -> Pico -> [Pico]` has a "step size" of `10^-12`. Hence, the list `[1..10] :: [Pico]` has the form [1.000000000000, 1.00000000001, 1.00000000002, ..., 10.000000000000] and contains `9 * 10^12 + 1` values. Since: base-2.1
Instance details Defined in Data.Fixed Methods succ :: Fixed a -> Fixed a Source # pred :: Fixed a -> Fixed a Source # toEnum :: Int -> Fixed a Source # fromEnum :: Fixed a -> Int Source # enumFrom :: Fixed a -> [Fixed a] Source # enumFromThen :: Fixed a -> Fixed a -> [Fixed a] Source # enumFromTo :: Fixed a -> Fixed a -> [Fixed a] Source # enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] Source #
Enum (Proxy s)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods succ :: Proxy s -> Proxy s Source # pred :: Proxy s -> Proxy s Source # toEnum :: Int -> Proxy s Source # fromEnum :: Proxy s -> Int Source # enumFrom :: Proxy s -> [Proxy s] Source # enumFromThen :: Proxy s -> Proxy s -> [Proxy s] Source # enumFromTo :: Proxy s -> Proxy s -> [Proxy s] Source # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] Source #
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods succ :: Const a b -> Const a b Source # pred :: Const a b -> Const a b Source # toEnum :: Int -> Const a b Source # fromEnum :: Const a b -> Int Source # enumFrom :: Const a b -> [Const a b] Source # enumFromThen :: Const a b -> Const a b -> [Const a b] Source # enumFromTo :: Const a b -> Const a b -> [Const a b] Source # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] Source #
Enum (f a) => Enum (Ap f a)	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods succ :: Ap f a -> Ap f a Source # pred :: Ap f a -> Ap f a Source # toEnum :: Int -> Ap f a Source # fromEnum :: Ap f a -> Int Source # enumFrom :: Ap f a -> [Ap f a] Source # enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source #
Enum (f a) => Enum (Alt f a)	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods succ :: Alt f a -> Alt f a Source # pred :: Alt f a -> Alt f a Source # toEnum :: Int -> Alt f a Source # fromEnum :: Alt f a -> Int Source # enumFrom :: Alt f a -> [Alt f a] Source # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source #
a ~ b => Enum (a :~: b)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Type.Equality Methods succ :: (a :~: b) -> a :~: b Source # pred :: (a :~: b) -> a :~: b Source # toEnum :: Int -> a :~: b Source # fromEnum :: (a :~: b) -> Int Source # enumFrom :: (a :~: b) -> [a :~: b] Source # enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] Source # enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] Source # enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] Source #
a ~~ b => Enum (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in GHC.Internal.Data.Type.Equality Methods succ :: (a :~~: b) -> a :~~: b Source # pred :: (a :~~: b) -> a :~~: b Source # toEnum :: Int -> a :~~: b Source # fromEnum :: (a :~~: b) -> Int Source # enumFrom :: (a :~~: b) -> [a :~~: b] Source # enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source # enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source # enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] Source #
Enum (f (g a)) => Enum (Compose f g a)	Since: base-4.19.0.0
Instance details Defined in Data.Functor.Compose Methods succ :: Compose f g a -> Compose f g a Source # pred :: Compose f g a -> Compose f g a Source # toEnum :: Int -> Compose f g a Source # fromEnum :: Compose f g a -> Int Source # enumFrom :: Compose f g a -> [Compose f g a] Source # enumFromThen :: Compose f g a -> Compose f g a -> [Compose f g a] Source # enumFromTo :: Compose f g a -> Compose f g a -> [Compose f g a] Source # enumFromThenTo :: Compose f g a -> Compose f g a -> Compose f g a -> [Compose f g a] Source #

class Eq a where Source #

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

The Haskell Report defines no laws for Eq. However, instances are encouraged to follow these properties:

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

Minimal complete definition

(==) | (/=)

