| Portability | portable |
|---|---|
| Stability | stable |
| Maintainer | libraries@haskell.org |
Prelude
Contents
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/.
- data Bool
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- otherwise :: Bool
- data Maybe a
- maybe :: b -> (a -> b) -> Maybe a -> b
- data Either a b
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- data Ordering
- 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
- class Eq a => Ord a where
- 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
- data Int
- data Integer
- data Float
- data Double
- type Rational = Ratio Integer
- class (Eq a, Show a) => Num a where
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- class (Real a, Enum a) => Integral a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class Fractional a => Floating a where
- class (Real a, Fractional a) => RealFrac a where
- 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, 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
- class Functor f where
- fmap :: (a -> b) -> f a -> f b
- mapM :: Monad m => (a -> m b) -> [a] -> m [b]
- mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
- sequence :: Monad m => [m a] -> m [a]
- sequence_ :: Monad m => [m a] -> m ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- id :: a -> a
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: (a -> b -> c) -> b -> a -> c
- ($) :: (a -> b) -> a -> b
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a -> a -> a
- error :: [Char] -> a
- undefined :: a
- seq :: a -> b -> b
- ($!) :: (a -> b) -> a -> b
- map :: (a -> b) -> [a] -> [b]
- (++) :: [a] -> [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [a] -> [a]
- null :: [a] -> Bool
- length :: [a] -> Int
- (!!) :: [a] -> Int -> a
- reverse :: [a] -> [a]
- foldl :: (a -> b -> a) -> a -> [b] -> a
- foldl1 :: (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: (a -> a -> a) -> [a] -> a
- and :: [Bool] -> Bool
- or :: [Bool] -> Bool
- any :: (a -> Bool) -> [a] -> Bool
- all :: (a -> Bool) -> [a] -> Bool
- sum :: Num a => [a] -> a
- product :: Num a => [a] -> a
- concat :: [[a]] -> [a]
- concatMap :: (a -> [b]) -> [a] -> [b]
- maximum :: Ord a => [a] -> a
- minimum :: Ord a => [a] -> a
- scanl :: (a -> b -> a) -> a -> [b] -> [a]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: [a] -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- elem :: Eq a => a -> [a] -> Bool
- notElem :: Eq a => a -> [a] -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- lines :: String -> [String]
- words :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- type ShowS = String -> String
- class Show a where
- 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
- 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
The Maybe type encapsulates an optional value. A value of type
Maybe aa (represented as Just aNothing). Using Maybe is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as error.
The Maybe type is also a monad. It is a simple kind of error
monad, where all errors are represented by Nothing. A richer
error monad can be built using the Data.Either.Either type.
Instances
| Monad Maybe | |
| Functor Maybe | |
| Typeable1 Maybe | |
| MonadFix Maybe | |
| MonadPlus Maybe | |
| Applicative Maybe | |
| Foldable Maybe | |
| Traversable Maybe | |
| Alternative Maybe | |
| Eq a => Eq (Maybe a) | |
| Data a => Data (Maybe a) | |
| Ord a => Ord (Maybe a) | |
| Read a => Read (Maybe a) | |
| Show a => Show (Maybe a) | |
| Generic (Maybe a) | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
The Either type represents values with two possibilities: a value of
type Either a bLeft aRight 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").
Instances
The character type Char is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) characters
(see http://www.unicode.org/ for details).
This set extends the ISO 8859-1 (Latin-1) character set
(the first 256 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 Prelude.toEnum and Prelude.fromEnum from the
Prelude.Enum class respectively (or equivalently ord and chr).
Tuples
curry :: ((a, b) -> c) -> a -> b -> cSource
curry converts an uncurried function to a curried function.
uncurry :: (a -> b -> c) -> (a, b) -> cSource
uncurry converts a curried function to a function on pairs.
Basic type classes
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.
