prelude-compat-0.0: 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.

(&&) :: 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

 Methods 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] # Methods(==) :: Bool -> Bool -> Bool #(/=) :: Bool -> Bool -> Bool # Methodscompare :: Bool -> Bool -> Ordering #(<) :: Bool -> Bool -> Bool #(<=) :: Bool -> Bool -> Bool #(>) :: Bool -> Bool -> Bool #(>=) :: Bool -> Bool -> Bool #max :: Bool -> Bool -> Bool #min :: Bool -> Bool -> Bool # Methods 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.

Minimal complete definition

Methods

minBound :: a #

maxBound :: a #

Instances

 Methods Methods Methods Methods Methods Bounded () MethodsminBound :: () #maxBound :: () # Methods Methods Methods Methods (Bounded a, Bounded b) => Bounded (a, b) MethodsminBound :: (a, b) #maxBound :: (a, b) # (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) MethodsminBound :: (a, b, c) #maxBound :: (a, b, c) # (~) k a b => Bounded ((:~:) k a b) MethodsminBound :: (k :~: a) b #maxBound :: (k :~: a) b # (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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

 Methods 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] # Methods(==) :: Char -> Char -> Bool #(/=) :: Char -> Char -> Bool # Methodscompare :: Char -> Char -> Ordering #(<) :: Char -> Char -> Bool #(<=) :: Char -> Char -> Bool #(>) :: Char -> Char -> Bool #(>=) :: Char -> Char -> Bool #max :: Char -> Char -> Char #min :: Char -> Char -> Char # Methods MethodsshowsPrec :: Int -> Char -> ShowS #show :: Char -> String #showList :: [Char] -> ShowS # Methodsfmap :: (a -> b) -> URec Char a -> URec Char b #(<$) :: a -> URec Char b -> URec Char a # 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 # 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) # Associated Typestype Rep1 (URec Char :: * -> *) :: * -> * # Methodsfrom1 :: URec Char a -> Rep1 (URec Char) a #to1 :: Rep1 (URec Char) a -> URec Char a # Eq (URec Char p) Methods(==) :: URec Char p -> URec Char p -> Bool #(/=) :: URec Char p -> URec Char p -> Bool # Ord (URec Char p) Methodscompare :: URec Char p -> URec Char p -> Ordering #(<) :: URec Char p -> URec Char p -> Bool #(<=) :: URec Char p -> URec Char p -> Bool #(>) :: URec Char p -> URec Char p -> Bool #(>=) :: URec Char p -> URec Char p -> Bool #max :: URec Char p -> URec Char p -> URec Char p #min :: URec Char p -> URec Char p -> URec Char p # Show (URec Char p) MethodsshowsPrec :: Int -> URec Char p -> ShowS #show :: URec Char p -> String #showList :: [URec Char p] -> ShowS # Associated Typestype Rep (URec Char p) :: * -> * # Methodsfrom :: URec Char p -> Rep (URec Char p) x #to :: Rep (URec Char p) x -> URec Char p # data URec Char Used for marking occurrences of Char# data URec Char = UChar {uChar# :: Char#} type Rep1 (URec Char) type Rep1 (URec Char) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UChar" PrefixI True) (S1 (MetaSel (Just Symbol "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UChar)) type Rep (URec Char p) type Rep (URec Char p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UChar" PrefixI True) (S1 (MetaSel (Just Symbol "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UChar)) 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  Methods(==) :: Double -> Double -> Bool #(/=) :: Double -> Double -> Bool # Methodsexp :: Double -> Double #log :: Double -> Double #(**) :: Double -> Double -> Double #sin :: Double -> Double #cos :: Double -> Double #tan :: Double -> Double # Methods(<) :: Double -> Double -> Bool #(<=) :: Double -> Double -> Bool #(>) :: Double -> Double -> Bool #(>=) :: Double -> Double -> Bool #max :: Double -> Double -> Double #min :: Double -> Double -> Double # Methods MethodsfloatRange :: Double -> (Int, Int) #decodeFloat :: Double -> (Integer, Int) #isNaN :: Double -> Bool #atan2 :: Double -> Double -> Double # Methodsfmap :: (a -> b) -> URec Double a -> URec Double b #(<$) :: a -> URec Double b -> URec Double a # 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 # 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) # Associated Typestype Rep1 (URec Double :: * -> *) :: * -> * # Methodsfrom1 :: URec Double a -> Rep1 (URec Double) a #to1 :: Rep1 (URec Double) a -> URec Double a # Eq (URec Double p) Methods(==) :: URec Double p -> URec Double p -> Bool #(/=) :: URec Double p -> URec Double p -> Bool # Methodscompare :: URec Double p -> URec Double p -> Ordering #(<) :: URec Double p -> URec Double p -> Bool #(<=) :: URec Double p -> URec Double p -> Bool #(>) :: URec Double p -> URec Double p -> Bool #(>=) :: URec Double p -> URec Double p -> Bool #max :: URec Double p -> URec Double p -> URec Double p #min :: URec Double p -> URec Double p -> URec Double p # MethodsshowsPrec :: Int -> URec Double p -> ShowS #show :: URec Double p -> String #showList :: [URec Double p] -> ShowS # Associated Typestype Rep (URec Double p) :: * -> * # Methodsfrom :: URec Double p -> Rep (URec Double p) x #to :: Rep (URec Double p) x -> URec Double p # data URec Double Used for marking occurrences of Double# data URec Double = UDouble {uDouble# :: Double#} type Rep1 (URec Double) type Rep1 (URec Double) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UDouble)) type Rep (URec Double p) type Rep (URec Double p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UDouble))