Methods

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

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

Instances

Instances details

Eq ByteArray	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods (==) :: ByteArray -> ByteArray -> Bool Source # (/=) :: ByteArray -> ByteArray -> Bool Source #
Eq Timeout
Instance details Defined in System.Timeout Methods (==) :: Timeout -> Timeout -> Bool Source # (/=) :: Timeout -> Timeout -> Bool Source #
Eq BigNat
Instance details Defined in GHC.Num.BigNat Methods (==) :: BigNat -> BigNat -> Bool Source # (/=) :: BigNat -> BigNat -> Bool Source #
Eq Void	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Base Methods (==) :: Void -> Void -> Bool Source # (/=) :: Void -> Void -> Bool Source #
Eq BlockReason	Since: base-4.3.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods (==) :: BlockReason -> BlockReason -> Bool Source # (/=) :: BlockReason -> BlockReason -> Bool Source #
Eq ThreadId	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods (==) :: ThreadId -> ThreadId -> Bool Source # (/=) :: ThreadId -> ThreadId -> Bool Source #
Eq ThreadStatus	Since: base-4.3.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods (==) :: ThreadStatus -> ThreadStatus -> Bool Source # (/=) :: ThreadStatus -> ThreadStatus -> Bool Source #
Eq Constr	Equality of constructors Since: base-4.0.0.0
Instance details Defined in GHC.Internal.Data.Data Methods (==) :: Constr -> Constr -> Bool Source # (/=) :: Constr -> Constr -> Bool Source #
Eq ConstrRep	Since: base-4.0.0.0
Instance details Defined in GHC.Internal.Data.Data Methods (==) :: ConstrRep -> ConstrRep -> Bool Source # (/=) :: ConstrRep -> ConstrRep -> Bool Source #
Eq DataRep	Since: base-4.0.0.0
Instance details Defined in GHC.Internal.Data.Data Methods (==) :: DataRep -> DataRep -> Bool Source # (/=) :: DataRep -> DataRep -> Bool Source #
Eq Fixity	Since: base-4.0.0.0
Instance details Defined in GHC.Internal.Data.Data Methods (==) :: Fixity -> Fixity -> Bool Source # (/=) :: Fixity -> Fixity -> Bool Source #
Eq All	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (==) :: All -> All -> Bool Source # (/=) :: All -> All -> Bool Source #
Eq Any	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool Source # (/=) :: Any -> Any -> Bool Source #
Eq SomeTypeRep
Instance details Defined in GHC.Internal.Data.Typeable.Internal Methods (==) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool Source #
Eq Unique
Instance details Defined in GHC.Internal.Data.Unique Methods (==) :: Unique -> Unique -> Bool Source # (/=) :: Unique -> Unique -> Bool Source #
Eq Version	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Version Methods (==) :: Version -> Version -> Bool Source # (/=) :: Version -> Version -> Bool Source #
Eq ErrorCall	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Exception Methods (==) :: ErrorCall -> ErrorCall -> Bool Source # (/=) :: ErrorCall -> ErrorCall -> Bool Source #
Eq ArithException	Since: base-3.0
Instance details Defined in GHC.Internal.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool Source # (/=) :: ArithException -> ArithException -> Bool Source #
Eq SpecConstrAnnotation	Since: base-4.3.0.0
Instance details Defined in GHC.Internal.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source #
Eq IntPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods (==) :: IntPtr -> IntPtr -> Bool Source # (/=) :: IntPtr -> IntPtr -> Bool Source #
Eq WordPtr
Instance details Defined in GHC.Internal.Foreign.Ptr Methods (==) :: WordPtr -> WordPtr -> Bool Source # (/=) :: WordPtr -> WordPtr -> Bool Source #
Eq Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: Associativity -> Associativity -> Bool Source # (/=) :: Associativity -> Associativity -> Bool Source #
Eq DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool Source #
Eq Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: Fixity -> Fixity -> Bool Source # (/=) :: Fixity -> Fixity -> Bool Source #
Eq SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool Source # (/=) :: SourceStrictness -> SourceStrictness -> Bool Source #
