prelude-compat-0.0.0.2: Provide Prelude and Data.List with fixed content across GHC versions

Prelude2010

Synopsis

Documentation

($!) :: (a -> b) -> a -> b infixr 0 # Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value. catch :: IO a -> (IOError -> IO a) -> IO a Source # gcd :: Integral a => a -> a -> a # gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.) Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types. ($) :: (a -> b) -> a -> b infixr 0 #

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

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

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

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

(&&) :: Bool -> Bool -> Bool infixr 3 #

Boolean "and"

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

Function composition.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as >>=, but with the arguments interchanged.

data Bool #

Constructors

 False True
Instances
 Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Bool -> Bool #pred :: Bool -> Bool #toEnum :: Int -> Bool #fromEnum :: Bool -> Int #enumFrom :: Bool -> [Bool] #enumFromThen :: Bool -> Bool -> [Bool] #enumFromTo :: Bool -> Bool -> [Bool] #enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] # Instance detailsDefined in GHC.Classes Methods(==) :: Bool -> Bool -> Bool #(/=) :: Bool -> Bool -> Bool # Instance detailsDefined in GHC.Classes Methodscompare :: Bool -> Bool -> Ordering #(<) :: Bool -> Bool -> Bool #(<=) :: Bool -> Bool -> Bool #(>) :: Bool -> Bool -> Bool #(>=) :: Bool -> Bool -> Bool #max :: Bool -> Bool -> Bool #min :: Bool -> Bool -> Bool # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Bool -> ShowS #show :: Bool -> String #showList :: [Bool] -> ShowS #

class Bounded a where #

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Methods

minBound :: a #

maxBound :: a #

Instances
 Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum Methods Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum Methods Bounded () Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: () #maxBound :: () # (Bounded a, Bounded b) => Bounded (a, b) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b) #maxBound :: (a, b) # (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c) #maxBound :: (a, b, c) # (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d) #maxBound :: (a, b, c, d) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e) #maxBound :: (a, b, c, d, e) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f) #maxBound :: (a, b, c, d, e, f) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g) #maxBound :: (a, b, c, d, e, f, g) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h) #maxBound :: (a, b, c, d, e, f, g, h) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i) #maxBound :: (a, b, c, d, e, f, g, h, i) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j) #maxBound :: (a, b, c, d, e, f, g, h, i, j) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

data Char #

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

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

Instances
 Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Char -> Char #pred :: Char -> Char #toEnum :: Int -> Char #fromEnum :: Char -> Int #enumFrom :: Char -> [Char] #enumFromThen :: Char -> Char -> [Char] #enumFromTo :: Char -> Char -> [Char] #enumFromThenTo :: Char -> Char -> Char -> [Char] # Instance detailsDefined in GHC.Classes Methods(==) :: Char -> Char -> Bool #(/=) :: Char -> Char -> Bool # Instance detailsDefined in GHC.Classes Methodscompare :: Char -> Char -> Ordering #(<) :: Char -> Char -> Bool #(<=) :: Char -> Char -> Bool #(>) :: Char -> Char -> Bool #(>=) :: Char -> Char -> Bool #max :: Char -> Char -> Char #min :: Char -> Char -> Char # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Char -> ShowS #show :: Char -> String #showList :: [Char] -> ShowS # Foldable (URec Char :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => URec Char m -> m #foldMap :: Monoid m => (a -> m) -> URec Char a -> m #foldr :: (a -> b -> b) -> b -> URec Char a -> b #foldr' :: (a -> b -> b) -> b -> URec Char a -> b #foldl :: (b -> a -> b) -> b -> URec Char a -> b #foldl' :: (b -> a -> b) -> b -> URec Char a -> b #foldr1 :: (a -> a -> a) -> URec Char a -> a #foldl1 :: (a -> a -> a) -> URec Char a -> a #toList :: URec Char a -> [a] #null :: URec Char a -> Bool #length :: URec Char a -> Int #elem :: Eq a => a -> URec Char a -> Bool #maximum :: Ord a => URec Char a -> a #minimum :: Ord a => URec Char a -> a #sum :: Num a => URec Char a -> a #product :: Num a => URec Char a -> a # Since: base-4.9.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) #sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) #mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) #sequence :: Monad m => URec Char (m a) -> m (URec Char a) #

data Double #

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

Instances
 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 detailsDefined in GHC.Classes Methods(==) :: Double -> Double -> Bool #(/=) :: Double -> Double -> Bool # Since: base-2.1 Instance detailsDefined in GHC.Float Methodsexp :: Double -> Double #log :: Double -> Double #(**) :: Double -> Double -> Double #sin :: Double -> Double #cos :: Double -> Double #tan :: Double -> Double # Note that due to the presence of NaN, Double's Ord instance does not satisfy reflexivity.>>> 0/0 <= (0/0 :: Double) False Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:>>> (0/0 :: Double) > 1 False >>> compare (0/0 :: Double) 1 GT  Instance detailsDefined in GHC.Classes Methods(<) :: Double -> Double -> Bool #(<=) :: Double -> Double -> Bool #(>) :: Double -> Double -> Bool #(>=) :: Double -> Double -> Bool #max :: Double -> Double -> Double #min :: Double -> Double -> Double # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Float MethodsfloatRange :: Double -> (Int, Int) #decodeFloat :: Double -> (Integer, Int) #isNaN :: Double -> Bool #atan2 :: Double -> Double -> Double # Since: base-4.9.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => URec Double m -> m #foldMap :: Monoid m => (a -> m) -> URec Double a -> m #foldr :: (a -> b -> b) -> b -> URec Double a -> b #foldr' :: (a -> b -> b) -> b -> URec Double a -> b #foldl :: (b -> a -> b) -> b -> URec Double a -> b #foldl' :: (b -> a -> b) -> b -> URec Double a -> b #foldr1 :: (a -> a -> a) -> URec Double a -> a #foldl1 :: (a -> a -> a) -> URec Double a -> a #toList :: URec Double a -> [a] #null :: URec Double a -> Bool #length :: URec Double a -> Int #elem :: Eq a => a -> URec Double a -> Bool #maximum :: Ord a => URec Double a -> a #minimum :: Ord a => URec Double a -> a #sum :: Num a => URec Double a -> a #product :: Num a => URec Double a -> a # Since: base-4.9.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) #sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) #mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) #sequence :: Monad m => URec Double (m a) -> m (URec Double a) #

data Either a b #

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

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

Examples

Expand

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

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


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

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


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

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


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

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

>>> parseMultiple
Right 3


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

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

>>> parseMultiple
Left "parse error"