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

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) 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 # Methodsfmap :: (a -> b) -> Either a a -> Either a b #(<$) :: a -> Either a b -> Either a a # Methodspure :: a -> Either e a #(<*>) :: Either e (a -> b) -> Either e a -> Either e b #(*>) :: Either e a -> Either e b -> Either e b #(<*) :: Either e a -> Either e b -> Either e a # Methodsfold :: Monoid m => Either a m -> m #foldMap :: Monoid m => (a -> m) -> Either a a -> m #foldr :: (a -> b -> b) -> b -> Either a a -> b #foldr' :: (a -> b -> b) -> b -> Either a a -> b #foldl :: (b -> a -> b) -> b -> Either a a -> b #foldl' :: (b -> a -> b) -> b -> Either a a -> b #foldr1 :: (a -> a -> a) -> Either a a -> a #foldl1 :: (a -> a -> a) -> Either a a -> a #toList :: Either a a -> [a] #null :: Either a a -> Bool #length :: Either a a -> Int #elem :: Eq a => a -> Either a a -> Bool #maximum :: Ord a => Either a a -> a #minimum :: Ord a => Either a a -> a #sum :: Num a => Either a a -> a #product :: Num a => Either a a -> a # Methodstraverse :: Applicative f => (a -> f b) -> Either a a -> f (Either a b) #sequenceA :: Applicative f => Either a (f a) -> f (Either a a) #mapM :: Monad m => (a -> m b) -> Either a a -> m (Either a b) #sequence :: Monad m => Either a (m a) -> m (Either a a) # Associated Typestype Rep1 (Either a :: * -> *) :: * -> * # Methodsfrom1 :: Either a a -> Rep1 (Either a) a #to1 :: Rep1 (Either a) a -> Either a a # (Eq b, Eq a) => Eq (Either a b) Methods(==) :: Either a b -> Either a b -> Bool #(/=) :: Either a b -> Either a b -> Bool # (Ord b, Ord a) => Ord (Either a b) 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 b, Read a) => Read (Either a b) MethodsreadsPrec :: Int -> ReadS (Either a b) #readList :: ReadS [Either a b] #readPrec :: ReadPrec (Either a b) #readListPrec :: ReadPrec [Either a b] # (Show b, Show a) => Show (Either a b) MethodsshowsPrec :: Int -> Either a b -> ShowS #show :: Either a b -> String #showList :: [Either a b] -> ShowS # Generic (Either a b) Associated Typestype Rep (Either a b) :: * -> * # Methodsfrom :: Either a b -> Rep (Either a b) x #to :: Rep (Either a b) x -> Either a b # type Rep1 (Either a) type Rep1 (Either a) = D1 (MetaData "Either" "Data.Either" "base" False) ((:+:) (C1 (MetaCons "Left" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) (C1 (MetaCons "Right" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))) type Rep (Either a b) type Rep (Either a b) = D1 (MetaData "Either" "Data.Either" "base" False) ((:+:) (C1 (MetaCons "Left" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) (C1 (MetaCons "Right" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b)))) type (==) (Either k k1) a b type (==) (Either k k1) a b = EqEither k k1 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..]. enumFromThen :: a -> a -> [a] # Used in Haskell's translation of [n,n'..]. enumFromTo :: a -> a -> [a] # Used in Haskell's translation of [n..m]. enumFromThenTo :: a -> a -> a -> [a] # Used in Haskell's translation of [n,n'..m]. Instances  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] # 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] # 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] # MethodsenumFrom :: Integer -> [Integer] #enumFromThen :: Integer -> Integer -> [Integer] #enumFromTo :: Integer -> Integer -> [Integer] #enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] # MethodsenumFrom :: Ordering -> [Ordering] #enumFromTo :: Ordering -> Ordering -> [Ordering] # 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] # Enum () Methodssucc :: () -> () #pred :: () -> () #toEnum :: Int -> () #fromEnum :: () -> Int #enumFrom :: () -> [()] #enumFromThen :: () -> () -> [()] #enumFromTo :: () -> () -> [()] #enumFromThenTo :: () -> () -> () -> [()] # Methods Methods Methods Methods Integral a => Enum (Ratio a) 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] # Enum (Proxy k s) Methodssucc :: Proxy k s -> Proxy k s #pred :: Proxy k s -> Proxy k s #toEnum :: Int -> Proxy k s #fromEnum :: Proxy k s -> Int #enumFrom :: Proxy k s -> [Proxy k s] #enumFromThen :: Proxy k s -> Proxy k s -> [Proxy k s] #enumFromTo :: Proxy k s -> Proxy k s -> [Proxy k s] #enumFromThenTo :: Proxy k s -> Proxy k s -> Proxy k s -> [Proxy k s] # (~) k a b => Enum ((:~:) k a b) Methodssucc :: (k :~: a) b -> (k :~: a) b #pred :: (k :~: a) b -> (k :~: a) b #toEnum :: Int -> (k :~: a) b #fromEnum :: (k :~: a) b -> Int #enumFrom :: (k :~: a) b -> [(k :~: a) b] #enumFromThen :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] #enumFromTo :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] #enumFromThenTo :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] # class Eq a where # The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq. Minimal complete definition: either == or /=. Minimal complete definition Methods (==) :: a -> a -> Bool infix 4 # (/=) :: a -> a -> Bool infix 4 # Instances  Methods(==) :: Bool -> Bool -> Bool #(/=) :: Bool -> Bool -> Bool # Methods(==) :: Char -> Char -> Bool #(/=) :: Char -> Char -> Bool # Methods(==) :: Double -> Double -> Bool #(/=) :: Double -> Double -> Bool # Methods(==) :: Float -> Float -> Bool #(/=) :: Float -> Float -> Bool # Methods(==) :: Int -> Int -> Bool #(/=) :: Int -> Int -> Bool # Methods(==) :: Integer -> Integer -> Bool #(/=) :: Integer -> Integer -> Bool # Methods Methods(==) :: Word -> Word -> Bool #(/=) :: Word -> Word -> Bool # Eq () Methods(==) :: () -> () -> Bool #(/=) :: () -> () -> Bool # Methods(==) :: TyCon -> TyCon -> Bool #(/=) :: TyCon -> TyCon -> Bool # Methods(==) :: BigNat -> BigNat -> Bool #(/=) :: BigNat -> BigNat -> Bool # Methods Methods Methods Methods Methods(==) :: Fixity -> Fixity -> Bool #(/=) :: Fixity -> Fixity -> Bool # Methods Methods Methods Methods Methods Methods Methods(==) :: SrcLoc -> SrcLoc -> Bool #(/=) :: SrcLoc -> SrcLoc -> Bool # Eq a => Eq [a] Methods(==) :: [a] -> [a] -> Bool #(/=) :: [a] -> [a] -> Bool # Eq a => Eq (Maybe a) Methods(==) :: Maybe a -> Maybe a -> Bool #(/=) :: Maybe a -> Maybe a -> Bool # Eq a => Eq (Ratio a) Methods(==) :: Ratio a -> Ratio a -> Bool #(/=) :: Ratio a -> Ratio a -> Bool # Eq (Ptr a) Methods(==) :: Ptr a -> Ptr a -> Bool #(/=) :: Ptr a -> Ptr a -> Bool # Eq (FunPtr a) Methods(==) :: FunPtr a -> FunPtr a -> Bool #(/=) :: FunPtr a -> FunPtr a -> Bool # Eq (V1 p) Methods(==) :: V1 p -> V1 p -> Bool #(/=) :: V1 p -> V1 p -> Bool # Eq (U1 p) Methods(==) :: U1 p -> U1 p -> Bool #(/=) :: U1 p -> U1 p -> Bool # Eq p => Eq (Par1 p) Methods(==) :: Par1 p -> Par1 p -> Bool #(/=) :: Par1 p -> Par1 p -> Bool # (Eq b, Eq a) => Eq (Either a b) Methods(==) :: Either a b -> Either a b -> Bool #(/=) :: Either a b -> Either a b -> Bool # Eq (f p) => Eq (Rec1 f p) Methods(==) :: Rec1 f p -> Rec1 f p -> Bool #(/=) :: Rec1 f p -> Rec1 f p -> Bool # Eq (URec Char p) Methods(==) :: URec Char p -> URec Char p -> Bool #(/=) :: URec Char p -> URec Char p -> Bool # Eq (URec Double p) Methods(==) :: URec Double p -> URec Double p -> Bool #(/=) :: URec Double p -> URec Double p -> Bool # Eq (URec Float p) Methods(==) :: URec Float p -> URec Float p -> Bool #(/=) :: URec Float p -> URec Float p -> Bool # Eq (URec Int p) Methods(==) :: URec Int p -> URec Int p -> Bool #(/=) :: URec Int p -> URec Int p -> Bool # Eq (URec Word p) Methods(==) :: URec Word p -> URec Word p -> Bool #(/=) :: URec Word p -> URec Word p -> Bool # Eq (URec (Ptr ()) p) Methods(==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (Eq a, Eq b) => Eq (a, b) Methods(==) :: (a, b) -> (a, b) -> Bool #(/=) :: (a, b) -> (a, b) -> Bool # Eq (Proxy k s) Methods(==) :: Proxy k s -> Proxy k s -> Bool #(/=) :: Proxy k s -> Proxy k s -> Bool # Eq c => Eq (K1 i c p) Methods(==) :: K1 i c p -> K1 i c p -> Bool #(/=) :: K1 i c p -> K1 i c p -> Bool # (Eq (g p), Eq (f p)) => Eq ((:+:) f g p) Methods(==) :: (f :+: g) p -> (f :+: g) p -> Bool #(/=) :: (f :+: g) p -> (f :+: g) p -> Bool # (Eq (g p), Eq (f p)) => Eq ((:*:) f g p) Methods(==) :: (f :*: g) p -> (f :*: g) p -> Bool #(/=) :: (f :*: g) p -> (f :*: g) p -> Bool # Eq (f (g p)) => Eq ((:.:) f g p) Methods(==) :: (f :.: g) p -> (f :.: g) p -> Bool #(/=) :: (f :.: g) p -> (f :.: g) p -> Bool # (Eq a, Eq b, Eq c) => Eq (a, b, c) Methods(==) :: (a, b, c) -> (a, b, c) -> Bool #(/=) :: (a, b, c) -> (a, b, c) -> Bool # Eq ((:~:) k a b) Methods(==) :: (k :~: a) b -> (k :~: a) b -> Bool #(/=) :: (k :~: a) b -> (k :~: a) b -> Bool # Eq (f p) => Eq (M1 i c f p) Methods(==) :: M1 i c f p -> M1 i c f p -> Bool #(/=) :: M1 i c f p -> M1 i c f p -> Bool # (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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  Methods(==) :: Float -> Float -> Bool #(/=) :: Float -> Float -> Bool # 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 # Methods(<) :: Float -> Float -> Bool #(<=) :: Float -> Float -> Bool #(>) :: Float -> Float -> Bool #(>=) :: Float -> Float -> Bool #max :: Float -> Float -> Float #min :: Float -> Float -> Float # Methods MethodsfloatRange :: Float -> (Int, Int) #decodeFloat :: Float -> (Integer, Int) #scaleFloat :: Int -> Float -> Float #isNaN :: Float -> Bool #isIEEE :: Float -> Bool #atan2 :: Float -> Float -> Float # Methodsfmap :: (a -> b) -> URec Float a -> URec Float b #(<$) :: a -> URec Float b -> URec Float a # 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 # 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) # Associated Typestype Rep1 (URec Float :: * -> *) :: * -> * # Methodsfrom1 :: URec Float a -> Rep1 (URec Float) a #to1 :: Rep1 (URec Float) a -> URec Float a # Eq (URec Float p) Methods(==) :: URec Float p -> URec Float p -> Bool #(/=) :: URec Float p -> URec Float p -> Bool # Ord (URec Float p) Methodscompare :: URec Float p -> URec Float p -> Ordering #(<) :: URec Float p -> URec Float p -> Bool #(<=) :: URec Float p -> URec Float p -> Bool #(>) :: URec Float p -> URec Float p -> Bool #(>=) :: URec Float p -> URec Float p -> Bool #max :: URec Float p -> URec Float p -> URec Float p #min :: URec Float p -> URec Float p -> URec Float p # MethodsshowsPrec :: Int -> URec Float p -> ShowS #show :: URec Float p -> String #showList :: [URec Float p] -> ShowS # Associated Typestype Rep (URec Float p) :: * -> * # Methodsfrom :: URec Float p -> Rep (URec Float p) x #to :: Rep (URec Float p) x -> URec Float p # data URec Float Used for marking occurrences of Float# data URec Float = UFloat {uFloat# :: Float#} type Rep1 (URec Float) type Rep1 (URec Float) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UFloat)) type Rep (URec Float p) type Rep (URec Float p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UFloat))