Eq SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source #
Eq MaskingState	Since: base-4.3.0.0
Instance details Defined in GHC.Internal.IO Methods (==) :: MaskingState -> MaskingState -> Bool Source # (/=) :: MaskingState -> MaskingState -> Bool Source #
Eq IODeviceType	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Device Methods (==) :: IODeviceType -> IODeviceType -> Bool Source # (/=) :: IODeviceType -> IODeviceType -> Bool Source #
Eq SeekMode	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Device Methods (==) :: SeekMode -> SeekMode -> Bool Source # (/=) :: SeekMode -> SeekMode -> Bool Source #
Eq CodingProgress	Since: base-4.4.0.0
Instance details Defined in GHC.Internal.IO.Encoding.Types Methods (==) :: CodingProgress -> CodingProgress -> Bool Source # (/=) :: CodingProgress -> CodingProgress -> Bool Source #
Eq ArrayException	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool Source # (/=) :: ArrayException -> ArrayException -> Bool Source #
Eq AsyncException	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool Source # (/=) :: AsyncException -> AsyncException -> Bool Source #
Eq ExitCode
Instance details Defined in GHC.Internal.IO.Exception Methods (==) :: ExitCode -> ExitCode -> Bool Source # (/=) :: ExitCode -> ExitCode -> Bool Source #
Eq IOErrorType	Since: base-4.1.0.0
Instance details Defined in GHC.Internal.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool Source # (/=) :: IOErrorType -> IOErrorType -> Bool Source #
Eq IOException	Since: base-4.1.0.0
Instance details Defined in GHC.Internal.IO.Exception Methods (==) :: IOException -> IOException -> Bool Source # (/=) :: IOException -> IOException -> Bool Source #
Eq HandlePosn	Since: base-4.1.0.0
Instance details Defined in GHC.Internal.IO.Handle Methods (==) :: HandlePosn -> HandlePosn -> Bool Source # (/=) :: HandlePosn -> HandlePosn -> Bool Source #
Eq BufferMode	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Handle.Types Methods (==) :: BufferMode -> BufferMode -> Bool Source # (/=) :: BufferMode -> BufferMode -> Bool Source #
Eq Handle	Since: base-4.1.0.0
Instance details Defined in GHC.Internal.IO.Handle.Types Methods (==) :: Handle -> Handle -> Bool Source # (/=) :: Handle -> Handle -> Bool Source #
Eq Newline	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Handle.Types Methods (==) :: Newline -> Newline -> Bool Source # (/=) :: Newline -> Newline -> Bool Source #
Eq NewlineMode	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.Handle.Types Methods (==) :: NewlineMode -> NewlineMode -> Bool Source # (/=) :: NewlineMode -> NewlineMode -> Bool Source #
Eq IOMode	Since: base-4.2.0.0
Instance details Defined in GHC.Internal.IO.IOMode Methods (==) :: IOMode -> IOMode -> Bool Source # (/=) :: IOMode -> IOMode -> Bool Source #
Eq Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int16 -> Int16 -> Bool Source # (/=) :: Int16 -> Int16 -> Bool Source #
Eq Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int32 -> Int32 -> Bool Source # (/=) :: Int32 -> Int32 -> Bool Source #
Eq Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int64 -> Int64 -> Bool Source # (/=) :: Int64 -> Int64 -> Bool Source #
Eq Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int8 -> Int8 -> Bool Source # (/=) :: Int8 -> Int8 -> Bool Source #
Eq SrcLoc	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Stack.Types Methods (==) :: SrcLoc -> SrcLoc -> Bool Source # (/=) :: SrcLoc -> SrcLoc -> Bool Source #
Eq CBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CBlkCnt -> CBlkCnt -> Bool Source # (/=) :: CBlkCnt -> CBlkCnt -> Bool Source #
Eq CBlkSize
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CBlkSize -> CBlkSize -> Bool Source # (/=) :: CBlkSize -> CBlkSize -> Bool Source #
Eq CCc
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CCc -> CCc -> Bool Source # (/=) :: CCc -> CCc -> Bool Source #
Eq CClockId
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CClockId -> CClockId -> Bool Source # (/=) :: CClockId -> CClockId -> Bool Source #
