| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Papa.Base.Export.Prelude
- class Applicative m => Monad m
- encodeFloat :: RealFloat a => Integer -> Int -> a
- ($) :: (a -> b) -> a -> b
- class Monoid a where
- (&&) :: Bool -> Bool -> Bool
- class Num a where
- (*) :: Num a => a -> a -> a
- class Eq a => Ord a where
- max :: Ord a => a -> a -> a
- sequenceA :: Traversable t => forall f a. Applicative f => t (f a) -> f (t a)
- (**) :: Floating a => a -> a -> a
- data Ordering :: *
- type Rational = Ratio Integer
- show :: Show a => a -> String
- (+) :: Num a => a -> a -> a
- even :: Integral a => a -> Bool
- maybe :: b -> (a -> b) -> Maybe a -> b
- exp :: Floating a => a -> a
- (-) :: Num a => a -> a -> a
- class (Num a, Ord a) => Real a where
- exponent :: RealFloat a => a -> Int
- mempty :: Monoid a => a
- showParen :: Bool -> ShowS -> ShowS
- class (RealFrac a, Floating a) => RealFloat a where
- min :: Ord a => a -> a -> a
- (/) :: Fractional a => a -> a -> a
- filter :: (a -> Bool) -> [a] -> [a]
- shows :: Show a => a -> ShowS
- (/=) :: Eq a => a -> a -> Bool
- showsPrec :: Show a => Int -> a -> ShowS
- (<) :: Ord a => a -> a -> Bool
- class Show a where
- floatDigits :: RealFloat a => a -> Int
- mod :: Integral a => a -> a -> a
- significand :: RealFloat a => a -> a
- (<$) :: Functor f => forall a b. a -> f b -> f a
- type ShowS = String -> String
- floatRadix :: RealFloat a => a -> Integer
- negate :: Num a => a -> a
- signum :: Num a => a -> a
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- floatRange :: RealFloat a => a -> (Int, Int)
- not :: Bool -> Bool
- sin :: Floating a => a -> a
- class (Functor t, Foldable t) => Traversable t where
- floor :: RealFrac a => forall b. Integral b => a -> b
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- sinh :: Floating a => a -> a
- (<*>) :: Applicative f => forall a b. f (a -> b) -> f a -> f b
- fmap :: Functor f => forall a b. (a -> b) -> f a -> f b
- null :: Foldable t => forall a. t a -> Bool
- (<=) :: Ord a => a -> a -> Bool
- data Word :: *
- foldMap :: Foldable t => forall m a. Monoid m => (a -> m) -> t a -> m
- odd :: Integral a => a -> Bool
- span :: (a -> Bool) -> [a] -> ([a], [a])
- (^) :: (Num a, Integral b) => a -> b -> a
- foldl :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b
- splitAt :: Int -> [a] -> ([a], [a])
- (==) :: Eq a => a -> a -> Bool
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- otherwise :: Bool
- sqrt :: Floating a => a -> a
- (>) :: Ord a => a -> a -> Bool
- abs :: Num a => a -> a
- foldr :: Foldable t => forall a b. (a -> b -> b) -> b -> t a -> b
- pi :: Floating a => a
- subtract :: Num a => a -> a -> a
- (>=) :: Ord a => a -> a -> Bool
- acos :: Floating a => a -> a
- acosh :: Floating a => a -> a
- sum :: Foldable t => forall a. Num a => t a -> a
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- fromInteger :: Num a => Integer -> a
- product :: Foldable t => forall a. Num a => t a -> a
- class Functor f => Applicative f where
- and :: Foldable t => t Bool -> Bool
- fromIntegral :: (Integral a, Num b) => a -> b
- properFraction :: RealFrac a => forall b. Integral b => a -> (b, a)
- take :: Int -> [a] -> [a]
- data Bool :: *
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- fromRational :: Fractional a => Rational -> a
- pure :: Applicative f => forall a. a -> f a
- takeWhile :: (a -> Bool) -> [a] -> [a]
- appendFile :: FilePath -> String -> IO ()
- putChar :: Char -> IO ()
- tan :: Floating a => a -> a
- data Char :: *
- gcd :: Integral a => a -> a -> a
- putStr :: String -> IO ()
- tanh :: Floating a => a -> a
