| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Yesod.Paginator.Prelude
Contents
Synopsis
- (++) :: [a] -> [a] -> [a]
- seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b
- filter :: (a -> Bool) -> [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- print :: Show a => a -> IO ()
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- otherwise :: Bool
- map :: (a -> b) -> [a] -> [b]
- ($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- guard :: Alternative f => Bool -> f ()
- join :: Monad m => m (m a) -> m a
- class Bounded a where
- class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
- class Eq a where
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class (Real a, Enum a) => Integral a where
- class Applicative m => Monad (m :: Type -> Type) where
- class Functor (f :: Type -> Type) where
- class Num a where
- class Eq a => Ord a where
- class Read a where
- 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
- class Monad m => MonadFail (m :: Type -> Type) where
- class Functor f => Applicative (f :: Type -> Type) where
- class Foldable (t :: Type -> Type) where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- null :: t a -> Bool
- length :: t a -> Int
- elem :: Eq a => a -> t a -> Bool
- maximum :: Ord a => t a -> a
- minimum :: Ord a => t a -> a
- sum :: Num a => t a -> a
- product :: Num a => t a -> a
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
- class Semigroup a where
- (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
- data Bool
- data Char
- data Double
- data Float
- data Int
- data Integer
- data Natural
- data Maybe a
- data Ordering
- type Rational = Ratio Integer
- data IO a
- data Word
- data Either a b
- type String = [Char]
- type ShowS = String -> String
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- id :: a -> a
- data Text
- forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- read :: Read a => String -> a
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
- unless :: Applicative f => Bool -> f () -> f ()
- replicateM_ :: Applicative m => Int -> m a -> m ()
- replicateM :: Applicative m => Int -> m a -> m [a]
- foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
- foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()
- zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]
- mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])
- forever :: Applicative f => f a -> f b
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
- forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- appendFile :: FilePath -> String -> IO ()
- writeFile :: FilePath -> String -> IO ()
- readFile :: FilePath -> IO String
- interact :: (String -> String) -> IO ()
- getContents :: IO String
- getLine :: IO String
- getChar :: IO Char
- putStrLn :: String -> IO ()
- putStr :: String -> IO ()
- putChar :: Char -> IO ()
- ioError :: IOError -> IO a
- type FilePath = String
- userError :: String -> IOError
- type IOError = IOException
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- or :: Foldable t => t Bool -> Bool
- and :: Foldable t => t Bool -> Bool
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- unwords :: [String] -> String
- words :: String -> [String]
- unlines :: [String] -> String
- lines :: String -> [String]
- genericReplicate :: Integral i => i -> a -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericTake :: Integral i => i -> [a] -> [a]
- genericLength :: Num i => [a] -> i
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- reads :: Read a => ReadS a
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- lex :: ReadS String