Eq CDev
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CDev -> CDev -> Bool Source # (/=) :: CDev -> CDev -> Bool Source #
Eq CFsBlkCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CFsBlkCnt -> CFsBlkCnt -> Bool Source # (/=) :: CFsBlkCnt -> CFsBlkCnt -> Bool Source #
Eq CFsFilCnt
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CFsFilCnt -> CFsFilCnt -> Bool Source # (/=) :: CFsFilCnt -> CFsFilCnt -> Bool Source #
Eq CGid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CGid -> CGid -> Bool Source # (/=) :: CGid -> CGid -> Bool Source #
Eq CId
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CId -> CId -> Bool Source # (/=) :: CId -> CId -> Bool Source #
Eq CIno
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CIno -> CIno -> Bool Source # (/=) :: CIno -> CIno -> Bool Source #
Eq CKey
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CKey -> CKey -> Bool Source # (/=) :: CKey -> CKey -> Bool Source #
Eq CMode
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CMode -> CMode -> Bool Source # (/=) :: CMode -> CMode -> Bool Source #
Eq CNfds
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CNfds -> CNfds -> Bool Source # (/=) :: CNfds -> CNfds -> Bool Source #
Eq CNlink
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CNlink -> CNlink -> Bool Source # (/=) :: CNlink -> CNlink -> Bool Source #
Eq COff
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: COff -> COff -> Bool Source # (/=) :: COff -> COff -> Bool Source #
Eq CPid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CPid -> CPid -> Bool Source # (/=) :: CPid -> CPid -> Bool Source #
Eq CRLim
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CRLim -> CRLim -> Bool Source # (/=) :: CRLim -> CRLim -> Bool Source #
Eq CSocklen
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CSocklen -> CSocklen -> Bool Source # (/=) :: CSocklen -> CSocklen -> Bool Source #
Eq CSpeed
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CSpeed -> CSpeed -> Bool Source # (/=) :: CSpeed -> CSpeed -> Bool Source #
Eq CSsize
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CSsize -> CSsize -> Bool Source # (/=) :: CSsize -> CSsize -> Bool Source #
Eq CTcflag
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CTcflag -> CTcflag -> Bool Source # (/=) :: CTcflag -> CTcflag -> Bool Source #
Eq CTimer
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CTimer -> CTimer -> Bool Source # (/=) :: CTimer -> CTimer -> Bool Source #
Eq CUid
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: CUid -> CUid -> Bool Source # (/=) :: CUid -> CUid -> Bool Source #
Eq Fd
Instance details Defined in GHC.Internal.System.Posix.Types Methods (==) :: Fd -> Fd -> Bool Source # (/=) :: Fd -> Fd -> Bool Source #
Eq GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Internal.Unicode Methods (==) :: GeneralCategory -> GeneralCategory -> Bool Source # (/=) :: GeneralCategory -> GeneralCategory -> Bool Source #
Eq Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word16 -> Word16 -> Bool Source # (/=) :: Word16 -> Word16 -> Bool Source #
Eq Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word32 -> Word32 -> Bool Source # (/=) :: Word32 -> Word32 -> Bool Source #
Eq Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word64 -> Word64 -> Bool Source # (/=) :: Word64 -> Word64 -> Bool Source #
Eq Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word8 -> Word8 -> Bool Source # (/=) :: Word8 -> Word8 -> Bool Source #
Eq Module
Instance details Defined in GHC.Classes Methods (==) :: Module -> Module -> Bool Source # (/=) :: Module -> Module -> Bool Source #
Eq Ordering
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool Source # (/=) :: Ordering -> Ordering -> Bool Source #
Eq TrName
Instance details Defined in GHC.Classes Methods (==) :: TrName -> TrName -> Bool Source # (/=) :: TrName -> TrName -> Bool Source #
Eq TyCon
Instance details Defined in GHC.Classes Methods (==) :: TyCon -> TyCon -> Bool Source # (/=) :: TyCon -> TyCon -> Bool Source #
Eq Integer
