Haskell Hierarchical Libraries (base package)ContentsIndex
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
log :: a -> a
sqrt :: a -> a
(**) :: a -> a -> a
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
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
($) :: (a -> b) -> a -> b
until :: (a -> Bool) -> (a -> a) -> a -> a
asTypeOf :: a -> a -> a
error :: String -> a
undefined :: a
seq :: a -> b -> b
($!) :: (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
The Bool type is an enumeration. It is defined with False first so that the corresponding Enum instance will give fromEnum False the value zero, and fromEnum True the value 1.
Constructors
False
True
show/hide Instances
(&&) :: Bool -> Bool -> Bool
Boolean "and"
(||) :: Bool -> Bool -> Bool
Boolean "or"
not :: Bool -> Bool
Boolean "not"
otherwise :: Bool

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

  f x | x < 0     = ...
      | otherwise = ...
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
show/hide Instances
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.
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").

Constructors
Left a
Right b
show/hide Instances
Typeable2 Either
(Data a, Data b) => Data (Either a b)
(Eq a, Eq b) => Eq (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 -> 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.
data Ordering
Represents an ordering relationship between two values: less than, equal to, or greater than. An Ordering is returned by compare.
Constructors
LT
EQ
GT
show/hide Instances
data Char

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO 10646) characters. This set extends the ISO 8859-1 (Latin-1) character set (the first 256 charachers), 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).

show/hide Instances
type String = [Char]
A String is a list of characters. String constants in Haskell are values of type String.
Tuples
fst :: (a, b) -> a
Extract the first component of a pair.
snd :: (a, b) -> b
Extract the second component of a pair.
curry :: ((a, b) -> c) -> a -> b -> c
curry converts an uncurried function to a curried function.
uncurry :: (a -> b -> c) -> (a, b) -> c
uncurry converts a curried function to a function on pairs.
Basic type classes
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 /=.

Methods
(==) :: a -> a -> Bool
(/=) :: a -> a -> Bool
show/hide Instances
Eq ArithException
Eq ArrayException
Eq AsyncException
Eq Bool
Eq BufferMode
Eq BufferState
Eq CCc
Eq CChar
Eq CClock
Eq CDev
Eq CDouble
Eq CFloat
Eq CGid
Eq CIno
Eq CInt
Eq CLDouble
Eq CLLong
Eq CLong
Eq CMode
Eq CNlink
Eq COff
Eq CPid
Eq CPtrdiff
Eq CRLim
Eq CSChar
Eq CShort
Eq CSigAtomic
Eq CSize
Eq CSpeed
Eq CSsize
Eq CTcflag
Eq CTime
Eq CUChar
Eq CUInt
Eq CULLong
Eq CULong
Eq CUShort
Eq CUid
Eq CWchar
Eq CalendarTime
Eq Char
Eq ClockTime
Eq Constr
Eq ConstrRep
Eq DataRep
Eq Day
Eq Double
Eq Errno
Eq Exception
Eq ExitCode
Eq FDType
Eq Fd
Eq Fixity
Eq Float
Eq GeneralCategory
Eq Handle
Eq HandlePosn
Eq IOErrorType
Eq IOException
Eq IOMode
Eq Int
Eq Int16
Eq Int32
Eq Int64
Eq Int8
Eq IntSet
Eq Integer
Eq Key
Eq KeyPr
Eq Lexeme
Eq Month
Eq Ordering
Eq PackedString
Eq Permissions
Eq SeekMode
Eq ThreadId
Eq TimeDiff
Eq TimeLocale
Eq TyCon
Eq TypeRep
Eq Unique
Eq Version
Eq Word
Eq Word16
Eq Word32
Eq Word64
Eq Word8
Eq ()
(Eq a, Eq b) => Eq (a, b)
(Eq a, Eq b, Eq c) => Eq (a, b, c)
(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)
(RealFloat a, Eq a) => Eq (Complex a)
Eq (ForeignPtr a)
Eq (FunPtr a)
Eq (IORef a)
Eq a => Eq (IntMap a)
Eq (MVar a)
Eq a => Eq (Maybe a)
Eq (Ptr a)
(Integral a, Eq a) => Eq (Ratio a)
Eq a => Eq (Set a)
Eq (StableName a)
Eq (StablePtr a)
Eq (TVar a)
Eq a => Eq (Tree a)
Eq a => Eq [a]
(Ix i, Eq e) => Eq (Array i e)
(Eq a, Eq b) => Eq (Either a b)
(Eq key, Eq elt) => Eq (FiniteMap key elt)
Eq (IOArray i e)
(Eq k, Eq a) => Eq (Map k a)
Eq (STRef s a)
Ix ix => Eq (UArray ix Bool)
Ix ix => Eq (UArray ix Char)
Ix ix => Eq (UArray ix Double)
Ix ix => Eq (UArray ix Float)
Ix ix => Eq (UArray ix (FunPtr a))
Ix ix => Eq (UArray ix Int)
Ix ix => Eq (UArray ix Int16)
Ix ix => Eq (UArray ix Int32)
Ix ix => Eq (UArray ix Int64)
Ix ix => Eq (UArray ix Int8)
Ix ix => Eq (UArray ix (Ptr a))
Ix ix => Eq (UArray ix (StablePtr a))
Ix ix => Eq (UArray ix Word)
Ix ix => Eq (UArray ix Word16)
Ix ix => Eq (UArray ix Word32)
Ix ix => Eq (UArray ix Word64)
Ix ix => Eq (UArray ix Word8)
Eq (STArray s i e)
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.