- data Double :: *
- asin :: Floating a => a -> a
- getChar :: IO Char
- putStrLn :: String -> IO ()
- asinh :: Floating a => a -> a
- getContents :: IO String
- quot :: Integral a => a -> a -> a
- toInteger :: Integral a => a -> Integer
- data Either a b :: * -> * -> *
- atan :: Floating a => a -> a
- getLine :: IO String
- quotRem :: Integral a => a -> a -> (a, a)
- toRational :: Real a => a -> Rational
- class Enum a
- atan2 :: RealFloat a => a -> a -> a
- traverse :: Traversable t => forall f a b. Applicative f => (a -> f b) -> t a -> f (t b)
- class Eq a where
- atanh :: Floating a => a -> a
- readFile :: FilePath -> IO String
- truncate :: RealFrac a => forall b. Integral b => a -> b
- break :: (a -> Bool) -> [a] -> ([a], [a])
- readIO :: Read a => String -> IO a
- uncurry :: (a -> b -> c) -> (a, b) -> c
- type FilePath = String
- ceiling :: RealFrac a => forall b. Integral b => a -> b
- interact :: (String -> String) -> IO ()
- data Float :: *
- compare :: Ord a => a -> a -> Ordering
- ioError :: IOError -> IO a
- unlines :: [String] -> String
- class Fractional a => Floating a where
- isDenormalized :: RealFloat a => a -> Bool
- until :: (a -> Bool) -> (a -> a) -> a -> a
- class Foldable t where
- isIEEE :: RealFloat a => a -> Bool
- unwords :: [String] -> String
- class Num a => Fractional a where
- isInfinite :: RealFloat a => a -> Bool
- class Functor f where
- cos :: Floating a => a -> a
- isNaN :: RealFloat a => a -> Bool
- realToFrac :: (Real a, Fractional b) => a -> b
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- cosh :: Floating a => a -> a
- isNegativeZero :: RealFloat a => a -> Bool
- recip :: Fractional a => a -> a
- data IO a :: * -> *
- curry :: ((a, b) -> c) -> a -> b -> c
- rem :: Integral a => a -> a -> a
- words :: String -> [String]
- type IOError = IOException
- cycle :: [a] -> [a]
- writeFile :: FilePath -> String -> IO ()
- data Int :: *
- decodeFloat :: RealFloat a => a -> (Integer, Int)
- lcm :: Integral a => a -> a -> a
- replicate :: Int -> a -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- data Integer :: *
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- class (Real a, Enum a) => Integral a where
- divMod :: Integral a => a -> a -> (a, a)
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- drop :: Int -> [a] -> [a]
- lines :: String -> [String]
- round :: RealFrac a => forall b. Integral b => a -> b
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- log :: Floating a => a -> a
- scaleFloat :: RealFloat a => Int -> a -> a
- (||) :: Bool -> Bool -> Bool
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- logBase :: Floating a => a -> a -> a
- data Maybe a :: * -> *
- elem :: Foldable t => forall a. Eq a => a -> t a -> Bool
Documentation
class Applicative m => Monad m #
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
Instances
| Monad [] | |
| Monad Maybe | |
| Monad IO | |
| Monad U1 | |
| Monad Par1 | |
| Monad Min | |
| Monad Max | |
| Monad First | |
| Monad Last | |
| Monad Option | |
| Monad NonEmpty | |
| Monad Dual | |
| Monad Sum | |
| Monad Product | |
| Monad First | |
| Monad Last | |
| Monad ((->) r) | |
| Monad (Either e) | |
| Monad f => Monad (Rec1 f) | |
| Monoid a => Monad ((,) a) | |
| Monad m => Monad (WrappedMonad m) | |
| (Monad f, Monad g) => Monad ((:*:) f g) | |
| Monad f => Monad (Alt * f) | |
| Monad f => Monad (M1 i c f) | |
encodeFloat :: RealFloat a => 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.
($) :: (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
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.
