| Safe Haskell | Trustworthy |
|---|---|
| Language | Haskell2010 |
Prelude
Contents
Description
The Haskell 2010 Prelude: a standard module imported by default into all Haskell modules. For more documentation, see the Haskell 2010 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 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 :: 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
- 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 :: (b -> a -> b) -> b -> [a] -> b
- 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 :: (b -> a -> b) -> b -> [a] -> [b]
- 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
data Bool :: *
data Maybe a :: * -> *
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 Either type.
data Either a b :: * -> * -> *
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").
data Ordering :: *
data Char :: *
The character type Char is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) characters (see
http://www.unicode.org/ for details). This set extends the ISO 8859-1
(Latin-1) character set (the first 256 characters), which is itself an extension
of the ASCII character set (the first 128 characters). A character literal in
Haskell has type Char.
To convert a Char to or from the corresponding Int value defined
by Unicode, use toEnum and fromEnum from the
Enum class respectively (or equivalently ord and chr).
Tuples
fst :: (a, b) -> a
Extract the first component of a pair.
snd :: (a, b) -> b
Extract the second component of a pair.
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.
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 Handle | |
| Eq HandlePosn | |
| Eq IOMode | |
| Eq Errno | |
| Eq AsyncException | |
| Eq ArrayException | |
| Eq ExitCode | |
| Eq IOErrorType | |
| Eq BufferMode | |
| Eq Newline | |
| Eq NewlineMode | |
| Eq IODeviceType | |
| Eq SeekMode | |
| Eq WordPtr | |
| Eq IntPtr | |
| Eq GeneralCategory | |
| Eq CChar | |
| Eq CSChar | |
| Eq CUChar | |
| Eq CShort | |
| Eq CUShort | |
| Eq CInt | |
| Eq CUInt | |
| Eq CLong | |
| Eq CULong | |
| Eq CLLong | |
| Eq CULLong | |
| Eq CFloat | |
| Eq CDouble | |
| Eq CPtrdiff | |
| Eq CSize | |
| Eq CWchar | |
| Eq CSigAtomic | |
| Eq CClock | |
| Eq CTime | |
| Eq CUSeconds | |
| Eq CSUSeconds | |
| Eq CIntPtr | |
| Eq CUIntPtr | |
| Eq CIntMax | |
| Eq CUIntMax | |
| Eq MaskingState | |
| Eq IOException | |
| Eq ErrorCall | |
| Eq ArithException | |
| Eq a => Eq [a] | |
| Eq a => Eq (Ratio a) | |
| Eq (StablePtr a) | |
| Eq (Ptr a) | |
| Eq (FunPtr a) | |
| Eq (ForeignPtr a) | |
| Eq a => Eq (Complex a) | |
| Eq a => Eq (ZipList a) | |
| Eq a => Eq (Maybe 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 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) |
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
(>=) :: a -> a -> Bool infix 4
(<=) :: a -> a -> Bool infix 4
max :: a -> a -> a
min :: a -> a -> a
Instances
| Ord Bool | |
| Ord Char | |
| Ord Double | |
| Ord Float | |
| Ord Int | |
| Ord Int8 | |
| Ord Int16 | |
| Ord Int32 | |
| Ord Int64 | |
| Ord Integer | |
| Ord Ordering | |
| Ord Word | |
| Ord Word8 | |
| Ord Word16 | |
| Ord Word32 | |
| Ord Word64 | |
| Ord () | |
| Ord IOMode | |
| Ord AsyncException | |
| Ord ArrayException | |
| Ord ExitCode | |
| Ord BufferMode | |
| Ord Newline | |
| Ord NewlineMode | |
| Ord SeekMode | |
| Ord WordPtr | |
| Ord IntPtr | |
| Ord GeneralCategory | |
| Ord CChar | |
| Ord CSChar | |
| Ord CUChar | |
| Ord CShort | |
| Ord CUShort | |
| Ord CInt | |
| Ord CUInt | |
| Ord CLong | |
| Ord CULong | |
| Ord CLLong | |
| Ord CULLong | |
| Ord CFloat | |
| Ord CDouble | |
| Ord CPtrdiff | |
| Ord CSize | |
| Ord CWchar | |
| Ord CSigAtomic | |
| Ord CClock | |
| Ord CTime | |
| Ord CUSeconds | |
| Ord CSUSeconds | |
| Ord CIntPtr | |
| Ord CUIntPtr | |
| Ord CIntMax | |
| Ord CUIntMax | |
| Ord ErrorCall | |
| Ord ArithException | |
| Ord a => Ord [a] | |
| Integral a => Ord (Ratio a) | |
| Ord (Ptr a) | |
| Ord (FunPtr a) | |
| Ord (ForeignPtr a) | |
| Ord a => Ord (ZipList a) | |
| Ord a => Ord (Maybe a) | |
| (Ord a, Ord b) => Ord (Either a b) | |
| (Ord a, Ord b) => Ord (a, b) | |
| (Ix i, Ord e) => Ord (Array i e) | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
| (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |
class Enum a 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
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould 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 = minBoundMethods
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.