Constructors

 Left a Right b
Instances
 Monad (Either e) Since: base-4.4.0.0 Instance detailsDefined in Data.Either Methods(>>=) :: Either e a -> (a -> Either e b) -> Either e b #(>>) :: Either e a -> Either e b -> Either e b #return :: a -> Either e a #fail :: String -> Either e a # Since: base-3.0 Instance detailsDefined in Data.Either Methodsfmap :: (a0 -> b) -> Either a a0 -> Either a b #(<$) :: a0 -> Either a b -> Either a a0 # Since: base-3.0 Instance detailsDefined in Data.Either Methodspure :: a -> Either e a #(<*>) :: Either e (a -> b) -> Either e a -> Either e b #liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c #(*>) :: Either e a -> Either e b -> Either e b #(<*) :: Either e a -> Either e b -> Either e a # Since: base-4.7.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => Either a m -> m #foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m #foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b #foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b #foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b #foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b #foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #toList :: Either a a0 -> [a0] #null :: Either a a0 -> Bool #length :: Either a a0 -> Int #elem :: Eq a0 => a0 -> Either a a0 -> Bool #maximum :: Ord a0 => Either a a0 -> a0 #minimum :: Ord a0 => Either a a0 -> a0 #sum :: Num a0 => Either a a0 -> a0 #product :: Num a0 => Either a a0 -> a0 # Since: base-4.7.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) #sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) #mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) #sequence :: Monad m => Either a (m a0) -> m (Either a a0) # (Eq a, Eq b) => Eq (Either a b) Since: base-2.1 Instance detailsDefined in Data.Either Methods(==) :: Either a b -> Either a b -> Bool #(/=) :: Either a b -> Either a b -> Bool # (Ord a, Ord b) => Ord (Either a b) Since: base-2.1 Instance detailsDefined in Data.Either Methodscompare :: Either a b -> Either a b -> Ordering #(<) :: Either a b -> Either a b -> Bool #(<=) :: Either a b -> Either a b -> Bool #(>) :: Either a b -> Either a b -> Bool #(>=) :: Either a b -> Either a b -> Bool #max :: Either a b -> Either a b -> Either a b #min :: Either a b -> Either a b -> Either a b # (Read a, Read b) => Read (Either a b) Since: base-3.0 Instance detailsDefined in Data.Either MethodsreadsPrec :: Int -> ReadS (Either a b) #readList :: ReadS [Either a b] #readPrec :: ReadPrec (Either a b) #readListPrec :: ReadPrec [Either a b] # (Show a, Show b) => Show (Either a b) Since: base-3.0 Instance detailsDefined in Data.Either MethodsshowsPrec :: Int -> Either a b -> ShowS #show :: Either a b -> String #showList :: [Either a b] -> ShowS # Semigroup (Either a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Either Methods(<>) :: Either a b -> Either a b -> Either a b #sconcat :: NonEmpty (Either a b) -> Either a b #stimes :: Integral b0 => b0 -> Either a b -> Either a b # class Enum a where # Class Enum defines operations on sequentially ordered types. The enumFrom... methods are used in Haskell's translation of arithmetic sequences. Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details. For any type that is an instance of class Bounded as well as Enum, the following should hold: • 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 Methods succ :: a -> a # the successor of a value. For numeric types, succ adds 1. pred :: a -> a # the predecessor of a value. For numeric types, pred subtracts 1. toEnum :: Int -> a # Convert from an Int. fromEnum :: a -> Int # Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int. enumFrom :: a -> [a] # Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n). For example: • enumFrom 4 :: [Integer] = [4,5,6,7,...] • enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int] enumFromThen :: a -> a -> [a] # Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y For example: • enumFromThen 4 6 :: [Integer] = [4,6,8,10...] • enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int] enumFromTo :: a -> a -> [a] # Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being enumFromTo n m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For example: • enumFromTo 6 10 :: [Int] = [6,7,8,9,10] • enumFromTo 42 1 :: [Integer] = [] enumFromThenTo :: a -> a -> a -> [a] # Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y and worker s c v m | c v m = v : worker s c (s v) m | otherwise = [] For example: • enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6] • enumFromThenTo 6 8 2 :: [Int] = [] Instances  Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Bool -> Bool #pred :: Bool -> Bool #toEnum :: Int -> Bool #fromEnum :: Bool -> Int #enumFrom :: Bool -> [Bool] #enumFromThen :: Bool -> Bool -> [Bool] #enumFromTo :: Bool -> Bool -> [Bool] #enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] # Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Char -> Char #pred :: Char -> Char #toEnum :: Int -> Char #fromEnum :: Char -> Int #enumFrom :: Char -> [Char] #enumFromThen :: Char -> Char -> [Char] #enumFromTo :: Char -> Char -> [Char] #enumFromThenTo :: Char -> Char -> Char -> [Char] # Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Int -> Int #pred :: Int -> Int #toEnum :: Int -> Int #fromEnum :: Int -> Int #enumFrom :: Int -> [Int] #enumFromThen :: Int -> Int -> [Int] #enumFromTo :: Int -> Int -> [Int] #enumFromThenTo :: Int -> Int -> Int -> [Int] # Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Integer -> [Integer] #enumFromThen :: Integer -> Integer -> [Integer] #enumFromTo :: Integer -> Integer -> [Integer] #enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] # Since: base-4.8.0.0 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Natural -> [Natural] #enumFromThen :: Natural -> Natural -> [Natural] #enumFromTo :: Natural -> Natural -> [Natural] #enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] # Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Ordering -> [Ordering] #enumFromTo :: Ordering -> Ordering -> [Ordering] # Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Word -> Word #pred :: Word -> Word #toEnum :: Int -> Word #fromEnum :: Word -> Int #enumFrom :: Word -> [Word] #enumFromThen :: Word -> Word -> [Word] #enumFromTo :: Word -> Word -> [Word] #enumFromThenTo :: Word -> Word -> Word -> [Word] # Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum MethodsenumFrom :: VecCount -> [VecCount] #enumFromTo :: VecCount -> VecCount -> [VecCount] # Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum MethodsenumFrom :: VecElem -> [VecElem] #enumFromThen :: VecElem -> VecElem -> [VecElem] #enumFromTo :: VecElem -> VecElem -> [VecElem] #enumFromThenTo :: VecElem -> VecElem -> VecElem -> [VecElem] # Enum () Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: () -> () #pred :: () -> () #toEnum :: Int -> () #fromEnum :: () -> Int #enumFrom :: () -> [()] #enumFromThen :: () -> () -> [()] #enumFromTo :: () -> () -> [()] #enumFromThenTo :: () -> () -> () -> [()] # Integral a => Enum (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodssucc :: Ratio a -> Ratio a #pred :: Ratio a -> Ratio a #toEnum :: Int -> Ratio a #fromEnum :: Ratio a -> Int #enumFrom :: Ratio a -> [Ratio a] #enumFromThen :: Ratio a -> Ratio a -> [Ratio a] #enumFromTo :: Ratio a -> Ratio a -> [Ratio a] #enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] # class Eq a where # The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq. The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties: Reflexivity x == x = True Symmetry x == y = y == x Transitivity if x == y && y == z = True, then x == z = True Substitutivity if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True Negation x /= y = not (x == y) Minimal complete definition: either == or /=. Minimal complete definition Methods (==) :: a -> a -> Bool infix 4 # (/=) :: a -> a -> Bool infix 4 # Instances  Instance detailsDefined in GHC.Classes Methods(==) :: Bool -> Bool -> Bool #(/=) :: Bool -> Bool -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: Char -> Char -> Bool #(/=) :: Char -> Char -> Bool # 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 detailsDefined in GHC.Classes Methods(==) :: Double -> Double -> Bool #(/=) :: Double -> Double -> Bool # Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.