class Fractional a => Floating a where #

Trigonometric and hyperbolic functions and related functions.

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

 Methodsexp :: Double -> Double #log :: Double -> Double #(**) :: Double -> Double -> Double #sin :: Double -> Double #cos :: Double -> Double #tan :: Double -> Double # 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.

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) Methods(/) :: Ratio a -> Ratio a -> Ratio a #recip :: Ratio a -> Ratio a #

class Functor f 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.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b #

Instances

 Functor [] Methodsfmap :: (a -> b) -> [a] -> [b] #(<$) :: a -> [b] -> [a] # Methodsfmap :: (a -> b) -> Maybe a -> Maybe b #(<$) :: a -> Maybe b -> Maybe a # Methodsfmap :: (a -> b) -> IO a -> IO b #(<$) :: a -> IO b -> IO a # Methodsfmap :: (a -> b) -> V1 a -> V1 b #(<$) :: a -> V1 b -> V1 a # Methodsfmap :: (a -> b) -> U1 a -> U1 b #(<$) :: a -> U1 b -> U1 a # Methodsfmap :: (a -> b) -> Par1 a -> Par1 b #(<$) :: a -> Par1 b -> Par1 a # Functor Id Methodsfmap :: (a -> b) -> Id a -> Id b #(<$) :: a -> Id b -> Id a # Methodsfmap :: (a -> b) -> P a -> P b #(<$) :: a -> P b -> P a # Methodsfmap :: (a -> b) -> ReadP a -> ReadP b #(<$) :: a -> ReadP b -> ReadP a # Functor ((->) r) Methodsfmap :: (a -> b) -> (r -> a) -> r -> b #(<$) :: a -> (r -> b) -> r -> a # Methodsfmap :: (a -> b) -> Either a a -> Either a b #(<$) :: a -> Either a b -> Either a a # Functor f => Functor (Rec1 f) Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b #(<$) :: a -> Rec1 f b -> Rec1 f a # Methodsfmap :: (a -> b) -> URec Char a -> URec Char b #(<$) :: a -> URec Char b -> URec Char a # Methodsfmap :: (a -> b) -> URec Double a -> URec Double b #(<$) :: a -> URec Double b -> URec Double a # Methodsfmap :: (a -> b) -> URec Float a -> URec Float b #(<$) :: a -> URec Float b -> URec Float a # Methodsfmap :: (a -> b) -> URec Int a -> URec Int b #(<$) :: a -> URec Int b -> URec Int a # Methodsfmap :: (a -> b) -> URec Word a -> URec Word b #(<$) :: a -> URec Word b -> URec Word a # Functor (URec (Ptr ())) Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a # Functor ((,) a) Methodsfmap :: (a -> b) -> (a, a) -> (a, b) #(<$) :: a -> (a, b) -> (a, a) # Functor (StateL s) Methodsfmap :: (a -> b) -> StateL s a -> StateL s b #(<$) :: a -> StateL s b -> StateL s a # Functor (StateR s) Methodsfmap :: (a -> b) -> StateR s a -> StateR s b #(<$) :: a -> StateR s b -> StateR s a # Methodsfmap :: (a -> b) -> Proxy * a -> Proxy * b #(<$) :: a -> Proxy * b -> Proxy * a # Functor (K1 i c) Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b #(<$) :: a -> K1 i c b -> K1 i c a # (Functor g, Functor f) => Functor ((:+:) f g) Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b #(<$) :: a -> (f :+: g) b -> (f :+: g) a # (Functor g, Functor f) => Functor ((:*:) f g) Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b #(<$) :: a -> (f :*: g) b -> (f :*: g) a # (Functor g, Functor f) => Functor ((:.:) f g) Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b #(<$) :: a -> (f :.: g) b -> (f :.: g) a # Functor f => Functor (M1 i c f) Methodsfmap :: (a -> b) -> M1 i c f a -> M1 i c f b #(<$) :: a -> M1 i c f b -> M1 i c f a # data IO a :: * -> * # A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a. There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main. IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class. Instances  Methods(>>=) :: IO a -> (a -> IO b) -> IO b #(>>) :: IO a -> IO b -> IO b #return :: a -> IO a #fail :: String -> IO a # Methodsfmap :: (a -> b) -> IO a -> IO b #(<$) :: a -> IO b -> IO a # Methodspure :: a -> IO a #(<*>) :: IO (a -> b) -> IO a -> IO b #(*>) :: IO a -> IO b -> IO b #(<*) :: IO a -> IO b -> IO a # Methodsempty :: IO a #(<|>) :: IO a -> IO a -> IO a #some :: IO a -> IO [a] #many :: IO a -> IO [a] # Methodsmzero :: IO a #mplus :: IO a -> IO a -> IO a # Monoid a => Monoid (IO a) 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 IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.

In Haskell 2010, this is an opaque type.

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

 Methods 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] # Methods(==) :: Int -> Int -> Bool #(/=) :: Int -> Int -> Bool # 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) # Methods(+) :: Int -> Int -> Int #(-) :: Int -> Int -> Int #(*) :: Int -> Int -> Int #negate :: Int -> Int #abs :: Int -> Int #signum :: Int -> Int # Methodscompare :: Int -> Int -> Ordering #(<) :: Int -> Int -> Bool #(<=) :: Int -> Int -> Bool #(>) :: Int -> Int -> Bool #(>=) :: Int -> Int -> Bool #max :: Int -> Int -> Int #min :: Int -> Int -> Int # Methods Methods MethodsshowsPrec :: Int -> Int -> ShowS #show :: Int -> String #showList :: [Int] -> ShowS # Methodsfmap :: (a -> b) -> URec Int a -> URec Int b #(<$) :: a -> URec Int b -> URec Int a # 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 # 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) # Associated Typestype Rep1 (URec Int :: * -> *) :: * -> * # Methodsfrom1 :: URec Int a -> Rep1 (URec Int) a #to1 :: Rep1 (URec Int) a -> URec Int a # Eq (URec Int p) Methods(==) :: URec Int p -> URec Int p -> Bool #(/=) :: URec Int p -> URec Int p -> Bool # Ord (URec Int p) Methodscompare :: URec Int p -> URec Int p -> Ordering #(<) :: URec Int p -> URec Int p -> Bool #(<=) :: URec Int p -> URec Int p -> Bool #(>) :: URec Int p -> URec Int p -> Bool #(>=) :: URec Int p -> URec Int p -> Bool #max :: URec Int p -> URec Int p -> URec Int p #min :: URec Int p -> URec Int p -> URec Int p # Show (URec Int p) MethodsshowsPrec :: Int -> URec Int p -> ShowS #show :: URec Int p -> String #showList :: [URec Int p] -> ShowS # Associated Typestype Rep (URec Int p) :: * -> * # Methodsfrom :: URec Int p -> Rep (URec Int p) x #to :: Rep (URec Int p) x -> URec Int p # data URec Int Used for marking occurrences of Int# data URec Int = UInt {uInt# :: Int#} type Rep1 (URec Int) type Rep1 (URec Int) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UInt)) type Rep (URec Int p) type Rep (URec Int p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UInt)) 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  MethodsenumFrom :: Integer -> [Integer] #enumFromThen :: Integer -> Integer -> [Integer] #enumFromTo :: Integer -> Integer -> [Integer] #enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] # Methods(==) :: Integer -> Integer -> Bool #(/=) :: Integer -> Integer -> Bool # MethodsquotRem :: Integer -> Integer -> (Integer, Integer) #divMod :: Integer -> Integer -> (Integer, Integer) # Methods Methods(<) :: Integer -> Integer -> Bool #(<=) :: Integer -> Integer -> Bool #(>) :: Integer -> Integer -> Bool #(>=) :: Integer -> Integer -> Bool # Methods Methods MethodsshowList :: [Integer] -> ShowS # class (Real a, Enum a) => Integral a where # Integral numbers, supporting integer division. 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  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) # MethodsquotRem :: Integer -> Integer -> (Integer, Integer) #divMod :: Integer -> Integer -> (Integer, Integer) # 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  Methods(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b #(>>) :: Maybe a -> Maybe b -> Maybe b #return :: a -> Maybe a #fail :: String -> Maybe a # Methodsfmap :: (a -> b) -> Maybe a -> Maybe b #(<$) :: a -> Maybe b -> Maybe a # Methodspure :: a -> Maybe a #(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b #(*>) :: Maybe a -> Maybe b -> Maybe b #(<*) :: Maybe a -> Maybe b -> Maybe a # 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 # 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) # Associated Typestype Rep1 (Maybe :: * -> *) :: * -> * # Methodsfrom1 :: Maybe a -> Rep1 Maybe a #to1 :: Rep1 Maybe a -> Maybe a # Methodsempty :: Maybe a #(<|>) :: Maybe a -> Maybe a -> Maybe a #some :: Maybe a -> Maybe [a] #many :: Maybe a -> Maybe [a] # Methodsmzero :: Maybe a #mplus :: Maybe a -> Maybe a -> Maybe a # Eq a => Eq (Maybe a) Methods(==) :: Maybe a -> Maybe a -> Bool #(/=) :: Maybe a -> Maybe a -> Bool # Ord a => Ord (Maybe a) 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) MethodsreadsPrec :: Int -> ReadS (Maybe a) #readList :: ReadS [Maybe a] # Show a => Show (Maybe a) MethodsshowsPrec :: Int -> Maybe a -> ShowS #show :: Maybe a -> String #showList :: [Maybe a] -> ShowS # Generic (Maybe a) Associated Typestype Rep (Maybe a) :: * -> * # Methodsfrom :: Maybe a -> Rep (Maybe a) x #to :: Rep (Maybe a) x -> Maybe a # Monoid 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 there is no "Semigroup" typeclass providing just mappend, we use Monoid instead. Methodsmempty :: Maybe a #mappend :: Maybe a -> Maybe a -> Maybe a #mconcat :: [Maybe a] -> Maybe a # SingI (Maybe a) (Nothing a) Methodssing :: Sing (Nothing a) a SingKind a (KProxy a) => SingKind (Maybe a) (KProxy (Maybe a)) Associated Typestype DemoteRep (KProxy (Maybe a)) (kparam :: KProxy (KProxy (Maybe a))) :: * MethodsfromSing :: Sing (KProxy (Maybe a)) a -> DemoteRep (KProxy (Maybe a)) kparam SingI a a1 => SingI (Maybe a) (Just a a1) Methodssing :: Sing (Just a a1) a type Rep1 Maybe type Rep1 Maybe = D1 (MetaData "Maybe" "GHC.Base" "base" False) ((:+:) (C1 (MetaCons "Nothing" PrefixI False) U1) (C1 (MetaCons "Just" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))) type Rep (Maybe a) type Rep (Maybe a) = D1 (MetaData "Maybe" "GHC.Base" "base" False) ((:+:) (C1 (MetaCons "Nothing" PrefixI False) U1) (C1 (MetaCons "Just" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))) data Sing (Maybe a) data Sing (Maybe a) whereSNothing :: Sing (Maybe a) (Nothing a)SJust :: Sing (Maybe a) (Just a a1) type (==) (Maybe k) a b type (==) (Maybe k) a b = EqMaybe k a b type DemoteRep (Maybe a) (KProxy (Maybe a)) type DemoteRep (Maybe a) (KProxy (Maybe a)) = Maybe (DemoteRep a (KProxy a))