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.
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
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.
Instances
Numbers
Numeric types
data Int :: *
data Integer :: *
Arbitrary-precision integers.
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.
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.
Numeric type classes
class Num a where
Basic numeric class.
Minimal complete definition: all except negate or (-)
Methods
(+) :: a -> a -> a infixl 6
(*) :: a -> a -> a infixl 7
(-) :: a -> a -> a infixl 6
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 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 WordPtr | |
| Num IntPtr | |
| Num CChar | |
| Num CSChar | |
| Num CUChar | |
| Num CShort | |
| Num CUShort | |
| Num CInt | |
| Num CUInt | |
| Num CLong | |
| Num CULong | |
| Num CLLong | |
| Num CULLong | |
| Num CFloat | |
| Num CDouble | |
| Num CPtrdiff | |
| Num CSize | |
| Num CWchar | |
| Num CSigAtomic | |
| Num CClock | |
| Num CTime | |
| Num CUSeconds | |
| Num CSUSeconds | |
| Num CIntPtr | |
| Num CUIntPtr | |
| Num CIntMax | |
| Num CUIntMax | |
| Integral a => Num (Ratio a) | |
| RealFloat a => Num (Complex a) |
class (Num a, Ord a) => Real a where
Instances
class (Real a, Enum a) => Integral a where
Methods
quot :: a -> a -> a infixl 7
integer division truncated toward zero
rem :: a -> a -> a infixl 7
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a)
divMod :: a -> a -> (a, a)
conversion to Integer
Instances
class Num a => Fractional a where
Fractional numbers, supporting real division.
Minimal complete definition: fromRational and (recip or ()/)
Minimal complete definition
fromRational, (recip | (/))
Methods
(/) :: a -> a -> a infixl 7
fractional division
recip :: a -> a
reciprocal fraction
fromRational :: Rational -> a
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional Double | |
| Fractional Float | |
| Fractional CFloat | |
| Fractional CDouble | |
| Integral a => Fractional (Ratio a) | |
| RealFloat a => Fractional (Complex 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
Minimal complete definition
pi, exp, log, sin, cos, asin, atan, acos, sinh, cosh, asinh, atanh, acosh
class (Real a, Fractional a) => RealFrac a where
Extracting components of fractions.
Minimal complete definition: properFraction
Minimal complete definition
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:
nis an integral number with the same sign asx; andfis 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 -> b
truncate xx between zero and x
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b
ceiling xx
floor xx
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
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
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(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) <= , where abs m < b^dd is
the value of floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite xTrue.
encodeFloat :: Integer -> Int -> a
encodeFloat performs the inverse of decodeFloat in the
sense that for finite x with the exception of -0.0,
uncurry encodeFloat (decodeFloat x) = xencodeFloat m nm*b^^n (or ±Infinity if overflow
occurs); usually the closer, but if m contains too many bits,
the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
significand x * b ^^ exponent xb is the
floating-point radix.
The behaviour is unspecified on infinite or NaN values.
significand :: a -> a
The first component of decodeFloat, scaled to lie in the open
interval (-1,1), either 0.0 or of absolute value >= 1/b,
where b is the floating-point radix.