>>> 0/0 == (0/0 :: Float) False Also note that Float's Eq instance does not satisfy substitutivity:>>> 0 == (-0 :: Float) True >>> recip 0 == recip (-0 :: Float) False  Instance detailsDefined in GHC.Classes Methods(==) :: Float -> Float -> Bool #(/=) :: Float -> Float -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: Int -> Int -> Bool #(/=) :: Int -> Int -> Bool # Instance detailsDefined in GHC.Integer.Type Methods(==) :: Integer -> Integer -> Bool #(/=) :: Integer -> Integer -> Bool # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods(==) :: Natural -> Natural -> Bool #(/=) :: Natural -> Natural -> Bool # Instance detailsDefined in GHC.Classes Methods Instance detailsDefined in GHC.Classes Methods(==) :: Word -> Word -> Bool #(/=) :: Word -> Word -> Bool # Eq () Instance detailsDefined in GHC.Classes Methods(==) :: () -> () -> Bool #(/=) :: () -> () -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: TyCon -> TyCon -> Bool #(/=) :: TyCon -> TyCon -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: Module -> Module -> Bool #(/=) :: Module -> Module -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: TrName -> TrName -> Bool #(/=) :: TrName -> TrName -> Bool # Instance detailsDefined in GHC.Integer.Type Methods(==) :: BigNat -> BigNat -> Bool #(/=) :: BigNat -> BigNat -> Bool # Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.3.0.0 Instance detailsDefined in GHC.IO Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Stack.Types Methods(==) :: SrcLoc -> SrcLoc -> Bool #(/=) :: SrcLoc -> SrcLoc -> Bool # Eq a => Eq [a] Instance detailsDefined in GHC.Classes Methods(==) :: [a] -> [a] -> Bool #(/=) :: [a] -> [a] -> Bool # Eq a => Eq (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Maybe Methods(==) :: Maybe a -> Maybe a -> Bool #(/=) :: Maybe a -> Maybe a -> Bool # Eq a => Eq (Ratio a) Since: base-2.1 Instance detailsDefined in GHC.Real Methods(==) :: Ratio a -> Ratio a -> Bool #(/=) :: Ratio a -> Ratio a -> Bool # Eq a => Eq (NonEmpty a) Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(==) :: NonEmpty a -> NonEmpty a -> Bool #(/=) :: NonEmpty a -> NonEmpty a -> Bool # (Eq a, Eq b) => Eq (Either a b) Since: base-2.1 Instance detailsDefined in Data.Either Methods(==) :: Either a b -> Either a b -> Bool #(/=) :: Either a b -> Either a b -> Bool # (Eq a, Eq b) => Eq (a, b) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b) -> (a, b) -> Bool #(/=) :: (a, b) -> (a, b) -> Bool # (Eq a, Eq b, Eq c) => Eq (a, b, c) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c) -> (a, b, c) -> Bool #(/=) :: (a, b, c) -> (a, b, c) -> Bool # (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # type FilePath = String # File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file. data Float # Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type. Instances  Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.>>> 0/0 == (0/0 :: Float) False Also note that Float's Eq instance does not satisfy substitutivity:>>> 0 == (-0 :: Float) True >>> recip 0 == recip (-0 :: Float) False  Instance detailsDefined in GHC.Classes Methods(==) :: Float -> Float -> Bool #(/=) :: Float -> Float -> Bool # Since: base-2.1 Instance detailsDefined in GHC.Float Methodspi :: Float #exp :: Float -> Float #log :: Float -> Float #sqrt :: Float -> Float #(**) :: Float -> Float -> Float #logBase :: Float -> Float -> Float #sin :: Float -> Float #cos :: Float -> Float #tan :: Float -> Float #asin :: Float -> Float #acos :: Float -> Float #atan :: Float -> Float #sinh :: Float -> Float #cosh :: Float -> Float #tanh :: Float -> Float #asinh :: Float -> Float #acosh :: Float -> Float #atanh :: Float -> Float #log1p :: Float -> Float #expm1 :: Float -> Float # Note that due to the presence of NaN, Float's Ord instance does not satisfy reflexivity.>>> 0/0 <= (0/0 :: Float) False Also note that, due to the same, Ord's operator interactions are not respected by Float's instance:>>> (0/0 :: Float) > 1 False >>> compare (0/0 :: Float) 1 GT  Instance detailsDefined in GHC.Classes Methods(<) :: Float -> Float -> Bool #(<=) :: Float -> Float -> Bool #(>) :: Float -> Float -> Bool #(>=) :: Float -> Float -> Bool #max :: Float -> Float -> Float #min :: Float -> Float -> Float # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Float MethodsfloatRange :: Float -> (Int, Int) #decodeFloat :: Float -> (Integer, Int) #scaleFloat :: Int -> Float -> Float #isNaN :: Float -> Bool #isIEEE :: Float -> Bool #atan2 :: Float -> Float -> Float # Since: base-4.9.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => URec Float m -> m #foldMap :: Monoid m => (a -> m) -> URec Float a -> m #foldr :: (a -> b -> b) -> b -> URec Float a -> b #foldr' :: (a -> b -> b) -> b -> URec Float a -> b #foldl :: (b -> a -> b) -> b -> URec Float a -> b #foldl' :: (b -> a -> b) -> b -> URec Float a -> b #foldr1 :: (a -> a -> a) -> URec Float a -> a #foldl1 :: (a -> a -> a) -> URec Float a -> a #toList :: URec Float a -> [a] #null :: URec Float a -> Bool #length :: URec Float a -> Int #elem :: Eq a => a -> URec Float a -> Bool #maximum :: Ord a => URec Float a -> a #minimum :: Ord a => URec Float a -> a #sum :: Num a => URec Float a -> a #product :: Num a => URec Float a -> a # Since: base-4.9.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) #sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) #mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) #sequence :: Monad m => URec Float (m a) -> m (URec Float a) # class Fractional a => Floating a where # Trigonometric and hyperbolic functions and related functions. The Haskell Report defines no laws for Floating. However, '(+)', '(*)' and exp are customarily expected to define an exponential field and have the following properties: • exp (a + b) = @exp a * exp b • exp (fromInteger 0) = fromInteger 1 Minimal complete definition Methods pi :: a # exp :: a -> a # log :: a -> a # sqrt :: a -> a # (**) :: a -> a -> a infixr 8 # logBase :: a -> a -> a # sin :: a -> a # cos :: a -> a # tan :: a -> a # asin :: a -> a # acos :: a -> a # atan :: a -> a # sinh :: a -> a # cosh :: a -> a # tanh :: a -> a # asinh :: a -> a # acosh :: a -> a # atanh :: a -> a # Instances  Since: base-2.1 Instance detailsDefined in GHC.Float Methodsexp :: Double -> Double #log :: Double -> Double #(**) :: Double -> Double -> Double #sin :: Double -> Double #cos :: Double -> Double #tan :: Double -> Double # Since: base-2.1 Instance detailsDefined in GHC.Float Methodspi :: Float #exp :: Float -> Float #log :: Float -> Float #sqrt :: Float -> Float #(**) :: Float -> Float -> Float #logBase :: Float -> Float -> Float #sin :: Float -> Float #cos :: Float -> Float #tan :: Float -> Float #asin :: Float -> Float #acos :: Float -> Float #atan :: Float -> Float #sinh :: Float -> Float #cosh :: Float -> Float #tanh :: Float -> Float #asinh :: Float -> Float #acosh :: Float -> Float #atanh :: Float -> Float #log1p :: Float -> Float #expm1 :: Float -> Float # class Num a => Fractional a where # 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 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 # fractional division recip :: a -> a # reciprocal fraction fromRational :: Rational -> a # 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  Integral a => Fractional (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods(/) :: Ratio a -> Ratio a -> Ratio a #recip :: Ratio a -> Ratio a # class Functor (f :: Type -> Type) where # The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws: fmap id == id fmap (f . g) == fmap f . fmap g The instances of Functor for lists, Maybe and IO satisfy these laws. Methods fmap :: (a -> b) -> f a -> f b # Instances  Functor [] Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> [a] -> [b] #(<$) :: a -> [b] -> [a] # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> Maybe a -> Maybe b #(<$) :: a -> Maybe b -> Maybe a # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> IO a -> IO b #(<$) :: a -> IO b -> IO a # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadP Methodsfmap :: (a -> b) -> ReadP a -> ReadP b #(<$) :: a -> ReadP b -> ReadP a # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b #(<$) :: a -> NonEmpty b -> NonEmpty a # Since: base-4.8.0.0 Instance detailsDefined in Text.ParserCombinators.ReadP Methodsfmap :: (a -> b) -> P a -> P b #(<$) :: a -> P b -> P a # Since: base-3.0 Instance detailsDefined in Data.Either Methodsfmap :: (a0 -> b) -> Either a a0 -> Either a b #(<$) :: a0 -> Either a b -> Either a a0 # Functor ((,) a) Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a0 -> b) -> (a, a0) -> (a, b) #(<$) :: a0 -> (a, b) -> (a, a0) # Functor ((->) r :: Type -> Type) Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> (r -> a) -> r -> b #(<$) :: a -> (r -> b) -> r -> a #

