| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | stable |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Prelude
Contents
Description
The Prelude: a standard module. The Prelude is imported by default into all Haskell modules unless either there is an explicit import statement for it, or the NoImplicitPrelude extension is enabled.
- 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
- data Word :: *
- 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 Monoid a where
- class Functor f where
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- class Functor f => Applicative f where
- class Applicative m => Monad m where
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- class Foldable t where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- null :: t a -> Bool
- length :: t a -> Int
- elem :: Eq a => a -> t a -> Bool
- maximum :: forall a. Ord a => t a -> a
- minimum :: forall a. Ord a => t a -> a
- sum :: Num a => t a -> a
- product :: Num a => t a -> a
- class (Functor t, Foldable t) => Traversable t where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
- id :: a -> a
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: (a -> b -> c) -> b -> a -> c
- ($) :: (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]
- (!!) :: [a] -> Int -> a
- reverse :: [a] -> [a]
- and :: Foldable t => t Bool -> Bool
- or :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- concat :: Foldable t => t [a] -> [a]
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- 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])
- notElem :: (Foldable t, Eq a) => a -> t 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
Standard types, classes and related functions
Basic data types
data Bool :: *
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.
Instances
| Monad Maybe Source | |
| Functor Maybe Source | |
| MonadFix Maybe Source | |
| Applicative Maybe Source | |
| Foldable Maybe Source | |
| Traversable Maybe Source | |
| Generic1 Maybe Source | |
| MonadPlus Maybe Source | |
| Alternative Maybe Source | |
| Eq a => Eq (Maybe a) Source | |
| Data a => Data (Maybe a) Source | |
| Ord a => Ord (Maybe a) Source | |
| Read a => Read (Maybe a) Source | |
| Show a => Show (Maybe a) Source | |
| Generic (Maybe a) Source | |
| Monoid a => Monoid (Maybe a) Source | Lift a semigroup into |
| type Rep1 Maybe Source | |
| type Rep (Maybe a) Source | |
| type (==) (Maybe k) a b Source | |
maybe :: b -> (a -> b) -> Maybe a -> b Source
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.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed,
return twice the integer; that is, apply (*2) to it. If instead
we fail to parse an integer, return 0 by default:
>>>import Text.Read ( readMaybe )>>>maybe 0 (*2) (readMaybe "5")10>>>maybe 0 (*2) (readMaybe "")0
Apply show to a Maybe Int. If we have Just n, we want to show
the underlying Int n. But if we have Nothing, we return the
empty string instead of (for example) "Nothing":
>>>maybe "" show (Just 5)"5">>>maybe "" show Nothing""
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").
Examples
The type Either String IntString or an Int. The Left constructor can be used only on
Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: Either String Int
The fmap from our Functor instance will ignore Left values, but
will apply the supplied function to values contained in a Right:
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>fmap (*2) sLeft "foo">>>fmap (*2) nRight 6
The Monad instance for Either allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int from a Char, or fail.
>>>import Data.Char ( digitToInt, isDigit )>>>:{let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>:}
The following should work, since both '1' and '2' can be
parsed as Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 3
But the following should fail overall, since the first operation where
we attempt to parse 'm' as an Int will fail:
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleLeft "parse error"
Instances
| Bifunctor Either Source | |
| Monad (Either e) Source | |
| Functor (Either a) Source | |
| MonadFix (Either e) Source | |
| Applicative (Either e) Source | |
| Foldable (Either a) Source | |
| Traversable (Either a) Source | |
| Generic1 (Either a) Source | |
| (Eq a, Eq b) => Eq (Either a b) Source | |
| (Data a, Data b) => Data (Either a b) Source | |
| (Ord a, Ord b) => Ord (Either a b) Source | |
| (Read a, Read b) => Read (Either a b) Source | |
| (Show a, Show b) => Show (Either a b) Source | |
| Generic (Either a b) Source | |
| type Rep1 (Either a) Source | |
| type Rep (Either a b) Source | |
| type (==) (Either k k1) a b Source | |
either :: (a -> c) -> (b -> c) -> Either a b -> c Source
Case analysis for the Either type.
If the value is Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft constructor and another using the Right constructor. Then
we apply "either" the length function (if we have a String)
or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
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
curry :: ((a, b) -> c) -> a -> b -> c Source
curry converts an uncurried function to a curried function.
uncurry :: (a -> b -> c) -> (a, b) -> c Source
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.
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 CallStack | |
| Eq TypeRep | |
| Eq () | |
| Eq BigNat | |
| Eq Number | |
| Eq Lexeme | |
| Eq GeneralCategory | |
| Eq Fingerprint | |
| Eq TyCon | |
| Eq Associativity | |
| Eq Fixity | |
| Eq Arity | |
| Eq Any | |
| Eq All | |
| Eq ArithException | |
| Eq ErrorCall | |
| Eq IOException | |
| Eq MaskingState | |
| 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 IntPtr | |
| Eq WordPtr | |
| Eq BufferState | |
| Eq CodingProgress | |
| Eq SeekMode | |
| Eq IODeviceType | |
| Eq NewlineMode | |
| Eq Newline | |
| Eq BufferMode | |
| Eq Handle | |
| Eq IOErrorType | |
| Eq ExitCode | |
| Eq ArrayException | |
| Eq AsyncException | |
| Eq Errno | |
| Eq Fd | |
| Eq CRLim | |
| Eq CTcflag | |
| Eq CSpeed | |
| Eq CCc | |
| Eq CUid | |
| Eq CNlink | |
| Eq CGid | |
| Eq CSsize | |
| Eq CPid | |
| Eq COff | |
| Eq CMode | |
| Eq CIno | |
| Eq CDev | |
| Eq ThreadStatus | |
| Eq BlockReason | |
| Eq ThreadId | |
| Eq IOMode | |
| Eq Lifetime | |
| Eq Event | |
| Eq FdKey | |
| Eq TimeoutKey | |
| Eq HandlePosn | |
| Eq Version | |
| Eq Fixity | |
| Eq ConstrRep | |
| Eq DataRep | |
| Eq Constr | Equality of constructors |
| Eq Natural | |
| Eq SomeSymbol | |
| Eq SomeNat | |
| Eq SrcLoc | |
| Eq SpecConstrAnnotation | |
| Eq Unique | |
| Eq Void | |
| Eq a => Eq [a] | |
| Eq a => Eq (Ratio a) | |
| Eq (StablePtr a) | |
| Eq (Ptr a) | |
| Eq (FunPtr a) | |
| Eq (U1 p) | |
| Eq p => Eq (Par1 p) | |
| Eq a => Eq (Maybe a) | |
| Eq a => Eq (Down a) | |
| Eq a => Eq (Last a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Product a) | |
| Eq a => Eq (Sum a) | |
| Eq a => Eq (Dual a) | |
| Eq (MVar a) | |
| Eq (IORef a) | |
| Eq (ForeignPtr a) | |
| Eq (TVar a) | |
| Eq a => Eq (ZipList a) | |
| Eq (Chan a) | |
| Eq a => Eq (Complex a) | |
| Eq (Fixed a) | |
| Eq a => Eq (Identity a) | |
| Eq (StableName a) | |
| (Eq a, Eq b) => Eq (Either a b) | |
| Eq (f p) => Eq (Rec1 f p) | |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq (STRef s a) | |
| Eq (Proxy k s) | |
| Eq a => Eq (Const a b) | |
| Eq c => Eq (K1 i c p) | |
| (Eq (f p), Eq (g p)) => Eq ((:+:) f g p) | |
| (Eq (f p), Eq (g p)) => Eq ((:*:) f g p) | |
| Eq (f (g p)) => Eq ((:.:) f g p) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| Eq ((:~:) k a b) | |
| Eq (Coercion k a b) | |
| Eq (f a) => Eq (Alt k f a) | |
| Eq (f p) => Eq (M1 i c f p) | |
| (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
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
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
data Int :: *
data 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.
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.
data Word :: *
Numeric type classes
Basic numeric class.
Methods
(+), (-), (*) :: a -> a -> a infixl 7 *infixl 6 +, - Source
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 -> a Source
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