- readParen :: Bool -> ReadS a -> ReadS a
- type ReadS a = String -> [(a, String)]
- lcm :: Integral a => a -> a -> a
- gcd :: Integral a => a -> a -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- odd :: Integral a => a -> Bool
- even :: Integral a => a -> Bool
- showParen :: Bool -> ShowS -> ShowS
- showString :: String -> ShowS
- showChar :: Char -> ShowS
- shows :: Show a => a -> ShowS
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip :: [(a, b)] -> ([a], [b])
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- (!!) :: [a] -> Int -> a
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- reverse :: [a] -> [a]
- break :: (a -> Bool) -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- splitAt :: Int -> [a] -> ([a], [a])
- drop :: Int -> [a] -> [a]
- take :: Int -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- cycle :: [a] -> [a]
- replicate :: Int -> a -> [a]
- repeat :: a -> [a]
- iterate :: (a -> a) -> a -> [a]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- init :: [a] -> [a]
- last :: [a] -> a
- tail :: [a] -> [a]
- head :: [a] -> a
- mapMaybe :: (a -> Maybe b) -> [a] -> [b]
- catMaybes :: [Maybe a] -> [a]
- listToMaybe :: [a] -> Maybe a
- maybeToList :: Maybe a -> [a]
- fromMaybe :: a -> Maybe a -> a
- fromJust :: HasCallStack => Maybe a -> a
- isNothing :: Maybe a -> Bool
- isJust :: Maybe a -> Bool
- maybe :: b -> (a -> b) -> Maybe a -> b
- void :: Functor f => f a -> f ()
- uncurry :: (a -> b -> c) -> (a, b) -> c
- curry :: ((a, b) -> c) -> a -> b -> c
- subtract :: Num a => a -> a -> a
- asTypeOf :: a -> a -> a
- until :: (a -> Bool) -> (a -> a) -> a -> a
- ($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- flip :: (a -> b -> c) -> b -> a -> c
- ap :: Monad m => m (a -> b) -> m a -> m b
- liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
- liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
- liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- when :: Applicative f => Bool -> f () -> f ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
- errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
- error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- foldl1Def' :: a -> (a -> a -> a) -> [a] -> a
- foldl1Def :: a -> (a -> a -> a) -> [a] -> a
- foldr1Def :: a -> (a -> a -> a) -> [a] -> a
- maximumByDef :: a -> (a -> a -> Ordering) -> [a] -> a
- minimumByDef :: a -> (a -> a -> Ordering) -> [a] -> a
- maximumDef :: Ord a => a -> [a] -> a
- minimumDef :: Ord a => a -> [a] -> a
- indexNote :: (Partial, Ix a) => String -> (a, a) -> a -> Int
- indexDef :: Ix a => Int -> (a, a) -> a -> Int
- indexMay :: Ix a => (a, a) -> a -> Maybe Int
- predSafe :: (Enum a, Eq a, Bounded a) => a -> a
- predNote :: (Partial, Enum a, Eq a, Bounded a) => String -> a -> a
- predDef :: (Enum a, Eq a, Bounded a) => a -> a -> a
- predMay :: (Enum a, Eq a, Bounded a) => a -> Maybe a
- succSafe :: (Enum a, Eq a, Bounded a) => a -> a
- succNote :: (Partial, Enum a, Eq a, Bounded a) => String -> a -> a
- succDef :: (Enum a, Eq a, Bounded a) => a -> a -> a
- succMay :: (Enum a, Eq a, Bounded a) => a -> Maybe a
- toEnumSafe :: (Enum a, Bounded a) => Int -> a
- toEnumNote :: (Partial, Enum a, Bounded a) => String -> Int -> a
- toEnumDef :: (Enum a, Bounded a) => a -> Int -> a
- toEnumMay :: (Enum a, Bounded a) => Int -> Maybe a
- findIndexJustNote :: Partial => String -> (a -> Bool) -> [a] -> Int
- findIndexJustDef :: Int -> (a -> Bool) -> [a] -> Int
- findIndexJust :: (a -> Bool) -> [a] -> Int
- elemIndexJustNote :: (Partial, Eq a) => String -> a -> [a] -> Int
- elemIndexJustDef :: Eq a => Int -> a -> [a] -> Int