data IO a #

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

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

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

Instances
 Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: IO a -> (a -> IO b) -> IO b #(>>) :: IO a -> IO b -> IO b #return :: a -> IO a #fail :: String -> IO a # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> IO a -> IO b #(<$) :: a -> IO b -> IO a # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: a -> IO a #(<*>) :: IO (a -> b) -> IO a -> IO b #liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c #(*>) :: IO a -> IO b -> IO b #(<*) :: IO a -> IO b -> IO a # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsempty :: IO a #(<|>) :: IO a -> IO a -> IO a #some :: IO a -> IO [a] #many :: IO a -> IO [a] # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsmzero :: IO a #mplus :: IO a -> IO a -> IO a # Semigroup a => Semigroup (IO a) Since: base-4.10.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: IO a -> IO a -> IO a #sconcat :: NonEmpty (IO a) -> IO a #stimes :: Integral b => b -> IO a -> IO a # Monoid a => Monoid (IO a) Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsmempty :: IO a #mappend :: IO a -> IO a -> IO a #mconcat :: [IO a] -> IO a # type IOError = IOException # The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOException instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception. In Haskell 2010, this is an opaque type. data Int # A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class. Instances  Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Int -> Int #pred :: Int -> Int #toEnum :: Int -> Int #fromEnum :: Int -> Int #enumFrom :: Int -> [Int] #enumFromThen :: Int -> Int -> [Int] #enumFromTo :: Int -> Int -> [Int] #enumFromThenTo :: Int -> Int -> Int -> [Int] # Instance detailsDefined in GHC.Classes Methods(==) :: Int -> Int -> Bool #(/=) :: Int -> Int -> Bool # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodsquot :: Int -> Int -> Int #rem :: Int -> Int -> Int #div :: Int -> Int -> Int #mod :: Int -> Int -> Int #quotRem :: Int -> Int -> (Int, Int) #divMod :: Int -> Int -> (Int, Int) # Since: base-2.1 Instance detailsDefined in GHC.Num Methods(+) :: Int -> Int -> Int #(-) :: Int -> Int -> Int #(*) :: Int -> Int -> Int #negate :: Int -> Int #abs :: Int -> Int #signum :: Int -> Int # Instance detailsDefined in GHC.Classes Methodscompare :: Int -> Int -> Ordering #(<) :: Int -> Int -> Bool #(<=) :: Int -> Int -> Bool #(>) :: Int -> Int -> Bool #(>=) :: Int -> Int -> Bool #max :: Int -> Int -> Int #min :: Int -> Int -> Int # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Int -> ShowS #show :: Int -> String #showList :: [Int] -> ShowS # Foldable (URec Int :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => URec Int m -> m #foldMap :: Monoid m => (a -> m) -> URec Int a -> m #foldr :: (a -> b -> b) -> b -> URec Int a -> b #foldr' :: (a -> b -> b) -> b -> URec Int a -> b #foldl :: (b -> a -> b) -> b -> URec Int a -> b #foldl' :: (b -> a -> b) -> b -> URec Int a -> b #foldr1 :: (a -> a -> a) -> URec Int a -> a #foldl1 :: (a -> a -> a) -> URec Int a -> a #toList :: URec Int a -> [a] #null :: URec Int a -> Bool #length :: URec Int a -> Int #elem :: Eq a => a -> URec Int a -> Bool #maximum :: Ord a => URec Int a -> a #minimum :: Ord a => URec Int a -> a #sum :: Num a => URec Int a -> a #product :: Num a => URec Int a -> a # Since: base-4.9.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) #sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) #mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) #sequence :: Monad m => URec Int (m a) -> m (URec Int a) # data Integer # Invariant: Jn# and Jp# are used iff value doesn't fit in S# Useful properties resulting from the invariants: • abs (S# _) <= abs (Jp# _) • abs (S# _) < abs (Jn# _) Instances  Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Integer -> [Integer] #enumFromThen :: Integer -> Integer -> [Integer] #enumFromTo :: Integer -> Integer -> [Integer] #enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] # Instance detailsDefined in GHC.Integer.Type Methods(==) :: Integer -> Integer -> Bool #(/=) :: Integer -> Integer -> Bool # Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsquotRem :: Integer -> Integer -> (Integer, Integer) #divMod :: Integer -> Integer -> (Integer, Integer) # Since: base-2.1 Instance detailsDefined in GHC.Num Methods Instance detailsDefined in GHC.Integer.Type Methods(<) :: Integer -> Integer -> Bool #(<=) :: Integer -> Integer -> Bool #(>) :: Integer -> Integer -> Bool #(>=) :: Integer -> Integer -> Bool # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowList :: [Integer] -> ShowS # class (Real a, Enum a) => Integral a where # Integral numbers, supporting integer division. The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the 'div'/'mod' and 'quot'/'rem' pairs, given suitable Euclidean functions f and g: • x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y • x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y An example of a suitable Euclidean function, for Integer's instance, is abs. Minimal complete definition Methods quot :: a -> a -> a infixl 7 # integer division truncated toward zero rem :: a -> a -> a infixl 7 # integer remainder, satisfying (x quot y)*y + (x rem y) == x div :: a -> a -> a infixl 7 # integer division truncated toward negative infinity mod :: a -> a -> a infixl 7 # integer modulus, satisfying (x div y)*y + (x mod y) == x quotRem :: a -> a -> (a, a) # simultaneous quot and rem divMod :: a -> a -> (a, a) # simultaneous div and mod toInteger :: a -> Integer # conversion to Integer Instances  Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodsquot :: Int -> Int -> Int #rem :: Int -> Int -> Int #div :: Int -> Int -> Int #mod :: Int -> Int -> Int #quotRem :: Int -> Int -> (Int, Int) #divMod :: Int -> Int -> (Int, Int) # Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsquotRem :: Integer -> Integer -> (Integer, Integer) #divMod :: Integer -> Integer -> (Integer, Integer) # Since: base-4.8.0.0 Instance detailsDefined in GHC.Real MethodsquotRem :: Natural -> Natural -> (Natural, Natural) #divMod :: Natural -> Natural -> (Natural, Natural) # Since: base-2.1 Instance detailsDefined in GHC.Real Methodsquot :: Word -> Word -> Word #rem :: Word -> Word -> Word #div :: Word -> Word -> Word #mod :: Word -> Word -> Word #quotRem :: Word -> Word -> (Word, Word) #divMod :: Word -> Word -> (Word, Word) # data Maybe a # The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error. The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type. Constructors  Nothing Just a Instances  Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b #(>>) :: Maybe a -> Maybe b -> Maybe b #return :: a -> Maybe a #fail :: String -> Maybe a # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> Maybe a -> Maybe b #(<$) :: a -> Maybe b -> Maybe a # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: a -> Maybe a #(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b #liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c #(*>) :: Maybe a -> Maybe b -> Maybe b #(<*) :: Maybe a -> Maybe b -> Maybe a # Since: base-2.1 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => Maybe m -> m #foldMap :: Monoid m => (a -> m) -> Maybe a -> m #foldr :: (a -> b -> b) -> b -> Maybe a -> b #foldr' :: (a -> b -> b) -> b -> Maybe a -> b #foldl :: (b -> a -> b) -> b -> Maybe a -> b #foldl' :: (b -> a -> b) -> b -> Maybe a -> b #foldr1 :: (a -> a -> a) -> Maybe a -> a #foldl1 :: (a -> a -> a) -> Maybe a -> a #toList :: Maybe a -> [a] #null :: Maybe a -> Bool #length :: Maybe a -> Int #elem :: Eq a => a -> Maybe a -> Bool #maximum :: Ord a => Maybe a -> a #minimum :: Ord a => Maybe a -> a #sum :: Num a => Maybe a -> a #product :: Num a => Maybe a -> a # Since: base-2.1 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) #sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) #mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) #sequence :: Monad m => Maybe (m a) -> m (Maybe a) # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsempty :: Maybe a #(<|>) :: Maybe a -> Maybe a -> Maybe a #some :: Maybe a -> Maybe [a] #many :: Maybe a -> Maybe [a] # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsmzero :: Maybe a #mplus :: Maybe a -> Maybe a -> Maybe a # Eq a => Eq (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Maybe Methods(==) :: Maybe a -> Maybe a -> Bool #(/=) :: Maybe a -> Maybe a -> Bool # Ord a => Ord (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Maybe Methodscompare :: Maybe a -> Maybe a -> Ordering #(<) :: Maybe a -> Maybe a -> Bool #(<=) :: Maybe a -> Maybe a -> Bool #(>) :: Maybe a -> Maybe a -> Bool #(>=) :: Maybe a -> Maybe a -> Bool #max :: Maybe a -> Maybe a -> Maybe a #min :: Maybe a -> Maybe a -> Maybe a # Read a => Read (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (Maybe a) #readList :: ReadS [Maybe a] # Show a => Show (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Maybe a -> ShowS #show :: Maybe a -> String #showList :: [Maybe a] -> ShowS # Semigroup a => Semigroup (Maybe a) Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: Maybe a -> Maybe a -> Maybe a #sconcat :: NonEmpty (Maybe a) -> Maybe a #stimes :: Integral b => b -> Maybe a -> Maybe a # Semigroup a => Monoid (Maybe a) Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S."Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.Since: base-2.1 Instance detailsDefined in GHC.Base Methodsmempty :: Maybe a #mappend :: Maybe a -> Maybe a -> Maybe a #mconcat :: [Maybe a] -> Maybe a #

