| Haskell Hierarchical Libraries (base package) | Contents | Index

Prelude

Portability | portable
Stability | stable
Maintainer | libraries@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 |

Instances

Bounded Bool
Data Bool
Enum Bool
Eq Bool
Ix Bool
NFData Bool
Ord Bool
Random Bool
Read Bool
Show Bool
Storable Bool
Typeable Bool
IArray UArray Bool
MArray IOUArray Bool IO
MArray (STUArray s) Bool (ST s)
Ix ix => Eq (UArray ix Bool)
Ix ix => Ord (UArray ix Bool)
(Ix ix, Show ix) => Show (UArray ix Bool)

(&&) :: 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 |

Instances

Functor Maybe
FunctorM Maybe
Monad Maybe
MonadFix Maybe
MonadPlus Maybe
Typeable1 Maybe
Data a => Data (Maybe a)
Eq a => Eq (Maybe a)
Ord a => Ord (Maybe a)
Read a => Read (Maybe a)
Show a => Show (Maybe a)

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 |

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 |

Instances

Bounded Ordering
Data Ordering
Enum Ordering
Eq Ordering
Ix Ordering
Monoid Ordering
Ord Ordering
Read Ordering
Show Ordering
Typeable Ordering

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`).

Instances

Bounded Char
Data Char
Enum Char
Eq Char
HTML Char
IsChar Char
Ix Char
NFData Char
Ord Char
PrintfArg Char
Random Char
Read Char
Show Char
Storable Char
Typeable Char
IArray UArray Char
MArray IOUArray Char IO
IArray (IOToDiffArray IOUArray) Char
MArray (STUArray s) Char (ST s)
Ix ix => Eq (UArray ix Char)
Ix ix => Ord (UArray ix Char)
(Ix ix, Show ix) => Show (DiffUArray ix Char)
(Ix ix, Show ix) => Show (UArray ix Char)

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

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

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:

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

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

Methods

succ :: a -> a
the successor of a value. For numeric types, `succ` adds 1.
pred :: a -> a
the predecessor of a value. For numeric types, `pred` subtracts 1.
toEnum :: Int -> a
Convert from an `Int`.
fromEnum :: a -> Int
Convert to an `Int`. It is implementation-dependent what `fromEnum` returns when applied to a value that is too large to fit in an `Int`.
enumFrom :: a -> [a]
Used in Haskell's translation of `[n..]`.
enumFromThen :: a -> a -> [a]
Used in Haskell's translation of `[n,n'..]`.
enumFromTo :: a -> a -> [a]
Used in Haskell's translation of `[n..m]`.
enumFromThenTo :: a -> a -> a -> [a]
Used in Haskell's translation of `[n,n'..m]`.

Instances

Enum Bool
Enum CCc
Enum CChar
Enum CClock
Enum CDev
Enum CDouble
Enum CFloat
Enum CGid
Enum CIno
Enum CInt
Enum CLDouble
Enum CLLong
Enum CLong
Enum CMode
Enum CNlink
Enum COff
Enum CPid
Enum CPtrdiff
Enum CRLim
Enum CSChar
Enum CShort
Enum CSigAtomic
Enum CSize
Enum CSpeed
Enum CSsize
Enum CTcflag
Enum CTime
Enum CUChar
Enum CUInt
Enum CULLong
Enum CULong
Enum CUShort
Enum CUid
Enum CWchar
Enum Char
Enum Day
Enum Double
Enum Fd
Enum Float
Enum GeneralCategory
Enum IOMode
Enum Int
Enum Int16
Enum Int32
Enum Int64
Enum Int8
Enum Integer
Enum Month
Enum Ordering
Enum SeekMode
Enum Word
Enum Word16
Enum Word32
Enum Word64
Enum Word8
Enum ()
Integral a => Enum (Ratio a)

class Bounded a where

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

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

Methods

minBound :: a
maxBound :: a

Instances

Bounded Bool
Bounded CChar
Bounded CGid
Bounded CIno
Bounded CInt
Bounded CLLong
Bounded CLong
Bounded CMode
Bounded CNlink
Bounded COff
Bounded CPid
Bounded CPtrdiff
Bounded CRLim
Bounded CSChar
Bounded CShort
Bounded CSigAtomic
Bounded CSize
Bounded CSsize
Bounded CTcflag
Bounded CUChar
Bounded CUInt
Bounded CULLong
Bounded CULong
Bounded CUShort
Bounded CUid
Bounded CWchar
Bounded Char
Bounded Day
Bounded Fd
Bounded GeneralCategory
Bounded Int
Bounded Int16
Bounded Int32
Bounded Int64
Bounded Int8
Bounded Month
Bounded Ordering
Bounded Word
Bounded Word16
Bounded Word32
Bounded Word64
Bounded Word8
Bounded ()
(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)

