| Safe Haskell | Safe |
|---|---|
| Language | Haskell98 |
Prelude2010
- ($!) :: (a -> b) -> a -> b
- catch :: IO a -> (IOError -> IO a) -> IO a
- gcd :: Integral a => a -> a -> a
- ($) :: (a -> b) -> a -> b
- (&&) :: Bool -> Bool -> Bool
- (.) :: (b -> c) -> (a -> b) -> a -> c
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- data Bool :: *
- class Bounded a where
- data Char :: *
- data Double :: *
- data Either a b :: * -> * -> *
- 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 Eq a where
- type FilePath = String
- data Float :: *
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class Functor f where
- fmap :: (a -> b) -> f a -> f b
- data IO a :: * -> *
- type IOError = IOException
- data Int :: *
- data Integer :: *
- class (Real a, Enum a) => Integral a where
- data Maybe a :: * -> *
- class Applicative m => Monad m where
- class Num a where
- class Eq a => Ord a where
- data Ordering :: *
- type Rational = Ratio Integer
- class Read a where
- type ReadS a = String -> [(a, String)]
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- 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
- class (Real a, Fractional a) => RealFrac a where
- class Show a where
- type ShowS = String -> String
- type String = [Char]
- (^) :: (Num a, Integral b) => a -> b -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- appendFile :: FilePath -> String -> IO ()
- asTypeOf :: a -> a -> a
- const :: a -> b -> a
- curry :: ((a, b) -> c) -> a -> b -> c
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- error :: [Char] -> a
- even :: Integral a => a -> Bool
- flip :: (a -> b -> c) -> b -> a -> c
- fromIntegral :: (Integral a, Num b) => a -> b
- fst :: (a, b) -> a
- getChar :: IO Char
- getContents :: IO String
- getLine :: IO String
- id :: a -> a
- interact :: (String -> String) -> IO ()
- ioError :: IOError -> IO a
- lcm :: Integral a => a -> a -> a
- lex :: ReadS String
- lines :: String -> [String]
- mapM :: Traversable t => forall a m b. Monad m => (a -> m b) -> t a -> m (t b)
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- maximum :: Foldable t => forall a. Ord a => t a -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- minimum :: Foldable t => forall a. Ord a => t a -> a
- not :: Bool -> Bool
- odd :: Integral a => a -> Bool
- otherwise :: Bool
- print :: Show a => a -> IO ()
- product :: Foldable t => forall a. Num a => t a -> a
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- read :: Read a => String -> a
- readFile :: FilePath -> IO String
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- readParen :: Bool -> ReadS a -> ReadS a
- reads :: Read a => ReadS a
- realToFrac :: (Real a, Fractional b) => a -> b
- seq :: a -> b -> b
- sequence :: Traversable t => forall m a. Monad m => t (m a) -> m (t a)
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- showChar :: Char -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- showString :: String -> ShowS
- shows :: Show a => a -> ShowS
- snd :: (a, b) -> b
- subtract :: Num a => a -> a -> a
- sum :: Foldable t => forall a. Num a => t a -> a
- uncurry :: (a -> b -> c) -> (a, b) -> c
- undefined :: a
- unlines :: [String] -> String
- until :: (a -> Bool) -> (a -> a) -> a -> a
- userError :: String -> IOError
- writeFile :: FilePath -> String -> IO ()
- (||) :: Bool -> Bool -> Bool
- (!!) :: [a] -> Int -> a
- (++) :: [a] -> [a] -> [a]
- all :: (a -> Bool) -> [a] -> Bool
- and :: [Bool] -> Bool
- any :: (a -> Bool) -> [a] -> Bool
- break :: (a -> Bool) -> [a] -> ([a], [a])
- concat :: [[a]] -> [a]
- concatMap :: (a -> [b]) -> [a] -> [b]
- cycle :: [a] -> [a]
- drop :: Int -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- elem :: Eq a => a -> [a] -> Bool
- filter :: (a -> Bool) -> [a] -> [a]
- foldl :: (a -> b -> a) -> a -> [b] -> a
- foldl1 :: (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: (a -> a -> a) -> [a] -> a
- head :: [a] -> a
- init :: [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- last :: [a] -> a
- length :: [a] -> Int
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- map :: (a -> b) -> [a] -> [b]
- notElem :: Eq a => a -> [a] -> Bool
- null :: [a] -> Bool
- or :: [Bool] -> Bool
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- reverse :: [a] -> [a]
- scanl :: (a -> b -> a) -> a -> [b] -> [a]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- splitAt :: Int -> [a] -> ([a], [a])
- tail :: [a] -> [a]
- take :: Int -> [a] -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- unwords :: [String] -> String
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- words :: String -> [String]
- 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]
Documentation
($!) :: (a -> b) -> a -> b infixr 0
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
gcd :: Integral a => a -> a -> a
gcd x yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 0 44. gcd 0 00.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0minBound0 or minBound
($) :: (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
(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9
Function composition.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1
Same as >>=, but with the arguments interchanged.
data Bool :: *
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
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).
