base-4.2.0.1: Basic librariesSource codeContentsIndex
Prelude
Portabilityportable
Stabilitystable
Maintainerlibraries@haskell.org
Contents
Standard types, classes and related functions
Basic data types
Tuples
Basic type classes
Numbers
Numeric types
Numeric type classes
Numeric functions
Monads and functors
Miscellaneous functions
List operations
Reducing lists (folds)
Special folds
Building lists
Scans
Infinite lists
Sublists
Searching lists
Zipping and unzipping lists
Functions on strings
Converting to and from String
Converting to String
Converting from String
Basic Input and output
Simple I/O operations
Output functions
Input functions
Files
Exception handling in the I/O monad
Description
The Prelude: a standard module imported by default into all Haskell modules. For more documentation, see the Haskell 98 Report http://www.haskell.org/onlinereport/.
Synopsis
data Bool
= False
| True
(&&) :: Bool -> Bool -> Bool
(||) :: Bool -> Bool -> Bool
not :: Bool -> Bool
otherwise :: Bool
data Maybe a
= Nothing
| Just a
maybe :: b -> (a -> b) -> Maybe a -> b
data Either a b
= Left a
| Right b
either :: (a -> c) -> (b -> c) -> Either a b -> c
data Ordering
= LT
| EQ
| GT
data Char
type String = [Char]
fst :: (a, b) -> a
snd :: (a, b) -> b
curry :: ((a, b) -> c) -> a -> b -> c
uncurry :: (a -> b -> c) -> (a, b) -> c
class Eq a where
(==) :: a -> a -> Bool
(/=) :: a -> a -> Bool
class Eq a => Ord a where
compare :: a -> a -> Ordering
(<) :: a -> a -> Bool
(>=) :: a -> a -> Bool
(>) :: a -> a -> Bool
(<=) :: a -> a -> Bool
max :: a -> a -> a
min :: a -> a -> a
class Enum a where
succ :: a -> a
pred :: a -> a
toEnum :: Int -> a
fromEnum :: a -> Int
enumFrom :: a -> [a]
enumFromThen :: a -> a -> [a]
enumFromTo :: a -> a -> [a]
enumFromThenTo :: a -> a -> a -> [a]
class Bounded a where
minBound :: a
maxBound :: a
data Int
data Integer
data Float
data Double
type Rational = Ratio Integer
class (Eq a, Show a) => Num a where
(+) :: a -> a -> a
(*) :: a -> a -> a
(-) :: a -> a -> a
negate :: a -> a
abs :: a -> a
signum :: a -> a
fromInteger :: Integer -> a
class (Num a, Ord a) => Real a where
toRational :: a -> Rational
class (Real a, Enum a) => Integral a where
quot :: a -> a -> a
rem :: a -> a -> a
div :: a -> a -> a
mod :: a -> a -> a
quotRem :: a -> a -> (a, a)
divMod :: a -> a -> (a, a)
toInteger :: a -> Integer
class Num a => Fractional a where
(/) :: a -> a -> a
recip :: a -> a
fromRational :: Rational -> a
class Fractional a => Floating a where
pi :: a
exp :: a -> a
sqrt :: a -> a
log :: a -> a
(**) :: a -> a -> a
logBase :: a -> a -> a
sin :: a -> a
tan :: a -> a
cos :: a -> a
asin :: a -> a
atan :: a -> a
acos :: a -> a
sinh :: a -> a
tanh :: a -> a
cosh :: a -> a
asinh :: a -> a
atanh :: a -> a
acosh :: a -> a
class (Real a, Fractional a) => RealFrac a where
properFraction :: Integral b => a -> (b, a)
truncate :: Integral b => a -> b
round :: Integral b => a -> b
ceiling :: Integral b => a -> b
floor :: Integral b => a -> b
class (RealFrac a, Floating a) => RealFloat a where
floatRadix :: a -> Integer
floatDigits :: a -> Int
floatRange :: a -> (Int, Int)
decodeFloat :: a -> (Integer, Int)
encodeFloat :: Integer -> Int -> a
exponent :: a -> Int
significand :: a -> a
scaleFloat :: Int -> a -> a
isNaN :: a -> Bool
isInfinite :: a -> Bool
isDenormalized :: a -> Bool
isNegativeZero :: a -> Bool
isIEEE :: a -> Bool
atan2 :: a -> a -> a
subtract :: Num a => a -> a -> a
even :: Integral a => a -> Bool
odd :: Integral a => a -> Bool
gcd :: Integral a => a -> a -> a
lcm :: Integral a => a -> a -> a
(^) :: (Num a, Integral b) => a -> b -> a
(^^) :: (Fractional a, Integral b) => a -> b -> a
fromIntegral :: (Integral a, Num b) => a -> b
realToFrac :: (Real a, Fractional b) => a -> b
class Monad m where
(>>=) :: forall a b. m a -> (a -> m b) -> m b
(>>) :: forall a b. m a -> m b -> m b
return :: a -> m a
fail :: String -> m a
class Functor f where
fmap :: (a -> b) -> f a -> f b
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
sequence :: Monad m => [m a] -> m [a]
sequence_ :: Monad m => [m a] -> m ()
(=<<) :: Monad m => (a -> m b) -> m a -> m b
id :: a -> a
const :: a -> b -> a
(.) :: (b -> c) -> (a -> b) -> a -> c
flip :: (a -> b -> c) -> b -> a -> c
($) :: (a -> b) -> a -> b
until :: (a -> Bool) -> (a -> a) -> a -> a
asTypeOf :: a -> a -> a
error :: [Char] -> a
undefined :: a
seq :: a -> b -> b
($!) :: (a -> b) -> a -> b
map :: (a -> b) -> [a] -> [b]
(++) :: [a] -> [a] -> [a]
filter :: (a -> Bool) -> [a] -> [a]
head :: [a] -> a
last :: [a] -> a
tail :: [a] -> [a]
init :: [a] -> [a]
null :: [a] -> Bool
length :: [a] -> Int
(!!) :: [a] -> Int -> a
reverse :: [a] -> [a]
foldl :: (a -> b -> a) -> a -> [b] -> a
foldl1 :: (a -> a -> a) -> [a] -> a
foldr :: (a -> b -> b) -> b -> [a] -> b
foldr1 :: (a -> a -> a) -> [a] -> a
and :: [Bool] -> Bool
or :: [Bool] -> Bool
any :: (a -> Bool) -> [a] -> Bool
all :: (a -> Bool) -> [a] -> Bool
sum :: Num a => [a] -> a
product :: Num a => [a] -> a
concat :: [[a]] -> [a]
concatMap :: (a -> [b]) -> [a] -> [b]
maximum :: Ord a => [a] -> a
minimum :: Ord a => [a] -> a
scanl :: (a -> b -> a) -> a -> [b] -> [a]
scanl1 :: (a -> a -> a) -> [a] -> [a]
scanr :: (a -> b -> b) -> b -> [a] -> [b]
scanr1 :: (a -> a -> a) -> [a] -> [a]
iterate :: (a -> a) -> a -> [a]
repeat :: a -> [a]
replicate :: Int -> a -> [a]
cycle :: [a] -> [a]
take :: Int -> [a] -> [a]
drop :: Int -> [a] -> [a]
splitAt :: Int -> [a] -> ([a], [a])
takeWhile :: (a -> Bool) -> [a] -> [a]
dropWhile :: (a -> Bool) -> [a] -> [a]
span :: (a -> Bool) -> [a] -> ([a], [a])
break :: (a -> Bool) -> [a] -> ([a], [a])
elem :: Eq a => a -> [a] -> Bool
notElem :: Eq a => a -> [a] -> Bool
lookup :: Eq a => a -> [(a, b)] -> Maybe b
zip :: [a] -> [b] -> [(a, b)]
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
unzip :: [(a, b)] -> ([a], [b])
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
lines :: String -> [String]
words :: String -> [String]
unlines :: [String] -> String
unwords :: [String] -> String
type ShowS = String -> String
class Show a where
showsPrec :: Int -> a -> ShowS
show :: a -> String
showList :: [a] -> ShowS
shows :: Show a => a -> ShowS
showChar :: Char -> ShowS
showString :: String -> ShowS
showParen :: Bool -> ShowS -> ShowS
type ReadS a = String -> [(a, String)]
class Read a where
readsPrec :: Int -> ReadS a
readList :: ReadS [a]
reads :: Read a => ReadS a
readParen :: Bool -> ReadS a -> ReadS a
read :: Read a => String -> a
lex :: ReadS String
data IO a
putChar :: Char -> IO ()
putStr :: String -> IO ()
putStrLn :: String -> IO ()
print :: Show a => a -> IO ()
getChar :: IO Char
getLine :: IO String
getContents :: IO String
interact :: (String -> String) -> IO ()
type FilePath = String
readFile :: FilePath -> IO String
writeFile :: FilePath -> String -> IO ()
appendFile :: FilePath -> String -> IO ()
readIO :: Read a => String -> IO a
readLn :: Read a => IO a
type IOError = IOException
ioError :: IOError -> IO a
userError :: String -> IOError
catch :: IO a -> (IOError -> IO a) -> IO a
Standard types, classes and related functions
Basic data types
data Bool Source
Constructors
False
True
show/hide Instances
(&&) :: Bool -> Bool -> BoolSource
Boolean "and"
(||) :: Bool -> Bool -> BoolSource
Boolean "or"
not :: Bool -> BoolSource
Boolean "not"
otherwise :: BoolSource