Instance details Defined in GHC.Num.Integer Methods (==) :: Integer -> Integer -> Bool Source # (/=) :: Integer -> Integer -> Bool Source #
Eq Natural
Instance details Defined in GHC.Num.Natural Methods (==) :: Natural -> Natural -> Bool Source # (/=) :: Natural -> Natural -> Bool Source #
Eq ()
Instance details Defined in GHC.Classes Methods (==) :: () -> () -> Bool Source # (/=) :: () -> () -> Bool Source #
Eq Bool
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool Source # (/=) :: Bool -> Bool -> Bool Source #
Eq Char
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool Source # (/=) :: Char -> Char -> Bool Source #
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 Source # (/=) :: Double -> Double -> Bool Source #
Eq Float	Note that due to the presence of `NaN`, `Float`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Float)`False Also note that `Float`'s `Eq` instance does not satisfy extensionality: `>>>` `0 == (-0 :: Float)`True `>>>` `recip 0 == recip (-0 :: Float)`False
Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool Source # (/=) :: Float -> Float -> Bool Source #
Eq Int
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool Source # (/=) :: Int -> Int -> Bool Source #
Eq Word
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool Source # (/=) :: Word -> Word -> Bool Source #
Eq (Chan a)	Since: base-4.4.0.0
Instance details Defined in Control.Concurrent.Chan Methods (==) :: Chan a -> Chan a -> Bool Source # (/=) :: Chan a -> Chan a -> Bool Source #
Eq (MutableByteArray s)	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods (==) :: MutableByteArray s -> MutableByteArray s -> Bool Source # (/=) :: MutableByteArray s -> MutableByteArray s -> Bool Source #
Eq a => Eq (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (==) :: Complex a -> Complex a -> Bool Source # (/=) :: Complex a -> Complex a -> Bool Source #
Eq a => Eq (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: First a -> First a -> Bool Source # (/=) :: First a -> First a -> Bool Source #
Eq a => Eq (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Last a -> Last a -> Bool Source # (/=) :: Last a -> Last a -> Bool Source #
Eq a => Eq (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Max a -> Max a -> Bool Source # (/=) :: Max a -> Max a -> Bool Source #
Eq a => Eq (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Min a -> Min a -> Bool Source # (/=) :: Min a -> Min a -> Bool Source #
Eq m => Eq (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #
Eq a => Eq (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (==) :: NonEmpty a -> NonEmpty a -> Bool Source # (/=) :: NonEmpty a -> NonEmpty a -> Bool Source #
Eq (TVar a)	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods (==) :: TVar a -> TVar a -> Bool Source # (/=) :: TVar a -> TVar a -> Bool Source #
Eq a => Eq (And a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: And a -> And a -> Bool Source # (/=) :: And a -> And a -> Bool Source #
Eq a => Eq (Iff a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: Iff a -> Iff a -> Bool Source # (/=) :: Iff a -> Iff a -> Bool Source #
Eq a => Eq (Ior a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: Ior a -> Ior a -> Bool Source # (/=) :: Ior a -> Ior a -> Bool Source #
Eq a => Eq (Xor a)	Since: base-4.16
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: Xor a -> Xor a -> Bool Source # (/=) :: Xor a -> Xor a -> Bool Source #
Eq a => Eq (Identity a)	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods (==) :: Identity a -> Identity a -> Bool Source # (/=) :: Identity a -> Identity a -> Bool Source #
Eq a => Eq (First a)	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Monoid Methods (==) :: First a -> First a -> Bool Source # (/=) :: First a -> First a -> Bool Source #
Eq a => Eq (Last a)	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Monoid Methods (==) :: Last a -> Last a -> Bool Source # (/=) :: Last a -> Last a -> Bool Source #