- elemIndexJust :: (Partial, Eq a) => a -> [a] -> Int
- findJustNote :: Partial => String -> (a -> Bool) -> [a] -> a
- findJustDef :: a -> (a -> Bool) -> [a] -> a
- findJust :: (a -> Bool) -> [a] -> a
- lookupJustNote :: (Partial, Eq a) => String -> a -> [(a, b)] -> b
- lookupJustDef :: Eq a => b -> a -> [(a, b)] -> b
- lookupJust :: (Eq a, Partial) => a -> [(a, b)] -> b
- readNote :: (Partial, Read a) => String -> String -> a
- readDef :: Read a => a -> String -> a
- readMay :: Read a => String -> Maybe a
- readEitherSafe :: Read a => String -> Either String a
- atNote :: Partial => String -> [a] -> Int -> a
- atDef :: a -> [a] -> Int -> a
- atMay :: [a] -> Int -> Maybe a
- at :: Partial => [a] -> Int -> a
- assertNote :: Partial => String -> Bool -> a -> a
- fromJustNote :: Partial => String -> Maybe a -> a
- fromJustDef :: a -> Maybe a -> a
- cycleNote :: Partial => String -> [a] -> [a]
- cycleDef :: [a] -> [a] -> [a]
- cycleMay :: [a] -> Maybe [a]
- scanl1Note :: Partial => String -> (a -> a -> a) -> [a] -> [a]
- scanr1Note :: Partial => String -> (a -> a -> a) -> [a] -> [a]
- scanl1Def :: [a] -> (a -> a -> a) -> [a] -> [a]
- scanr1Def :: [a] -> (a -> a -> a) -> [a] -> [a]
- scanl1May :: (a -> a -> a) -> [a] -> Maybe [a]
- scanr1May :: (a -> a -> a) -> [a] -> Maybe [a]
- foldl1Note' :: Partial => String -> (a -> a -> a) -> [a] -> a
- foldl1Note :: Partial => String -> (a -> a -> a) -> [a] -> a
- foldr1Note :: Partial => String -> (a -> a -> a) -> [a] -> a
- foldl1May' :: (a -> a -> a) -> [a] -> Maybe a
- foldl1May :: (a -> a -> a) -> [a] -> Maybe a
- foldr1May :: (a -> a -> a) -> [a] -> Maybe a
- minimumBounded :: (Ord a, Bounded a) => [a] -> a
- maximumBounded :: (Ord a, Bounded a) => [a] -> a
- minimumBound :: Ord a => a -> [a] -> a
- maximumBound :: Ord a => a -> [a] -> a
- minimumBoundBy :: a -> (a -> a -> Ordering) -> [a] -> a
- maximumBoundBy :: a -> (a -> a -> Ordering) -> [a] -> a
- maximumByNote :: Partial => String -> (a -> a -> Ordering) -> [a] -> a
- minimumByNote :: Partial => String -> (a -> a -> Ordering) -> [a] -> a
- maximumByMay :: (a -> a -> Ordering) -> [a] -> Maybe a
- minimumByMay :: (a -> a -> Ordering) -> [a] -> Maybe a
- maximumNote :: (Partial, Ord a) => String -> [a] -> a
- minimumNote :: (Partial, Ord a) => String -> [a] -> a
- maximumMay :: Ord a => [a] -> Maybe a
- minimumMay :: Ord a => [a] -> Maybe a
- lastNote :: Partial => String -> [a] -> a
- headNote :: Partial => String -> [a] -> a
- lastDef :: a -> [a] -> a
- headDef :: a -> [a] -> a
- lastMay :: [a] -> Maybe a
- headMay :: [a] -> Maybe a
- initSafe :: [a] -> [a]
- initNote :: Partial => String -> [a] -> [a]
- initDef :: [a] -> [a] -> [a]
- initMay :: [a] -> Maybe [a]
- tailSafe :: [a] -> [a]
- tailNote :: Partial => String -> [a] -> [a]
- tailDef :: [a] -> [a] -> [a]
- tailMay :: [a] -> Maybe [a]
- abort :: Partial => String -> a
- pack :: String -> Text
- unpack :: Text -> String
- tshow :: Show a => a -> Text
- nubOn :: Eq b => (a -> b) -> [a] -> [a]
Documentation
(++) :: [a] -> [a] -> [a] infixr 5 #
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b infixr 0 #
The value of seq a b is bottom if a is bottom, and
otherwise equal to b. In other words, it evaluates the first
argument a to weak head normal form (WHNF). 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.
filter :: (a -> Bool) -> [a] -> [a] #
\(\mathcal{O}(n)\). 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]
>>>filter odd [1, 2, 3][1,3]
zip :: [a] -> [b] -> [(a, b)] #
\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of
corresponding pairs.
zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]
If one input list is short, excess elements of the longer list are discarded:
zip [1] ['a', 'b'] = [(1, 'a')] zip [1, 2] ['a'] = [(1, 'a')]
zip is right-lazy:
zip [] _|_ = [] zip _|_ [] = _|_
zip is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
print :: Show a => a -> IO () #
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]])
map :: (a -> b) -> [a] -> [b] #
\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to
each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>>map (+1) [1, 2, 3]
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (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
Note that ( is levity-polymorphic in its result type, so that
$)foo where $ Truefoo :: Bool -> Int# is well-typed.
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
guard :: Alternative f => Bool -> f () #
Conditional failure of Alternative computations. Defined by
guard True =pure() guard False =empty
Examples
Common uses of guard include conditionally signaling an error in
an error monad and conditionally rejecting the current choice in an
Alternative-based parser.
As an example of signaling an error in the error monad Maybe,
consider a safe division function safeDiv x y that returns
Nothing when the denominator y is zero and Just (x `div`
y)
>>> safeDiv 4 0 Nothing >>> safeDiv 4 2 Just 2
A definition of safeDiv using guards, but not guard:
safeDiv :: Int -> Int -> Maybe Int
safeDiv x y | y /= 0 = Just (x `div` y)
| otherwise = Nothing
A definition of safeDiv using guard and Monad do-notation:
safeDiv :: Int -> Int -> Maybe Int safeDiv x y = do guard (y /= 0) return (x `div` y)
join :: Monad m => m (m a) -> m a #
The join function is the conventional monad join operator. It
is used to remove one level of monadic structure, projecting its
bound argument into the outer level.
'join bssdo expression
do bs <- bss bs
Examples
A common use of join is to run an IO computation returned from
an STM transaction, since STM transactions
can't perform IO directly. Recall that
atomically :: STM a -> IO a
is used to run STM transactions atomically. So, by
specializing the types of atomically and join to
atomically:: STM (IO b) -> IO (IO b)join:: IO (IO b) -> IO b
we can compose them as
join.atomically:: STM (IO b) -> IO b
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
| Bounded Bool | Since: base-2.1 |
| Bounded Char | Since: base-2.1 |
| Bounded Int | Since: base-2.1 |
| Bounded Ordering | Since: base-2.1 |
| Bounded Word | Since: base-2.1 |
| Bounded VecCount | Since: base-4.10.0.0 |
| Bounded VecElem | Since: base-4.10.0.0 |
| Bounded () | Since: base-2.1 |
| Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded UTF32_Invalid | |
Defined in Basement.String.Encoding.UTF32 | |
| Bounded Encoding | |
| Bounded IPv4 | |
| Bounded IPv6 | |
| Bounded PortNumber | |
Defined in Network.Socket.Types | |
| Bounded Checkmark | |
| Bounded VarType | |
| Bounded Format | |
| Bounded Method | |
| Bounded CompressionStrategy | |
Defined in Codec.Compression.Zlib.Stream | |
| Bounded a => Bounded (Solo a) | |
| SizeValid n => Bounded (Bits n) | |
| (Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
| (Bounded a, Bounded b) => Bounded (Pair a b) | |
| (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
| Bounded b => Bounded (Tagged s b) | |
| (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum from 0 through n-1.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum,
the following should hold:
- The calls
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBoundMethods
the successor of a value. For numeric types, succ adds 1.
the predecessor of a value. For numeric types, pred subtracts 1.
Convert from an Int.
Convert to an Int.
It is implementation-dependent what fromEnum returns when
applied to a value that is too large to fit in an Int.
Used in Haskell's translation of [n..] with [n..] = enumFrom n,
a possible implementation being enumFrom n = n : enumFrom (succ n).
For example:
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n', a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n'),
worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
For example:
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] #
Used in Haskell's translation of [n..m] with
[n..m] = enumFromTo n m, a possible implementation being
enumFromTo n m
| n <= m = n : enumFromTo (succ n) m
| otherwise = [].