Instances
| Eq Bool | |
| Eq Char | |
| Eq Double | |
| Eq Float | |
| Eq Int | |
| Eq Int8 | |
| Eq Int16 | |
| Eq Int32 | |
| Eq Int64 | |
| Eq Integer | |
| Eq Ordering | |
| Eq Word | |
| Eq Word8 | |
| Eq Word16 | |
| Eq Word32 | |
| Eq Word64 | |
| Eq () | |
| Eq Arity | |
| Eq Fixity | |
| Eq Associativity | |
| Eq TyCon | |
| Eq TypeRep | |
| Eq ArithException | |
| Eq IOException | |
| Eq MaskingState | |
| Eq Lexeme | |
| Eq Fingerprint | |
| Eq IOMode | |
| Eq SeekMode | |
| Eq IODeviceType | |
| Eq CUIntMax | |
| Eq CIntMax | |
| Eq CUIntPtr | |
| Eq CIntPtr | |
| Eq CSUSeconds | |
| Eq CUSeconds | |
| Eq CTime | |
| Eq CClock | |
| Eq CSigAtomic | |
| Eq CWchar | |
| Eq CSize | |
| Eq CPtrdiff | |
| Eq CDouble | |
| Eq CFloat | |
| Eq CULLong | |
| Eq CLLong | |
| Eq CULong | |
| Eq CLong | |
| Eq CUInt | |
| Eq CInt | |
| Eq CUShort | |
| Eq CShort | |
| Eq CUChar | |
| Eq CSChar | |
| Eq CChar | |
| Eq Any | |
| Eq All | |
| Eq GeneralCategory | |
| Eq TypeRepKey | |
| Eq Finalizers | |
| Eq IntPtr | |
| Eq WordPtr | |
| Eq Inserts | |
| Eq HashData | |
| Eq BufferState | |
| Eq CodingProgress | |
| Eq NewlineMode | |
| Eq Newline | |
| Eq BufferMode | |
| Eq Handle | |
| Eq IOErrorType | |
| Eq ExitCode | |
| Eq ArrayException | |
| Eq AsyncException | |
| Eq Errno | |
| Eq ThreadStatus | |
| Eq BlockReason | |
| Eq ThreadId | |
| Eq Fd | |
| Eq CRLim | |
| Eq CTcflag | |
| Eq CSpeed | |
| Eq CCc | |
| Eq CUid | |
| Eq CNlink | |
| Eq CGid | |
| Eq CSsize | |
| Eq CPid | |
| Eq COff | |
| Eq CMode | |
| Eq CIno | |
| Eq CDev | |
| Eq ControlMessage | |
| Eq Event | |
| Eq EventType | |
| Eq EPollFd | |
| Eq Unique | |
| Eq State | |
| Eq TimeoutKey | |
| Eq FdKey | |
| Eq HandlePosn | |
| Eq Fixity | |
| Eq ConstrRep | |
| Eq DataRep | |
| Eq Constr | Equality of constructors |
| Eq SpecConstrAnnotation | |
| Eq Unique | |
| Eq QSem | |
| Eq QSemN | |
| Eq Timeout | |
| Eq Version | |
| Eq Exception | |
| Eq Event | |
| Eq a => Eq [a] | |
| Eq a => Eq (Ratio a) | |
| Eq (StablePtr a) | |
| Eq (Ptr a) | |
| Eq (FunPtr a) | |
| Eq a => Eq (Maybe a) | |
| Eq (MVar a) | |
| Eq (IORef a) | |
| Eq a => Eq (Last a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Product a) | |
| Eq a => Eq (Sum a) | |
| Eq a => Eq (Dual a) | |
| Eq (ForeignPtr a) | |
| Eq (TVar a) | |
| Eq a => Eq (IntMap a) | |
| Eq a => Eq (LTree a) | |
| Eq a => Eq (PSQ a) | |
| Eq a => Eq (Elem a) | |
| Eq a => Eq (Down a) | |
| Eq (Chan a) | |
| Eq (SampleVar a) | |
| Eq a => Eq (Complex a) | |
| Eq (Fixed a) | |
| Eq (StableName a) | |
| (Eq a, Eq b) => Eq (Either a b) | |
| (Eq a, Eq b) => Eq (a, b) | |
| (Ix i, Eq e) => Eq (Array i e) | |
| Eq (IOArray i e) | |
| Eq (STRef s a) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| Eq (STArray s i e) | |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |
class Eq a => Ord a whereSource
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined
datatype whose constituent types are in Ord. The declared order
of the constructors in the data declaration determines the ordering
in derived Ord instances. The Ordering datatype allows a single
comparison to determine the precise ordering of two objects.