class Applicative m => Monad m 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.

fail :: 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.

Instances

class Num a where #

Basic numeric class.

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

 Methods(+) :: Int -> Int -> Int #(-) :: Int -> Int -> Int #(*) :: Int -> Int -> Int #negate :: Int -> Int #abs :: Int -> Int #signum :: Int -> Int # Methods Methods(+) :: Word -> Word -> Word #(-) :: Word -> Word -> Word #(*) :: Word -> Word -> Word #negate :: Word -> Word #abs :: Word -> Word #signum :: Word -> Word # Integral a => Num (Ratio a) 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.

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

 Methodscompare :: Bool -> Bool -> Ordering #(<) :: Bool -> Bool -> Bool #(<=) :: Bool -> Bool -> Bool #(>) :: Bool -> Bool -> Bool #(>=) :: Bool -> Bool -> Bool #max :: Bool -> Bool -> Bool #min :: Bool -> Bool -> Bool # Methodscompare :: Char -> Char -> Ordering #(<) :: Char -> Char -> Bool #(<=) :: Char -> Char -> Bool #(>) :: Char -> Char -> Bool #(>=) :: Char -> Char -> Bool #max :: Char -> Char -> Char #min :: Char -> Char -> Char # Methods(<) :: Double -> Double -> Bool #(<=) :: Double -> Double -> Bool #(>) :: Double -> Double -> Bool #(>=) :: Double -> Double -> Bool #max :: Double -> Double -> Double #min :: Double -> Double -> Double # Methods(<) :: Float -> Float -> Bool #(<=) :: Float -> Float -> Bool #(>) :: Float -> Float -> Bool #(>=) :: Float -> Float -> Bool #max :: Float -> Float -> Float #min :: Float -> Float -> Float # Methodscompare :: Int -> Int -> Ordering #(<) :: Int -> Int -> Bool #(<=) :: Int -> Int -> Bool #(>) :: Int -> Int -> Bool #(>=) :: Int -> Int -> Bool #max :: Int -> Int -> Int #min :: Int -> Int -> Int # Methods(<) :: Integer -> Integer -> Bool #(<=) :: Integer -> Integer -> Bool #(>) :: Integer -> Integer -> Bool #(>=) :: Integer -> Integer -> Bool # Methods(<) :: Ordering -> Ordering -> Bool #(>) :: Ordering -> Ordering -> Bool # 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 () Methodscompare :: () -> () -> Ordering #(<) :: () -> () -> Bool #(<=) :: () -> () -> Bool #(>) :: () -> () -> Bool #(>=) :: () -> () -> Bool #max :: () -> () -> () #min :: () -> () -> () # Methods(<) :: TyCon -> TyCon -> Bool #(<=) :: TyCon -> TyCon -> Bool #(>) :: TyCon -> TyCon -> Bool #(>=) :: TyCon -> TyCon -> Bool #max :: TyCon -> TyCon -> TyCon #min :: TyCon -> TyCon -> TyCon # Methods(<) :: BigNat -> BigNat -> Bool #(<=) :: BigNat -> BigNat -> Bool #(>) :: BigNat -> BigNat -> Bool #(>=) :: BigNat -> BigNat -> Bool #max :: BigNat -> BigNat -> BigNat #min :: BigNat -> BigNat -> BigNat # Methods Methods Methods(<) :: ExitCode -> ExitCode -> Bool #(>) :: ExitCode -> ExitCode -> Bool # Methods(<) :: Fixity -> Fixity -> Bool #(<=) :: Fixity -> Fixity -> Bool #(>) :: Fixity -> Fixity -> Bool #(>=) :: Fixity -> Fixity -> Bool #max :: Fixity -> Fixity -> Fixity #min :: Fixity -> Fixity -> Fixity # Methods Methods Methods Methods Ord a => Ord [a] 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) 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) 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 (Ptr a) Methodscompare :: Ptr a -> Ptr a -> Ordering #(<) :: Ptr a -> Ptr a -> Bool #(<=) :: Ptr a -> Ptr a -> Bool #(>) :: Ptr a -> Ptr a -> Bool #(>=) :: Ptr a -> Ptr a -> Bool #max :: Ptr a -> Ptr a -> Ptr a #min :: Ptr a -> Ptr a -> Ptr a # Ord (FunPtr a) Methodscompare :: FunPtr a -> FunPtr a -> Ordering #(<) :: FunPtr a -> FunPtr a -> Bool #(<=) :: FunPtr a -> FunPtr a -> Bool #(>) :: FunPtr a -> FunPtr a -> Bool #(>=) :: FunPtr a -> FunPtr a -> Bool #max :: FunPtr a -> FunPtr a -> FunPtr a #min :: FunPtr a -> FunPtr a -> FunPtr a # Ord (V1 p) Methodscompare :: V1 p -> V1 p -> Ordering #(<) :: V1 p -> V1 p -> Bool #(<=) :: V1 p -> V1 p -> Bool #(>) :: V1 p -> V1 p -> Bool #(>=) :: V1 p -> V1 p -> Bool #max :: V1 p -> V1 p -> V1 p #min :: V1 p -> V1 p -> V1 p # Ord (U1 p) Methodscompare :: U1 p -> U1 p -> Ordering #(<) :: U1 p -> U1 p -> Bool #(<=) :: U1 p -> U1 p -> Bool #(>) :: U1 p -> U1 p -> Bool #(>=) :: U1 p -> U1 p -> Bool #max :: U1 p -> U1 p -> U1 p #min :: U1 p -> U1 p -> U1 p # Ord p => Ord (Par1 p) Methodscompare :: Par1 p -> Par1 p -> Ordering #(<) :: Par1 p -> Par1 p -> Bool #(<=) :: Par1 p -> Par1 p -> Bool #(>) :: Par1 p -> Par1 p -> Bool #(>=) :: Par1 p -> Par1 p -> Bool #max :: Par1 p -> Par1 p -> Par1 p #min :: Par1 p -> Par1 p -> Par1 p # (Ord b, Ord a) => Ord (Either a b) 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 (f p) => Ord (Rec1 f p) Methodscompare :: Rec1 f p -> Rec1 f p -> Ordering #(<) :: Rec1 f p -> Rec1 f p -> Bool #(<=) :: Rec1 f p -> Rec1 f p -> Bool #(>) :: Rec1 f p -> Rec1 