For example:
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] #
Used in Haskell's translation of [n,n'..m] with
[n,n'..m] = enumFromThenTo n n' m, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m,
x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
For example:
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
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.
The Haskell Report defines no laws for Eq. However, == is customarily
expected to implement an equivalence relationship where two values comparing
equal are indistinguishable by "public" functions, with a "public" function
being one not allowing to see implementation details. For example, for a
type representing non-normalised natural numbers modulo 100, a "public"
function doesn't make the difference between 1 and 201. It is expected to
have the following properties:
Instances
class Fractional a => Floating a where #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (, +)(
and *)exp are customarily expected to define an exponential field and have
the following properties:
exp (a + b)=exp a * exp bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
| Floating Double | Since: base-2.1 |
| Floating Float | Since: base-2.1 |
| Floating a => Floating (Tagged s a) | |
Defined in Data.Tagged Methods exp :: Tagged s a -> Tagged s a # log :: Tagged s a -> Tagged s a # sqrt :: Tagged s a -> Tagged s a # (**) :: Tagged s a -> Tagged s a -> Tagged s a # logBase :: Tagged s a -> Tagged s a -> Tagged s a # sin :: Tagged s a -> Tagged s a # cos :: Tagged s a -> Tagged s a # tan :: Tagged s a -> Tagged s a # asin :: Tagged s a -> Tagged s a # acos :: Tagged s a -> Tagged s a # atan :: Tagged s a -> Tagged s a # sinh :: Tagged s a -> Tagged s a # cosh :: Tagged s a -> Tagged s a # tanh :: Tagged s a -> Tagged s a # asinh :: Tagged s a -> Tagged s a # acosh :: Tagged s a -> Tagged s a # atanh :: Tagged s a -> Tagged s a # log1p :: Tagged s a -> Tagged s a # expm1 :: Tagged s a -> Tagged s a # | |
class Num a => Fractional a where #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, ( and
+)( are customarily expected to define a division ring and have the
following properties:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1
Note that it isn't customarily expected that a type instance of
Fractional implement a field. However, all instances in base do.
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
| Fractional Scientific | WARNING: These methods also compute
|
Defined in Data.Scientific Methods (/) :: Scientific -> Scientific -> Scientific # recip :: Scientific -> Scientific # fromRational :: Rational -> Scientific # | |
| Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
| Fractional a => Fractional (Tagged s a) | |
class (Real a, Enum a) => Integral a where #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div/mod and quot/rem pairs, given
suitable Euclidean functions f and g:
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for Integer's instance, is
abs.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
conversion to Integer
Instances
class Applicative m => Monad (m :: Type -> Type) 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:
- Left identity
returna>>=k = k a- Right identity
m>>=return= m- Associativity
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
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.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
(>>) :: 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.
'as ' can be understood as the >> bsdo expression
do as bs
Inject a value into the monadic type.