Minimal complete definition: either compare or <=.
Using compare can be more efficient for complex types.
Instances
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
succmaxBoundpredminBound -
fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::Bool -
enumFromandenumFromThenshould 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
the successor of a value. For numeric types, succ adds 1.
the predecessor of a value. For numeric types, pred subtracts 1.
Convert from an 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.
Used in Haskell's translation of [n..].
enumFromThen :: a -> a -> [a]Source
Used in Haskell's translation of [n,n'..].
enumFromTo :: a -> a -> [a]Source
Used in Haskell's translation of [n..m].
enumFromThenTo :: a -> a -> a -> [a]Source
Used in Haskell's translation of [n,n'..m].
Instances
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.
Instances
Numbers
Numeric types
A fixed-precision integer type with at least the range [-2^29 .. 2^29-1].
The exact range for a given implementation can be determined by using
Prelude.minBound and Prelude.maxBound from the Prelude.Bounded class.
Arbitrary-precision integers.
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.
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.
Numeric type classes
class (Eq a, Show a) => Num a whereSource
Basic numeric class.
Minimal complete definition: all except negate or (-)
Methods
(+), (*), (-) :: a -> a -> aSource
Unary negation.
Absolute value.
Sign of a number.
The functions abs and signum should satisfy the law:
abs x * signum x == x
For real numbers, the signum is either -1 (negative), 0 (zero)
or 1 (positive).
fromInteger :: Integer -> aSource
Conversion from an Integer.
An integer literal represents the application of the function
fromInteger to the appropriate value of type Integer,
so such literals have type (.
Num a) => a
Instances
| Num Double | |
| Num Float | |
| Num Int | |
| Num Int8 | |
| Num Int16 | |
| Num Int32 | |
| Num Int64 | |
| Num Integer | |
| Num Word | |
| Num Word8 | |
| Num Word16 | |
| Num Word32 | |
| Num Word64 | |
| Num CUIntMax | |
| Num CIntMax | |
| Num CUIntPtr | |
| Num CIntPtr | |
| Num CSUSeconds | |
| Num CUSeconds | |
| Num CTime | |
| Num CClock | |
| Num CSigAtomic | |
| Num CWchar | |
| Num CSize | |
| Num CPtrdiff | |
| Num CDouble | |
| Num CFloat | |
| Num CULLong | |
| Num CLLong | |
| Num CULong | |
| Num CLong | |
| Num CUInt | |
| Num CInt | |
| Num CUShort | |
| Num CShort | |
| Num CUChar | |
| Num CSChar | |
| Num CChar | |
| Num IntPtr | |
| Num WordPtr | |
| Num Fd | |
| Num CRLim | |
| Num CTcflag | |
| Num CSpeed | |
| Num CCc | |
| Num CUid | |
| Num CNlink | |
| Num CGid | |
| Num CSsize | |
| Num CPid | |
| Num COff | |
| Num CMode | |
| Num CIno | |
| Num CDev | |
| Num EventType | |
| Num Unique | |
| Num Event | |
| Integral a => Num (Ratio a) | |
| RealFloat a => Num (Complex a) | |
| HasResolution a => Num (Fixed a) |
class (Num a, Ord a) => Real a whereSource
Methods
toRational :: a -> RationalSource
the rational equivalent of its real argument with full precision
Instances
class (Real a, Enum a) => Integral a whereSource
Methods
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a)Source
divMod :: a -> a -> (a, a)Source
toInteger :: a -> IntegerSource
conversion to Integer
Instances
class Num a => Fractional a whereSource
Fractional numbers, supporting real division.