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.
Instances

Bits Int
Bounded Int
Data Int
Enum Int
Eq Int
Integral Int
Ix Int
NFData Int
NFDataIntegral Int
NFDataOrd Int
Num Int
Ord Int
PrintfArg Int
Random Int
Read Int
Real Int
Show Int
Storable Int
Typeable Int
IArray UArray Int
MArray IOUArray Int IO
IArray (IOToDiffArray IOUArray) Int
MArray (STUArray s) Int (ST s)
Ix ix => Eq (UArray ix Int)
Ix ix => Ord (UArray ix Int)
(Ix ix, Show ix) => Show (DiffUArray ix Int)
(Ix ix, Show ix) => Show (UArray ix Int)

data Integer

Arbitrary-precision integers.
Instances

Bits Integer
Data Integer
Enum Integer
Eq Integer
Integral Integer
Ix Integer
NFData Integer
Num Integer
Ord Integer
PrintfArg Integer
Random Integer
Read Integer
Real Integer
Show Integer
Typeable Integer

data Float

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

Data Float
Enum Float
Eq Float
Floating Float
Fractional Float
NFData Float
Num Float
Ord Float
PrintfArg Float
Random Float
Read Float
Real Float
RealFloat Float
RealFrac Float
Show Float
Storable Float
Typeable Float
IArray UArray Float
MArray IOUArray Float IO
IArray (IOToDiffArray IOUArray) Float
MArray (STUArray s) Float (ST s)
Ix ix => Eq (UArray ix Float)
Ix ix => Ord (UArray ix Float)
(Ix ix, Show ix) => Show (DiffUArray ix Float)
(Ix ix, Show ix) => Show (UArray ix Float)

data Double

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

Data Double
Enum Double
Eq Double
Floating Double
Fractional Double
NFData Double
Num Double
Ord Double
PrintfArg Double
Random Double
Read Double
Real Double
RealFloat Double
RealFrac Double
Show Double
Storable Double
Typeable Double
IArray UArray Double
MArray IOUArray Double IO
IArray (IOToDiffArray IOUArray) Double
MArray (STUArray s) Double (ST s)
Ix ix => Eq (UArray ix Double)
Ix ix => Ord (UArray ix Double)
(Ix ix, Show ix) => Show (DiffUArray ix Double)
(Ix ix, Show ix) => Show (UArray ix Double)

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`.

Instances

Num CCc
Num CChar
Num CClock
Num CDev
Num CDouble
Num CFloat
Num CGid
Num CIno
Num CInt
Num CLDouble
Num CLLong
Num CLong
Num CMode
Num CNlink
Num COff
Num CPid
Num CPtrdiff
Num CRLim
Num CSChar
Num CShort
Num CSigAtomic
Num CSize
Num CSpeed
Num CSsize
Num CTcflag
Num CTime
Num CUChar
Num CUInt
Num CULLong
Num CULong
Num CUShort
Num CUid
Num CWchar
Num Double
Num Fd
Num Float
Num Int
Num Int16
Num Int32
Num Int64
Num Int8
Num Integer
Num Word
Num Word16
Num Word32
Num Word64
Num Word8
RealFloat a => Num (Complex a)
Integral a => Num (Ratio a)

class (Num a, Ord a) => Real a where

Methods

toRational :: a -> Rational
the rational equivalent of its real argument with full precision

Instances

Real CCc
Real CChar
Real CClock
Real CDev
Real CDouble
Real CFloat
Real CGid
Real CIno
Real CInt
Real CLDouble
Real CLLong
Real CLong
Real CMode
Real CNlink
Real COff
Real CPid
Real CPtrdiff
Real CRLim
Real CSChar
Real CShort
Real CSigAtomic
Real CSize
Real CSpeed
Real CSsize
Real CTcflag
Real CTime
Real CUChar
Real CUInt
Real CULLong
Real CULong
Real CUShort
Real CUid
Real CWchar
Real Double
Real Fd
Real Float
Real Int
Real Int16
Real Int32
Real Int64
Real Int8
Real Integer
Real Word
Real Word16
Real Word32
Real Word64
Real Word8
Integral a => Real (Ratio a)

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`

Instances

Integral CChar
Integral CGid
Integral CIno
Integral CInt
Integral CLLong
Integral CLong
Integral CMode
Integral CNlink
Integral COff
Integral CPid
Integral CPtrdiff
Integral CRLim
Integral CSChar
Integral CShort
Integral CSigAtomic
Integral CSize
Integral CSsize
Integral CTcflag
Integral CUChar
Integral CUInt
Integral CULLong
Integral CULong
Integral CUShort
Integral CUid
Integral CWchar
Integral Fd
Integral Int
Integral Int16
Integral Int32
Integral Int64
Integral Int8
Integral Integer
Integral Word
Integral Word16
Integral Word32
Integral Word64
Integral Word8

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`.