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 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").
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
| Monad (Either e) | |
| Functor (Either a) | |
| Applicative (Either e) | |
| Foldable (Either a) | |
| Traversable (Either a) | |
| Generic1 (Either a) | |
| (Eq a, Eq b) => Eq (Either a b) | |
| (Ord a, Ord b) => Ord (Either a b) | |
| (Read a, Read b) => Read (Either a b) | |
| (Show a, Show b) => Show (Either a b) | |
| Generic (Either a b) | |
| type Rep1 (Either a) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector Par1))) | |
| type Rep (Either a b) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector (Rec0 b)))) | |
| type (==) (Either k k1) a b = EqEither k k1 a b |
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].
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 Integer | |
| Eq Ordering | |
| Eq Word | |
| Eq () | |
| Eq BigNat | |
| Eq AsyncException | |
| Eq ArrayException | |
| Eq ExitCode | |
| Eq IOErrorType | |
| Eq MaskingState | |
| Eq IOException | |
| Eq Arity | |
| Eq Fixity | |
| Eq Associativity | |
| Eq a => Eq [a] | |
| Eq a => Eq (Ratio a) | |
| Eq (U1 p) | |
| Eq p => Eq (Par1 p) | |
| Eq a => Eq (ZipList a) | |
| Eq a => Eq (Maybe a) | |
| (Eq a, Eq b) => Eq (Either a b) | |
| Eq (f p) => Eq (Rec1 f p) | |
| (Eq a, Eq b) => Eq (a, b) | |
| (Ix i, Eq e) => Eq (Array i e) | |
| Eq a => Eq (Const a b) | |
| Eq (Proxy k s) | |
| 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 (STArray s i e) | |
| Eq ((:~:) 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) | |
| (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) |
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.
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.
class Fractional a => Floating a where
Trigonometric and hyperbolic functions and related functions.
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
class Num a => Fractional a where
Fractional numbers, supporting real division.
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
| Integral a => Fractional (Ratio a) |
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
Instances
| Functor [] | |
| Functor IO | |
| Functor Id | |
| Functor P | |
| Functor ZipList | |
| Functor ReadP | |
| Functor Maybe | |
| Functor ((->) r) | |
| Functor (Either a) | |
| Functor ((,) a) | |
| Functor (StateL s) | |
| Functor (StateR s) | |
| Ix i => Functor (Array i) | |
| Functor (Const m) | |
| Monad m => Functor (WrappedMonad m) | |
| Functor (Proxy *) | |
| Arrow a => Functor (WrappedArrow a b) |
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.
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.
data Int :: *
data Integer :: *
class (Real a, Enum a) => Integral a where
Integral numbers, supporting integer division.
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
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.
Instances
| Monad Maybe | |
| Functor Maybe | |
| Applicative Maybe | |
| Foldable Maybe | |
| Traversable Maybe | |
| Generic1 Maybe | |
| Alternative Maybe | |
| MonadPlus Maybe | |
| Eq a => Eq (Maybe a) | |
| Ord a => Ord (Maybe a) | |
| Read a => Read (Maybe a) | |
| Show a => Show (Maybe a) | |
| Generic (Maybe a) | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| type Rep1 Maybe = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector Par1))) | |
| type Rep (Maybe a) = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector (Rec0 a)))) | |
| type (==) (Maybe k) a b = EqMaybe k a b |
class Applicative m => 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.
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
(>>=) :: 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 Num a where
Basic numeric class.
Methods
(+) :: a -> a -> a infixl 6
(-) :: a -> a -> a infixl 6
(*) :: a -> a -> a infixl 7
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
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 Integer | |
| Ord Ordering | |
| Ord Word | |
| Ord () | |
| Ord BigNat | |
| Ord AsyncException | |
| Ord ArrayException | |
| Ord ExitCode | |
| Ord Arity | |
| Ord Fixity | |
| Ord Associativity | |
| Ord a => Ord [a] | |
| Integral a => Ord (Ratio a) | |
| Ord (U1 p) | |
| Ord p => Ord (Par1 p) | |
| Ord a => Ord (ZipList a) | |
| Ord a => Ord (Maybe a) | |
| (Ord a, Ord b) => Ord (Either a b) | |
| Ord (f p) => Ord (Rec1 f p) | |
| (Ord a, Ord b) => Ord (a, b) | |
| (Ix i, Ord e) => Ord (Array i e) | |
| Ord a => Ord (Const a b) | |
| Ord (Proxy k s) | |
| Ord c => Ord (K1 i c p) | |
| (Ord (f p), Ord (g p)) => Ord ((:+:) f g p) | |
| (Ord (f p), Ord (g p)) => Ord ((:*:) f g p) | |
| Ord (f (g p)) => Ord ((:.:) f g p) | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
| Ord ((:~:) k a b) | |
| Ord (f p) => Ord (M1 i c f p) | |
| (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) |
data Ordering :: *
class Read a where
Parsing of Strings, producing values.