class Applicative m => Monad (m :: Type -> Type) where #

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

• return a >>= k  =  k a
• m >>= return  =  m
• m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return
• (<*>) = ap

The above laws imply:

• fmap f xs  =  xs >>= return . f
• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1 #

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a #

Inject a value into the monadic type.

Instances

fail :: Monad m => String -> m a #

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

class Num a where #

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)

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 #

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

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

negate :: a -> a #

Unary negation.

abs :: a -> a #

Absolute value.

signum :: a -> a #

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 #

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
 Since: base-2.1 Instance detailsDefined in GHC.Num Methods(+) :: Int -> Int -> Int #(-) :: Int -> Int -> Int #(*) :: Int -> Int -> Int #negate :: Int -> Int #abs :: Int -> Int #signum :: Int -> Int # Since: base-2.1 Instance detailsDefined in GHC.Num Methods 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 detailsDefined in GHC.Num Methods Since: base-2.1 Instance detailsDefined in GHC.Num Methods(+) :: Word -> Word -> Word #(-) :: Word -> Word -> Word #(*) :: Word -> Word -> Word #negate :: Word -> Word #abs :: Word -> Word #signum :: Word -> Word # Integral a => Num (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods(+) :: Ratio a -> Ratio a -> Ratio a #(-) :: Ratio a -> Ratio a -> Ratio a #(*) :: Ratio a -> Ratio a -> Ratio a #negate :: Ratio a -> Ratio a #abs :: Ratio a -> Ratio a #signum :: Ratio a -> Ratio a #

class Eq a => Ord a where #

The Ord class is used for totally ordered datatypes.

Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.

The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:

Transitivity
if x <= y && y <= z = True, then x <= z = True
Reflexivity
x <= x = True
Antisymmetry
if x <= y && y <= x = True, then x == y = True

Note that the following operator interactions are expected to hold:

1. x >= y = y <= x
2. x < y = x <= y && x /= y
3. x > y = y < x
4. x < y = compare x y == LT
5. x > y = compare x y == GT
6. x == y = compare x y == EQ
7. min x y == if x <= y then x else y = True
8. max x y == if x >= y then x else y = True

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Minimal complete definition

Methods

compare :: a -> a -> Ordering #

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

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

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

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

max :: a -> a -> a #

min :: a -> a -> a #

Instances
 Instance detailsDefined in GHC.Classes Methodscompare :: Bool -> Bool -> Ordering #(<) :: Bool -> Bool -> Bool #(<=) :: Bool -> Bool -> Bool #(>) :: Bool -> Bool -> Bool #(>=) :: Bool -> Bool -> Bool #max :: Bool -> Bool -> Bool #min :: Bool -> Bool -> Bool # Instance detailsDefined in GHC.Classes Methodscompare :: Char -> Char -> Ordering #(<) :: Char -> Char -> Bool #(<=) :: Char -> Char -> Bool #(>) :: Char -> Char -> Bool #(>=) :: Char -> Char -> Bool #max :: Char -> Char -> Char #min :: Char -> Char -> Char # Note that due to the presence of NaN, Double's Ord instance does not satisfy reflexivity.>>> 0/0 <= (0/0 :: Double) False Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:>>> (0/0 :: Double) > 1 False >>> compare (0/0 :: Double) 1 GT  Instance detailsDefined in GHC.Classes Methods(<) :: Double -> Double -> Bool #(<=) :: Double -> Double -> Bool #(>) :: Double -> Double -> Bool #(>=) :: Double -> Double -> Bool #max :: Double -> Double -> Double #min :: Double -> Double -> Double # Note that due to the presence of NaN, Float's Ord instance does not satisfy reflexivity.>>> 0/0 <= (0/0 :: Float) False Also note that, due to the same, Ord's operator interactions are not respected by Float's instance:>>> (0/0 :: Float) > 1 False >>> compare (0/0 :: Float) 1 GT  Instance detailsDefined in GHC.Classes Methods(<) :: Float -> Float -> Bool #(<=) :: Float -> Float -> Bool #(>) :: Float -> Float -> Bool #(>=) :: Float -> Float -> Bool #max :: Float -> Float -> Float #min :: Float -> Float -> Float # Instance detailsDefined in GHC.Classes Methodscompare :: Int -> Int -> Ordering #(<) :: Int -> Int -> Bool #(<=) :: Int -> Int -> Bool #(>) :: Int -> Int -> Bool #(>=) :: Int -> Int -> Bool #max :: Int -> Int -> Int #min :: Int -> Int -> Int # Instance detailsDefined in GHC.Integer.Type Methods(<) :: Integer -> Integer -> Bool #(<=) :: Integer -> Integer -> Bool #(>) :: Integer -> Integer -> Bool #(>=) :: Integer -> Integer -> Bool # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods(<) :: Natural -> Natural -> Bool #(<=) :: Natural -> Natural -> Bool #(>) :: Natural -> Natural -> Bool #(>=) :: Natural -> Natural -> Bool # Instance detailsDefined in GHC.Classes Methods(<) :: Ordering -> Ordering -> Bool #(>) :: Ordering -> Ordering -> Bool # Instance detailsDefined in GHC.Classes Methodscompare :: Word -> Word -> Ordering #(<) :: Word -> Word -> Bool #(<=) :: Word -> Word -> Bool #(>) :: Word -> Word -> Bool #(>=) :: Word -> Word -> Bool #max :: Word -> Word -> Word #min :: Word -> Word -> Word # Ord () Instance detailsDefined in GHC.Classes Methodscompare :: () -> () -> Ordering #(<) :: () -> () -> Bool #(<=) :: () -> () -> Bool #(>) :: () -> () -> Bool #(>=) :: () -> () -> Bool #max :: () -> () -> () #min :: () -> () -> () # Instance detailsDefined in GHC.Classes Methods(<) :: TyCon -> TyCon -> Bool #(<=) :: TyCon -> TyCon -> Bool #(>) :: TyCon -> TyCon -> Bool #(>=) :: TyCon -> TyCon -> Bool #max :: TyCon -> TyCon -> TyCon #min :: TyCon -> TyCon -> TyCon # Instance detailsDefined in GHC.Integer.Type Methods(<) :: BigNat -> BigNat -> Bool #(<=) :: BigNat -> BigNat -> Bool #(>) :: BigNat -> BigNat -> Bool #(>=) :: BigNat -> BigNat -> Bool #max :: BigNat -> BigNat -> BigNat #min :: BigNat -> BigNat -> BigNat # Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Instance detailsDefined in GHC.IO.Exception Methods(<) :: ExitCode -> ExitCode -> Bool #(>) :: ExitCode -> ExitCode -> Bool # Ord a => Ord [a] Instance detailsDefined in GHC.Classes Methodscompare :: [a] -> [a] -> Ordering #(<) :: [a] -> [a] -> Bool #(<=) :: [a] -> [a] -> Bool #(>) :: [a] -> [a] -> Bool #(>=) :: [a] -> [a] -> Bool #max :: [a] -> [a] -> [a] #min :: [a] -> [a] -> [a] # Ord a => Ord (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Maybe Methodscompare :: Maybe a -> Maybe a -> Ordering #(<) :: Maybe a -> Maybe a -> Bool #(<=) :: Maybe a -> Maybe a -> Bool #(>) :: Maybe a -> Maybe a -> Bool #(>=) :: Maybe a -> Maybe a -> Bool #max :: Maybe a -> Maybe a -> Maybe a #min :: Maybe a -> Maybe a -> Maybe a # Integral a => Ord (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodscompare :: Ratio a -> Ratio a -> Ordering #(<) :: Ratio a -> Ratio a -> Bool #(<=) :: Ratio a -> Ratio a -> Bool #(>) :: Ratio a -> Ratio a -> Bool #(>=) :: Ratio a -> Ratio a -> Bool #max :: Ratio a -> Ratio a -> Ratio a #min :: Ratio a -> Ratio a -> Ratio a # Ord a => Ord (NonEmpty a) Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodscompare :: NonEmpty a -> NonEmpty a -> Ordering #(<) :: NonEmpty a -> NonEmpty a -> Bool #(<=) :: NonEmpty a -> NonEmpty a -> Bool #(>) :: NonEmpty a -> NonEmpty a -> Bool #(>=) :: NonEmpty a -> NonEmpty a -> Bool #max :: NonEmpty a -> NonEmpty a -> NonEmpty a #min :: NonEmpty a -> NonEmpty a -> NonEmpty a # (Ord a, Ord b) => Ord (Either a b) Since: base-2.1 Instance detailsDefined in Data.Either Methodscompare :: Either a b -> Either a b -> Ordering #(<) :: Either a b -> Either a b -> Bool #(<=) :: Either a b -> Either a b -> Bool #(>) :: Either a b -> Either a b -> Bool #(>=) :: Either a b -> Either a b -> Bool #max :: Either a b -> Either a b -> Either a b #min :: Either a b -> Either a b -> Either a b # (Ord a, Ord b) => Ord (a, b) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b) -> (a, b) -> Ordering #(<) :: (a, b) -> (a, b) -> Bool #(<=) :: (a, b) -> (a, b) -> Bool #(>) :: (a, b) -> (a, b) -> Bool #(>=) :: (a, b) -> (a, b) -> Bool #max :: (a, b) -> (a, b) -> (a, b) #min :: (a, b) -> (a, b) -> (a, b) # (Ord a, Ord b, Ord c) => Ord (a, b, c) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c) -> (a, b, c) -> Ordering #(<) :: (a, b, c) -> (a, b, c) -> Bool #(<=) :: (a, b, c) -> (a, b, c) -> Bool #(>) :: (a, b, c) -> (a, b, c) -> Bool #(>=) :: (a, b, c) -> (a, b, c) -> Bool #max :: (a, b, c) -> (a, b, c) -> (a, b, c) #min :: (a, b, c) -> (a, b, c) -> (a, b, c) # (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d) -> (a, b, c, d) -> Ordering #(<) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(>) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering #(<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering #(<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering #(<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering #(<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) #min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) #min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) #min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) #min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) #min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) #min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