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

  f x | x < 0     = ...
      | otherwise = ...
data Maybe a Source

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 Data.Either.Either type.

Constructors
Nothing
Just a
show/hide Instances
maybe :: b -> (a -> b) -> Maybe a -> bSource
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.
data Either a b Source

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").

Constructors
Left a
Right b
show/hide Instances
Typeable2 Either
Functor (Either a)
(Eq a, Eq b) => Eq (Either a b)
(Data a, Data b) => Data (Either a b)
(Ord a, Ord b) => Ord (Either a b)
(Read a, Read b) => Read (Either a b)
(Show a, Show b) => Show (Either a b)
either :: (a -> c) -> (b -> c) -> Either a b -> cSource
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.
data Ordering Source
Constructors
LT
EQ
GT
show/hide Instances
data Char Source
show/hide Instances
type String = [Char]Source
A String is a list of characters. String constants in Haskell are values of type String.
Tuples
fst :: (a, b) -> aSource
Extract the first component of a pair.
snd :: (a, b) -> bSource
Extract the second component of a pair.
curry :: ((a, b) -> c) -> a -> b -> cSource
curry converts an uncurried function to a curried function.
uncurry :: (a -> b -> c) -> (a, b) -> cSource
uncurry converts a curried function to a function on pairs.
Basic type classes
class Eq a whereSource

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 /=.