Instances

Fractional CDouble
Fractional CFloat
Fractional CLDouble
Fractional Double
Fractional Float
RealFloat a => Fractional (Complex a)
Integral a => Fractional (Ratio a)

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

Instances

Floating CDouble
Floating CFloat
Floating CLDouble
Floating Double
Floating Float
RealFloat a => Floating (Complex a)

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`

Instances

RealFrac CDouble
RealFrac CFloat
RealFrac CLDouble
RealFrac Double
RealFrac Float
Integral a => RealFrac (Ratio a)

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.

Instances

RealFloat CDouble
RealFloat CFloat
RealFloat CLDouble
RealFloat Double
RealFloat Float

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.

Instances

Monad IO
Monad Maybe
Monad P
Monad ReadP
Monad ReadPrec
Monad STM
Monad []
ArrowApply a => Monad (ArrowMonad a)
Monad (ST s)
Monad (ST s)

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

Instances

Functor IO
Functor IntMap
Functor Maybe
Functor Queue
Functor ReadP
Functor ReadPrec
Functor STM
Functor Tree
Functor []
Ix i => Functor (Array i)
Functor (FiniteMap k)
Functor (Map k)
Functor (ST s)
Functor (ST s)

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 `String`s.

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

:: Int | the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> a | the value to be converted to a `String`
-> ShowS |

Convert a value to a readable `String`.

`showsPrec` should satisfy the law

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

Derived instances of `Read` and `Show` satisfy the following:

- `(x,"")` is an element of `(`readsPrec` d (`showsPrec` d x ""))`.

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

show :: a -> String
A specialised variant of `showsPrec`, using precedence context zero, and returning an ordinary `String`.
showList :: [a] -> ShowS
The method `showList` is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined `Show` instance of the `Char` type, where values of type `String` should be shown in double quotes, rather than between square brackets.

Instances

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 `String`s, 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

:: Int | the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> ReadS a |

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

Derived instances of `Read` and `Show` satisfy the following:

- `(x,"")` is an element of `(`readsPrec` d (`showsPrec` d x ""))`.

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

readList :: ReadS [a]
The method `readList` is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined `Read` instance of the `Char` type, where values of type `String` should be are expected to use double quotes, rather than square brackets.

Instances

Read Bool
Read BufferMode
Read CCc
Read CChar
Read CClock
Read CDev
Read CDouble
Read CFloat
Read CGid
Read CIno
Read CInt
Read CLDouble
Read CLLong
Read CLong
Read CMode
Read CNlink
Read COff
Read CPid
Read CPtrdiff
Read CRLim
Read CSChar
Read CShort
Read CSigAtomic
Read CSize
Read CSpeed
Read CSsize
Read CTcflag
Read CTime
Read CUChar
Read CUInt
Read CULLong
Read CULong
Read CUShort
Read CUid
Read CWchar
Read CalendarTime
Read Char
Read Day
Read Double
Read ExitCode
Read Fd
Read Float
Read GeneralCategory
Read IOMode
Read Int
Read Int16
Read Int32
Read Int64
Read Int8
Read Integer
Read Lexeme
Read Month
Read Ordering
Read Permissions
Read SeekMode
Read StdGen
Read TimeDiff
Read Version
Read Word
Read Word16
Read Word32
Read Word64
Read Word8
Read ()
(Read a, Read b) => Read (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)
(RealFloat a, Read a) => Read (Complex a)
Read a => Read (Maybe a)
(Integral a, Read a) => Read (Ratio a)
Read a => Read (Tree a)
Read a => Read [a]
(Ix a, Read a, Read b) => Read (Array a b)
(Read a, Read b) => Read (Either a b)

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.

Instances

Functor IO
Monad IO
MonadFix IO
Typeable1 IO
MArray IOArray e IO
MArray IOUArray Bool IO
MArray IOUArray Char IO
MArray IOUArray Double IO
MArray IOUArray Float IO
MArray IOUArray Int IO
MArray IOUArray Int16 IO
MArray IOUArray Int32 IO
MArray IOUArray Int64 IO
MArray IOUArray Int8 IO
MArray IOUArray Word IO
MArray IOUArray Word16 IO
MArray IOUArray Word32 IO
MArray IOUArray Word64 IO
MArray IOUArray Word8 IO
Storable e => MArray StorableArray e IO
MArray IOUArray (FunPtr a) IO
MArray IOUArray (Ptr a) IO
MArray IOUArray (StablePtr a) IO
Typeable a => Data (IO a)
HPrintfType (IO a)
PrintfType (IO a)

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 `IOError`s 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.

Produced by Haddock version 0.7