f p -> Bool #(>=) :: Rec1 f p -> Rec1 f p -> Bool #max :: Rec1 f p -> Rec1 f p -> Rec1 f p #min :: Rec1 f p -> Rec1 f p -> Rec1 f p # Ord (URec Char p) Methodscompare :: URec Char p -> URec Char p -> Ordering #(<) :: URec Char p -> URec Char p -> Bool #(<=) :: URec Char p -> URec Char p -> Bool #(>) :: URec Char p -> URec Char p -> Bool #(>=) :: URec Char p -> URec Char p -> Bool #max :: URec Char p -> URec Char p -> URec Char p #min :: URec Char p -> URec Char p -> URec Char p # Methodscompare :: URec Double p -> URec Double p -> Ordering #(<) :: URec Double p -> URec Double p -> Bool #(<=) :: URec Double p -> URec Double p -> Bool #(>) :: URec Double p -> URec Double p -> Bool #(>=) :: URec Double p -> URec Double p -> Bool #max :: URec Double p -> URec Double p -> URec Double p #min :: URec Double p -> URec Double p -> URec Double p # Ord (URec Float p) Methodscompare :: URec Float p -> URec Float p -> Ordering #(<) :: URec Float p -> URec Float p -> Bool #(<=) :: URec Float p -> URec Float p -> Bool #(>) :: URec Float p -> URec Float p -> Bool #(>=) :: URec Float p -> URec Float p -> Bool #max :: URec Float p -> URec Float p -> URec Float p #min :: URec Float p -> URec Float p -> URec Float p # Ord (URec Int p) Methodscompare :: URec Int p -> URec Int p -> Ordering #(<) :: URec Int p -> URec Int p -> Bool #(<=) :: URec Int p -> URec Int p -> Bool #(>) :: URec Int p -> URec Int p -> Bool #(>=) :: URec Int p -> URec Int p -> Bool #max :: URec Int p -> URec Int p -> URec Int p #min :: URec Int p -> URec Int p -> URec Int p # Ord (URec Word p) Methodscompare :: URec Word p -> URec Word p -> Ordering #(<) :: URec Word p -> URec Word p -> Bool #(<=) :: URec Word p -> URec Word p -> Bool #(>) :: URec Word p -> URec Word p -> Bool #(>=) :: URec Word p -> URec Word p -> Bool #max :: URec Word p -> URec Word p -> URec Word p #min :: URec Word p -> URec Word p -> URec Word p # Ord (URec (Ptr ()) p) Methodscompare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering #(<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # (Ord a, Ord b) => Ord (a, b) 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 (Proxy k s) Methodscompare :: Proxy k s -> Proxy k s -> Ordering #(<) :: Proxy k s -> Proxy k s -> Bool #(<=) :: Proxy k s -> Proxy k s -> Bool #(>) :: Proxy k s -> Proxy k s -> Bool #(>=) :: Proxy k s -> Proxy k s -> Bool #max :: Proxy k s -> Proxy k s -> Proxy k s #min :: Proxy k s -> Proxy k s -> Proxy k s # Ord c => Ord (K1 i c p) Methodscompare :: K1 i c p -> K1 i c p -> Ordering #(<) :: K1 i c p -> K1 i c p -> Bool #(<=) :: K1 i c p -> K1 i c p -> Bool #(>) :: K1 i c p -> K1 i c p -> Bool #(>=) :: K1 i c p -> K1 i c p -> Bool #max :: K1 i c p -> K1 i c p -> K1 i c p #min :: K1 i c p -> K1 i c p -> K1 i c p # (Ord (g p), Ord (f p)) => Ord ((:+:) f g p) Methodscompare :: (f :+: g) p -> (f :+: g) p -> Ordering #(<) :: (f :+: g) p -> (f :+: g) p -> Bool #(<=) :: (f :+: g) p -> (f :+: g) p -> Bool #(>) :: (f :+: g) p -> (f :+: g) p -> Bool #(>=) :: (f :+: g) p -> (f :+: g) p -> Bool #max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p # (Ord (g p), Ord (f p)) => Ord ((:*:) f g p) Methodscompare :: (f :*: g) p -> (f :*: g) p -> Ordering #(<) :: (f :*: g) p -> (f :*: g) p -> Bool #(<=) :: (f :*: g) p -> (f :*: g) p -> Bool #(>) :: (f :*: g) p -> (f :*: g) p -> Bool #(>=) :: (f :*: g) p -> (f :*: g) p -> Bool #max :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #min :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p # Ord (f (g p)) => Ord ((:.:) f g p) Methodscompare :: (f :.: g) p -> (f :.: g) p -> Ordering #(<) :: (f :.: g) p -> (f :.: g) p -> Bool #(<=) :: (f :.: g) p -> (f :.: g) p -> Bool #(>) :: (f :.: g) p -> (f :.: g) p -> Bool #(>=) :: (f :.: g) p -> (f :.: g) p -> Bool #max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # (Ord a, Ord b, Ord c) => Ord (a, b, c) 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 ((:~:) k a b) Methodscompare :: (k :~: a) b -> (k :~: a) b -> Ordering #(<) :: (k :~: a) b -> (k :~: a) b -> Bool #(<=) :: (k :~: a) b -> (k :~: a) b -> Bool #(>) :: (k :~: a) b -> (k :~: a) b -> Bool #(>=) :: (k :~: a) b -> (k :~: a) b -> Bool #max :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b #min :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b # Ord (f p) => Ord (M1 i c f p) Methodscompare :: M1 i c f p -> M1 i c f p -> Ordering #(<) :: M1 i c f p -> M1 i c f p -> Bool #(<=) :: M1 i c f p -> M1 i c f p -> Bool #(>) :: M1 i c f p -> M1 i c f p -> Bool #(>=) :: M1 i c f p -> M1 i c f p -> Bool #max :: M1 i c f p -> M1 i c f p -> M1 i c f p #min :: M1 i c f p -> M1 i c f p -> M1 i c f p # (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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