Instances
| Monoid Ordering | |
| Monoid () | |
| Monoid All | |
| Monoid Any | |
| Monoid [a] | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| Monoid a => Monoid (IO a) | |
| Ord a => Monoid (Max a) | |
| Ord a => Monoid (Min a) | |
| (Ord a, Bounded a) => Monoid (Min a) | |
| (Ord a, Bounded a) => Monoid (Max a) | |
| Monoid m => Monoid (WrappedMonoid m) | |
| Semigroup a => Monoid (Option a) | |
| Monoid a => Monoid (Dual a) | |
| Monoid (Endo a) | |
| Num a => Monoid (Sum a) | |
| Num a => Monoid (Product a) | |
| Monoid (First a) | |
| Monoid (Last a) | |
| Monoid b => Monoid (a -> b) | |
| (Monoid a, Monoid b) => Monoid (a, b) | |
| Monoid (Proxy k s) | |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |
| Monoid a => Monoid (Const k a b) | |
| Alternative f => Monoid (Alt * f a) | |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | |
Basic numeric class.
Methods
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 #
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
compare :: a -> a -> Ordering #
(<) :: a -> a -> Bool infix 4 #
(<=) :: a -> a -> Bool infix 4 #
(>) :: a -> a -> Bool infix 4 #
Instances
| Ord Bool | |
| Ord Char | |
| Ord Double | |
| Ord Float | |
| Ord Int | |
| Ord Int8 | |
| Ord Int16 | |
| Ord Int32 | |
| Ord Int64 | |
| Ord Integer | |
| Ord Ordering | |
| Ord Word | |
| Ord () | |
| Ord TyCon | |
| Ord BigNat | |
| Ord Void | |
| Ord Version | |
| Ord AsyncException | |
| Ord ArrayException | |
| Ord ExitCode | |
| Ord All | |
| Ord Any | |
| Ord Fixity | |
| Ord Associativity | |
| Ord SourceUnpackedness | |
| Ord SourceStrictness | |
| Ord DecidedStrictness | |
| Ord SomeNat | |
| Ord SomeSymbol | |
| Ord GeneralCategory | |
| Ord a => Ord [a] | |
| Ord a => Ord (Maybe a) | |
| Integral a => Ord (Ratio a) | |
| Ord (Ptr a) | |
| Ord (FunPtr a) | |
| Ord (V1 p) | |
| Ord (U1 p) | |
| Ord p => Ord (Par1 p) | |
| Ord a => Ord (Min a) | |
| Ord a => Ord (Max a) | |
| Ord a => Ord (First a) | |
| Ord a => Ord (Last a) | |
| Ord m => Ord (WrappedMonoid m) | |
| Ord a => Ord (Option a) | |
| Ord a => Ord (NonEmpty a) | |
| Ord a => Ord (ZipList a) | |
| Ord a => Ord (Dual a) | |
| Ord a => Ord (Sum a) | |
| Ord a => Ord (Product a) | |
| Ord a => Ord (First a) | |
| Ord a => Ord (Last a) | |
| Ord a => Ord (Down a) | |
| (Ord b, Ord a) => Ord (Either a b) | |
| Ord (f p) => Ord (Rec1 f p) | |
| Ord (URec Char p) | |
| Ord (URec Double p) | |
| Ord (URec Float p) | |
| Ord (URec Int p) | |
| Ord (URec Word p) | |
| Ord (URec (Ptr ()) p) | |
| (Ord a, Ord b) => Ord (a, b) | |
| Ord a => Ord (Arg a b) | |
| Ord (Proxy k s) | |
| Ord c => Ord (K1 i c p) | |
| (Ord (g p), Ord (f p)) => Ord ((:+:) f g p) | |
| (Ord (g p), Ord (f p)) => Ord ((:*:) f g p) | |
| Ord (f (g p)) => Ord ((:.:) f g p) | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
| Ord a => Ord (Const k a b) | |
| Ord (f a) => Ord (Alt k f a) | |
| 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) | |
sequenceA :: Traversable t => forall f a. Applicative f => t (f a) -> f (t a) #
Evaluate each action in the structure from left to right, and
and collect the results. For a version that ignores the results
see sequenceA_.
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""
class (Num a, Ord a) => Real a where #
Minimal complete definition
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
exponent :: RealFloat a => a -> Int #
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.
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
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.
(/) :: Fractional a => a -> a -> a #
fractional division
filter :: (a -> Bool) -> [a] -> [a] #
filter, applied to a predicate and a list, returns the list of
those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
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
Instances
| Show Bool | |
| Show Char | |
| Show Int | |
| Show Int8 | |
| Show Int16 | |
| Show Int32 | |
| Show Int64 | |
| Show Integer | |
| Show Ordering | |
| Show Word | |
| Show CallStack | |
| Show () | |
| Show TyCon | |
| Show Module | |
| Show TrName | |
| Show Void | |
| Show Version | |
| Show BlockedIndefinitelyOnMVar | |
| Show BlockedIndefinitelyOnSTM | |
| Show Deadlock | |
| Show AllocationLimitExceeded | |
| Show AssertionFailed | |
| Show SomeAsyncException | |
| Show AsyncException | |
| Show ArrayException | |
| Show ExitCode | |
| Show IOErrorType | |
| Show All | |
| Show Any | |
| Show Fixity | |
| Show Associativity | |
| Show SourceUnpackedness | |
| Show SourceStrictness | |
| Show DecidedStrictness | |
| Show MaskingState | |
| Show IOException | |
| Show SomeNat | |
| Show SomeSymbol | |
| Show GeneralCategory | |
| Show SrcLoc | |
| Show a => Show [a] | |
| Show a => Show (Maybe a) | |
| Show a => Show (Ratio a) | |
| Show (Ptr a) | |
| Show (FunPtr a) | |
| Show (V1 p) | |
| Show (U1 p) | |
| Show p => Show (Par1 p) | |
| Show a => Show (Min a) | |
| Show a => Show (Max a) | |
| Show a => Show (First a) | |
| Show a => Show (Last a) | |
| Show m => Show (WrappedMonoid m) | |
| Show a => Show (Option a) | |
| Show a => Show (NonEmpty a) | |
| Show a => Show (ZipList a) | |
| Show a => Show (Dual a) | |
| Show a => Show (Sum a) | |
| Show a => Show (Product a) | |
| Show a => Show (First a) | |
| Show a => Show (Last a) | |
| Show a => Show (Down a) | |
| (Show b, Show a) => Show (Either a b) | |
| Show (f p) => Show (Rec1 f p) | |
| Show (URec Char p) | |
| Show (URec Double p) | |
| Show (URec Float p) | |
| Show (URec Int p) | |
| Show (URec Word p) | |
| (Show a, Show b) => Show (a, b) | |
| (Show b, Show a) => Show (Arg a b) | |
| Show (Proxy k s) | |
| Show c => Show (K1 i c p) | |
| (Show (g p), Show (f p)) => Show ((:+:) f g p) | |
| (Show (g p), Show (f p)) => Show ((:*:) f g p) | |
| Show (f (g p)) => Show ((:.:) f g p) | |
| (Show a, Show b, Show c) => Show (a, b, c) | |
| Show a => Show (Const k a b) | This instance would be equivalent to the derived instances of the
|
| Show (f a) => Show (Alt k f a) | |
| 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) | |
floatDigits :: RealFloat a => a -> Int #
a constant function, returning the number of digits of
floatRadix in the significand
significand :: RealFloat a => 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.
floatRadix :: RealFloat a => a -> Integer #
a constant function, returning the radix of the representation
(often 2)
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
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 <$> (2,2)(2,True)
floatRange :: RealFloat a => a -> (Int, Int) #
a constant function, returning the lowest and highest values the exponent may assume
class (Functor t, Foldable t) => Traversable t where #
Functors representing data structures that can be traversed from left to right.
A definition of traverse must satisfy the following laws:
- naturality
t .for every applicative transformationtraversef =traverse(t . f)t- identity
traverseIdentity = Identity- composition
traverse(Compose .fmapg . f) = Compose .fmap(traverseg) .traversef
A definition of sequenceA must satisfy the following laws:
- naturality
t .for every applicative transformationsequenceA=sequenceA.fmaptt- identity
sequenceA.fmapIdentity = Identity- composition
sequenceA.fmapCompose = Compose .fmapsequenceA.sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative operations, i.e.
and the identity functor Identity and composition of functors Compose
are defined as
newtype Identity a = Identity a
instance Functor Identity where
fmap f (Identity x) = Identity (f x)
instance Applicative Identity where
pure x = Identity x
Identity f <*> Identity x = Identity (f x)
newtype Compose f g a = Compose (f (g a))
instance (Functor f, Functor g) => Functor (Compose f g) where
fmap f (Compose x) = Compose (fmap (fmap f) x)
instance (Applicative f, Applicative g) => Applicative (Compose f g) where
pure x = Compose (pure (pure x))
Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)(The naturality law is implied by parametricity.)
Instances are similar to Functor, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*>
imply a form of associativity.
The superclass instances should satisfy the following:
- In the
Functorinstance,fmapshould be equivalent to traversal with the identity applicative functor (fmapDefault). - In the
Foldableinstance,foldMapshould be equivalent to traversal with a constant applicative functor (foldMapDefault).
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_.
sequenceA :: Applicative f => t (f a) -> f (t a) #
Evaluate each action in the structure from left to right, and
and collect the results. For a version that ignores the results
see sequenceA_.
Instances
| Traversable [] | |
| Traversable Maybe | |
| Traversable V1 | |
| Traversable U1 | |
| Traversable Par1 | |
| Traversable Min | |
| Traversable Max | |
| Traversable First | |
| Traversable Last | |
| Traversable Option | |
| Traversable NonEmpty | |
| Traversable ZipList | |
| Traversable Dual | |
| Traversable Sum | |
| Traversable Product | |
| Traversable First | |
| Traversable Last | |
| Traversable (Either a) | |
| Traversable f => Traversable (Rec1 f) | |
| Traversable (URec Char) | |
| Traversable (URec Double) | |
| Traversable (URec Float) | |
| Traversable (URec Int) | |
| Traversable (URec Word) | |
| Traversable (URec (Ptr ())) | |
| Traversable ((,) a) | |
| Ix i => Traversable (Array i) | |
| Traversable (Arg a) | |
| Traversable (Proxy *) | |
| Traversable (K1 i c) | |
| (Traversable f, Traversable g) => Traversable ((:+:) f g) | |
| (Traversable f, Traversable g) => Traversable ((:*:) f g) | |
| (Traversable f, Traversable g) => Traversable ((:.:) f g) | |
| Traversable (Const * m) | |
| Traversable f => Traversable (M1 i c f) | |
floor :: RealFrac a => forall b. Integral b => a -> b #
floor xx
(<*>) :: Applicative f => forall a b. f (a -> b) -> f a -> f b #
Sequential application.
null :: Foldable t => forall a. t a -> Bool #
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.
Instances
| Bounded Word | |
| Enum Word | |
| Eq Word | |
| Integral Word | |
| Num Word | |
| Ord Word | |
| Read Word | |
| Real Word | |
| Show Word | |
| Functor (URec Word) | |
| Foldable (URec Word) | |
| Traversable (URec Word) | |
| Generic1 (URec Word) | |
| Eq (URec Word p) | |
| Ord (URec Word p) | |
| Show (URec Word p) | |
| Generic (URec Word p) | |
| data URec Word | Used for marking occurrences of |
| type Rep1 (URec Word) | |
| type Rep (URec Word p) | |
foldMap :: Foldable t => forall m a. Monoid m => (a -> m) -> t a -> m #
Map each element of the structure to a monoid, and combine the results.
span :: (a -> Bool) -> [a] -> ([a], [a]) #
span, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
satisfy p and second element is the remainder of the list:
span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4]) span (< 9) [1,2,3] == ([1,2,3],[]) span (< 0) [1,2,3] == ([],[1,2,3])
foldl :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b #
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
splitAt :: Int -> [a] -> ([a], [a]) #
splitAt n xs returns a tuple where first element is xs prefix of
length n and second element is the remainder of the list:
splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])It is equivalent to ( when take n xs, drop n xs)n is not _|_
(splitAt _|_ xs = _|_).
splitAt is an instance of the more general genericSplitAt,
in which n may be of any integral type.
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
foldr :: Foldable t => forall a b. (a -> b -> b) -> b -> t a -> b #
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
sum :: Foldable t => forall a. Num a => t a -> a #
The sum function computes the sum of the numbers of a structure.
all :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether all elements of the structure satisfy the predicate.
fromInteger :: Num a => 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
product :: Foldable t => forall a. Num a => t a -> a #
The product function computes the product of the numbers of a
structure.
class Functor f => Applicative f where #
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).
Instances
| Applicative [] | |
| Applicative Maybe | |
| Applicative IO | |
| Applicative U1 | |
| Applicative Par1 | |
| Applicative Id | |
| Applicative Min | |
| Applicative Max | |
| Applicative First | |
| Applicative Last | |
| Applicative Option | |
| Applicative NonEmpty | |
| Applicative ZipList | |
| Applicative Dual | |
| Applicative Sum | |
| Applicative Product | |
| Applicative First | |
| Applicative Last | |
| Applicative ((->) a) | |
| Applicative (Either e) | |
| Applicative f => Applicative (Rec1 f) | |
| Monoid a => Applicative ((,) a) | |
| Applicative (StateL s) | |
| Applicative (StateR s) | |
| Monad m => Applicative (WrappedMonad m) | |
| Applicative (Proxy *) | |
| (Applicative f, Applicative g) => Applicative ((:*:) f g) | |
| (Applicative f, Applicative g) => Applicative ((:.:) f g) | |
| Arrow a => Applicative (WrappedArrow a b) | |
| Monoid m => Applicative (Const * m) | |
| Applicative f => Applicative (Alt * f) | |
| Applicative f => Applicative (M1 i c f) | |
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
properFraction :: RealFrac a => forall b. 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.
take n, applied to a list xs, returns the prefix of xs
of length n, or xs itself if n > :length xs
take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []
It is an instance of the more general genericTake,
in which n may be of any integral type.
any :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether any element of the structure satisfies the predicate.
fromRational :: Fractional a => Rational -> a #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
pure :: Applicative f => forall a. a -> f a #
Lift a value.
takeWhile :: (a -> Bool) -> [a] -> [a] #
takeWhile, applied to a predicate p and a list xs, returns the
longest prefix (possibly empty) of xs of elements that satisfy p:
takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2] takeWhile (< 9) [1,2,3] == [1,2,3] takeWhile (< 0) [1,2,3] == []
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]])
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 | |
| Enum Char | |
| Eq Char | |
| Ord Char | |
| Read Char | |
| Show Char | |
| Functor (URec Char) | |
| Foldable (URec Char) | |
| Traversable (URec Char) | |
| Generic1 (URec Char) | |
| Eq (URec Char p) | |
| Ord (URec Char p) | |
| Show (URec Char p) | |
| Generic (URec Char p) | |
| data URec Char | Used for marking occurrences of |
| type Rep1 (URec Char) | |
| type Rep (URec Char p) | |
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
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 | |
| Ord Double | |
| Read Double | |
| RealFloat Double | |
| Functor (URec Double) | |
| Foldable (URec Double) | |
| Traversable (URec Double) | |
| Generic1 (URec Double) | |
| Eq (URec Double p) | |
| Ord (URec Double p) | |
| Show (URec Double p) | |
| Generic (URec Double p) | |
| data URec Double | Used for marking occurrences of |
| type Rep1 (URec Double) | |
| type Rep (URec Double p) | |
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).
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 b, Eq a) => Eq (Either a b) | |
| (Ord b, Ord a) => Ord (Either a b) | |
| (Read b, Read a) => Read (Either a b) | |
| (Show b, Show a) => Show (Either a b) | |
| Generic (Either a b) | |
| Semigroup (Either a b) | |
| type Rep1 (Either a) | |
| type Rep (Either a b) | |
| type (==) (Either k k1) a b | |
toRational :: Real a => a -> Rational #
the rational equivalent of its real argument with full precision
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 = minBoundInstances
| Enum Bool | |
| Enum Char | |
| Enum Int | |
| Enum Int8 | |
| Enum Int16 | |
| Enum Int32 | |
| Enum Int64 | |
| Enum Integer | |
| Enum Ordering | |
| Enum Word | |
| Enum () | |
| Enum Associativity | |
| Enum SourceUnpackedness | |
| Enum SourceStrictness | |
| Enum DecidedStrictness | |
| Enum GeneralCategory | |
| Integral a => Enum (Ratio a) | |
| Enum a => Enum (Min a) | |
| Enum a => Enum (Max a) | |
| Enum a => Enum (First a) | |
| Enum a => Enum (Last a) | |
| Enum a => Enum (WrappedMonoid a) | |
| Enum (Proxy k s) | |
| Enum a => Enum (Const k a b) | |
| Enum (f a) => Enum (Alt k f a) | |
| (~) k a b => Enum ((:~:) k a b) | |
atan2 :: RealFloat a => 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.
traverse :: Traversable t => forall f a b. Applicative f => (a -> f b) -> t a -> f (t b) #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_.