Instances
| Monad [] | Since: base-2.1 |
| Monad Maybe | Since: base-2.1 |
| Monad IO | Since: base-2.1 |
| Monad Par1 | Since: base-4.9.0.0 |
| Monad Q | |
| Monad Solo | |
| Monad IResult | |
| Monad Result | |
| Monad Parser | |
| Monad ReadPrec | Since: base-2.1 |
| Monad ReadP | Since: base-2.1 |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Monad MarkupM | |
| Monad CryptoFailable | |
Defined in Crypto.Error.Types Methods (>>=) :: CryptoFailable a -> (a -> CryptoFailable b) -> CryptoFailable b # (>>) :: CryptoFailable a -> CryptoFailable b -> CryptoFailable b # return :: a -> CryptoFailable a # | |
| Monad DNonEmpty | |
| Monad DList | |
| Monad SmallArray | |
Defined in Data.Primitive.SmallArray Methods (>>=) :: SmallArray a -> (a -> SmallArray b) -> SmallArray b # (>>) :: SmallArray a -> SmallArray b -> SmallArray b # return :: a -> SmallArray a # | |
| Monad Array | |
| Monad Vector | |
| Monad Stream | |
| Monad P | Since: base-2.1 |
| Monad (Either e) | Since: base-4.4.0.0 |
| Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
| Monad (Parser i) | |
| Monad m => Monad (MaybeT m) | |
| Monad m => Monad (ResourceT m) | |
| Monad m => Monad (ListT m) | |
| Monad m => Monad (NoLoggingT m) | |
Defined in Control.Monad.Logger Methods (>>=) :: NoLoggingT m a -> (a -> NoLoggingT m b) -> NoLoggingT m b # (>>) :: NoLoggingT m a -> NoLoggingT m b -> NoLoggingT m b # return :: a -> NoLoggingT m a # | |
| Monad m => Monad (WriterLoggingT m) | |
Defined in Control.Monad.Logger Methods (>>=) :: WriterLoggingT m a -> (a -> WriterLoggingT m b) -> WriterLoggingT m b # (>>) :: WriterLoggingT m a -> WriterLoggingT m b -> WriterLoggingT m b # return :: a -> WriterLoggingT m a # | |
| Monad m => Monad (LoggingT m) | |
| Monad f => Monad (WrappedPoly f) | |
Defined in Data.MonoTraversable Methods (>>=) :: WrappedPoly f a -> (a -> WrappedPoly f b) -> WrappedPoly f b # (>>) :: WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f b # return :: a -> WrappedPoly f a # | |
| Semigroup a => Monad (These a) | |
| Semigroup a => Monad (These a) | |
| Monad (HandlerFor site) | |
Defined in Yesod.Core.Types Methods (>>=) :: HandlerFor site a -> (a -> HandlerFor site b) -> HandlerFor site b # (>>) :: HandlerFor site a -> HandlerFor site b -> HandlerFor site b # return :: a -> HandlerFor site a # | |
| Monad (WidgetFor site) | |
| Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
| Monad m => Monad (IdentityT m) | |
| (Monoid w, Monad m) => Monad (WriterT w m) | |
| (Monoid w, Monad m) => Monad (WriterT w m) | |
| Monad m => Monad (StateT s m) | |
| Monad m => Monad (StateT s m) | |
| Monad m => Monad (ReaderT r m) | |
| Monad m => Monad (ExceptT e m) | |
| (Monad m, Error e) => Monad (ErrorT e m) | |
| Monad (Tagged s) | |
| Monad (SubHandlerFor child master) | |
Defined in Yesod.Core.Types Methods (>>=) :: SubHandlerFor child master a -> (a -> SubHandlerFor child master b) -> SubHandlerFor child master b # (>>) :: SubHandlerFor child master a -> SubHandlerFor child master b -> SubHandlerFor child master b # return :: a -> SubHandlerFor child master a # | |
| Monad ((->) r :: Type -> Type) | Since: base-2.1 |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| Monad (ConduitT i o m) | |
| Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
| (Monoid w, Monad m) => Monad (RWST r w s m) | |
| (Monoid w, Monad m) => Monad (RWST r w s m) | |
| Monad state => Monad (Builder collection mutCollection step state err) | |
Defined in Basement.MutableBuilder Methods (>>=) :: Builder collection mutCollection step state err a -> (a -> Builder collection mutCollection step state err b) -> Builder collection mutCollection step state err b # (>>) :: Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err b # return :: a -> Builder collection mutCollection step state err a # | |
| Monad m => Monad (Pipe l i o u m) | |
class Functor (f :: Type -> Type) where #
A type f is a Functor if it provides a function fmap which, given any types a and b
lets you apply any function from (a -> b) to turn an f a into an f b, preserving the
structure of f. Furthermore f needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b #
Using ApplicativeDo: 'fmap f asdo expression
do a <- as pure (f a)
with an inferred Functor constraint.