 Methods MethodsenumFrom :: Ordering -> [Ordering] #enumFromTo :: Ordering -> Ordering -> [Ordering] # Methods Methods(<) :: Ordering -> Ordering -> Bool #(>) :: Ordering -> Ordering -> Bool # Methods MethodsshowList :: [Ordering] -> ShowS # Associated Typestype Rep Ordering :: * -> * # Methodsto :: Rep Ordering x -> Ordering # Methodsmconcat :: [Ordering] -> Ordering # type Rep Ordering type Rep Ordering = D1 (MetaData "Ordering" "GHC.Types" "ghc-prim" False) ((:+:) (C1 (MetaCons "LT" PrefixI False) U1) ((:+:) (C1 (MetaCons "EQ" PrefixI False) U1) (C1 (MetaCons "GT" PrefixI False) U1))) type (==) Ordering a b type (==) Ordering a b = EqOrdering a b

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 Minimal complete definition Methods readsPrec :: Int -> 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  Methods Methods Methods Methods Methods Methods Methods Methods Read () MethodsreadsPrec :: Int -> ReadS () #readList :: ReadS [()] #readListPrec :: ReadPrec [()] # Methods Methods Methods Methods Methods Methods Methods Methods Read a => Read [a] MethodsreadsPrec :: Int -> ReadS [a] #readList :: ReadS [[a]] #readPrec :: ReadPrec [a] #readListPrec :: ReadPrec [[a]] # Read a => Read (Maybe a) MethodsreadsPrec :: Int -> ReadS (Maybe a) #readList :: ReadS [Maybe a] # (Integral a, Read a) => Read (Ratio a) MethodsreadsPrec :: Int -> ReadS (Ratio a) #readList :: ReadS [Ratio a] # Read (V1 p) MethodsreadsPrec :: Int -> ReadS (V1 p) #readList :: ReadS [V1 p] #readPrec :: ReadPrec (V1 p) # Read (U1 p) MethodsreadsPrec :: Int -> ReadS (U1 p) #readList :: ReadS [U1 p] #readPrec :: ReadPrec (U1 p) # Read p => Read (Par1 p) MethodsreadsPrec :: Int -> ReadS (Par1 p) #readList :: ReadS [Par1 p] # (Read b, Read a) => Read (Either a b) MethodsreadsPrec :: Int -> ReadS (Either a b) #readList :: ReadS [Either a b] #readPrec :: ReadPrec (Either a b) #readListPrec :: ReadPrec [Either a b] # Read (f p) => Read (Rec1 f p) MethodsreadsPrec :: Int -> ReadS (Rec1 f p) #readList :: ReadS [Rec1 f p] #readPrec :: ReadPrec (Rec1 f p) #readListPrec :: ReadPrec [Rec1 f p] # (Read a, Read b) => Read (a, b) 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) MethodsreadsPrec :: Int -> ReadS (Array a b) #readList :: ReadS [Array a b] #readPrec :: ReadPrec (Array a b) #readListPrec :: ReadPrec [Array a b] # Read (Proxy k s) MethodsreadsPrec :: Int -> ReadS (Proxy k s) #readList :: ReadS [Proxy k s] #readPrec :: ReadPrec (Proxy k s) #readListPrec :: ReadPrec [Proxy k s] # Read c => Read (K1 i c p) MethodsreadsPrec :: Int -> ReadS (K1 i c p) #readList :: ReadS [K1 i c p] #readPrec :: ReadPrec (K1 i c p) #readListPrec :: ReadPrec [K1 i c p] # (Read (g p), Read (f p)) => Read ((:+:) f g p) MethodsreadsPrec :: Int -> ReadS ((f :+: g) p) #readList :: ReadS [(f :+: g) p] #readPrec :: ReadPrec ((f :+: g) p) #readListPrec :: ReadPrec [(f :+: g) p] # (Read (g p), Read (f p)) => Read ((:*:) f g p) MethodsreadsPrec :: Int -> ReadS ((f :*: g) p) #readList :: ReadS [(f :*: g) p] #readPrec :: ReadPrec ((f :*: g) p) #readListPrec :: ReadPrec [(f :*: g) p] # Read (f (g p)) => Read ((:.:) f g p) MethodsreadsPrec :: Int -> ReadS ((f :.: g) p) #readList :: ReadS [(f :.: g) p] #readPrec :: ReadPrec ((f :.: g) p) #readListPrec :: ReadPrec [(f :.: g) p] # (Read a, Read b, Read c) => Read (a, b, c) MethodsreadsPrec :: Int -> ReadS (a, b, c) #readList :: ReadS [(a, b, c)] #readPrec :: ReadPrec (a, b, c) #readListPrec :: ReadPrec [(a, b, c)] # (~) k a b => Read ((:~:) k a b) MethodsreadsPrec :: Int -> ReadS ((k :~: a) b) #readList :: ReadS [(k :~: a) b] #readPrec :: ReadPrec ((k :~: a) b) #readListPrec :: ReadPrec [(k :~: a) b] # Read (f p) => Read (M1 i c f p) MethodsreadsPrec :: Int -> ReadS (M1 i c f p) #readList :: ReadS [M1 i c f p] #readPrec :: ReadPrec (M1 i c f p) #readListPrec :: ReadPrec [M1 i c f p] # (Read a, Read b, Read c, Read d) => Read (a, b, c, d) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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 # Minimal complete definition toRational Methods toRational :: a -> Rational # the rational equivalent of its real argument with full precision Instances  Methods Methods Methods Integral a => Real (Ratio a) 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  MethodsfloatRange :: Double -> (Int, Int) #decodeFloat :: Double -> (Integer, Int) #isNaN :: Double -> Bool #atan2 :: Double -> Double -> Double # 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) 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