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 () | |
| Eq TyCon | |
| Eq BigNat | |
| Eq SpecConstrAnnotation | |
| Eq Void | |
| Eq Version | |
| Eq AsyncException | |
| Eq ArrayException | |
| Eq ExitCode | |
| Eq IOErrorType | |
| Eq All | |
| Eq Any | |
| Eq Fixity | |
| Eq Associativity | |
| Eq SourceUnpackedness | |
| Eq SourceStrictness | |
| Eq DecidedStrictness | |
| Eq MaskingState | |
| Eq IOException | |
| Eq SomeNat | |
| Eq SomeSymbol | |
| Eq GeneralCategory | |
| Eq SrcLoc | |
| Eq a => Eq [a] | |
| Eq a => Eq (Maybe a) | |
| Eq a => Eq (Ratio a) | |
| Eq (Ptr a) | |
| Eq (FunPtr a) | |
| Eq (V1 p) | |
| Eq (U1 p) | |
| Eq p => Eq (Par1 p) | |
| Eq a => Eq (Min a) | |
| Eq a => Eq (Max a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Last a) | |
| Eq m => Eq (WrappedMonoid m) | |
| Eq a => Eq (Option a) | |
| Eq a => Eq (NonEmpty a) | |
| Eq a => Eq (ZipList a) | |
| Eq a => Eq (Dual a) | |
| Eq a => Eq (Sum a) | |
| Eq a => Eq (Product a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Last a) | |
| Eq a => Eq (Down a) | |
| (Eq b, Eq a) => 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 a => Eq (Arg a b) | |
| Eq (Proxy k s) | |
| Eq c => Eq (K1 i c p) | |
| (Eq (g p), Eq (f p)) => Eq ((:+:) f g p) | |
| (Eq (g p), Eq (f p)) => Eq ((:*:) f g p) | |
| Eq (f (g p)) => Eq ((:.:) f g p) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| Eq a => Eq (Const k a b) | |
| Eq (f a) => Eq (Alt k f a) | |
| 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) | |
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.
truncate :: RealFrac a => forall b. Integral b => a -> b #
truncate xx between zero and x
break :: (a -> Bool) -> [a] -> ([a], [a]) #
break, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
do not satisfy p and second element is the remainder of the list:
break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])
uncurry :: (a -> b -> c) -> (a, b) -> c #
uncurry converts a curried function to a function on pairs.
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.
ceiling :: RealFrac a => forall b. Integral b => a -> b #
ceiling xx
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.
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 | |
| Ord Float | |
| Read Float | |
| RealFloat Float | |
| Functor (URec Float) | |
| Foldable (URec Float) | |
| Traversable (URec Float) | |
| Generic1 (URec Float) | |
| Eq (URec Float p) | |
| Ord (URec Float p) | |
| Show (URec Float p) | |
| Generic (URec Float p) | |
| data URec Float | Used for marking occurrences of |
| type Rep1 (URec Float) | |
| type Rep (URec Float p) | |
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
isDenormalized :: RealFloat a => a -> Bool #
True if the argument is too small to be represented in
normalized format
until :: (a -> Bool) -> (a -> a) -> a -> a #
until p ff until p holds.
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 #
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b #
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 #
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
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.
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
The sum function computes the sum of the numbers of a structure.
product :: Num a => t a -> a #
The product function computes the product of the numbers of a
structure.
Instances
| Foldable [] | |
| Foldable Maybe | |
| Foldable V1 | |
| Foldable U1 | |
| Foldable Par1 | |
| Foldable Min | |
| Foldable Max | |
| Foldable First | |
| Foldable Last | |
| Foldable Option | |
| Foldable NonEmpty | |
| Foldable ZipList | |
| Foldable Dual | |
| Foldable Sum | |
| Foldable Product | |
| Foldable First | |
| Foldable Last | |
| Foldable (Either a) | |
| Foldable f => Foldable (Rec1 f) | |
| Foldable (URec Char) | |
| Foldable (URec Double) | |
| Foldable (URec Float) | |
| Foldable (URec Int) | |
| Foldable (URec Word) | |
| Foldable (URec (Ptr ())) | |
| Foldable ((,) a) | |
| Foldable (Array i) | |
| Foldable (Arg a) | |
| Foldable (Proxy *) | |
| Foldable (K1 i c) | |
| (Foldable f, Foldable g) => Foldable ((:+:) f g) | |
| (Foldable f, Foldable g) => Foldable ((:*:) f g) | |
| (Foldable f, Foldable g) => Foldable ((:.:) f g) | |
| Foldable (Const * m) | |
| Foldable f => Foldable (M1 i c f) | |
class Num a => Fractional a where #
Fractional numbers, supporting real division.