Methods
compare :: a -> a -> Ordering
(<) :: a -> a -> Bool
(<=) :: a -> a -> Bool
(>) :: a -> a -> Bool
(>=) :: a -> a -> Bool
max :: a -> a -> a
min :: a -> a -> a
show/hide Instances
Ord ArithException
Ord ArrayException
Ord AsyncException
Ord Bool
Ord BufferMode
Ord CCc
Ord CChar
Ord CClock
Ord CDev
Ord CDouble
Ord CFloat
Ord CGid
Ord CIno
Ord CInt
Ord CLDouble
Ord CLLong
Ord CLong
Ord CMode
Ord CNlink
Ord COff
Ord CPid
Ord CPtrdiff
Ord CRLim
Ord CSChar
Ord CShort
Ord CSigAtomic
Ord CSize
Ord CSpeed
Ord CSsize
Ord CTcflag
Ord CTime
Ord CUChar
Ord CUInt
Ord CULLong
Ord CULong
Ord CUShort
Ord CUid
Ord CWchar
Ord CalendarTime
Ord Char
Ord ClockTime
Ord Day
Ord Double
Ord ExitCode
Ord Fd
Ord Float
Ord GeneralCategory
Ord IOMode
Ord Int
Ord Int16
Ord Int32
Ord Int64
Ord Int8
Ord IntSet
Ord Integer
Ord Month
Ord Ordering
Ord PackedString
Ord Permissions
Ord SeekMode
Ord ThreadId
Ord TimeDiff
Ord TimeLocale
Ord Unique
Ord Version
Ord Word
Ord Word16
Ord Word32
Ord Word64
Ord Word8
Ord ()
(Ord a, Ord b) => Ord (a, b)
(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)
Ord (ForeignPtr a)
Ord (FunPtr a)
Ord a => Ord (IntMap a)
Ord a => Ord (Maybe a)
Ord (Ptr a)
Integral a => Ord (Ratio a)
Ord a => Ord (Set a)
Ord a => Ord [a]
(Ix i, Ord e) => Ord (Array i e)
(Ord a, Ord b) => Ord (Either a b)
(Ord k, Ord v) => Ord (Map k v)
Ix ix => Ord (UArray ix Bool)
Ix ix => Ord (UArray ix Char)
Ix ix => Ord (UArray ix Double)
Ix ix => Ord (UArray ix Float)
Ix ix => Ord (UArray ix (FunPtr a))
Ix ix => Ord (UArray ix Int)
Ix ix => Ord (UArray ix Int16)
Ix ix => Ord (UArray ix Int32)
Ix ix => Ord (UArray ix Int64)
Ix ix => Ord (UArray ix Int8)
Ix ix => Ord (UArray ix (Ptr a))
Ix ix => Ord (UArray ix Word)
Ix ix => Ord (UArray ix Word16)
Ix ix => Ord (UArray ix Word32)
Ix ix => Ord (UArray ix Word64)
Ix ix => Ord (UArray ix Word8)
class Enum a where

Class Enum defines operations on sequentially ordered types.