Minimal complete definition: fromRational and (recip or ()
/)
Methods
fractional division
reciprocal fraction
fromRational :: Rational -> aSource
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.
Fractional a) => a
Instances
| Fractional Double | |
| Fractional Float | |
| Fractional CDouble | |
| Fractional CFloat | |
| Integral a => Fractional (Ratio a) | |
| RealFloat a => Fractional (Complex a) | |
| HasResolution a => Fractional (Fixed a) |
class Fractional a => Floating a whereSource
Trigonometric and hyperbolic functions and related functions.
Minimal complete definition:
pi, exp, log, sin, cos, sinh, cosh,
asin, acos, atan, asinh, acosh and atanh
class (Real a, Fractional a) => RealFrac a whereSource
Extracting components of fractions.
Minimal complete definition: properFraction
Methods
properFraction :: Integral b => a -> (b, a)Source
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
-
nis an integral number with the same sign asx; and -
fis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> bSource
truncate xx between zero and x
round :: Integral b => a -> bSource
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> bSource
ceiling xx
floor :: Integral b => a -> bSource
floor xx
class (RealFrac a, Floating a) => RealFloat a whereSource
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition:
all except exponent, significand, scaleFloat and atan2
Methods
floatRadix :: a -> IntegerSource
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> IntSource
a constant function, returning the number of digits of
floatRadix in the significand
floatRange :: a -> (Int, Int)Source
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int)Source
The function decodeFloat applied to a real floating-point
number returns the significand expressed as an Integer and an
appropriately scaled exponent (an Int). If decodeFloat x(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 xdecodeFloat 0 = (0,0)
encodeFloat :: Integer -> Int -> aSource
encodeFloat performs the inverse of decodeFloat
the second component of decodeFloat.
significand :: a -> aSource
the first component of decodeFloat, scaled to lie in the open
interval (-1,1)
scaleFloat :: Int -> a -> aSource
multiplies a floating-point number by an integer power of the radix
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> BoolSource
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> BoolSource
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> BoolSource
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloat, should return the same value as atan yatan2 is provided, but implementors
can provide a more accurate implementation.
Numeric functions
gcd :: Integral a => a -> a -> aSource
gcd x yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 0 44. gcd 0 00.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0minBound0 or minBound
lcm :: Integral a => a -> a -> aSource
lcm x yx and y divide.
(^^) :: (Fractional a, Integral b) => a -> b -> aSource
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> bSource
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> bSource
general coercion to fractional types
Monads and functors
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Minimal complete definition: >>= and return.
Instances of Monad should satisfy the following laws:
return a >>= k == k a m >>= return == m m >>= (\x -> k x >>= h) == (m >>= k) >>= h
Instances of both Monad and Functor should additionally satisfy the law:
fmap f xs == xs >>= return . f
The instances of Monad for lists, Data.Maybe.Maybe and System.IO.IO
defined in the Prelude satisfy these laws.
Methods
(>>=) :: forall a b. m a -> (a -> m b) -> m bSource
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: forall a b. m a -> m b -> m bSource
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
Inject a value into the monadic type.
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.
The Functor class is used for types that can be mapped over.
Instances of Functor should satisfy the following laws:
fmap id == id fmap (f . g) == fmap f . fmap g
The instances of Functor for lists, Data.Maybe.Maybe and System.IO.IO
satisfy these laws.
Instances
| Functor [] | |
| Functor IO | |
| Functor Maybe | |
| Functor ReadP | |
| Functor ReadPrec | |
| Functor STM | |
| Functor ZipList | |
| Functor Id | |
| Functor ((->) r) | |
| Functor (Either a) | |
| Functor ((,) a) | |
| Functor (ST s) | |
| Ix i => Functor (Array i) | |
| Functor (ST s) | |
| Monad m => Functor (WrappedMonad m) | |
| Functor (Const m) | |
| Functor (StateR s) | |
| Functor (StateL s) | |
| Arrow a => Functor (WrappedArrow a b) |
sequence :: Monad m => [m a] -> m [a]Source
Evaluate each action in the sequence from left to right, and collect the results.
sequence_ :: Monad m => [m a] -> m ()Source
Evaluate each action in the sequence from left to right, and ignore the results.