showsPrec :: Int -> a -> ShowS #

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

• (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

 MethodsshowsPrec :: Int -> Bool -> ShowS #show :: Bool -> String #showList :: [Bool] -> ShowS # MethodsshowsPrec :: Int -> Char -> ShowS #show :: Char -> String #showList :: [Char] -> ShowS # MethodsshowsPrec :: Int -> Int -> ShowS #show :: Int -> String #showList :: [Int] -> ShowS # MethodsshowList :: [Integer] -> ShowS # MethodsshowList :: [Ordering] -> ShowS # MethodsshowsPrec :: Int -> Word -> ShowS #show :: Word -> String #showList :: [Word] -> ShowS # MethodsshowList :: [CallStack] -> ShowS # Show () MethodsshowsPrec :: Int -> () -> ShowS #show :: () -> String #showList :: [()] -> ShowS # MethodsshowsPrec :: Int -> TyCon -> ShowS #show :: TyCon -> String #showList :: [TyCon] -> ShowS # MethodsshowsPrec :: Int -> Module -> ShowS #showList :: [Module] -> ShowS # MethodsshowsPrec :: Int -> TrName -> ShowS #showList :: [TrName] -> ShowS # Methods Methods MethodsshowList :: [Deadlock] -> ShowS # Methods MethodsshowList :: [AssertionFailed] -> ShowS # MethodsshowList :: [SomeAsyncException] -> ShowS # MethodsshowList :: [AsyncException] -> ShowS # MethodsshowList :: [ArrayException] -> ShowS # MethodsshowList :: [ExitCode] -> ShowS # MethodsshowList :: [IOErrorType] -> ShowS # MethodsshowsPrec :: Int -> Fixity -> ShowS #showList :: [Fixity] -> ShowS # MethodsshowList :: [Associativity] -> ShowS # MethodsshowList :: [SourceUnpackedness] -> ShowS # MethodsshowList :: [SourceStrictness] -> ShowS # MethodsshowList :: [DecidedStrictness] -> ShowS # MethodsshowList :: [MaskingState] -> ShowS # MethodsshowList :: [IOException] -> ShowS # MethodsshowsPrec :: Int -> SrcLoc -> ShowS #showList :: [SrcLoc] -> ShowS # Show a => Show [a] MethodsshowsPrec :: Int -> [a] -> ShowS #show :: [a] -> String #showList :: [[a]] -> ShowS # Show a => Show (Maybe a) MethodsshowsPrec :: Int -> Maybe a -> ShowS #show :: Maybe a -> String #showList :: [Maybe a] -> ShowS # Show a => Show (Ratio a) MethodsshowsPrec :: Int -> Ratio a -> ShowS #show :: Ratio a -> String #showList :: [Ratio a] -> ShowS # Show (Ptr a) MethodsshowsPrec :: Int -> Ptr a -> ShowS #show :: Ptr a -> String #showList :: [Ptr a] -> ShowS # Show (FunPtr a) MethodsshowsPrec :: Int -> FunPtr a -> ShowS #show :: FunPtr a -> String #showList :: [FunPtr a] -> ShowS # Show (V1 p) MethodsshowsPrec :: Int -> V1 p -> ShowS #show :: V1 p -> String #showList :: [V1 p] -> ShowS # Show (U1 p) MethodsshowsPrec :: Int -> U1 p -> ShowS #show :: U1 p -> String #showList :: [U1 p] -> ShowS # Show p => Show (Par1 p) MethodsshowsPrec :: Int -> Par1 p -> ShowS #show :: Par1 p -> String #showList :: [Par1 p] -> ShowS # (Show b, Show a) => Show (Either a b) MethodsshowsPrec :: Int -> Either a b -> ShowS #show :: Either a b -> String #showList :: [Either a b] -> ShowS # Show (f p) => Show (Rec1 f p) MethodsshowsPrec :: Int -> Rec1 f p -> ShowS #show :: Rec1 f p -> String #showList :: [Rec1 f p] -> ShowS # Show (URec Char p) MethodsshowsPrec :: Int -> URec Char p -> ShowS #show :: URec Char p -> String #showList :: [URec Char p] -> ShowS # MethodsshowsPrec :: Int -> URec Double p -> ShowS #show :: URec Double p -> String #showList :: [URec Double p] -> ShowS # MethodsshowsPrec :: Int -> URec Float p -> ShowS #show :: URec Float p -> String #showList :: [URec Float p] -> ShowS # Show (URec Int p) MethodsshowsPrec :: Int -> URec Int p -> ShowS #show :: URec Int p -> String #showList :: [URec Int p] -> ShowS # Show (URec Word p) MethodsshowsPrec :: Int -> URec Word p -> ShowS #show :: URec Word p -> String #showList :: [URec Word p] -> ShowS # (Show a, Show b) => Show (a, b) MethodsshowsPrec :: Int -> (a, b) -> ShowS #show :: (a, b) -> String #showList :: [(a, b)] -> ShowS # Show (Proxy k s) MethodsshowsPrec :: Int -> Proxy k s -> ShowS #show :: Proxy k s -> String #showList :: [Proxy k s] -> ShowS # Show c => Show (K1 i c p) MethodsshowsPrec :: Int -> K1 i c p -> ShowS #show :: K1 i c p -> String #showList :: [K1 i c p] -> ShowS # (Show (g p), Show (f p)) => Show ((:+:) f g p) MethodsshowsPrec :: Int -> (f :+: g) p -> ShowS #show :: (f :+: g) p -> String #showList :: [(f :+: g) p] -> ShowS # (Show (g p), Show (f p)) => Show ((:*:) f g p) MethodsshowsPrec :: Int -> (f :*: g) p -> ShowS #show :: (f :*: g) p -> String #showList :: [(f :*: g) p] -> ShowS # Show (f (g p)) => Show ((:.:) f g p) MethodsshowsPrec :: Int -> (f :.: g) p -> ShowS #show :: (f :.: g) p -> String #showList :: [(f :.: g) p] -> ShowS # (Show a, Show b, Show c) => Show (a, b, c) MethodsshowsPrec :: Int -> (a, b, c) -> ShowS #show :: (a, b, c) -> String #showList :: [(a, b, c)] -> ShowS # Show ((:~:) k a b) MethodsshowsPrec :: Int -> (k :~: a) b -> ShowS #show :: (k :~: a) b -> String #showList :: [(k :~: a) b] -> ShowS # Show (f p) => Show (M1 i c f p) MethodsshowsPrec :: Int -> M1 i c f p -> ShowS #show :: M1 i c f p -> String #showList :: [M1 i c f p] -> ShowS # (Show a, Show b, Show c, Show d) => Show (a, b, c, d) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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.

For instance,

>>> 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.

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

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.

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.

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 IOError 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 => forall m a b. 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 => forall a. 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

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 => forall a. 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 => forall a. 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.

The read function reads input from a string, which must be completely consumed by the input process.

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.

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

The readLn function combines getLine and readIO.

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

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. 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 => forall m a. 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 => forall a. 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.

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.

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

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

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

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

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 #