Eq a => Eq (Down a)	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods (==) :: Down a -> Down a -> Bool Source # (/=) :: Down a -> Down a -> Bool Source #
Eq a => Eq (Dual a)	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool Source # (/=) :: Dual a -> Dual a -> Bool Source #
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool Source # (/=) :: Product a -> Product a -> Bool Source #
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool Source # (/=) :: Sum a -> Sum a -> Bool Source #
Eq (ForeignPtr a)	Since: base-2.1
Instance details Defined in GHC.Internal.ForeignPtr Methods (==) :: ForeignPtr a -> ForeignPtr a -> Bool Source # (/=) :: ForeignPtr a -> ForeignPtr a -> Bool Source #
Eq a => Eq (ZipList a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Functor.ZipList Methods (==) :: ZipList a -> ZipList a -> Bool Source # (/=) :: ZipList a -> ZipList a -> Bool Source #
Eq p => Eq (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: Par1 p -> Par1 p -> Bool Source # (/=) :: Par1 p -> Par1 p -> Bool Source #
Eq (IORef a)	Pointer equality. Since: base-4.0.0.0
Instance details Defined in GHC.Internal.IORef Methods (==) :: IORef a -> IORef a -> Bool Source # (/=) :: IORef a -> IORef a -> Bool Source #
Eq (MVar a)	Compares the underlying pointers. Since: base-4.1.0.0
Instance details Defined in GHC.Internal.MVar Methods (==) :: MVar a -> MVar a -> Bool Source # (/=) :: MVar a -> MVar a -> Bool Source #
Eq (FunPtr a)
Instance details Defined in GHC.Internal.Ptr Methods (==) :: FunPtr a -> FunPtr a -> Bool Source # (/=) :: FunPtr a -> FunPtr a -> Bool Source #
Eq (Ptr a)	Since: base-2.1
Instance details Defined in GHC.Internal.Ptr Methods (==) :: Ptr a -> Ptr a -> Bool Source # (/=) :: Ptr a -> Ptr a -> Bool Source #
Eq a => Eq (Ratio a)	Since: base-2.1
Instance details Defined in GHC.Internal.Real Methods (==) :: Ratio a -> Ratio a -> Bool Source # (/=) :: Ratio a -> Ratio a -> Bool Source #
Eq (StablePtr a)	Since: base-2.1
Instance details Defined in GHC.Internal.Stable Methods (==) :: StablePtr a -> StablePtr a -> Bool Source # (/=) :: StablePtr a -> StablePtr a -> Bool Source #
Eq (StableName a)	Since: base-2.1
Instance details Defined in GHC.Internal.StableName Methods (==) :: StableName a -> StableName a -> Bool Source # (/=) :: StableName a -> StableName a -> Bool Source #
Eq a => Eq (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Internal.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool Source # (/=) :: Maybe a -> Maybe a -> Bool Source #
Eq a => Eq (Solo a)
Instance details Defined in GHC.Classes Methods (==) :: Solo a -> Solo a -> Bool Source # (/=) :: Solo a -> Solo a -> Bool Source #
Eq a => Eq [a]
Instance details Defined in GHC.Classes Methods (==) :: [a] -> [a] -> Bool Source # (/=) :: [a] -> [a] -> Bool Source #
Eq (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (==) :: Fixed a -> Fixed a -> Bool Source # (/=) :: Fixed a -> Fixed a -> Bool Source #
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 Source # (/=) :: Arg a b -> Arg a b -> Bool Source #
(Eq a, Eq b) => Eq (Either a b)	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Either Methods (==) :: Either a b -> Either a b -> Bool Source # (/=) :: Either a b -> Either a b -> Bool Source #
Eq (Proxy s)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods (==) :: Proxy s -> Proxy s -> Bool Source # (/=) :: Proxy s -> Proxy s -> Bool Source #
Eq (TypeRep a)	Since: base-2.1
Instance details Defined in GHC.Internal.Data.Typeable.Internal Methods (==) :: TypeRep a -> TypeRep a -> Bool Source # (/=) :: TypeRep a -> TypeRep a -> Bool Source #
Eq (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: U1 p -> U1 p -> Bool Source # (/=) :: U1 p -> U1 p -> Bool Source #
Eq (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: V1 p -> V1 p -> Bool Source # (/=) :: V1 p -> V1 p -> Bool Source #
Eq (STRef s a)	Pointer equality. Since: base-2.1
Instance details Defined in GHC.Internal.STRef Methods (==) :: STRef s a -> STRef s a -> Bool Source # (/=) :: STRef s a -> STRef s a -> Bool Source #
(Eq a, Eq b) => Eq (a, b)