Methods
(==) :: a -> a -> BoolSource
(/=) :: a -> a -> BoolSource
show/hide Instances
Eq Bool
Eq Char
Eq Double
Eq Float
Eq Int
Eq Int8
Eq Int16
Eq Int32
Eq Int64
Eq Integer
Eq Ordering
Eq Word
Eq Word8
Eq Word16
Eq Word32
Eq Word64
Eq ()
Eq TyCon
Eq TypeRep
Eq ArithException
Eq IOException
Eq Lexeme
Eq IOMode
Eq SeekMode
Eq IODeviceType
Eq CUIntMax
Eq CIntMax
Eq CUIntPtr
Eq CIntPtr
Eq CTime
Eq CClock
Eq CSigAtomic
Eq CWchar
Eq CSize
Eq CPtrdiff
Eq CDouble
Eq CFloat
Eq CULLong
Eq CLLong
Eq CULong
Eq CLong
Eq CUInt
Eq CInt
Eq CUShort
Eq CShort
Eq CUChar
Eq CSChar
Eq CChar
Eq GeneralCategory
Eq Inserts
Eq HashData
Eq KeyPr
Eq Key
Eq Finalizers
Eq IntPtr
Eq WordPtr
Eq BufferState
Eq NewlineMode
Eq Newline
Eq BufferMode
Eq Handle
Eq IOErrorType
Eq ExitCode
Eq ArrayException
Eq AsyncException
Eq Errno
Eq Fd
Eq CRLim
Eq CTcflag
Eq CSpeed
Eq CCc
Eq CUid
Eq CNlink
Eq CGid
Eq CSsize
Eq CPid
Eq COff
Eq CMode
Eq CIno
Eq CDev
Eq ThreadStatus
Eq BlockReason
Eq ThreadId
Eq HandlePosn
Eq Fixity
Eq ConstrRep
Eq DataRep
Eq Constr
Eq Unique
Eq Any
Eq All
Eq Timeout
Eq Version
Eq Exception
Eq a => Eq [a]
Integral a => Eq (Ratio a)
Eq (StablePtr a)
Eq (Ptr a)
Eq (FunPtr a)
Eq a => Eq ([::] a)
Eq a => Eq (Maybe a)
Eq (MVar a)
Eq (IORef a)
Eq (ForeignPtr a)
Eq (TVar a)
Eq a => Eq (Down a)
Eq a => Eq (Last a)
Eq a => Eq (First a)
Eq a => Eq (Product a)
Eq a => Eq (Sum a)
Eq a => Eq (Dual a)
RealFloat a => Eq (Complex a)
Eq (Fixed a)
Eq (StableName a)
(Eq a, Eq b) => Eq (Either a b)
(Eq a, Eq b) => Eq (a, b)
(Ix i, Eq e) => Eq (Array i e)
Eq (IOArray i e)
Eq (STRef s a)
(Eq a, Eq b, Eq c) => Eq (a, b, c)
Eq (STArray s i e)
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d)
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)
class Eq a => Ord a whereSource

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.

Methods
compare :: a -> a -> OrderingSource
(<) :: a -> a -> BoolSource
(>=) :: a -> a -> BoolSource
(>) :: a -> a -> BoolSource
(<=) :: a -> a -> BoolSource
max :: a -> a -> aSource
min :: a -> a -> aSource
show/hide Instances
Ord Bool
Ord Char
Ord Double
Ord Float
Ord Int
Ord Int8
Ord Int16
Ord Int32
Ord Int64
Ord Integer
Ord Ordering
Ord Word
Ord Word8
Ord Word16
Ord Word32
Ord Word64
Ord ()
Ord ArithException
Ord IOMode
Ord SeekMode
Ord CUIntMax
Ord CIntMax
Ord CUIntPtr
Ord CIntPtr
Ord CTime
Ord CClock
Ord CSigAtomic
Ord CWchar
Ord CSize
Ord CPtrdiff
Ord CDouble
Ord CFloat
Ord CULLong
Ord CLLong
Ord CULong
Ord CLong
Ord CUInt
Ord CInt
Ord CUShort
Ord CShort
Ord CUChar
Ord CSChar
Ord CChar
Ord GeneralCategory
Ord IntPtr
Ord WordPtr
Ord BufferMode
Ord ExitCode
Ord ArrayException
Ord AsyncException
Ord Fd
Ord CRLim
Ord CTcflag
Ord CSpeed
Ord CCc
Ord CUid
Ord CNlink
Ord CGid
Ord CSsize
Ord CPid
Ord COff
Ord CMode
Ord CIno
Ord CDev
Ord ThreadStatus
Ord BlockReason
Ord ThreadId
Ord Unique
Ord Any
Ord All
Ord Version
Ord a => Ord [a]
Integral a => Ord (Ratio a)
Ord (Ptr a)
Ord (FunPtr a)
Ord a => Ord ([::] a)
Ord a => Ord (Maybe a)
Ord (ForeignPtr a)
Ord a => Ord (Down a)
Ord a => Ord (Last a)
Ord a => Ord (First a)
Ord a => Ord (Product a)
Ord a => Ord (Sum a)
Ord a => Ord (Dual a)
Ord (Fixed a)
(Ord a, Ord b) => Ord (Either a b)
(Ord a, Ord b) => Ord (a, b)
(Ix i, Ord e) => Ord (Array i e)
(Ord a, Ord b, Ord c) => Ord (a, b, c)
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e)
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
class Enum a whereSource

Class Enum defines operations on sequentially ordered types.

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

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

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

    enumFrom     x   = enumFromTo     x maxBound
    enumFromThen x y = enumFromThenTo x y bound
      where
        bound | fromEnum y >= fromEnum x = maxBound
              | otherwise                = minBound
Methods
succ :: a -> aSource
the successor of a value. For numeric types, succ adds 1.
pred :: a -> aSource
the predecessor of a value. For numeric types, pred subtracts 1.
toEnum :: Int -> aSource
Convert from an Int.
fromEnum :: a -> IntSource
Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.
enumFrom :: a -> [a]Source
Used in Haskell's translation of [n..].
enumFromThen :: a -> a -> [a]Source
Used in Haskell's translation of [n,n'..].
enumFromTo :: a -> a -> [a]Source
Used in Haskell's translation of [n..m].
enumFromThenTo :: a -> a -> a -> [a]Source
Used in Haskell's translation of [n,n'..m].
show/hide Instances
class Bounded a whereSource

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

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

Methods
minBound :: aSource
maxBound :: aSource
show/hide Instances
Bounded Bool
Bounded Char
Bounded Int
Bounded Int8
Bounded Int16
Bounded Int32
Bounded Int64
Bounded Ordering
Bounded Word
Bounded Word8
Bounded Word16
Bounded Word32
Bounded Word64
Bounded ()
Bounded CUIntMax
Bounded CIntMax
Bounded CUIntPtr
Bounded CIntPtr
Bounded CSigAtomic
Bounded CWchar
Bounded CSize
Bounded CPtrdiff
Bounded CULLong
Bounded CLLong
Bounded CULong
Bounded CLong
Bounded CUInt
Bounded CInt
Bounded CUShort
Bounded CShort
Bounded CUChar
Bounded CSChar
Bounded CChar
Bounded GeneralCategory
Bounded IntPtr
Bounded WordPtr
Bounded Fd
Bounded CRLim
Bounded CTcflag
Bounded CUid
Bounded CNlink
Bounded CGid
Bounded CSsize
Bounded CPid
Bounded COff
Bounded CMode
Bounded CIno
Bounded Any
Bounded All
Bounded a => Bounded (Product a)
Bounded a => Bounded (Sum a)
Bounded a => Bounded (Dual a)
(Bounded a, Bounded b) => Bounded (a, b)
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
Numbers
Numeric types
data Int Source
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 Prelude.minBound and Prelude.maxBound from the Prelude.Bounded class.
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data Integer Source
Arbitrary-precision integers.
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data Float Source
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.
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data Double Source
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.
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type Rational = Ratio IntegerSource
Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.
Numeric type classes
class (Eq a, Show a) => Num a whereSource

Basic numeric class.

Minimal complete definition: all except negate or (-)

Methods
(+) :: a -> a -> aSource
(*) :: a -> a -> aSource
(-) :: a -> a -> aSource
negate :: a -> aSource
Unary negation.
abs :: a -> aSource
Absolute value.
signum :: a -> aSource

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 -> aSource
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.
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class (Num a, Ord a) => Real a whereSource
Methods
toRational :: a -> RationalSource
the rational equivalent of its real argument with full precision
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class (Real a, Enum a) => Integral a whereSource

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

Methods
quot :: a -> a -> aSource
integer division truncated toward zero
rem :: a -> a -> aSource

integer remainder, satisfying

 (x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> aSource
integer division truncated toward negative infinity
mod :: a -> a -> aSource

integer modulus, satisfying

 (x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a)Source
simultaneous quot and rem
divMod :: a -> a -> (a, a)Source
simultaneous div and mod
toInteger :: a -> IntegerSource
conversion to Integer
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class Num a => Fractional a whereSource

Fractional numbers, supporting real division.

Minimal complete definition: fromRational and (recip or (/))

Methods
(/) :: a -> a -> aSource
fractional division
recip :: a -> aSource
reciprocal fraction
fromRational :: Rational -> aSource
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.
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class Fractional a => Floating a whereSource

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition: pi, exp, log, sin, cos, sinh, cosh, asin, acos, atan, asinh, acosh and atanh

Methods
pi :: aSource
exp :: a -> aSource
sqrt :: a -> aSource
log :: a -> aSource
(**) :: a -> a -> aSource
logBase :: a -> a -> aSource
sin :: a -> aSource
tan :: a -> aSource
cos :: a -> aSource
asin :: a -> aSource
atan :: a -> aSource
acos :: a -> aSource
sinh :: a -> aSource
tanh :: a -> aSource
cosh :: a -> aSource
asinh :: a -> aSource
atanh :: a -> aSource
acosh :: a -> aSource
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class (Real a, Fractional a) => RealFrac a whereSource

Extracting components of fractions.

Minimal complete definition: properFraction

Methods
properFraction :: Integral b => a -> (b, a)Source

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

  • 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 -> bSource
truncate x returns the integer nearest x between zero and x
round :: Integral b => a -> bSource
round x returns the nearest integer to x; the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> bSource
ceiling x returns the least integer not less than x
floor :: Integral b => a -> bSource
floor x returns the greatest integer not greater than x
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class (RealFrac a, Floating a) => RealFloat a whereSource

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition: all except exponent, significand, scaleFloat and atan2

Methods
floatRadix :: a -> IntegerSource
a constant function, returning the radix of the representation (often 2)
floatDigits :: a -> IntSource
a constant function, returning the number of digits of floatRadix in the significand
floatRange :: a -> (Int, Int)Source
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int)Source
The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x 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) <= m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0).
encodeFloat :: Integer -> Int -> aSource
encodeFloat performs the inverse of decodeFloat
exponent :: a -> IntSource
the second component of decodeFloat.
significand :: a -> aSource
the first component of decodeFloat, scaled to lie in the open interval (-1,1)
scaleFloat :: Int -> a -> aSource
multiplies a floating-point number by an integer power of the radix
isNaN :: a -> BoolSource
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> BoolSource
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> BoolSource
True if the argument is too small to be represented in normalized format
isNegativeZero :: a -> BoolSource
True if the argument is an IEEE negative zero
isIEEE :: a -> BoolSource
True if the argument is an IEEE floating point number
atan2 :: a -> a -> aSource
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.
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Numeric functions
subtract :: Num a => a -> a -> aSource

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.

even :: Integral a => a -> BoolSource
odd :: Integral a => a -> BoolSource
gcd :: Integral a => a -> a -> aSource
gcd x y is the greatest (positive) integer that divides both x and y; for example gcd (-3) 6 = 3, gcd (-3) (-6) = 3, gcd 0 4 = 4. gcd 0 0 raises a runtime error.
lcm :: Integral a => a -> a -> aSource
lcm x y is the smallest positive integer that both x and y divide.
(^) :: (Num a, Integral b) => a -> b -> aSource
raise a number to a non-negative integral power
(^^) :: (Fractional a, Integral b) => a -> b -> aSource
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> bSource
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> bSource
general coercion to fractional types
Monads and functors
class Monad m whereSource

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.

Minimal complete definition: >>= and return.

Instances of Monad should satisfy the following laws:

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

Instances of both Monad and Functor should additionally satisfy the law:

 fmap f xs  ==  xs >>= return . f

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

Methods
(>>=) :: forall a b. m a -> (a -> m b) -> m bSource
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: forall a b. m a -> m b -> m bSource
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
return :: a -> m aSource
Inject a value into the monadic type.
fail :: String -> m aSource
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.
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class Functor f whereSource

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, Data.Maybe.Maybe and System.IO.IO defined in the Prelude satisfy these laws.

Methods
fmap :: (a -> b) -> f a -> f bSource
show/hide Instances
mapM :: Monad m => (a -> m b) -> [a] -> m [b]Source
mapM f is equivalent to sequence . map f.
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()Source
mapM_ f is equivalent to sequence_ . map f.
sequence :: Monad m => [m a] -> m [a]Source
Evaluate each action in the sequence from left to right, and collect the results.
sequence_ :: Monad m => [m a] -> m ()Source
Evaluate each action in the sequence from left to right, and ignore the results.
(=<<) :: Monad m => (a -> m b) -> m a -> m bSource
Same as >>=, but with the arguments interchanged.
Miscellaneous functions
id :: a -> aSource
Identity function.
const :: a -> b -> aSource
Constant function.
(.) :: (b -> c) -> (a -> b) -> a -> cSource
Function composition.
flip :: (a -> b -> c) -> b -> a -> cSource
flip f takes its (first) two arguments in the reverse order of f.
($) :: (a -> b) -> a -> bSource

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 Data.List.zipWith ($) fs xs.

until :: (a -> Bool) -> (a -> a) -> a -> aSource
until p f yields the result of applying f until p holds.
asTypeOf :: a -> a -> aSource
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.
error :: [Char] -> aSource
error stops execution and displays an error message.
undefined :: aSource
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.
seq :: a -> b -> bSource
Evaluates its first argument to head normal form, and then returns its second argument as the result.
($!) :: (a -> b) -> a -> bSource
Strict (call-by-value) application, defined in terms of seq.
List operations
map :: (a -> b) -> [a] -> [b]Source

map f xs is the list obtained by applying f to each element of xs, i.e.,

 map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
 map f [x1, x2, ...] == [f x1, f x2, ...]
(++) :: [a] -> [a] -> [a]Source

Append two lists, i.e.,

 [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
 [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

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

filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

 filter p xs = [ x | x <- xs, p x]
head :: [a] -> aSource
Extract the first element of a list, which must be non-empty.
last :: [a] -> aSource
Extract the last element of a list, which must be finite and non-empty.
tail :: [a] -> [a]Source
Extract the elements after the head of a list, which must be non-empty.
init :: [a] -> [a]Source
Return all the elements of a list except the last one. The list must be non-empty.
null :: [a] -> BoolSource
Test whether a list is empty.
length :: [a] -> IntSource
O(n). length returns the length of a finite list as an Int. It is an instance of the more general Data.List.genericLength, the result type of which may be any kind of number.
(!!) :: [a] -> Int -> aSource
List index (subscript) operator, starting from 0. It is an instance of the more general Data.List.genericIndex, which takes an index of any integral type.
reverse :: [a] -> [a]Source
reverse xs returns the elements of xs in reverse order. xs must be finite.
Reducing lists (folds)
foldl :: (a -> b -> a) -> a -> [b] -> aSource

foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

 foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

The list must be finite.

foldl1 :: (a -> a -> a) -> [a] -> aSource
foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty lists.
foldr :: (a -> b -> b) -> b -> [a] -> bSource

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

 foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
foldr1 :: (a -> a -> a) -> [a] -> aSource
foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty lists.
Special folds
and :: [Bool] -> BoolSource
and returns the conjunction of a Boolean list. For the result to be True, the list must be finite; False, however, results from a False value at a finite index of a finite or infinite list.
or :: [Bool] -> BoolSource
or returns the disjunction of a Boolean list. For the result to be False, the list must be finite; True, however, results from a True value at a finite index of a finite or infinite list.
any :: (a -> Bool) -> [a] -> BoolSource
Applied to a predicate and a list, any determines if any element of the list satisfies the predicate.
all :: (a -> Bool) -> [a] -> BoolSource
Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate.
sum :: Num a => [a] -> aSource
The sum function computes the sum of a finite list of numbers.
product :: Num a => [a] -> aSource
The product function computes the product of a finite list of numbers.
concat :: [[a]] -> [a]Source
Concatenate a list of lists.
concatMap :: (a -> [b]) -> [a] -> [b]Source
Map a function over a list and concatenate the results.
maximum :: Ord a => [a] -> aSource
maximum returns the maximum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of maximumBy, which allows the programmer to supply their own comparison function.
minimum :: Ord a => [a] -> aSource
minimum returns the minimum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of minimumBy, which allows the programmer to supply their own comparison function.
Building lists
Scans
scanl :: (a -> b -> a) -> a -> [b] -> [a]Source

scanl is similar to foldl, but returns a list of successive reduced values from the left:

 scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

 last (scanl f z xs) == foldl f z xs.
scanl1 :: (a -> a -> a) -> [a] -> [a]Source

scanl1 is a variant of scanl that has no starting value argument:

 scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
scanr :: (a -> b -> b) -> b -> [a] -> [b]Source

scanr is the right-to-left dual of scanl. Note that

 head (scanr f z xs) == foldr f z xs.
scanr1 :: (a -> a -> a) -> [a] -> [a]Source
scanr1 is a variant of scanr that has no starting value argument.
Infinite lists
iterate :: (a -> a) -> a -> [a]Source

iterate f x returns an infinite list of repeated applications of f to x:

 iterate f x == [x, f x, f (f x), ...]
repeat :: a -> [a]Source
repeat x is an infinite list, with x the value of every element.
replicate :: Int -> a -> [a]Source
replicate n x is a list of length n with x the value of every element. It is an instance of the more general Data.List.genericReplicate, in which n may be of any integral type.
cycle :: [a] -> [a]Source
cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.
Sublists
take :: Int -> [a] -> [a]Source

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

 take 5 "Hello World!" == "Hello"
 take 3 [1,2,3,4,5] == [1,2,3]
 take 3 [1,2] == [1,2]
 take 3 [] == []
 take (-1) [1,2] == []
 take 0 [1,2] == []

It is an instance of the more general Data.List.genericTake, in which n may be of any integral type.

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

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

 drop 6 "Hello World!" == "World!"
 drop 3 [1,2,3,4,5] == [4,5]
 drop 3 [1,2] == []
 drop 3 [] == []
 drop (-1) [1,2] == [1,2]
 drop 0 [1,2] == [1,2]

It is an instance of the more general Data.List.genericDrop, in which n may be of any integral type.

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

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

 splitAt 6 "Hello World!" == ("Hello ","World!")
 splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
 splitAt 1 [1,2,3] == ([1],[2,3])
 splitAt 3 [1,2,3] == ([1,2,3],[])
 splitAt 4 [1,2,3] == ([1,2,3],[])
 splitAt 0 [1,2,3] == ([],[1,2,3])
 splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to (take n xs, drop n xs). splitAt is an instance of the more general Data.List.genericSplitAt, in which n may be of any integral type.

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

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

 takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
 takeWhile (< 9) [1,2,3] == [1,2,3]
 takeWhile (< 0) [1,2,3] == []
dropWhile :: (a -> Bool) -> [a] -> [a]Source

dropWhile p xs returns the suffix remaining after takeWhile p xs:

 dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
 dropWhile (< 9) [1,2,3] == []
 dropWhile (< 0) [1,2,3] == [1,2,3]
span :: (a -> Bool) -> [a] -> ([a], [a])Source

span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

 span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
 span (< 9) [1,2,3] == ([1,2,3],[])
 span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

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

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

 break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
 break (< 9) [1,2,3] == ([],[1,2,3])
 break (> 9) [1,2,3] == ([1,2,3],[])

break p is equivalent to span (not . p).

Searching lists
elem :: Eq a => a -> [a] -> BoolSource
elem is the list membership predicate, usually written in infix form, e.g., x `elem` xs.
notElem :: Eq a => a -> [a] -> BoolSource
notElem is the negation of elem.
lookup :: Eq a => a -> [(a, b)] -> Maybe bSource
lookup key assocs looks up a key in an association list.
Zipping and unzipping lists
zip :: [a] -> [b] -> [(a, b)]Source
zip takes two lists and returns a list of corresponding pairs. If one input list is short, excess elements of the longer list are discarded.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]Source
zip3 takes three lists and returns a list of triples, analogous to zip.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]Source
zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]Source
The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith.
unzip :: [(a, b)] -> ([a], [b])Source
unzip transforms a list of pairs into a list of first components and a list of second components.
unzip3 :: [(a, b, c)] -> ([a], [b], [c])Source
The unzip3 function takes a list of triples and returns three lists, analogous to unzip.
Functions on strings
lines :: String -> [String]Source
lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.
words :: String -> [String]Source
words breaks a string up into a list of words, which were delimited by white space.
unlines :: [String] -> StringSource
unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.
unwords :: [String] -> StringSource
unwords is an inverse operation to words. It joins words with separating spaces.
Converting to and from String
Converting to String
type ShowS = String -> StringSource
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.
class Show a whereSource

Conversion of values to readable Strings.

Minimal complete definition: showsPrec or show.

Derived instances of Show have the following properties, which are compatible with derived instances of Text.Read.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)".
Methods
showsPrecSource
:: Intthe operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.
-> athe value to be converted to a String
-> ShowS

Convert a value to a readable String.

showsPrec should satisfy the law

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

Derived instances of Text.Read.Read and Show satisfy the following:

  • (x,"") is an element of (Text.Read.readsPrec d (showsPrec d x "")).

That is, Text.Read.readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> StringSource
A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.
showList :: [a] -> ShowSSource
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.
show/hide Instances
Show Bool
Show Char
Show Double
Show Float
Show Int
Show Int8
Show Int16
Show Int32
Show Int64
Show Integer
Show Ordering
Show Word
Show Word8
Show Word16
Show Word32
Show Word64
Show ()
Show TyCon
Show TypeRep
Show ArithException
Show ErrorCall
Show SomeException
Show IOException
Show Lexeme
Show IOMode
Show SeekMode
Show CUIntMax
Show CIntMax
Show CUIntPtr
Show CIntPtr
Show CTime
Show CClock
Show CSigAtomic
Show CWchar
Show CSize
Show CPtrdiff
Show CDouble
Show CFloat
Show CULLong
Show CLLong
Show CULong
Show CLong
Show CUInt
Show CInt
Show CUShort
Show CShort
Show CUChar
Show CSChar
Show CChar
Show GeneralCategory
Show HashData
Show Dynamic
Show IntPtr
Show WordPtr
Show BufferMode
Show HandleType
Show Handle
Show IOErrorType
Show ExitCode
Show ArrayException
Show AsyncException
Show AssertionFailed
Show Deadlock
Show BlockedIndefinitelyOnSTM
Show BlockedIndefinitelyOnMVar
Show BlockedIndefinitely
Show BlockedOnDeadMVar
Show Fd
Show CRLim
Show CTcflag
Show CSpeed
Show CCc
Show CUid
Show CNlink
Show CGid
Show CSsize
Show CPid
Show COff
Show CMode
Show CIno
Show CDev
Show ThreadStatus
Show BlockReason
Show ThreadId
Show NestedAtomically
Show NonTermination
Show NoMethodError
Show RecUpdError
Show RecConError
Show RecSelError
Show PatternMatchFail
Show FD
Show HandlePosn
Show Fixity
Show ConstrRep
Show DataRep
Show Constr
Show DataType
Show Any
Show All
Show Timeout
Show Version
Show Exception
Show a => Show [a]
Integral a => Show (Ratio a)
Show (Ptr a)
Show (FunPtr a)
Show a => Show ([::] a)
Show a => Show (Maybe a)
Show (ForeignPtr a)
Show a => Show (Last a)
Show a => Show (First a)
Show a => Show (Product a)
Show a => Show (Sum a)
Show a => Show (Dual a)
RealFloat a => Show (Complex a)
HasResolution a => Show (Fixed a)
Show (a -> b)
(Show a, Show b) => Show (Either a b)
(Show a, Show b) => Show (a, b)
Show (ST s a)
(Ix a, Show a, Show b) => Show (Array a b)
(Show a, Show b, Show c) => Show (a, b, c)
(Show a, Show b, Show c, Show d) => Show (a, b, c, d)
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
shows :: Show a => a -> ShowSSource
equivalent to showsPrec with a precedence of 0.
showChar :: Char -> ShowSSource
utility function converting a Char to a show function that simply prepends the character unchanged.
showString :: String -> ShowSSource
utility function converting a String to a show function that simply prepends the string unchanged.
showParen :: Bool -> ShowS -> ShowSSource
utility function that surrounds the inner show function with parentheses when the Bool parameter is True.
Converting from String
type ReadS a = String -> [(a, String)]Source

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 Read a whereSource

Parsing of Strings, producing values.

Minimal complete definition: readsPrec (or, for GHC only, readPrec)

Derived instances of Read make the following assumptions, which derived instances of Text.Show.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 98 is equivalent to

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

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

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

           where app_prec = 10
                 up_prec = 5

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

The derived instance in GHC is equivalent to

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

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

                      +++ (prec up_prec $ do
                                  u <- step readPrec
                                  Symbol ":^:" <- lexP
                                  v <- step readPrec
                                  return (u :^: v))

           where app_prec = 10
                 up_prec = 5

         readListPrec = readListPrecDefault
Methods
readsPrecSource
:: Intthe operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.
-> ReadS a

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Text.Show.Show satisfy the following:

  • (x,"") is an element of (readsPrec d (Text.Show.showsPrec d x "")).

That is, readsPrec parses the string produced by Text.Show.showsPrec, and delivers the value that Text.Show.showsPrec started with.

readList :: ReadS [a]Source
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.
show/hide Instances
Read Bool
Read Char
Read Double
Read Float
Read Int
Read Int8
Read Int16
Read Int32
Read Int64
Read Integer
Read Ordering
Read Word
Read Word8
Read Word16
Read Word32
Read Word64
Read ()
Read Lexeme
Read IOMode
Read SeekMode
Read CUIntMax
Read CIntMax
Read CUIntPtr
Read CIntPtr
Read CTime
Read CClock
Read CSigAtomic
Read CWchar
Read CSize
Read CPtrdiff
Read CDouble
Read CFloat
Read CULLong
Read CLLong
Read CULong
Read CLong
Read CUInt
Read CInt
Read CUShort
Read CShort
Read CUChar
Read CSChar
Read CChar
Read GeneralCategory
Read IntPtr
Read WordPtr
Read BufferMode
Read ExitCode
Read Fd
Read CRLim
Read CTcflag
Read CSpeed
Read CCc
Read CUid
Read CNlink
Read CGid
Read CSsize
Read CPid
Read COff
Read CMode
Read CIno
Read CDev
Read Any
Read All
Read Version
Read a => Read [a]
(Integral a, Read a) => Read (Ratio a)
Read a => Read ([::] a)
Read a => Read (Maybe a)
Read a => Read (Last a)
Read a => Read (First a)
Read a => Read (Product a)
Read a => Read (Sum a)
Read a => Read (Dual a)
(Read a, RealFloat a) => Read (Complex a)
(Read a, Read b) => Read (Either a b)
(Read a, Read b) => Read (a, b)
(Ix a, Read a, Read b) => Read (Array a b)
(Read a, Read b, Read c) => Read (a, b, c)
(Read a, Read b, Read c, Read d) => Read (a, b, c, d)
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e)
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
reads :: Read a => ReadS aSource
equivalent to readsPrec with a precedence of 0.
readParen :: Bool -> ReadS a -> ReadS aSource

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

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

read :: Read a => String -> aSource
The read function reads input from a string, which must be completely consumed by the input process.
lex :: ReadS StringSource

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
Basic Input and output
data IO a Source

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.

show/hide Instances
Simple I/O operations
Output functions
putChar :: Char -> IO ()Source
Write a character to the standard output device (same as hPutChar stdout).
putStr :: String -> IO ()Source
Write a string to the standard output device (same as hPutStr stdout).
putStrLn :: String -> IO ()Source
The same as putStr, but adds a newline character.
print :: Show a => a -> IO ()Source

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

 main = print ([(n, 2^n) | n <- [0..19]])
Input functions
getChar :: IO CharSource
Read a character from the standard input device (same as hGetChar stdin).
getLine :: IO StringSource
Read a line from the standard input device (same as hGetLine stdin).
getContents :: IO StringSource
The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).
interact :: (String -> String) -> IO ()Source
The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.
Files
type FilePath = StringSource
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.
readFile :: FilePath -> IO StringSource
The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.
writeFile :: FilePath -> String -> IO ()Source
The computation writeFile file str function writes the string str, to the file file.
appendFile :: FilePath -> String -> IO ()Source

The computation appendFile file str function appends the string str, to the file file.

Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.

 main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
readIO :: Read a => String -> IO aSource
The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.
readLn :: Read a => IO aSource
The readLn function combines getLine and readIO.
Exception handling in the I/O monad
type IOError = IOExceptionSource

The Haskell 98 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 Control.Exception.Exception.

In Haskell 98, this is an opaque type.

ioError :: IOError -> IO aSource
Raise an IOError in the IO monad.
userError :: String -> IOErrorSource

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)
catch :: IO a -> (IOError -> IO a) -> IO aSource

The catch function establishes a handler that receives any IOError raised in the action protected by catch. An IOError is caught by the most recent handler established by catch. These handlers are not selective: all IOErrors are caught. Exception propagation must be explicitly provided in a handler by re-raising any unwanted exceptions. For example, in

 f = catch g (\e -> if IO.isEOFError e then return [] else ioError e)

the function f returns [] when an end-of-file exception (cf. isEOFError) occurs in g; otherwise, the exception is propagated to the next outer handler.

When an exception propagates outside the main program, the Haskell system prints the associated IOError value and exits the program.

Non-I/O exceptions are not caught by this variant; to catch all exceptions, use Control.Exception.catch from Control.Exception.

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