Miscellaneous functions
flip :: (a -> b -> c) -> b -> a -> cSource
flip ff.
($) :: (a -> b) -> a -> bSource
Application operator. This operator is redundant, since ordinary
application (f x) means the same as (f . However, $ x)$ 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) xsData.List.zipWith ($) fs xs
until :: (a -> Bool) -> (a -> a) -> a -> aSource
until p ff until p holds.
Evaluates its first argument to head normal form, and then returns its second argument as the result.
List operations
map :: (a -> b) -> [a] -> [b]Source
map f xs is the list obtained by applying f to each element
of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
(++) :: [a] -> [a] -> [a]Source
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
filter :: (a -> Bool) -> [a] -> [a]Source
filter, applied to a predicate and a list, returns the list of
those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
Return all the elements of a list except the last one. The list must be non-empty.
List index (subscript) operator, starting from 0.
It is an instance of the more general Data.List.genericIndex,
which takes an index of any integral type.
reverse xs returns the elements of xs in reverse order.
xs must be finite.
Reducing lists (folds)
foldl :: (a -> b -> a) -> a -> [b] -> aSource
foldl, applied to a binary operator, a starting value (typically
the left-identity of the operator), and a list, reduces the list
using the binary operator, from left to right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
The list must be finite.
foldr :: (a -> b -> b) -> b -> [a] -> bSource
foldr, applied to a binary operator, a starting value (typically
the right-identity of the operator), and a list, reduces the list
using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Special folds
product :: Num a => [a] -> aSource
The product function computes the product of a finite list of numbers.
Building lists
Scans
Infinite lists
iterate :: (a -> a) -> a -> [a]Source
iterate f x returns an infinite list of repeated applications
of f to x:
iterate f x == [x, f x, f (f x), ...]
replicate :: Int -> a -> [a]Source
replicate n x is a list of length n with x the value of
every element.
It is an instance of the more general Data.List.genericReplicate,
in which n may be of any integral type.
cycle ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.
Sublists
take :: Int -> [a] -> [a]Source
take n, applied to a list xs, returns the prefix of xs
of length n, or xs itself if n > :
length xs
take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []
It is an instance of the more general Data.List.genericTake,
in which n may be of any integral type.
drop :: Int -> [a] -> [a]Source
drop n xs returns the suffix of xs
after the first n elements, or [] if n > :
length xs
drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]
It is an instance of the more general Data.List.genericDrop,
in which n may be of any integral type.
splitAt :: Int -> [a] -> ([a], [a])Source
splitAt n xs returns a tuple where first element is xs prefix of
length n and second element is the remainder of the list:
splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])
It is equivalent to ( when take n xs, drop n xs)n is not _|_
(splitAt _|_ xs = _|_).
splitAt is an instance of the more general Data.List.genericSplitAt,
in which n may be of any integral type.
takeWhile :: (a -> Bool) -> [a] -> [a]Source
takeWhile, applied to a predicate p and a list xs, returns the
longest prefix (possibly empty) of xs of elements that satisfy p:
takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2] takeWhile (< 9) [1,2,3] == [1,2,3] takeWhile (< 0) [1,2,3] == []
span :: (a -> Bool) -> [a] -> ([a], [a])Source
span, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
satisfy p and second element is the remainder of the list:
span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4]) span (< 9) [1,2,3] == ([1,2,3],[]) span (< 0) [1,2,3] == ([],[1,2,3])
break :: (a -> Bool) -> [a] -> ([a], [a])Source
break, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
do not satisfy p and second element is the remainder of the list:
break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])
Searching lists
lookup :: Eq a => a -> [(a, b)] -> Maybe bSource
lookup key assocs looks up a key in an association list.