Minimal complete definition
fromRational, (recip | (/))
Methods
fractional division
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) | |
| Fractional a => Fractional (Const k a b) | |
isInfinite :: RealFloat a => a -> Bool #
True if the argument is an IEEE infinity or negative infinity
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 [] | |
| Functor Maybe | |
| Functor IO | |
| Functor V1 | |
| Functor U1 | |
| Functor Par1 | |
| Functor Id | |
| Functor Min | |
| Functor Max | |
| Functor First | |
| Functor Last | |
| Functor Option | |
| Functor NonEmpty | |
| Functor ZipList | |
| Functor Dual | |
| Functor Sum | |
| Functor Product | |
| Functor First | |
| Functor Last | |
| Functor ((->) r) | |
| Functor (Either a) | |
| Functor f => Functor (Rec1 f) | |
| Functor (URec Char) | |
| Functor (URec Double) | |
| Functor (URec Float) | |
| Functor (URec Int) | |
| Functor (URec Word) | |
| Functor (URec (Ptr ())) | |
| Functor ((,) a) | |
| Functor (StateL s) | |
| Functor (StateR s) | |
| Functor (Arg a) | |
| Monad m => Functor (WrappedMonad m) | |
| Functor (Proxy *) | |
| Functor (K1 i c) | |
| (Functor g, Functor f) => Functor ((:+:) f g) | |
| (Functor g, Functor f) => Functor ((:*:) f g) | |
| (Functor g, Functor f) => Functor ((:.:) f g) | |
| Arrow a => Functor (WrappedArrow a b) | |
| Functor (Const * m) | |
| Functor f => Functor (Alt * f) | |
| Functor f => Functor (M1 i c f) | |
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
isNegativeZero :: RealFloat a => a -> Bool #
True if the argument is an IEEE negative zero
recip :: Fractional a => a -> a #
reciprocal fraction
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.
words breaks a string up into a list of words, which were delimited
by white space.
type IOError = IOException #
cycle ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.
writeFile :: FilePath -> String -> IO () #
The computation writeFile file str function writes the string str,
to the file file.
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 | |
| Enum Int | |
| Eq Int | |
| Integral Int | |
| Num Int | |
| Ord Int | |
| Read Int | |
| Real Int | |
| Show Int | |
| Functor (URec Int) | |
| Foldable (URec Int) | |
| Traversable (URec Int) | |
| Generic1 (URec Int) | |
| Eq (URec Int p) | |
| Ord (URec Int p) | |
| Show (URec Int p) | |
| Generic (URec Int p) | |
| data URec Int | Used for marking occurrences of |
| type Rep1 (URec Int) | |
| type Rep (URec Int p) | |
decodeFloat :: RealFloat a => 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.
lcm :: Integral a => a -> a -> a #
lcm x yx and y divide.
replicate :: Int -> a -> [a] #
replicate n x is a list of length n with x the value of
every element.
It is an instance of the more general genericReplicate,
in which n may be of any integral type.
class (Real a, Enum a) => Integral a where #
Integral numbers, supporting integer division.
drop n xs returns the suffix of xs
after the first n elements, or [] if n > :length xs
drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]
It is an instance of the more general genericDrop,
in which n may be of any integral type.
lines breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,
lines "" == [] lines "\n" == [""] lines "one" == ["one"] lines "one\n" == ["one"] lines "one\n\n" == ["one",""] lines "one\ntwo" == ["one","two"] lines "one\ntwo\n" == ["one","two"]
Thus lines ss.
round :: RealFrac a => forall b. Integral b => a -> b #
round xx;
the even integer if x is equidistant between two integers
scaleFloat :: RealFloat a => Int -> a -> a #
multiplies a floating-point number by an integer power of the radix
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
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) | |
| Semigroup a => Semigroup (Maybe a) | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| SingI (Maybe a) (Nothing a) | |
| SingKind a (KProxy a) => SingKind (Maybe a) (KProxy (Maybe a)) | |
| SingI a a1 => SingI (Maybe a) (Just a a1) | |
| type Rep1 Maybe | |
| type Rep (Maybe a) | |
| data Sing (Maybe a) | |
| type (==) (Maybe k) a b | |
| type DemoteRep (Maybe a) (KProxy (Maybe a)) | |