Instance details Defined in GHC.Classes Methods (==) :: (a, b) -> (a, b) -> Bool Source # (/=) :: (a, b) -> (a, b) -> Bool Source #
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool Source # (/=) :: Const a b -> Const a b -> Bool Source #
Eq (f a) => Eq (Ap f a)	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (==) :: Ap f a -> Ap f a -> Bool Source # (/=) :: Ap f a -> Ap f a -> Bool Source #
Eq (f a) => Eq (Alt f a)	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (==) :: Alt f a -> Alt f a -> Bool Source # (/=) :: Alt f a -> Alt f a -> Bool Source #
Eq (a :~: b)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Type.Equality Methods (==) :: (a :~: b) -> (a :~: b) -> Bool Source # (/=) :: (a :~: b) -> (a :~: b) -> Bool Source #
(Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a)	Since: base-4.18.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: Generically1 f a -> Generically1 f a -> Bool Source # (/=) :: Generically1 f a -> Generically1 f a -> Bool Source #
Eq (f p) => Eq (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: Rec1 f p -> Rec1 f p -> Bool Source # (/=) :: Rec1 f p -> Rec1 f p -> Bool Source #
Eq (URec (Ptr ()) p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # (/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source #
Eq (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec Char p -> URec Char p -> Bool Source # (/=) :: URec Char p -> URec Char p -> Bool Source #
Eq (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec Double p -> URec Double p -> Bool Source # (/=) :: URec Double p -> URec Double p -> Bool Source #
Eq (URec Float p)
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec Float p -> URec Float p -> Bool Source # (/=) :: URec Float p -> URec Float p -> Bool Source #
Eq (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec Int p -> URec Int p -> Bool Source # (/=) :: URec Int p -> URec Int p -> Bool Source #
Eq (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec Word p -> URec Word p -> Bool Source # (/=) :: URec Word p -> URec Word p -> Bool Source #
(Eq a, Eq b, Eq c) => Eq (a, b, c)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c) -> (a, b, c) -> Bool Source # (/=) :: (a, b, c) -> (a, b, c) -> Bool Source #
(Eq (f a), Eq (g a)) => Eq (Product f g a)	Since: base-4.18.0.0
Instance details Defined in Data.Functor.Product Methods (==) :: Product f g a -> Product f g a -> Bool Source # (/=) :: Product f g a -> Product f g a -> Bool Source #
(Eq (f a), Eq (g a)) => Eq (Sum f g a)	Since: base-4.18.0.0
Instance details Defined in Data.Functor.Sum Methods (==) :: Sum f g a -> Sum f g a -> Bool Source # (/=) :: Sum f g a -> Sum f g a -> Bool Source #
Eq (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in GHC.Internal.Data.Type.Equality Methods (==) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (/=) :: (a :~~: b) -> (a :~~: b) -> Bool Source #
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: (f :: g) p -> (f :: g) p -> Bool Source # (/=) :: (f :: g) p -> (f :: g) p -> Bool Source #
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: (f :+: g) p -> (f :+: g) p -> Bool Source # (/=) :: (f :+: g) p -> (f :+: g) p -> Bool Source #
Eq c => Eq (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: K1 i c p -> K1 i c p -> Bool Source # (/=) :: K1 i c p -> K1 i c p -> Bool Source #
(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 Source # (/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #
Eq (f (g a)) => Eq (Compose f g a)	Since: base-4.18.0.0
Instance details Defined in Data.Functor.Compose Methods (==) :: Compose f g a -> Compose f g a -> Bool Source # (/=) :: Compose f g a -> Compose f g a -> Bool Source #
Eq (f (g p)) => Eq ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: (f :.: g) p -> (f :.: g) p -> Bool Source # (/=) :: (f :.: g) p -> (f :.: g) p -> Bool Source #
Eq (f p) => Eq (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: M1 i c f p -> M1 i c f p -> Bool Source # (/=) :: M1 i c f p -> M1 i c f p -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source #