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
| Read Bool | |
| Read Char | |
| Read Double | |
| Read Float | |
| Read Int | |
| Read Integer | |
| Read Ordering | |
| Read Word | |
| Read () | |
| Read ExitCode | |
| Read Arity | |
| Read Fixity | |
| Read Associativity | |
| Read Lexeme | |
| Read a => Read [a] | |
| (Integral a, Read a) => Read (Ratio a) | |
| Read (U1 p) | |
| Read p => Read (Par1 p) | |
| Read a => Read (ZipList a) | |
| Read a => Read (Maybe a) | |
| (Read a, Read b) => Read (Either a b) | |
| Read (f p) => Read (Rec1 f p) | |
| (Read a, Read b) => Read (a, b) | |
| (Ix a, Read a, Read b) => Read (Array a b) | |
| Read a => Read (Const a b) | |
| Read (Proxy k s) | |
| Read c => Read (K1 i c p) | |
| (Read (f p), Read (g p)) => Read ((:+:) f g p) | |
| (Read (f p), Read (g p)) => Read ((:*:) f g p) | |
| Read (f (g p)) => Read ((:.:) f g p) | |
| (Read a, Read b, Read c) => Read (a, b, c) | |
| (~) k a b => Read ((:~:) k a b) | |
| Read (f p) => Read (M1 i c f p) | |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |
class (RealFrac a, Floating a) => RealFloat a where
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
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.
class (Real a, Fractional a) => RealFrac a where
Extracting components of fractions.
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 Show a where
Conversion of values to readable Strings.
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
| Show Bool | |
| Show Char | |
| Show Int | |
| Show Integer | |
| Show Ordering | |
| Show Word | |
| Show () | |
| Show BlockedIndefinitelyOnMVar | |
| Show BlockedIndefinitelyOnSTM | |
| Show Deadlock | |
| Show AllocationLimitExceeded | |
| Show AssertionFailed | |
| Show SomeAsyncException | |
| Show AsyncException | |
| Show ArrayException | |
| Show ExitCode | |
| Show IOErrorType | |
| Show MaskingState | |
| Show IOException | |
| Show Arity | |
| Show Fixity | |
| Show Associativity | |
| Show a => Show [a] | |
| (Integral a, Show a) => Show (Ratio a) | |
| Show (U1 p) | |
| Show p => Show (Par1 p) | |
| Show a => Show (ZipList a) | |
| Show a => Show (Maybe a) | |
| (Show a, Show b) => Show (Either a b) | |
| Show (f p) => Show (Rec1 f p) | |
| (Show a, Show b) => Show (a, b) | |
| (Ix a, Show a, Show b) => Show (Array a b) | |
| Show a => Show (Const a b) | |
| Show (Proxy k s) | |
| Show c => Show (K1 i c p) | |
| (Show (f p), Show (g p)) => Show ((:+:) f g p) | |
| (Show (f p), Show (g p)) => Show ((:*:) f g p) | |
| Show (f (g p)) => Show ((:.:) f g p) | |
| (Show a, Show b, Show c) => Show (a, b, c) | |
| Show ((:~:) k a b) | |
| Show (f p) => Show (M1 i c f p) | |
| (Show a, Show b, Show c, Show d) => Show (a, b, c, d) | |
| (Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) | |
| (Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8
raise a number to an integral power
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]])
asTypeOf :: a -> a -> a
const :: a -> b -> a
Constant function.
either :: (a -> c) -> (b -> c) -> Either a b -> c
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
flip :: (a -> b -> c) -> b -> a -> c
flip ff.
fromIntegral :: (Integral a, Num b) => a -> b
general coercion from integral types
fst :: (a, b) -> a
Extract the first component of a pair.
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).
id :: a -> a
Identity function.
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.
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
lines breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
mapM :: Traversable t => forall a m b. Monad m => (a -> m b) -> t a -> m (t b)
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_.
maybe :: b -> (a -> b) -> Maybe a -> b
The maybe function takes a default value, a function, and a Maybe
value. If the Maybe value is Nothing, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just and returns the result.
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 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]])
product :: Foldable t => forall a. Num a => t a -> a
The product function computes the product of the numbers of a
structure.
The read function reads input from a string, which must be
completely consumed by the input process.
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.
realToFrac :: (Real a, Fractional b) => a -> b
general coercion to fractional types
seq :: a -> b -> b
The value of seq a b is bottom if a is bottom, and
otherwise equal to b. seq is usually introduced to
improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does
not guarantee that a will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
sequence :: Traversable t => forall m a. Monad m => t (m a) -> m (t a)
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
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.
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.
snd :: (a, b) -> b
Extract the second component of a pair.
sum :: Foldable t => forall a. Num a => t a -> a
The sum function computes the sum of the numbers of a structure.
undefined :: a