Zipping and unzipping lists
zip :: [a] -> [b] -> [(a, b)]Source
zip takes two lists and returns a list of corresponding pairs.
If one input list is short, excess elements of the longer list are
discarded.
unzip :: [(a, b)] -> ([a], [b])Source
unzip transforms a list of pairs into a list of first components
and a list of second components.
Functions on strings
lines :: String -> [String]Source
lines breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
words :: String -> [String]Source
words breaks a string up into a list of words, which were delimited
by white space.
Converting to and from String
Converting to String
Conversion of values to readable Strings.
Minimal complete definition: showsPrec or show.
Derived instances of Show have the following properties, which
are compatible with derived instances of Text.Read.Read:
- The result of
showis 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
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill 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)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> a | the value to be converted to a |
| -> ShowS |
Convert a value to a readable String.
showsPrec should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Text.Read.Read and Show satisfy the following:
-
(x,"")is an element of(.Text.Read.readsPrecd (showsPrecd x ""))
That is, Text.Read.readsPrec parses the string produced by
showsPrec, and delivers the value that showsPrec started with.
Instances
showChar :: Char -> ShowSSource
utility function converting a Char to a show function that
simply prepends the character unchanged.
showString :: String -> ShowSSource
utility function converting a String to a show function that
simply prepends the string unchanged.
Converting from String
Parsing of Strings, producing values.
Minimal complete definition: readsPrec (or, for GHC only, readPrec)
Derived instances of Read make the following assumptions, which
derived instances of Text.Show.Show obey:
- If the constructor is defined to be an infix operator, then the
derived
Readinstance 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
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Readinstance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read in Haskell 98 is equivalent to
instance (Read a) => Read (Tree a) where
readsPrec d r = readParen (d > app_prec)
(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r
++ readParen (d > up_prec)
(\r -> [(u:^:v,w) |
(u,s) <- readsPrec (up_prec+1) r,
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r
where app_prec = 10
up_prec = 5
Note that right-associativity of :^: is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefault
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> ReadS a |
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read and Text.Show.Show satisfy the following:
-
(x,"")is an element of(.readsPrecd (Text.Show.showsPrecd x ""))
That is, readsPrec parses the string produced by
Text.Show.showsPrec, and delivers the value that
Text.Show.showsPrec started with.
Instances
read :: Read a => String -> aSource
The read function reads input from a string, which must be
completely consumed by the input process.
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 "" = [("","")]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
A value of type IO aa.
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
| Monad IO | |
| Functor IO | |
| Typeable1 IO | |
| MonadFix IO | |
| Applicative IO | |
| HPrintfType (IO a) | |
| PrintfType (IO a) |
Simple I/O operations
Output functions
print :: Show a => a -> IO ()Source
The print function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class Show; print
converts values to strings for output using the show operation and
adds a newline.
For example, a program to print the first 20 integers and their powers of 2 could be written as:
main = print ([(n, 2^n) | n <- [0..19]])
Input functions
getContents :: IO StringSource
The getContents operation returns all user input as a single string,
which is read lazily as it is needed
(same as hGetContents stdin).
interact :: (String -> String) -> IO ()Source
The interact function takes a function of type String->String
as its argument. The entire input from the standard input device is
passed to this function as its argument, and the resulting string is
output on the standard output device.
Files
File and directory names are values of type String, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.
readFile :: FilePath -> IO StringSource
The readFile function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with getContents.
writeFile :: FilePath -> String -> IO ()Source
The computation writeFile file str function writes the string str,
to the file file.
appendFile :: FilePath -> String -> IO ()Source
The computation appendFile file str function appends the string str,
to the file file.
Note that writeFile and appendFile write a literal string
to a file. To write a value of any printable type, as with print,
use the show function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
Exception handling in the I/O monad
type IOError = IOExceptionSource
The Haskell 98 type for exceptions in the IO monad.
Any I/O operation may raise an IOError instead of returning a result.
For a more general type of exception, including also those that arise
in pure code, see Control.Exception.Exception.
In Haskell 98, this is an opaque type.