The behaviour is unspecified on infinite or NaN values.
scaleFloat :: Int -> a -> a
multiplies a floating-point number by an integer power of the radix
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
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(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
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8
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
(>>=) :: m a -> (a -> m b) -> m b infixl 1
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: m a -> m b -> m b infixl 1
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
return :: a -> m a
Inject a value into the monadic type.
Fail 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.
class Functor f where
The Functor class is used for types that can be mapped over.
Instances of Functor should satisfy the following laws:
fmap id == id fmap (f . g) == fmap f . fmap g
The instances of Functor for lists, Maybe and IO
satisfy these laws.
Methods
fmap :: (a -> b) -> f a -> f b
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 infixr 1
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 infixr 9
Function composition.
flip :: (a -> b -> c) -> b -> a -> c
flip ff.
($) :: (a -> b) -> a -> b infixr 0
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) xszipWith ($) fs xs
asTypeOf :: a -> a -> a
undefined :: a
seq :: a -> b -> b
Evaluates its first argument to head normal form, and then returns its second argument as the result.
($!) :: (a -> b) -> a -> b infixr 0 Source
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] infixr 5
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 non-empty.
O(n). 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 infixl 9
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex,
which takes an index of any integral type.
Reducing lists (folds)
foldl :: (b -> a -> b) -> b -> [a] -> b
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
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
Special folds
concat :: [[a]] -> [a]
Concatenate a list of lists.
concatMap :: (a -> [b]) -> [a] -> [b]
Map a function over a list and concatenate the results.
Building lists
Scans
scanl :: (b -> a -> b) -> b -> [a] -> [b]
scanl1 :: (a -> a -> a) -> [a] -> [a]
scanr :: (a -> b -> b) -> b -> [a] -> [b]
scanr1 :: (a -> a -> a) -> [a] -> [a]
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), ...]
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 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 genericTake,
in which n may be of any integral type.
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 genericDrop,
in which n may be of any integral type.
splitAt :: Int -> [a] -> ([a], [a]) Source
splitAt n xs returns a tuple where first element is xs prefix of
length n and second element is the remainder of the list:
splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])It is equivalent to (.
take n xs, drop n xs)splitAt is an instance of the more general 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:
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])
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])
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
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)]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
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])
Functions on strings
lines breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
words breaks a string up into a list of words, which were delimited
by white space.
Converting to and from String
Converting to String
class Show a where
Conversion of values to readable Strings.
Minimal complete definition: showsPrec or show.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
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 = 5Note 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 Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that showsPrec started with.
Instances
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.
Converting from String
class Read a where
Parsing of Strings, producing values.
Minimal complete definition: readsPrec (or, for GHC only, readPrec)
Derived instances of Read make the following assumptions, which
derived instances of Show obey:
- If the constructor is defined to be an infix operator, then the
derived
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 2010 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 = 5Note 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 = readListPrecDefaultMethods
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 Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that
showsPrec started with.
Instances
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
data IO a :: * -> *
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.
Simple I/O operations
Output functions
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 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
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]])
Exception handling in the I/O monad
type IOError = IOException
The Haskell 2010 type for exceptions in the IO monad.
Any I/O operation may raise an IOError instead of returning a result.
For a more general type of exception, including also those that arise
in pure code, see Control.Exception.Exception.
In Haskell 2010, this is an opaque type.
catch :: IO a -> (IOError -> IO a) -> IO a Source
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 one of the exception handling
functions. These handlers are
not selective: all IOErrors are caught. Exception propagation
must be explicitly provided in a handler by re-raising any unwanted
exceptions. For example, in
f = catch g (\e -> if IO.isEOFError e then return [] else ioError e)
the function f returns [] when an end-of-file exception
(cf. isEOFError) occurs in g; otherwise, the
exception is propagated to the next outer handler.
When an exception propagates outside the main program, the Haskell
system prints the associated IOError value and exits the program.
Non-I/O exceptions are not caught by this variant; to catch all
exceptions, use catch from Control.Exception.