class Arrow a => ArrowApply (a :: Type -> Type -> Type) where Source #

Some arrows allow application of arrow inputs to other inputs. Instances should satisfy the following laws:

first (arr (\x -> arr (\y -> (x,y)))) >>> app = id

first (arr (g >>>)) >>> app = second g >>> app

```
first (arr (>>> h)) >>> app = app >>> h
```

Such arrows are equivalent to monads (see ArrowMonad).

Methods

app :: a (a b c, b) c Source #

Instances

Instances details

Monad m => ArrowApply (Kleisli m)	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods app :: Kleisli m (Kleisli m b c, b) c Source #
ArrowApply (->)	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods app :: (b -> c, b) -> c Source #

class Arrow a => ArrowChoice (a :: Type -> Type -> Type) where Source #

Choice, for arrows that support it. This class underlies the if and case constructs in arrow notation.

Instances should satisfy the following laws:

```
left (arr f) = arr (left f)
```
```
left (f >>> g) = left f >>> left g
```
```
f >>> arr Left = arr Left >>> left f
```

left f >>> arr (id +++ g) = arr (id +++ g) >>> left f

left (left f) >>> arr assocsum = arr assocsum >>> left f

where

assocsum (Left (Left x)) = Left x
assocsum (Left (Right y)) = Right (Left y)
assocsum (Right z) = Right (Right z)

The other combinators have sensible default definitions, which may be overridden for efficiency.

Minimal complete definition

(left | (+++))

Methods

left :: a b c -> a (Either b d) (Either c d) Source #

Feed marked inputs through the argument arrow, passing the rest through unchanged to the output.

right :: a b c -> a (Either d b) (Either d c) Source #

A mirror image of left.

The default definition may be overridden with a more efficient version if desired.

(+++) :: a b c -> a b' c' -> a (Either b b') (Either c c') infixr 2 Source #

Split the input between the two argument arrows, retagging and merging their outputs. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

(|||) :: a b d -> a c d -> a (Either b c) d infixr 2 Source #

Fanin: Split the input between the two argument arrows and merge their outputs.

The default definition may be overridden with a more efficient version if desired.

Instances

Instances details

Monad m => ArrowChoice (Kleisli m)	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods left :: Kleisli m b c -> Kleisli m (Either b d) (Either c d) Source # right :: Kleisli m b c -> Kleisli m (Either d b) (Either d c) Source # (+++) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c') Source # (\|\|\|) :: Kleisli m b d -> Kleisli m c d -> Kleisli m (Either b c) d Source #
ArrowChoice (->)	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods left :: (b -> c) -> Either b d -> Either c d Source # right :: (b -> c) -> Either d b -> Either d c Source # (+++) :: (b -> c) -> (b' -> c') -> Either b b' -> Either c c' Source # (\|\|\|) :: (b -> d) -> (c -> d) -> Either b c -> d Source #

class Arrow a => ArrowLoop (a :: Type -> Type -> Type) where Source #

The loop operator expresses computations in which an output value is fed back as input, although the computation occurs only once. It underlies the rec value recursion construct in arrow notation. loop should satisfy the following laws:

extension: loop (arr f) = arr (\ b -> fst (fix (\ (c,d) -> f (b,d))))
left tightening: loop (first h >>> f) = h >>> loop f
right tightening: loop (f >>> first h) = loop f >>> h
sliding: loop (f >>> arr (id *** k)) = loop (arr (id *** k) >>> f)
vanishing: loop (loop f) = loop (arr unassoc >>> f >>> arr assoc)
superposing: second (loop f) = loop (arr assoc >>> second f >>> arr unassoc)

where

assoc ((a,b),c) = (a,(b,c))
unassoc (a,(b,c)) = ((a,b),c)

Methods

loop :: a (b, d) (c, d) -> a b c Source #

Instances

Instances details

MonadFix m => ArrowLoop (Kleisli m)	Beware that for many monads (those for which the `>>=` operation is strict) this instance will not satisfy the right-tightening law required by the `ArrowLoop` class. Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods loop :: Kleisli m (b, d) (c, d) -> Kleisli m b c Source #
ArrowLoop (->)	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Arrow Methods loop :: ((b, d) -> (c, d)) -> b -> c Source #

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

General coercion from Integral types.

WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.

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

General coercion to Fractional types.

WARNING: This function goes through the Rational type, which does not have values for NaN for example. This means it does not round-trip.

For Double it also behaves differently with or without -O0:

Prelude> realToFrac nan -- With -O0
-Infinity
Prelude> realToFrac nan
NaN

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

Integral numbers, supporting integer division.

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

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

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

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

Minimal complete definition

quotRem, toInteger

Methods

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

Integer division truncated toward zero.