data Ordering #

Constructors

 LT EQ GT
Instances
 Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Ordering -> [Ordering] #enumFromTo :: Ordering -> Ordering -> [Ordering] # Instance detailsDefined in GHC.Classes Methods Instance detailsDefined in GHC.Classes Methods(<) :: Ordering -> Ordering -> Bool #(>) :: Ordering -> Ordering -> Bool # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowList :: [Ordering] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsstimes :: Integral b => b -> Ordering -> Ordering # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsmconcat :: [Ordering] -> Ordering #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

Parsing of Strings, producing values.

Derived instances of Read make the following assumptions, which derived instances of Show obey:

• If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form).
• Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
• If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
• The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where

(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r

(\r -> [(u:^:v,w) |
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r

where app_prec = 10
up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where

readPrec = parens $(prec app_prec$ do
Ident "Leaf" <- lexP
return (Leaf m))

+++ (prec up_prec $do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault Why do both readsPrec and readPrec exist, and why does GHC opt to implement readPrec in derived Read instances instead of readsPrec? The reason is that readsPrec is based on the ReadS type, and although ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient parser data structure. readPrec, on the other hand, is based on a much more efficient ReadPrec datatype (a.k.a "new-style parsers"), but its definition relies on the use of the RankNTypes language extension. Therefore, readPrec (and its cousin, readListPrec) are marked as GHC-only. Nevertheless, it is recommended to use readPrec instead of readsPrec whenever possible for the efficiency improvements it brings. As mentioned above, derived Read instances in GHC will implement readPrec instead of readsPrec. The default implementations of readsPrec (and its cousin, readList) will simply use readPrec under the hood. If you are writing a Read instance by hand, it is recommended to write it like so: instance Read T where readPrec = ... readListPrec = readListPrecDefault  Minimal complete definition Methods Arguments  :: Int the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10. -> ReadS a attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty. Derived instances of Read and Show satisfy the following: • (x,"") is an element of (readsPrec d (showsPrec d x "")). That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with. readList :: ReadS [a] # The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets. Instances  Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-4.8.0.0 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-4.5.0.0 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Read () Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS () #readList :: ReadS [()] #readListPrec :: ReadPrec [()] # Instance detailsDefined in GHC.IO.Exception Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Since: base-2.1 Instance detailsDefined in GHC.Read Methods Read a => Read [a] Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS [a] #readList :: ReadS [[a]] #readPrec :: ReadPrec [a] #readListPrec :: ReadPrec [[a]] # Read a => Read (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (Maybe a) #readList :: ReadS [Maybe a] # (Integral a, Read a) => Read (Ratio a) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (Ratio a) #readList :: ReadS [Ratio a] # Read a => Read (NonEmpty a) Since: base-4.11.0.0 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (NonEmpty a) # (Read a, Read b) => Read (Either a b) Since: base-3.0 Instance detailsDefined in Data.Either MethodsreadsPrec :: Int -> ReadS (Either a b) #readList :: ReadS [Either a b] #readPrec :: ReadPrec (Either a b) #readListPrec :: ReadPrec [Either a b] # (Read a, Read b) => Read (a, b) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b) #readList :: ReadS [(a, b)] #readPrec :: ReadPrec (a, b) #readListPrec :: ReadPrec [(a, b)] # (Ix a, Read a, Read b) => Read (Array a b) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (Array a b) #readList :: ReadS [Array a b] #readPrec :: ReadPrec (Array a b) #readListPrec :: ReadPrec [Array a b] # (Read a, Read b, Read c) => Read (a, b, c) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c) #readList :: ReadS [(a, b, c)] #readPrec :: ReadPrec (a, b, c) #readListPrec :: ReadPrec [(a, b, c)] # (Read a, Read b, Read c, Read d) => Read (a, b, c, d) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d) #readList :: ReadS [(a, b, c, d)] #readPrec :: ReadPrec (a, b, c, d) #readListPrec :: ReadPrec [(a, b, c, d)] # (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e) #readList :: ReadS [(a, b, c, d, e)] #readPrec :: ReadPrec (a, b, c, d, e) #readListPrec :: ReadPrec [(a, b, c, d, e)] # (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f) #readList :: ReadS [(a, b, c, d, e, f)] #readPrec :: ReadPrec (a, b, c, d, e, f) #readListPrec :: ReadPrec [(a, b, c, d, e, f)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g) #readList :: ReadS [(a, b, c, d, e, f, g)] #readPrec :: ReadPrec (a, b, c, d, e, f, g) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h) #readList :: ReadS [(a, b, c, d, e, f, g, h)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i) #readList :: ReadS [(a, b, c, d, e, f, g, h, i)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j) #readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k) #readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l) #readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m) #readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] # (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Since: base-2.1 Instance detailsDefined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] #readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] # type ReadS a = String -> [(a, String)] # A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs. Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP). class (Num a, Ord a) => Real a where # Methods toRational :: a -> Rational # the rational equivalent of its real argument with full precision Instances  Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Since: base-4.8.0.0 Instance detailsDefined in GHC.Real Methods Since: base-2.1 Instance detailsDefined in GHC.Real Methods Integral a => Real (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodstoRational :: Ratio a -> Rational # class (RealFrac a, Floating a) => RealFloat a where # Efficient, machine-independent access to the components of a floating-point number. Minimal complete definition Methods floatRadix :: a -> Integer # a constant function, returning the radix of the representation (often 2) floatDigits :: a -> Int # a constant function, returning the number of digits of floatRadix in the significand floatRange :: a -> (Int, Int) # a constant function, returning the lowest and highest values the exponent may assume decodeFloat :: a -> (Integer, Int) # The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True. encodeFloat :: Integer -> Int -> a # encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction. exponent :: a -> Int # exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values. significand :: a -> a # The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values. scaleFloat :: Int -> a -> a # multiplies a floating-point number by an integer power of the radix isNaN :: a -> Bool # True if the argument is an IEEE "not-a-number" (NaN) value isInfinite :: a -> Bool # True if the argument is an IEEE infinity or negative infinity isDenormalized :: a -> Bool # True if the argument is too small to be represented in normalized format isNegativeZero :: a -> Bool # True if the argument is an IEEE negative zero isIEEE :: a -> Bool # True if the argument is an IEEE floating point number atan2 :: a -> a -> a # a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation. Instances  Since: base-2.1 Instance detailsDefined in GHC.Float MethodsfloatRange :: Double -> (Int, Int) #decodeFloat :: Double -> (Integer, Int) #isNaN :: Double -> Bool #atan2 :: Double -> Double -> Double # Since: base-2.1 Instance detailsDefined in GHC.Float MethodsfloatRange :: Float -> (Int, Int) #decodeFloat :: Float -> (Integer, Int) #scaleFloat :: Int -> Float -> Float #isNaN :: Float -> Bool #isIEEE :: Float -> Bool #atan2 :: Float -> Float -> Float # class (Real a, Fractional a) => RealFrac a where # Extracting components of fractions. Minimal complete definition properFraction Methods properFraction :: Integral b => a -> (b, a) # The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and: • n is an integral number with the same sign as x; and • f is a fraction with the same type and sign as x, and with absolute value less than 1. The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction. truncate :: Integral b => a -> b # truncate x returns the integer nearest x between zero and x round :: Integral b => a -> b # round x returns the nearest integer to x; the even integer if x is equidistant between two integers ceiling :: Integral b => a -> b # ceiling x returns the least integer not less than x floor :: Integral b => a -> b # floor x returns the greatest integer not greater than x Instances  Integral a => RealFrac (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsproperFraction :: Integral b => Ratio a -> (b, Ratio a) #truncate :: Integral b => Ratio a -> b #round :: Integral b => Ratio a -> b #ceiling :: Integral b => Ratio a -> b #floor :: Integral b => Ratio a -> b # class Show a where # Conversion of values to readable Strings. Derived instances of Show have the following properties, which are compatible with derived instances of Read: • The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. • If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor. • the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression. • If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration. For example, given the declarations infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a the derived instance of Show is equivalent to instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec)$
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10

