| 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
- 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
- class (Real a, Enum a) => Integral a where
- class Num a => Fractional a where
- class Fractional a => Floating a where
- class (Real a, Fractional a) => RealFrac a where
- class (RealFrac a, Floating a) => RealFloat a where
- 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
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- class Functor f => Applicative f where
- class Applicative m => Monad m where
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- class Foldable t where
- class (Functor t, Foldable t) => Traversable t where
- id :: a -> a
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: (a -> b -> c) -> b -> a -> c
- ($) :: (a -> b) -> a -> b
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a -> a -> a
- error :: forall r. forall a. HasCallStack => [Char] -> a
- errorWithoutStackTrace :: forall r. forall a. [Char] -> a
- undefined :: forall r. forall a. HasCallStack => 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 :: Foldable t => t a -> Bool
- length :: Foldable t => t a -> Int
- (!!) :: [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
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
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 # | |
| Show2 Either Source # | |
| Read2 Either Source # | |
| Ord2 Either Source # | |
| Eq2 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 # | |
| Show a => Show1 (Either a) Source # | |
| Read a => Read1 (Either a) Source # | |
| Ord a => Ord1 (Either a) Source # | |
| Eq a => Eq1 (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 # | |
| Semigroup (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
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 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).
Instances
| Bounded Char Source # | |
| Enum Char Source # | |
| Eq Char | |
| Data Char Source # | |
| Ord Char | |
| Read Char Source # | |
| Show Char Source # | |
| Ix Char Source # | |
| Storable Char Source # | |
| IsChar Char Source # | |
| PrintfArg Char Source # | |
| Functor (URec Char) Source # | |
| Foldable (URec Char) Source # | |
| Traversable (URec Char) Source # | |
| Generic1 (URec Char) Source # | |
| Eq (URec Char p) # | |
| Ord (URec Char p) # | |
| Show (URec Char p) Source # | |
| Generic (URec Char p) Source # | |
| data URec Char Source # | Used for marking occurrences of |
| type Rep1 (URec Char) Source # | |
| type Rep (URec Char p) Source # | |
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
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 TypeRep # | |
| Eq () | |
| Eq TyCon | |
| Eq BigNat | |
| Eq SrcLoc # | |
| Eq GeneralCategory # | |
| Eq Number # | |
| Eq Lexeme # | |
| Eq IOMode # | |
| Eq SomeSymbol # | |
| Eq SomeNat # | |
| Eq Fingerprint # | |
| Eq ArithException # | |
| Eq ErrorCall # | |
| Eq IOException # | |
| Eq MaskingState # | |
| Eq DecidedStrictness # | |
| Eq SourceStrictness # | |
| Eq SourceUnpackedness # | |
| Eq Associativity # | |
| Eq Fixity # | |
| Eq Any # | |
| Eq All # | |
| 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 IntPtr # | |
| Eq WordPtr # | |
| 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 Lifetime # | |
| Eq Event # | |
| Eq FdKey # | |
| Eq TimeoutKey # | |
| Eq HandlePosn # | |
| Eq Unique # | |
| Eq Version # | |
| Eq Fixity # | |
| Eq ConstrRep # | |
| Eq DataRep # | |
| Eq Constr # | Equality of constructors |
| Eq Void # | |
| Eq Natural # | |
| Eq SpecConstrAnnotation # | |
| Eq a => Eq [a] | |
| Eq a => Eq (Maybe a) # | |
| Eq a => Eq (Ratio a) # | |
| Eq (StablePtr a) # | |
| Eq (Ptr a) # | |
| Eq (FunPtr a) # | |
| Eq (V1 p) # | |
| Eq (U1 p) # | |
| Eq p => Eq (Par1 p) # | |
| Eq (MVar a) # | |
| Eq a => Eq (Down 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 (ZipList a) # | |
| Eq (Chan a) # | |
| Eq (StableName a) # | |
| Eq a => Eq (Complex a) # | |
| Eq (Fixed a) # | |
| Eq a => Eq (NonEmpty a) # | |
| Eq a => Eq (Option a) # | |
| Eq m => Eq (WrappedMonoid m) # | |
| Eq a => Eq (Last a) # | |
| Eq a => Eq (First a) # | |
| Eq a => Eq (Max a) # | |
| Eq a => Eq (Min a) # | |
| Eq a => Eq (Identity a) # | |
| (Eq a, Eq b) => Eq (Either a b) # | |
| Eq (f p) => Eq (Rec1 f p) # | |
| Eq (URec Char p) # | |
| Eq (URec Double p) # | |
| Eq (URec Float p) # | |
| Eq (URec Int p) # | |
| Eq (URec Word p) # | |
| Eq (URec (Ptr ()) p) # | |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq (STRef s a) # | |
| Eq (Proxy k s) # | |
| Eq a => Eq (Arg 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 a => Eq (Const k a b) # | |
| Eq (f p) => Eq (M1 i c f p) # | |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Product * f g a) # | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Sum * f g a) # | |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Compose * * f g a) # | |
| (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.
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
class Bounded a where Source #
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
minBound and maxBound from the Bounded class.
Instances
| Bounded Int Source # | |
| Enum Int Source # | |
| Eq Int | |
| Integral Int Source # | |
| Data Int Source # | |
| Num Int Source # | |
| Ord Int | |
| Read Int Source # | |
| Real Int Source # | |
| Show Int Source # | |
| Ix Int Source # | |
| FiniteBits Int Source # | |
| Bits Int Source # | |
| Storable Int Source # | |
| PrintfArg Int Source # | |
| Functor (URec Int) Source # | |
| Foldable (URec Int) Source # | |
| Traversable (URec Int) Source # | |
| Generic1 (URec Int) Source # | |
| Eq (URec Int p) # | |
| Ord (URec Int p) # | |
| Show (URec Int p) Source # | |
| Generic (URec Int p) Source # | |
| data URec Int Source # | Used for marking occurrences of |
| type Rep1 (URec Int) Source # | |
| type Rep (URec Int p) Source # | |
Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.
Instances
| Eq Float | |
| Floating Float Source # | |
| Data Float Source # | |
| Ord Float | |
| Read Float Source # | |
| RealFloat Float Source # | |
| Storable Float Source # | |
| PrintfArg Float Source # | |
| Functor (URec Float) Source # | |
| Foldable (URec Float) Source # | |
| Traversable (URec Float) Source # | |
| Generic1 (URec Float) Source # | |
| Eq (URec Float p) # | |
| Ord (URec Float p) # | |
| Show (URec Float p) Source # | |
| Generic (URec Float p) Source # | |
| data URec Float Source # | Used for marking occurrences of |
| type Rep1 (URec Float) Source # | |
| type Rep (URec Float p) Source # | |
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
Instances
| Eq Double | |
| Floating Double Source # | |
| Data Double Source # | |
| Ord Double | |
| Read Double Source # | |
| RealFloat Double Source # | |
| Storable Double Source # | |
| PrintfArg Double Source # | |
| Functor (URec Double) Source # | |
| Foldable (URec Double) Source # | |
| Traversable (URec Double) Source # | |
| Generic1 (URec Double) Source # | |
| Eq (URec Double p) # | |
| Ord (URec Double p) # | |
| Show (URec Double p) Source # | |
| Generic (URec Double p) Source # | |
| data URec Double Source # | Used for marking occurrences of |
| type Rep1 (URec Double) Source # | |
| type Rep (URec Double p) Source # | |
Instances
| Bounded Word Source # | |
| Enum Word Source # | |
| Eq Word | |
| Integral Word Source # | |
| Data Word Source # | |
| Num Word Source # | |
| Ord Word | |
| Read Word Source # | |
| Real Word Source # | |
| Show Word Source # | |
| Ix Word Source # | |
| FiniteBits Word Source # | |
| Bits Word Source # | |
| Storable Word Source # | |
| PrintfArg Word Source # | |
| Functor (URec Word) Source # | |
| Foldable (URec Word) Source # | |
| Traversable (URec Word) Source # | |
| Generic1 (URec Word) Source # | |
| Eq (URec Word p) # | |
| Ord (URec Word p) # | |
| Show (URec Word p) Source # | |
| Generic (URec Word p) Source # | |
| data URec Word Source # | Used for marking occurrences of |
| type Rep1 (URec Word) Source # | |
| type Rep (URec Word p) Source # | |
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
class (Num a, Ord a) => Real a where Source #
Minimal complete definition
Methods
toRational :: a -> Rational Source #
the rational equivalent of its real argument with full precision
Instances
class (Real a, Enum a) => Integral a where Source #
Integral numbers, supporting integer division.
Methods
quot :: a -> a -> a infixl 7 Source #
integer division truncated toward zero
rem :: a -> a -> a infixl 7 Source #
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7 Source #
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7 Source #
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 -> Integer Source #
conversion to Integer
Instances
class Num a => Fractional a where Source #
Fractional numbers, supporting real division.
Minimal complete definition
fromRational, (recip | (/))
Methods
(/) :: a -> a -> a infixl 7 Source #
fractional division
reciprocal fraction
fromRational :: Rational -> a Source #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional CDouble Source # | |
| Fractional CFloat Source # | |
| Integral a => Fractional (Ratio a) Source # | |
| RealFloat a => Fractional (Complex a) Source # | |
| HasResolution a => Fractional (Fixed a) Source # | |
| Fractional a => Fractional (Identity a) Source # | |
| Fractional a => Fractional (Const k a b) Source # | |
class Fractional a => Floating a where Source #
Trigonometric and hyperbolic functions and related functions.
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
class (Real a, Fractional a) => RealFrac a where Source #
Extracting components of fractions.
Minimal complete definition
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; 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 Source #
truncate xx between zero and x
round :: Integral b => a -> b Source #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b Source #
ceiling xx
floor :: Integral b => a -> b Source #
floor xx
class (RealFrac a, Floating a) => RealFloat a where Source #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer Source #
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> Int Source #
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) <= , 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 Source #
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 Source #
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 Source #
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 Source #
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool Source #
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool Source #
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 -> a Source #
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 -> a Source #
lcm x yx and y divide.
(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to a non-negative integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b Source #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b Source #
general coercion to fractional types
Monoids
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
mappend mempty x = x
mappend x mempty = x
mappend x (mappend y z) = mappend (mappend x y) z
mconcat =
foldrmappend mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtypes and make those instances
of Monoid, e.g. Sum and Product.
Methods
Identity of mappend
mappend :: a -> a -> a Source #
An associative operation
Fold a list using the monoid.
For most types, the default definition for mconcat will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
Instances
Monads and functors
class Functor f where Source #
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.
Minimal complete definition
Instances
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #
An infix synonym for fmap.
The name of this operator is an allusion to $.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
class Functor f => Applicative f where Source #
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying the following laws:
- identity
pureid<*>v = v- composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- homomorphism
puref<*>purex =pure(f x)- interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #
Sequential application.
(*>) :: f a -> f b -> f b infixl 4 Source #
Sequence actions, discarding the value of the first argument.
(<*) :: f a -> f b -> f a infixl 4 Source #
Sequence actions, discarding the value of the second argument.
Instances
class Applicative m => Monad m where Source #
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.
Instances of Monad should satisfy the following laws:
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1 Source #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: forall a b. m a -> m b -> m b infixl 1 Source #
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 :: String -> m a Source #
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.
As part of the MonadFail proposal (MFP), this function is moved
to its own class MonadFail (see Control.Monad.Fail for more
details). The definition here will be removed in a future
release.
Instances
| Monad [] Source # | |
| Monad Maybe Source # | |
| Monad IO Source # | |
| Monad U1 Source # | |
| Monad Par1 Source # | |
| Monad ReadP Source # | |
| Monad ReadPrec Source # | |
| Monad Last Source # | |
| Monad First Source # | |
| Monad Product Source # | |
| Monad Sum Source # | |
| Monad Dual Source # | |
| Monad STM Source # | |
| Monad Complex Source # | |
| Monad NonEmpty Source # | |
| Monad Option Source # | |
| Monad Last Source # | |
| Monad First Source # | |
| Monad Max Source # | |
| Monad Min Source # | |
| Monad Identity Source # | |
| Monad ((->) r) Source # | |
| Monad (Either e) Source # | |
| Monad f => Monad (Rec1 f) Source # | |
| Monoid a => Monad ((,) a) Source # | |
| Monad (ST s) Source # | |
| Monad (Proxy *) Source # | |
| ArrowApply a => Monad (ArrowMonad a) Source # | |
| Monad m => Monad (WrappedMonad m) Source # | |
| Monad (ST s) Source # | |
| (Monad f, Monad g) => Monad ((:*:) f g) Source # | |
| Monad f => Monad (Alt * f) Source # | |
| Monad f => Monad (M1 i c f) Source # | |
| (Monad f, Monad g) => Monad (Product * f g) Source # | |
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence.
As of base 4.8.0.0, sequence_ is just sequenceA_, specialized
to Monad.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #
Same as >>=, but with the arguments interchanged.
Folds and traversals
class Foldable t where Source #
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed
to satisfy the monoid laws. Alternatively, one could define foldr:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
sum, product, maximum, and minimum should all be essentially
equivalent to foldMap forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a Functor instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m Source #
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b Source #
Right-associative fold of a structure.
In the case of lists, foldr, when 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)...)
Note that, since the head of the resulting expression is produced by
an application of the operator to the first element of the list,
foldr can produce a terminating expression from an infinite list.
For a general Foldable structure this should be semantically identical
to,
foldr f z =foldrf z .toList
foldl :: (b -> a -> b) -> b -> t a -> b Source #
Left-associative fold of a structure.
In the case of lists, foldl, when 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
Note that to produce the outermost application of the operator the
entire input list must be traversed. This means that foldl' will
diverge if given an infinite list.
Also note that if you want an efficient left-fold, you probably want to
use foldl' instead of foldl. The reason for this is that latter does
not force the "inner" results (e.g. z in the above example)
before applying them to the operator (e.g. to f x1(). This results
in a thunk chain f x2)O(n) elements long, which then must be evaluated from
the outside-in.
For a general Foldable structure this should be semantically identical
to,
foldl f z =foldlf z .toList
foldr1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
foldr1f =foldr1f .toList
foldl1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
foldl1f =foldl1f .toList
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
Returns the size/length of a finite structure as an Int. The
default implementation is optimized for structures that are similar to
cons-lists, because there is no general way to do better.
elem :: Eq a => a -> t a -> Bool infix 4 Source #
Does the element occur in the structure?
maximum :: forall a. Ord a => t a -> a Source #
The largest element of a non-empty structure.
minimum :: forall a. Ord a => t a -> a Source #
The least element of a non-empty structure.
sum :: Num a => t a -> a Source #
The sum function computes the sum of the numbers of a structure.
product :: Num a => t a -> a Source #
The product function computes the product of the numbers of a
structure.