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

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

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

	enumFrom     x   = enumFromTo     x maxBound
	enumFromThen x y = enumFromThenTo x y bound
	  where
	    bound | fromEnum y >= fromEnum x = maxBound
	          | otherwise                = minBound
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].
show/hide Instances
class Bounded a where

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

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

Methods
minBound :: a
maxBound :: a
show/hide Instances
Numbers
Numeric types
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.
show/hide Instances
data Integer
Arbitrary-precision integers.
show/hide Instances
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.
show/hide Instances
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.
show/hide Instances
type Rational = Ratio Integer
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 where

Basic numeric class.

Minimal complete definition: all except negate or (-)

Methods
(+) :: a -> a -> a
(-) :: a -> a -> a
(*) :: a -> a -> a
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.
show/hide Instances
class (Num a, Ord a) => Real a where
Methods
toRational :: a -> Rational
the rational equivalent of its real argument with full precision
show/hide Instances
class (Real a, Enum a) => Integral a where

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

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

integer remainder, satisfying 

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

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
show/hide Instances
class Num a => Fractional a where

Fractional numbers, supporting real division.

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

Methods
(/) :: a -> a -> a
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.
show/hide Instances
class Fractional a => Floating a where

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 :: a
exp :: a -> a
log :: a -> a
sqrt :: a -> a
(**) :: a -> a -> a
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
show/hide Instances
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
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
show/hide Instances
class (RealFrac a, Floating a) => RealFloat a where

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 -> 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) <= m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0).
encodeFloat :: Integer -> Int -> a
encodeFloat performs the inverse of decodeFloat
exponent :: a -> Int
the second component of decodeFloat.
significand :: a -> a
the first component of decodeFloat, scaled to lie in the open interval (-1,1)
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.
show/hide Instances
Numeric functions
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.

even :: Integral a => a -> Bool
odd :: Integral a => a -> Bool
gcd :: Integral a => a -> a -> a
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 -> a
lcm x y is the smallest positive integer that both x and y divide.
(^) :: (Num a, Integral b) => a -> b -> a
raise a number to a non-negative integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b
general coercion to fractional types
Monads and functors
class 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.

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

Methods
(>>=) :: forall a b . m a -> (a -> m b) -> m b
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 b
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.
show/hide Instances
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 defined in the Prelude satisfy these laws.

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

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.

until :: (a -> Bool) -> (a -> a) -> a -> a
until p f yields the result of applying f until p holds.
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.
error :: String -> a
error stops execution and displays an error message.
undefined :: 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.
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 -> b) -> a -> b
Strict (call-by-value) application, defined in terms of seq.
List operations
map :: (a -> b) -> [a] -> [b]

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]

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]

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

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] -> a
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] -> b

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] -> a
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] -> Bool
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] -> Bool
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] -> Bool
Applied to a predicate and a list, any determines if any element of the list satisfies the predicate.
all :: (a -> Bool) -> [a] -> Bool
Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate.
sum :: Num a => [a] -> a
The sum function computes the sum of a finite list of numbers.
product :: Num a => [a] -> a
The product function computes the product of a finite list of numbers.
concat :: [[a]] -> [a]
Concatenate a list of lists.
concatMap :: (a -> [b]) -> [a] -> [b]
Map a function over a list and concatenate the results.
maximum :: Ord a => [a] -> a
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] -> a
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]

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]

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]

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]
scanr1 is a variant of scanr that has no starting value argument.
Infinite lists
iterate :: (a -> a) -> a -> [a]

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

 iterate f x == [x, f x, f (f x), ...]
repeat :: a -> [a]
repeat x is an infinite list, with x the value of every element.
replicate :: Int -> a -> [a]
replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.
cycle :: [a] -> [a]
cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.
Sublists
take :: Int -> [a] -> [a]
take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs. It is an instance of the more general genericTake, in which n may be of any integral type.
drop :: Int -> [a] -> [a]
drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs. It is an instance of the more general genericDrop, in which n may be of any integral type.
splitAt :: Int -> [a] -> ([a], [a])
splitAt n xs is equivalent to (take n xs, drop n xs). It is an instance of the more general genericSplitAt, in which n may be of any integral type.
takeWhile :: (a -> Bool) -> [a] -> [a]
takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p.
dropWhile :: (a -> Bool) -> [a] -> [a]
dropWhile p xs returns the suffix remaining after takeWhile p xs.
span :: (a -> Bool) -> [a] -> ([a], [a])
span p xs is equivalent to (takeWhile p xs, dropWhile p xs)
break :: (a -> Bool) -> [a] -> ([a], [a])
break p is equivalent to span (not . p).
Searching lists
elem :: Eq a => a -> [a] -> Bool
elem is the list membership predicate, usually written in infix form, e.g., x elem xs.
notElem :: Eq a => a -> [a] -> Bool
notElem is the negation of elem.
lookup :: Eq a => a -> [(a, b)] -> Maybe b
lookup key assocs looks up a key in an association list.
Zipping and unzipping lists
zip :: [a] -> [b] -> [(a, b)]
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)]
zip3 takes three lists and returns a list of triples, analogous to zip.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
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]
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])
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])
The unzip3 function takes a list of triples and returns three lists, analogous to unzip.
Functions on strings
lines :: String -> [String]
lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.
words :: String -> [String]
words breaks a string up into a list of words, which were delimited by white space.
unlines :: [String] -> String
unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.
unwords :: [String] -> String
unwords is an inverse operation to words. It joins words with separating spaces.
Converting to and from String
Converting to String
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.
class Show a where

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 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
showsPrec
:: 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 Read and Show satisfy the following:

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

show :: a -> String
A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.
showList :: [a] -> ShowS
The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.
show/hide Instances
Show ArithException
Show ArrayException
Show AsyncException
Show Bool
Show BufferMode
Show CCc
Show CChar
Show CClock
Show CDev
Show CDouble
Show CFloat
Show CGid
Show CIno
Show CInt
Show CLDouble
Show CLLong
Show CLong
Show CMode
Show CNlink
Show COff
Show CPid
Show CPtrdiff
Show CRLim
Show CSChar
Show CShort
Show CSigAtomic
Show CSize
Show CSpeed
Show CSsize
Show CTcflag
Show CTime
Show CUChar
Show CUInt
Show CULLong
Show CULong
Show CUShort
Show CUid
Show CWchar
Show CalendarTime
Show Char
Show ClockTime
Show Constr
Show ConstrRep
Show DataRep
Show DataType
Show Day
Show Doc
Show Double
Show Dynamic
Show Exception
Show ExitCode
Show Fd
Show Fixity
Show Float
Show GeneralCategory
Show Handle
Show HandlePosn
Show HandleType
Show HotLink
Show Html
Show HtmlAttr
Show HtmlTable
Show IOErrorType
Show IOException
Show IOMode
Show Int
Show Int16
Show Int32
Show Int64
Show Int8
Show IntSet
Show Integer
Show Lexeme
Show Month
Show Ordering
Show PackedString
Show Permissions
Show SeekMode
Show StdGen
Show ThreadId
Show TimeDiff
Show TimeLocale
Show TyCon
Show TypeRep
Show Version
Show Word
Show Word16
Show Word32
Show Word64
Show Word8
Show ()
(Show a, Show b) => Show (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 -> b)
Show a => Show (BlockTable a)
(RealFloat a, Show a) => Show (Complex a)
Show (ForeignPtr a)
Show (FunPtr a)
Show a => Show (IntMap a)
Show a => Show (Maybe a)
Show (Ptr a)
Integral a => Show (Ratio a)
Show a => Show (Set a)
Show a => Show (Tree a)
Show a => Show [a]
(Ix a, Show a, Show b) => Show (Array a b)
(Ix ix, Show ix, Show e) => Show (DiffArray ix e)
(Ix ix, Show ix) => Show (DiffUArray ix Char)
(Ix ix, Show ix) => Show (DiffUArray ix Double)
(Ix ix, Show ix) => Show (DiffUArray ix Float)
(Ix ix, Show ix) => Show (DiffUArray ix Int)
(Ix ix, Show ix) => Show (DiffUArray ix Int16)
(Ix ix, Show ix) => Show (DiffUArray ix Int32)
(Ix ix, Show ix) => Show (DiffUArray ix Int64)
(Ix ix, Show ix) => Show (DiffUArray ix Int8)
(Ix ix, Show ix) => Show (DiffUArray ix Word)
(Ix ix, Show ix) => Show (DiffUArray ix Word16)
(Ix ix, Show ix) => Show (DiffUArray ix Word32)
(Ix ix, Show ix) => Show (DiffUArray ix Word64)
(Ix ix, Show ix) => Show (DiffUArray ix Word8)
(Show a, Show b) => Show (Either a b)
(Show k, Show e) => Show (FiniteMap k e)
(Show k, Show a) => Show (Map k a)
Show (ST s a)
(Ix ix, Show ix) => Show (UArray ix Bool)
(Ix ix, Show ix) => Show (UArray ix Char)
(Ix ix, Show ix) => Show (UArray ix Double)
(Ix ix, Show ix) => Show (UArray ix Float)
(Ix ix, Show ix) => Show (UArray ix Int)
(Ix ix, Show ix) => Show (UArray ix Int16)
(Ix ix, Show ix) => Show (UArray ix Int32)
(Ix ix, Show ix) => Show (UArray ix Int64)
(Ix ix, Show ix) => Show (UArray ix Int8)
(Ix ix, Show ix) => Show (UArray ix Word)
(Ix ix, Show ix) => Show (UArray ix Word16)
(Ix ix, Show ix) => Show (UArray ix Word32)
(Ix ix, Show ix) => Show (UArray ix Word64)
(Ix ix, Show ix) => Show (UArray ix Word8)
shows :: Show a => a -> ShowS
equivalent to showsPrec with a precedence of 0.
showChar :: Char -> ShowS
utility function converting a Char to a show function that simply prepends the character unchanged.
showString :: String -> ShowS
utility function converting a String to a show function that simply prepends the string unchanged.
showParen :: Bool -> ShowS -> ShowS
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)]

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 where

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 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 is equivalent to 

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

         readsPrec d 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

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

           where up_prec = 5
                 app_prec = 10

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

Methods
readsPrec
:: 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 Show satisfy the following:

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

readList :: ReadS [a]
The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.
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reads :: Read a => ReadS a
equivalent to readsPrec with a precedence of 0.
readParen :: Bool -> ReadS a -> ReadS a

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

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

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

The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

  • Qualified names are not handled properly
  • Octal and hexadecimal numerics are not recognized as a single token
  • Comments are not treated properly
Basic Input and output
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.

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Simple I/O operations
Output functions
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.
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]])
Input functions
getChar :: IO Char
Read a character from the standard input device (same as hGetChar stdin).
getLine :: IO String
Read a line from the standard input device (same as hGetLine stdin).
getContents :: IO String
The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).
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.
Files
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.
readFile :: FilePath -> IO String
The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.
writeFile :: FilePath -> String -> IO ()
The computation writeFile file str function writes the string str, to the file file.
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]])
readIO :: Read a => String -> IO a
The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.
readLn :: Read a => IO a
The readLn function combines getLine and readIO.
Exception handling in the I/O monad
type IOError = IOException

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 Exception.

In Haskell 98, this is an opaque type.

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

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

 instance Monad IO where 
   ...
   fail s = ioError (userError s)
catch :: IO a -> (IOError -> IO a) -> IO a

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 catch from Control.Exception.

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