showsPrec d (u :^: v) = showParen (d > up_prec) $showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5 Note that right-associativity of :^: is ignored. For example, • show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)". Minimal complete definition Methods Arguments  :: Int the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10. -> a the value to be converted to a String -> ShowS Convert a value to a readable String. showsPrec should satisfy the law showsPrec d x r ++ s == showsPrec d x (r ++ s) Derived instances of Read and Show satisfy the following: • (x,"") is an element of (readsPrec d (showsPrec d x "")). That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with. show :: a -> String # A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String. showList :: [a] -> ShowS # The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets. Instances  Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Bool -> ShowS #show :: Bool -> String #showList :: [Bool] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Char -> ShowS #show :: Char -> String #showList :: [Char] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Int -> ShowS #show :: Int -> String #showList :: [Int] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowList :: [Integer] -> ShowS # Since: base-4.8.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [Natural] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowList :: [Ordering] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Word -> ShowS #show :: Word -> String #showList :: [Word] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [RuntimeRep] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [VecCount] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [VecElem] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [CallStack] -> ShowS # Show () Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> () -> ShowS #show :: () -> String #showList :: [()] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> TyCon -> ShowS #show :: TyCon -> String #showList :: [TyCon] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Module -> ShowS #showList :: [Module] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> TrName -> ShowS #showList :: [TrName] -> ShowS # Instance detailsDefined in GHC.Show MethodsshowList :: [KindRep] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [TypeLitSort] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [Deadlock] -> ShowS # Since: base-4.7.1.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.10.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [CompactionFailed] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [AssertionFailed] -> ShowS # Since: base-4.7.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [SomeAsyncException] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [AsyncException] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [ArrayException] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [FixIOException] -> ShowS # Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [ExitCode] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [IOErrorType] -> ShowS # Since: base-4.3.0.0 Instance detailsDefined in GHC.IO MethodsshowList :: [MaskingState] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [IOException] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> SrcLoc -> ShowS #showList :: [SrcLoc] -> ShowS # Show a => Show [a] Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> [a] -> ShowS #show :: [a] -> String #showList :: [[a]] -> ShowS # Show a => Show (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Maybe a -> ShowS #show :: Maybe a -> String #showList :: [Maybe a] -> ShowS # Show a => Show (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsshowsPrec :: Int -> Ratio a -> ShowS #show :: Ratio a -> String #showList :: [Ratio a] -> ShowS # Show a => Show (NonEmpty a) Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> NonEmpty a -> ShowS #show :: NonEmpty a -> String #showList :: [NonEmpty a] -> ShowS # (Show a, Show b) => Show (Either a b) Since: base-3.0 Instance detailsDefined in Data.Either MethodsshowsPrec :: Int -> Either a b -> ShowS #show :: Either a b -> String #showList :: [Either a b] -> ShowS # (Show a, Show b) => Show (a, b) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b) -> ShowS #show :: (a, b) -> String #showList :: [(a, b)] -> ShowS # (Show a, Show b, Show c) => Show (a, b, c) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c) -> ShowS #show :: (a, b, c) -> String #showList :: [(a, b, c)] -> ShowS # (Show a, Show b, Show c, Show d) => Show (a, b, c, d) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d) -> ShowS #show :: (a, b, c, d) -> String #showList :: [(a, b, c, d)] -> ShowS # (Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e) -> ShowS #show :: (a, b, c, d, e) -> String #showList :: [(a, b, c, d, e)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f) -> ShowS #show :: (a, b, c, d, e, f) -> String #showList :: [(a, b, c, d, e, f)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS #show :: (a, b, c, d, e, f, g) -> String #showList :: [(a, b, c, d, e, f, g)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS #show :: (a, b, c, d, e, f, g, h) -> String #showList :: [(a, b, c, d, e, f, g, h)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS #show :: (a, b, c, d, e, f, g, h, i) -> String #showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS #show :: (a, b, c, d, e, f, g, h, i, j) -> String #showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS #show :: (a, b, c, d, e, f, g, h, i, j, k) -> String #showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS #show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String #showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS #show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String #showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS #show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String #showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS # (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS #show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String #showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS # type ShowS = String -> String # The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition. type String = [Char] # A String is a list of characters. String constants in Haskell are values of type String. (^) :: (Num a, Integral b) => a -> b -> a infixr 8 # raise a number to a non-negative integral power (^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 # raise a number to an integral power appendFile :: FilePath -> String -> IO () # The computation appendFile file str function appends the string str, to the file file. Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first. main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]]) asTypeOf :: a -> a -> a # asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second. const :: a -> b -> a # const x is a unary function which evaluates to x for all inputs. >>> const 42 "hello" 42  >>> map (const 42) [0..3] [42,42,42,42]  curry :: ((a, b) -> c) -> a -> b -> c # curry converts an uncurried function to a curried function. Examples Expand >>> curry fst 1 2 1  either :: (a -> c) -> (b -> c) -> Either a b -> c # Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b. Examples Expand We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int): >>> let s = Left "foo" :: Either String Int >>> let n = Right 3 :: Either String Int >>> either length (*2) s 3 >>> either length (*2) n 6  error :: HasCallStack => [Char] -> a # error stops execution and displays an error message. even :: Integral a => a -> Bool # flip :: (a -> b -> c) -> b -> a -> c # flip f takes its (first) two arguments in the reverse order of f. >>> flip (++) "hello" "world" "worldhello"  fromIntegral :: (Integral a, Num b) => a -> b # general coercion from integral types fst :: (a, b) -> a # Extract the first component of a pair. Read a character from the standard input device (same as hGetChar stdin). The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin). Read a line from the standard input device (same as hGetLine stdin). id :: a -> a # Identity function. id x = x interact :: (String -> String) -> IO () # The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device. ioError :: IOError -> IO a # Raise an IOException in the IO monad. lcm :: Integral a => a -> a -> a # lcm x y is the smallest positive integer that both x and y divide. The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []). This lexer is not completely faithful to the Haskell lexical syntax in the following respects: • Qualified names are not handled properly • Octal and hexadecimal numerics are not recognized as a single token • Comments are not treated properly lines :: String -> [String] # lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines. Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example, >>> lines "" []  >>> lines "\n" [""]  >>> lines "one" ["one"]  >>> lines "one\n" ["one"]  >>> lines "one\n\n" ["one",""]  >>> lines "one\ntwo" ["one","two"]  >>> lines "one\ntwo\n" ["one","two"]  Thus lines s contains at least as many elements as newlines in s. mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b) # Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_. mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () # Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM. As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad. maximum :: (Foldable t, Ord a) => t a -> a # The largest element of a non-empty structure. maybe :: b -> (a -> b) -> Maybe a -> b # The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result. Examples Expand Basic usage: >>> maybe False odd (Just 3) True  >>> maybe False odd Nothing False  Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default: >>> import Text.Read ( readMaybe ) >>> maybe 0 (*2) (readMaybe "5") 10 >>> maybe 0 (*2) (readMaybe "") 0  Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing": >>> maybe "" show (Just 5) "5" >>> maybe "" show Nothing ""  minimum :: (Foldable t, Ord a) => t a -> a # The least element of a non-empty structure. not :: Bool -> Bool # Boolean "not" odd :: Integral a => a -> Bool # otherwise is defined as the value True. It helps to make guards more readable. eg.  f x | x < 0 = ... | otherwise = ... print :: Show a => a -> IO () # The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline. For example, a program to print the first 20 integers and their powers of 2 could be written as: main = print ([(n, 2^n) | n <- [0..19]]) product :: (Foldable t, Num a) => t a -> a # The product function computes the product of the numbers of a structure. putChar :: Char -> IO () # Write a character to the standard output device (same as hPutChar stdout). putStr :: String -> IO () # Write a string to the standard output device (same as hPutStr stdout). putStrLn :: String -> IO () # The same as putStr, but adds a newline character. read :: Read a => String -> a # The read function reads input from a string, which must be completely consumed by the input process. read fails with an error if the parse is unsuccessful, and it is therefore discouraged from being used in real applications. Use readMaybe or readEither for safe alternatives. >>> read "123" :: Int 123  >>> read "hello" :: Int *** Exception: Prelude.read: no parse  The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents. readIO :: Read a => String -> IO a # The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program. readLn :: Read a => IO a # The readLn function combines getLine and readIO. readParen :: Bool -> ReadS a -> ReadS a # readParen True p parses what p parses, but surrounded with parentheses. readParen False p parses what p parses, but optionally surrounded with parentheses. reads :: Read a => ReadS a # equivalent to readsPrec with a precedence of 0. realToFrac :: (Real a, Fractional b) => a -> b # general coercion to fractional types seq :: a -> b -> b # 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. sequence :: (Traversable t, Monad m) => t (m a) -> m (t a) # Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_. sequence_ :: (Foldable t, Monad m) => t (m a) -> m () # Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence. As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad. utility function converting a Char to a show function that simply prepends the character unchanged. showParen :: Bool -> ShowS -> ShowS # utility function that surrounds the inner show function with parentheses when the Bool parameter is True. utility function converting a String to a show function that simply prepends the string unchanged. shows :: Show a => a -> ShowS # equivalent to showsPrec with a precedence of 0. snd :: (a, b) -> b # Extract the second component of a pair. subtract :: Num a => a -> a -> a # the same as flip (-). Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section. sum :: (Foldable t, Num a) => t a -> a # The sum function computes the sum of the numbers of a structure. uncurry :: (a -> b -> c) -> (a, b) -> c # uncurry converts a curried function to a function on pairs. Examples Expand >>> uncurry (+) (1,2) 3  >>> uncurry ($) (show, 1)
"1"

>>> map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]


undefined :: HasCallStack => a #

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

unlines :: [String] -> String #

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"


until :: (a -> Bool) -> (a -> a) -> a -> a #

until p f yields the result of applying f until p holds.

Construct an IOException value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

instance Monad IO where
...
fail s = ioError (userError s)

writeFile :: FilePath -> String -> IO () #

The computation writeFile file str function writes the string str, to the file file`.

(||) :: Bool -> Bool -> Bool infixr 2 #

Boolean "or"

(!!) :: [a] -> Int -> a Source #

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

all :: (a -> Bool) -> [a] -> Bool Source #

and :: [Bool] -> Bool Source #

any :: (a -> Bool) -> [a] -> Bool Source #

break :: (a -> Bool) -> [a] -> ([a], [a]) Source #

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

concatMap :: (a -> [b]) -> [a] -> [b] Source #

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

drop :: Int -> [a] -> [a] Source #

dropWhile :: (a -> Bool) -> [a] -> [a] Source #

elem :: Eq a => a -> [a] -> Bool Source #

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

foldl :: (a -> b -> a) -> a -> [b] -> a Source #

foldl1 :: (a -> a -> a) -> [a] -> a Source #

foldr :: (a -> b -> b) -> b -> [a] -> b Source #

foldr1 :: (a -> a -> a) -> [a] -> a Source #

head :: [a] -> a Source #

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

iterate :: (a -> a) -> a -> [a] Source #

last :: [a] -> a Source #

length :: [a] -> Int Source #

lookup :: Eq a => a -> [(a, b)] -> Maybe b Source #

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

notElem :: Eq a => a -> [a] -> Bool Source #

null :: [a] -> Bool Source #

or :: [Bool] -> Bool Source #

repeat :: a -> [a] Source #

replicate :: Int -> a -> [a] Source #

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

scanl :: (a -> b -> a) -> a -> [b] -> [a] Source #

scanl1 :: (a -> a -> a) -> [a] -> [a] Source #

scanr :: (a -> b -> b) -> b -> [a] -> [b] Source #

scanr1 :: (a -> a -> a) -> [a] -> [a] Source #

span :: (a -> Bool) -> [a] -> ([a], [a]) Source #

splitAt :: Int -> [a] -> ([a], [a]) Source #

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

take :: Int -> [a] -> [a] Source #

takeWhile :: (a -> Bool) -> [a] -> [a] Source #

unzip :: [(a, b)] -> ([a], [b]) Source #

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) Source #

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

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] Source #

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source #

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #