Safe Haskell | Safe-Inferred |
---|---|
Language | GHC2021 |
Imports
Description
Imports that are supposed to be used in all wire-server code.
Synopsis
- data Double
- data Float
- data Integer
- data IO a
- class (Real a, Enum a) => Integral a where
- type Rational = Ratio Integer
- class Read a where
- class Show a where
- 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 Num a where
- class Eq a => Ord 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
- type ShowS = String -> String
- type ReadS a = String -> [(a, String)]
- type FilePath = String
- error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
- even :: Integral a => a -> Bool
- seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- (^) :: (Num a, Integral b) => a -> b -> a
- undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
- ($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- subtract :: Num a => a -> a -> a
- shows :: Show a => a -> ShowS
- showChar :: Char -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- odd :: Integral a => a -> Bool
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- lex :: ReadS String
- readParen :: Bool -> ReadS a -> ReadS a
- reads :: Read a => ReadS a
- read :: Read a => String -> a
- class Functor f => Applicative (f :: Type -> Type) where
- class Applicative f => Alternative (f :: Type -> Type) where
- (<|>) :: f a -> f a -> f a
- newtype Const a (b :: k) = Const {
- getConst :: a
- newtype ZipList a = ZipList {
- getZipList :: [a]
- newtype WrappedArrow (a :: Type -> Type -> Type) b c = WrapArrow {
- unwrapArrow :: a b c
- newtype WrappedMonad (m :: Type -> Type) a = WrapMonad {
- unwrapMonad :: m a
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- (<$) :: Functor f => a -> f b -> f a
- (<**>) :: Applicative f => f a -> f (a -> b) -> f b
- liftA :: Applicative f => (a -> b) -> f a -> f b
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- asum :: (Foldable t, Alternative f) => t (f a) -> f a
- class Functor (f :: Type -> Type) where
- class Applicative m => Monad (m :: Type -> Type) where
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- class Monad m => MonadFail (m :: Type -> Type) where
- join :: Monad m => m (m a) -> m a
- forever :: Applicative f => f a -> f b
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- guard :: Alternative f => Bool -> f ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- when :: Applicative f => Bool -> f () -> f ()
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
- liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
- liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
- ap :: Monad m => m (a -> b) -> m a -> m b
- void :: Functor f => f a -> f ()
- filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])
- zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]
- zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()
- foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
- replicateM :: Applicative m => Int -> m a -> m [a]
- replicateM_ :: Applicative m => Int -> m a -> m ()
- unless :: Applicative f => Bool -> f () -> f ()
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
- mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
- module Data.Functor
- class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
- module Data.Function
- module Data.Functor.Identity
- module Data.Int
- module Data.Word
- module Data.Void
- module Data.Bool
- module Data.Char
- module Data.Ord
- newtype Any = Any {}
- class Semigroup a where
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype Last a = Last {
- getLast :: a
- newtype First a = First {
- getFirst :: a
- newtype Min a = Min {
- getMin :: a
- newtype Max a = Max {
- getMax :: a
- newtype All = All {}
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype Dual a = Dual {
- getDual :: a
- newtype WrappedMonoid m = WrapMonoid {
- unwrapMonoid :: m
- type ArgMax a b = Max (Arg a b)
- type ArgMin a b = Min (Arg a b)
- data Arg a b = Arg a b
- stimesIdempotent :: Integral b => b -> a -> a
- stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
- stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
- cycle1 :: Semigroup m => m -> m
- mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
- newtype Any = Any {}
- class Semigroup a => Monoid a where
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype Alt (f :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
- newtype All = All {}
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype Dual a = Dual {
- getDual :: a
- newtype Ap (f :: k -> Type) (a :: k) = Ap {
- getAp :: f a
- (<>) :: Semigroup a => a -> a -> a
- module Data.Maybe
- module Data.Either
- fromLeft' :: Either a b -> a
- fromRight' :: Either a b -> b
- mapBoth :: (a -> c) -> (b -> d) -> Either a b -> Either c d
- mapLeft :: (a -> c) -> Either a b -> Either c b
- mapRight :: (b -> c) -> Either a b -> Either a c
- whenLeft :: Applicative m => Either a b -> (a -> m ()) -> m ()
- whenRight :: Applicative m => Either a b -> (b -> m ()) -> m ()
- unlessLeft :: Applicative m => Either a b -> (b -> m ()) -> m ()
- unlessRight :: Applicative m => Either a b -> (a -> m ()) -> m ()
- leftToMaybe :: Either a b -> Maybe a
- rightToMaybe :: Either a b -> Maybe b
- maybeToLeft :: b -> Maybe a -> Either a b
- maybeToRight :: b -> Maybe a -> Either b a
- eitherToError :: MonadError e m => Either e a -> m a
- swapEither :: Either e a -> Either a e
- module Data.Foldable
- module Data.Traversable
- module Data.Tuple
- module Data.String
- (++) :: [a] -> [a] -> [a]
- foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
- length :: Foldable t => t a -> Int
- foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
- null :: Foldable t => t a -> Bool
- foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
- sum :: (Foldable t, Num a) => t a -> a
- product :: (Foldable t, Num a) => t a -> a
- foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
- maximum :: (Foldable t, Ord a) => t a -> a
- minimum :: (Foldable t, Ord a) => t a -> a
- elem :: (Foldable t, Eq a) => a -> t a -> Bool
- map :: (a -> b) -> [a] -> [b]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- genericLength :: Num i => [a] -> i
- maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- genericReplicate :: Integral i => i -> a -> [a]
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericIndex :: Integral i => [a] -> i -> a
- head :: HasCallStack => [a] -> a
- group :: Eq a => [a] -> [[a]]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- filter :: (a -> Bool) -> [a] -> [a]
- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
- transpose :: [[a]] -> [[a]]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- cycle :: HasCallStack => [a] -> [a]
- concat :: Foldable t => t [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- uncons :: [a] -> Maybe (a, [a])
- tail :: HasCallStack => [a] -> [a]
- last :: HasCallStack => [a] -> a
- init :: HasCallStack => [a] -> [a]
- foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- reverse :: [a] -> [a]
- and :: Foldable t => t Bool -> Bool
- or :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- (!!) :: HasCallStack => [a] -> Int -> a
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- find :: Foldable t => (a -> Bool) -> t a -> Maybe a
- dropWhileEnd :: (a -> Bool) -> [a] -> [a]
- stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
- elemIndex :: Eq a => a -> [a] -> Maybe Int
- elemIndices :: Eq a => a -> [a] -> [Int]
- findIndex :: (a -> Bool) -> [a] -> Maybe Int
- findIndices :: (a -> Bool) -> [a] -> [Int]
- isPrefixOf :: Eq a => [a] -> [a] -> Bool
- isSuffixOf :: Eq a => [a] -> [a] -> Bool
- isInfixOf :: Eq a => [a] -> [a] -> Bool
- nub :: Eq a => [a] -> [a]
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
- (\\) :: Eq a => [a] -> [a] -> [a]
- union :: Eq a => [a] -> [a] -> [a]
- unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersect :: Eq a => [a] -> [a] -> [a]
- intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- partition :: (a -> Bool) -> [a] -> ([a], [a])
- mapAccumL :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- mapAccumR :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
- zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
- zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]
- zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]
- zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]
- zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
- zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]
- zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]
- zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]
- unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
- unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])
- unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])
- unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])
- deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- inits :: [a] -> [[a]]
- tails :: [a] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- sort :: Ord a => [a] -> [a]
- lines :: String -> [String]
- unlines :: [String] -> String
- words :: String -> [String]
- unwords :: [String] -> String
- isSubsequenceOf :: Eq a => [a] -> [a] -> Bool
- class Generic a
- class Typeable (a :: k)
- type HasCallStack = ?callStack :: CallStack
- readMaybe :: Read a => String -> Maybe a
- readEither :: Read a => String -> Either String a
- module Control.Monad.Trans
- module Control.Monad.Reader.Class
- newtype ReaderT r (m :: Type -> Type) a = ReaderT {
- runReaderT :: r -> m a
- type Reader r = ReaderT r Identity
- runReader :: Reader r a -> r -> a
- mapReader :: (a -> b) -> Reader r a -> Reader r b
- withReader :: (r' -> r) -> Reader r a -> Reader r' a
- mapReaderT :: (m a -> n b) -> ReaderT r m a -> ReaderT r n b
- withReaderT :: forall r' r (m :: Type -> Type) a. (r' -> r) -> ReaderT r m a -> ReaderT r' m a
- module Control.Monad.IO.Unlift
- class NFData a where
- rnf :: a -> ()
- deepseq :: NFData a => a -> b -> b
- data IOMode
- data SeekMode
- data BufferMode
- openFile :: MonadIO m => FilePath -> IOMode -> m Handle
- stdout :: Handle
- stdin :: Handle
- stderr :: Handle
- hSeek :: MonadIO m => Handle -> SeekMode -> Integer -> m ()
- hFlush :: MonadIO m => Handle -> m ()
- hClose :: MonadIO m => Handle -> m ()
- hWaitForInput :: MonadIO m => Handle -> Int -> m Bool
- withFile :: MonadUnliftIO m => FilePath -> IOMode -> (Handle -> m a) -> m a
- withBinaryFile :: MonadUnliftIO m => FilePath -> IOMode -> (Handle -> m a) -> m a
- hFileSize :: MonadIO m => Handle -> m Integer
- hSetFileSize :: MonadIO m => Handle -> Integer -> m ()
- hIsEOF :: MonadIO m => Handle -> m Bool
- hSetBuffering :: MonadIO m => Handle -> BufferMode -> m ()
- hTell :: MonadIO m => Handle -> m Integer
- hIsOpen :: MonadIO m => Handle -> m Bool
- hIsClosed :: MonadIO m => Handle -> m Bool
- hIsReadable :: MonadIO m => Handle -> m Bool
- hIsWritable :: MonadIO m => Handle -> m Bool
- hGetBuffering :: MonadIO m => Handle -> m BufferMode
- hIsSeekable :: MonadIO m => Handle -> m Bool
- hSetEcho :: MonadIO m => Handle -> Bool -> m ()
- hGetEcho :: MonadIO m => Handle -> m Bool
- hIsTerminalDevice :: MonadIO m => Handle -> m Bool
- hReady :: MonadIO m => Handle -> m Bool
- data XdgDirectoryList
- data XdgDirectory
- getDirectoryContents :: MonadIO m => FilePath -> m [FilePath]
- removeDirectory :: MonadIO m => FilePath -> m ()
- removeFile :: MonadIO m => FilePath -> m ()
- readable :: Permissions -> Bool
- writable :: Permissions -> Bool
- executable :: Permissions -> Bool
- searchable :: Permissions -> Bool
- emptyPermissions :: Permissions
- setOwnerReadable :: Bool -> Permissions -> Permissions
- setOwnerWritable :: Bool -> Permissions -> Permissions
- setOwnerExecutable :: Bool -> Permissions -> Permissions
- setOwnerSearchable :: Bool -> Permissions -> Permissions
- getPermissions :: MonadIO m => FilePath -> m Permissions
- setPermissions :: MonadIO m => FilePath -> Permissions -> m ()
- copyPermissions :: MonadIO m => FilePath -> FilePath -> m ()
- createDirectory :: MonadIO m => FilePath -> m ()
- createDirectoryIfMissing :: MonadIO m => Bool -> FilePath -> m ()
- removeDirectoryRecursive :: MonadIO m => FilePath -> m ()
- removePathForcibly :: MonadIO m => FilePath -> m ()
- renameDirectory :: MonadIO m => FilePath -> FilePath -> m ()
- renameFile :: MonadIO m => FilePath -> FilePath -> m ()
- renamePath :: MonadIO m => FilePath -> FilePath -> m ()
- copyFile :: MonadIO m => FilePath -> FilePath -> m ()
- copyFileWithMetadata :: MonadIO m => FilePath -> FilePath -> m ()
- canonicalizePath :: MonadIO m => FilePath -> m FilePath
- makeAbsolute :: MonadIO m => FilePath -> m FilePath
- makeRelativeToCurrentDirectory :: MonadIO m => FilePath -> m FilePath
- findExecutable :: MonadIO m => String -> m (Maybe FilePath)
- findExecutables :: MonadIO m => String -> m [FilePath]
- findExecutablesInDirectories :: MonadIO m => [FilePath] -> String -> m [FilePath]
- findFile :: MonadIO m => [FilePath] -> String -> m (Maybe FilePath)
- findFiles :: MonadIO m => [FilePath] -> String -> m [FilePath]
- findFileWith :: MonadUnliftIO m => (FilePath -> m Bool) -> [FilePath] -> String -> m (Maybe FilePath)
- findFilesWith :: MonadUnliftIO m => (FilePath -> m Bool) -> [FilePath] -> String -> m [FilePath]
- exeExtension :: String
- listDirectory :: MonadIO m => FilePath -> m [FilePath]
- getCurrentDirectory :: MonadIO m => m FilePath
- setCurrentDirectory :: MonadIO m => FilePath -> m ()
- withCurrentDirectory :: MonadUnliftIO m => FilePath -> m a -> m a
- getFileSize :: MonadIO m => FilePath -> m Integer
- doesPathExist :: MonadIO m => FilePath -> m Bool
- doesDirectoryExist :: MonadIO m => FilePath -> m Bool
- doesFileExist :: MonadIO m => FilePath -> m Bool
- createFileLink :: MonadIO m => FilePath -> FilePath -> m ()
- createDirectoryLink :: MonadIO m => FilePath -> FilePath -> m ()
- removeDirectoryLink :: MonadIO m => FilePath -> m ()
- pathIsSymbolicLink :: MonadIO m => FilePath -> m Bool
- getSymbolicLinkTarget :: MonadIO m => FilePath -> m FilePath
- getAccessTime :: MonadIO m => FilePath -> m UTCTime
- getModificationTime :: MonadIO m => FilePath -> m UTCTime
- setAccessTime :: MonadIO m => FilePath -> UTCTime -> m ()
- setModificationTime :: MonadIO m => FilePath -> UTCTime -> m ()
- getHomeDirectory :: MonadIO m => m FilePath
- getXdgDirectory :: MonadIO m => XdgDirectory -> FilePath -> m FilePath
- getXdgDirectoryList :: MonadIO m => XdgDirectoryList -> m [FilePath]
- getAppUserDataDirectory :: MonadIO m => FilePath -> m FilePath
- getUserDocumentsDirectory :: MonadIO m => m FilePath
- getTemporaryDirectory :: MonadIO m => m FilePath
- putStr :: MonadIO m => String -> m ()
- putStrLn :: MonadIO m => String -> m ()
- print :: (Show a, MonadIO m) => a -> m ()
- getLine :: MonadIO m => m String
- readFile :: MonadIO m => FilePath -> m String
- writeFile :: MonadIO m => FilePath -> String -> m ()
- appendFile :: MonadIO m => FilePath -> String -> m ()
- getArgs :: MonadIO m => m [String]
- getEnv :: MonadIO m => String -> m String
- lookupEnv :: MonadIO m => String -> m (Maybe String)
- setEnv :: MonadIO m => String -> String -> m ()
- unsetEnv :: MonadIO m => String -> m ()
- data ThreadId
- forkIO :: MonadUnliftIO m => m () -> m ThreadId
- forkOS :: MonadUnliftIO m => m () -> m ThreadId
- killThread :: MonadIO m => ThreadId -> m ()
- threadDelay :: MonadIO m => Int -> m ()
- module UnliftIO.IORef
- module UnliftIO.MVar
- class (Typeable e, Show e) => Exception e where
- toException :: e -> SomeException
- fromException :: SomeException -> Maybe e
- displayException :: e -> String
- data SomeException = Exception e => SomeException e
- data SomeAsyncException = Exception e => SomeAsyncException e
- data IOException
- module UnliftIO.STM
- data Map k a
- data Set a
- data HashMap k v
- data HashSet a
- data ByteString
- type LByteString = ByteString
- data Text
- type LText = Text
- whenM :: Monad m => m Bool -> m () -> m ()
- unlessM :: Monad m => m Bool -> m () -> m ()
- (<$$>) :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b)
- (<$$$>) :: (Functor f, Functor g, Functor h) => (a -> b) -> f (g (h a)) -> f (g (h b))
- todo :: forall {r :: RuntimeRep} (a :: TYPE r). HasCallStack => a
- pattern TODO :: forall (a :: Type). HasCallStack => forall. a
- data TodoException = TodoException
Base
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
Floating Double | Since: base-2.1 |
RealFloat Double | Since: base-2.1 |
Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # | |
Read Double | Since: base-2.1 |
NFData Double | |
Defined in Control.DeepSeq | |
Eq Double | Note that due to the presence of
Also note that
|
Ord Double | Note that due to the presence of
Also note that, due to the same,
|
Hashable Double | Note: prior to The Since: hashable-1.3.0.0 |
Lift Double | |
Generic1 (URec Double :: k -> Type) | |
Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
Generic (URec Double p) | |
Show (URec Double p) | Since: base-4.9.0.0 |
Eq (URec Double p) | Since: base-4.9.0.0 |
Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # | |
data URec Double (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
type Rep1 (URec Double :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics |
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
Floating Float | Since: base-2.1 |
RealFloat Float | Since: base-2.1 |
Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # | |
Read Float | Since: base-2.1 |
NFData Float | |
Defined in Control.DeepSeq | |
Eq Float | Note that due to the presence of
Also note that
|
Ord Float | Note that due to the presence of
Also note that, due to the same,
|
Hashable Float | Note: prior to The Since: hashable-1.3.0.0 |
Lift Float | |
Generic1 (URec Float :: k -> Type) | |
Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
Generic (URec Float p) | |
Show (URec Float p) | |
Eq (URec Float p) | |
Ord (URec Float p) | |
Defined in GHC.Generics | |
data URec Float (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
type Rep1 (URec Float :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (URec Float p) | |
Defined in GHC.Generics |
Arbitrary precision integers. In contrast with fixed-size integral types
such as Int
, the Integer
type represents the entire infinite range of
integers.
Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.
If the value is small (fit into an Int
), IS
constructor is used.
Otherwise Integer
and IN
constructors are used to store a BigNat
representing respectively the positive or the negative value magnitude.
Invariant: Integer
and IN
are used iff value doesn't fit in IS
Instances
Enum Integer | Since: base-2.1 |
Num Integer | Since: base-2.1 |
Read Integer | Since: base-2.1 |
Integral Integer | Since: base-2.0.1 |
Defined in GHC.Real | |
Real Integer | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Integer -> Rational # | |
Show Integer | Since: base-2.1 |
NFData Integer | |
Defined in Control.DeepSeq | |
Eq Integer | |
Ord Integer | |
Hashable Integer | |
Lift Integer | |
A value of type
is a computation which, when performed,
does some I/O before returning 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.
Instances
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 y
withrem x y
=fromInteger 0
org (rem x y)
<g y
x
=y * div x y + mod x y
withmod x y
=fromInteger 0
orf (mod x y)
<f y
An example of a suitable Euclidean function, for Integer
's instance, is
abs
.
In addition, toInteger
should be total, and fromInteger
should be a left
inverse for it, i.e. fromInteger (toInteger i) = i
.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
integer division truncated toward negative infinity
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
conversion to Integer
Instances
Parsing of String
s, producing values.
Derived instances of Read
make the following assumptions, which
derived instances of Show
obey:
- If the constructor is defined to be an infix operator, then the
derived
Read
instance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
Read
will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Read
instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read
in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5
Note that right-associativity of :^:
is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where readPrec = parens $ (prec app_prec $ do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec $ do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault
Why do both readsPrec
and readPrec
exist, and why does GHC opt to
implement readPrec
in derived Read
instances instead of readsPrec
?
The reason is that readsPrec
is based on the ReadS
type, and although
ReadS
is mentioned in the Haskell 2010 Report, it is not a very efficient
parser data structure.
readPrec
, on the other hand, is based on a much more efficient ReadPrec
datatype (a.k.a "new-style parsers"), but its definition relies on the use
of the RankNTypes
language extension. Therefore, readPrec
(and its
cousin, readListPrec
) are marked as GHC-only. Nevertheless, it is
recommended to use readPrec
instead of readsPrec
whenever possible
for the efficiency improvements it brings.
As mentioned above, derived Read
instances in GHC will implement
readPrec
instead of readsPrec
. The default implementations of
readsPrec
(and its cousin, readList
) will simply use readPrec
under
the hood. If you are writing a Read
instance by hand, it is recommended
to write it like so:
instanceRead
T wherereadPrec
= ...readListPrec
=readListPrecDefault
Methods
Arguments
:: Int | the operator precedence of the enclosing
context (a number from |
-> ReadS a |
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read
and Show
satisfy the following:
That is, readsPrec
parses the string produced by
showsPrec
, and delivers the value that
showsPrec
started with.
Instances
Read All | Since: base-2.1 |
Read Any | Since: base-2.1 |
Read Version | Since: base-2.1 |
Read CBool | |
Read CChar | |
Read CClock | |
Read CDouble | |
Read CFloat | |
Read CInt | |
Read CIntMax | |
Read CIntPtr | |
Read CLLong | |
Read CLong | |
Read CPtrdiff | |
Read CSChar | |
Read CSUSeconds | |
Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSUSeconds # readList :: ReadS [CSUSeconds] # readPrec :: ReadPrec CSUSeconds # readListPrec :: ReadPrec [CSUSeconds] # | |
Read CShort | |
Read CSigAtomic | |
Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSigAtomic # readList :: ReadS [CSigAtomic] # readPrec :: ReadPrec CSigAtomic # readListPrec :: ReadPrec [CSigAtomic] # | |
Read CSize | |
Read CTime | |
Read CUChar | |
Read CUInt | |
Read CUIntMax | |
Read CUIntPtr | |
Read CULLong | |
Read CULong | |
Read CUSeconds | |
Read CUShort | |
Read CWchar | |
Read Void | Reading a Since: base-4.8.0.0 |
Read Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Associativity # readList :: ReadS [Associativity] # | |
Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness # readList :: ReadS [DecidedStrictness] # | |
Read Fixity | Since: base-4.6.0.0 |
Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness # readList :: ReadS [SourceStrictness] # | |
Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceUnpackedness # readList :: ReadS [SourceUnpackedness] # | |
Read SeekMode | Since: base-4.2.0.0 |
Read ExitCode | |
Read BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS BufferMode # readList :: ReadS [BufferMode] # readPrec :: ReadPrec BufferMode # readListPrec :: ReadPrec [BufferMode] # | |
Read Newline | Since: base-4.3.0.0 |
Read NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS NewlineMode # readList :: ReadS [NewlineMode] # readPrec :: ReadPrec NewlineMode # readListPrec :: ReadPrec [NewlineMode] # | |
Read IOMode | Since: base-4.2.0.0 |
Read Int16 | Since: base-2.1 |
Read Int32 | Since: base-2.1 |
Read Int64 | Since: base-2.1 |
Read Int8 | Since: base-2.1 |
Read GeneralCategory | Since: base-2.1 |
Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory # readList :: ReadS [GeneralCategory] # | |
Read Word16 | Since: base-2.1 |
Read Word32 | Since: base-2.1 |
Read Word64 | Since: base-2.1 |
Read Word8 | Since: base-2.1 |
Read Lexeme | Since: base-2.1 |
Read ByteString | |
Defined in Data.ByteString.Internal.Type Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
Read ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
Read ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods readsPrec :: Int -> ReadS ShortByteString # readList :: ReadS [ShortByteString] # | |
Read IntSet | |
Read FileType | |
Read Permissions | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS Permissions # readList :: ReadS [Permissions] # readPrec :: ReadPrec Permissions # readListPrec :: ReadPrec [Permissions] # | |
Read XdgDirectory | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS XdgDirectory # readList :: ReadS [XdgDirectory] # | |
Read XdgDirectoryList | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS XdgDirectoryList # readList :: ReadS [XdgDirectoryList] # | |
Read Ordering | Since: base-2.1 |
Read Integer | Since: base-2.1 |
Read Natural | Since: base-4.8.0.0 |
Read () | Since: base-2.1 |
Read Bool | Since: base-2.1 |
Read Char | Since: base-2.1 |
Read Double | Since: base-2.1 |
Read Float | Since: base-2.1 |
Read Int | Since: base-2.1 |
Read Word | Since: base-4.5.0.0 |
Read a => Read (ZipList a) | Since: base-4.7.0.0 |
Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
Read a => Read (First a) | Since: base-2.1 |
Read a => Read (Last a) | Since: base-2.1 |
Read a => Read (Down a) | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
Read a => Read (First a) | Since: base-4.9.0.0 |
Read a => Read (Last a) | Since: base-4.9.0.0 |
Read a => Read (Max a) | Since: base-4.9.0.0 |
Read a => Read (Min a) | Since: base-4.9.0.0 |
Read m => Read (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] # | |
Read a => Read (Dual a) | Since: base-2.1 |
Read a => Read (Product a) | Since: base-2.1 |
Read a => Read (Sum a) | Since: base-2.1 |
Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
Read p => Read (Par1 p) | Since: base-4.7.0.0 |
(Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
Read e => Read (IntMap e) | |
Read a => Read (Seq a) | |
Read a => Read (ViewL a) | |
Read a => Read (ViewR a) | |
(Read a, Ord a) => Read (Set a) | |
Read a => Read (Tree a) | |
(Eq a, Hashable a, Read a) => Read (HashSet a) | |
Read a => Read (Maybe a) | Since: base-2.1 |
Read a => Read (a) | Since: base-4.15 |
Read a => Read [a] | Since: base-2.1 |
(Read a, Read b) => Read (Either a b) | Since: base-3.0 |
(Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0 |
(Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
Read (U1 p) | Since: base-4.9.0.0 |
Read (V1 p) | Since: base-4.9.0.0 |
(Ord k, Read k, Read e) => Read (Map k e) | |
(Read1 m, Read a) => Read (MaybeT m a) | |
(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) | |
(Read a, Read b) => Read (a, b) | Since: base-2.1 |
Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
Read (f a) => Read (Ap f a) | Since: base-4.12.0.0 |
Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 |
Read (f p) => Read (Rec1 f p) | Since: base-4.7.0.0 |
(Read e, Read1 m, Read a) => Read (ExceptT e m a) | |
(Read1 f, Read a) => Read (IdentityT f a) | |
(Read w, Read1 m, Read a) => Read (WriterT w m a) | |
(Read w, Read1 m, Read a) => Read (WriterT w m a) | |
(Read a, Read b, Read c) => Read (a, b, c) | Since: base-2.1 |
(Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
(Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
Read c => Read (K1 i c p) | Since: base-4.7.0.0 |
(Read a, Read b, Read c, Read d) => Read (a, b, c, d) | Since: base-2.1 |
Read (f (g p)) => Read ((f :.: g) p) | Since: base-4.7.0.0 |
Read (f p) => Read (M1 i c f p) | Since: base-4.7.0.0 |
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Defined in GHC.Read |
Conversion of values to readable String
s.
Derived instances of Show
have the following properties, which
are compatible with derived instances of Read
:
- The result of
show
is 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
showsPrec
will produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
x
is less thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
show
will 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 = 5
Note that right-associativity of :^:
is ignored. For example,
produces the stringshow
(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"
.
Methods
Arguments
:: Int | the operator precedence of the enclosing
context (a number from |
-> a | the value to be converted to a |
-> ShowS |
Convert a value to a readable String
.
showsPrec
should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read
and Show
satisfy the following:
That is, readsPrec
parses the string produced by
showsPrec
, and delivers the value that showsPrec
started with.
Instances
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 All | Since: base-2.1 |
Bounded Any | Since: base-2.1 |
Bounded CBool | |
Bounded CChar | |
Bounded CInt | |
Bounded CIntMax | |
Bounded CIntPtr | |
Bounded CLLong | |
Bounded CLong | |
Bounded CPtrdiff | |
Bounded CSChar | |
Bounded CShort | |
Bounded CSigAtomic | |
Defined in Foreign.C.Types | |
Bounded CSize | |
Bounded CUChar | |
Bounded CUInt | |
Bounded CUIntMax | |
Bounded CUIntPtr | |
Bounded CULLong | |
Bounded CULong | |
Bounded CUShort | |
Bounded CWchar | |
Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded Int16 | Since: base-2.1 |
Bounded Int32 | Since: base-2.1 |
Bounded Int64 | Since: base-2.1 |
Bounded Int8 | Since: base-2.1 |
Bounded GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode | |
Bounded Word16 | Since: base-2.1 |
Bounded Word32 | Since: base-2.1 |
Bounded Word64 | Since: base-2.1 |
Bounded Word8 | Since: base-2.1 |
Bounded FileType | |
Bounded XdgDirectory | |
Defined in System.Directory.Internal.Common | |
Bounded XdgDirectoryList | |
Defined in System.Directory.Internal.Common | |
Bounded Extension | |
Bounded Ordering | Since: base-2.1 |
Bounded () | Since: base-2.1 |
Bounded Bool | Since: base-2.1 |
Bounded Char | Since: base-2.1 |
Bounded Int | Since: base-2.1 |
Bounded Levity | Since: base-4.16.0.0 |
Bounded VecCount | Since: base-4.10.0.0 |
Bounded VecElem | Since: base-4.10.0.0 |
Bounded Word | Since: base-2.1 |
Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Down a) | Swaps Since: base-4.14.0.0 |
Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Last a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Max a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Min a) | Since: base-4.9.0.0 |
Bounded m => Bounded (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Bounded a => Bounded (Dual a) | Since: base-2.1 |
Bounded a => Bounded (Product a) | Since: base-2.1 |
Bounded a => Bounded (Sum a) | Since: base-2.1 |
Bounded a => Bounded (a) | |
(Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
(Applicative f, Bounded a) => Bounded (Ap f a) | Since: base-4.12.0.0 |
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
(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
andsucc
maxBound
should result in a runtime error.pred
minBound
fromEnum
andtoEnum
should give a runtime error if the result value is not representable in the result type. For example,
is an error.toEnum
7 ::Bool
enumFrom
andenumFromThen
should 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 = minBound
Methods
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, instances are
encouraged to follow these properties:
Instances
Eq ByteArray | Since: base-4.17.0.0 |
Eq All | Since: base-2.1 |
Eq Any | Since: base-2.1 |
Eq SomeTypeRep | |
Defined in Data.Typeable.Internal | |
Eq Version | Since: base-2.1 |
Eq CBool | |
Eq CChar | |
Eq CClock | |
Eq CDouble | |
Eq CFloat | |
Eq CInt | |
Eq CIntMax | |
Eq CIntPtr | |
Eq CLLong | |
Eq CLong | |
Eq CPtrdiff | |
Eq CSChar | |
Eq CSUSeconds | |
Defined in Foreign.C.Types | |
Eq CShort | |
Eq CSigAtomic | |
Defined in Foreign.C.Types | |
Eq CSize | |
Eq CTime | |
Eq CUChar | |
Eq CUInt | |
Eq CUIntMax | |
Eq CUIntPtr | |
Eq CULLong | |
Eq CULong | |
Eq CUSeconds | |
Eq CUShort | |
Eq CWchar | |
Eq Void | Since: base-4.8.0.0 |
Eq BlockReason | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync | |
Eq ThreadId | Since: base-4.2.0.0 |
Eq ThreadStatus | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync | |
Eq ErrorCall | Since: base-4.7.0.0 |
Eq ArithException | Since: base-3.0 |
Defined in GHC.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool # (/=) :: ArithException -> ArithException -> Bool # | |
Eq SpecConstrAnnotation | Since: base-4.3.0.0 |
Defined in GHC.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # | |
Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods (==) :: Associativity -> Associativity -> Bool # (/=) :: Associativity -> Associativity -> Bool # | |
Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
Eq Fixity | Since: base-4.6.0.0 |
Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
Eq MaskingState | Since: base-4.3.0.0 |
Defined in GHC.IO | |
Eq IODeviceType | Since: base-4.2.0.0 |
Defined in GHC.IO.Device | |
Eq SeekMode | Since: base-4.2.0.0 |
Eq ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool # (/=) :: ArrayException -> ArrayException -> Bool # | |
Eq AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool # (/=) :: AsyncException -> AsyncException -> Bool # | |
Eq ExitCode | |
Eq IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
Eq IOException | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
Eq BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types | |
Eq Handle | Since: base-4.1.0.0 |
Eq Newline | Since: base-4.2.0.0 |
Eq NewlineMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types | |
Eq IOMode | Since: base-4.2.0.0 |
Eq Int16 | Since: base-2.1 |
Eq Int32 | Since: base-2.1 |
Eq Int64 | Since: base-2.1 |
Eq Int8 | Since: base-2.1 |
Eq SrcLoc | Since: base-4.9.0.0 |
Eq GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode Methods (==) :: GeneralCategory -> GeneralCategory -> Bool # (/=) :: GeneralCategory -> GeneralCategory -> Bool # | |
Eq Word16 | Since: base-2.1 |
Eq Word32 | Since: base-2.1 |
Eq Word64 | Since: base-2.1 |
Eq Word8 | Since: base-2.1 |
Eq ByteString | |
Defined in Data.ByteString.Internal.Type | |
Eq ByteString | |
Defined in Data.ByteString.Lazy.Internal | |
Eq ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods (==) :: ShortByteString -> ShortByteString -> Bool # (/=) :: ShortByteString -> ShortByteString -> Bool # | |
Eq IntSet | |
Eq FileType | |
Eq Permissions | |
Defined in System.Directory.Internal.Common | |
Eq XdgDirectory | |
Defined in System.Directory.Internal.Common | |
Eq XdgDirectoryList | |
Defined in System.Directory.Internal.Common Methods (==) :: XdgDirectoryList -> XdgDirectoryList -> Bool # (/=) :: XdgDirectoryList -> XdgDirectoryList -> Bool # | |
Eq OsChar | Byte equality of the internal representation. |
Eq OsString | Byte equality of the internal representation. |
Eq PosixChar | |
Eq PosixString | |
Defined in System.OsString.Internal.Types.Hidden | |
Eq WindowsChar | |
Defined in System.OsString.Internal.Types.Hidden | |
Eq WindowsString | |
Defined in System.OsString.Internal.Types.Hidden Methods (==) :: WindowsString -> WindowsString -> Bool # (/=) :: WindowsString -> WindowsString -> Bool # | |
Eq ForeignSrcLang | |
Defined in GHC.ForeignSrcLang.Type Methods (==) :: ForeignSrcLang -> ForeignSrcLang -> Bool # (/=) :: ForeignSrcLang -> ForeignSrcLang -> Bool # | |
Eq Extension | |
Eq Module | |
Eq Ordering | |
Eq TrName | |
Eq TyCon | |
Eq TodoException Source # | |
Defined in Imports Methods (==) :: TodoException -> TodoException -> Bool # (/=) :: TodoException -> TodoException -> Bool # | |
Eq OsChar | Byte equality of the internal representation. |
Eq OsString | Byte equality of the internal representation. |
Eq PosixChar | |
Eq PosixString | |
Defined in System.OsString.Internal.Types | |
Eq WindowsChar | |
Defined in System.OsString.Internal.Types | |
Eq WindowsString | |
Defined in System.OsString.Internal.Types Methods (==) :: WindowsString -> WindowsString -> Bool # (/=) :: WindowsString -> WindowsString -> Bool # | |
Eq Mode | |
Eq Style | |
Eq TextDetails | |
Defined in Text.PrettyPrint.Annotated.HughesPJ | |
Eq Doc | |
Eq AnnLookup | |
Eq AnnTarget | |
Eq Bang | |
Eq Body | |
Eq Bytes | |
Eq Callconv | |
Eq Clause | |
Eq Con | |
Eq Dec | |
Eq DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
Eq DerivClause | |
Defined in Language.Haskell.TH.Syntax | |
Eq DerivStrategy | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DerivStrategy -> DerivStrategy -> Bool # (/=) :: DerivStrategy -> DerivStrategy -> Bool # | |
Eq DocLoc | |
Eq Exp | |
Eq FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FamilyResultSig -> FamilyResultSig -> Bool # (/=) :: FamilyResultSig -> FamilyResultSig -> Bool # | |
Eq Fixity | |
Eq FixityDirection | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FixityDirection -> FixityDirection -> Bool # (/=) :: FixityDirection -> FixityDirection -> Bool # | |
Eq Foreign | |
Eq FunDep | |
Eq Guard | |
Eq Info | |
Eq InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: InjectivityAnn -> InjectivityAnn -> Bool # (/=) :: InjectivityAnn -> InjectivityAnn -> Bool # | |
Eq Inline | |
Eq Lit | |
Eq Loc | |
Eq Match | |
Eq ModName | |
Eq Module | |
Eq ModuleInfo | |
Defined in Language.Haskell.TH.Syntax | |
Eq Name | |
Eq NameFlavour | |
Defined in Language.Haskell.TH.Syntax | |
Eq NameSpace | |
Eq OccName | |
Eq Overlap | |
Eq Pat | |
Eq PatSynArgs | |
Defined in Language.Haskell.TH.Syntax | |
Eq PatSynDir | |
Eq Phases | |
Eq PkgName | |
Eq Pragma | |
Eq Range | |
Eq Role | |
Eq RuleBndr | |
Eq RuleMatch | |
Eq Safety | |
Eq SourceStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
Eq SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
Eq Specificity | |
Defined in Language.Haskell.TH.Syntax | |
Eq Stmt | |
Eq TyLit | |
Eq TySynEqn | |
Eq Type | |
Eq TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (/=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # | |
Eq UTCTime | |
Eq LocalTime | |
Eq StringException | Since: unliftio-0.2.19 |
Defined in UnliftIO.Exception Methods (==) :: StringException -> StringException -> Bool # (/=) :: StringException -> StringException -> Bool # | |
Eq Integer | |
Eq () | |
Eq Bool | |
Eq Char | |
Eq Double | Note that due to the presence of
Also note that
|
Eq Float | Note that due to the presence of
Also note that
|
Eq Int | |
Eq Word | |
Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
Eq (Chan a) | Since: base-4.4.0.0 |
Eq (MutableByteArray s) | Since: base-4.17.0.0 |
Defined in Data.Array.Byte Methods (==) :: MutableByteArray s -> MutableByteArray s -> Bool # (/=) :: MutableByteArray s -> MutableByteArray s -> Bool # | |
Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
Eq a => Eq (First a) | Since: base-2.1 |
Eq a => Eq (Last a) | Since: base-2.1 |
Eq a => Eq (Down a) | Since: base-4.6.0.0 |
Eq a => Eq (First a) | Since: base-4.9.0.0 |
Eq a => Eq (Last a) | Since: base-4.9.0.0 |
Eq a => Eq (Max a) | Since: base-4.9.0.0 |
Eq a => Eq (Min a) | Since: base-4.9.0.0 |
Eq m => Eq (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # | |
Eq a => Eq (Dual a) | Since: base-2.1 |
Eq a => Eq (Product a) | Since: base-2.1 |
Eq a => Eq (Sum a) | Since: base-2.1 |
Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
Eq (TVar a) | Since: base-4.8.0.0 |
Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
Eq (IORef a) | Pointer equality. Since: base-4.0.0.0 |
Eq (MVar a) | Since: base-4.1.0.0 |
Eq (FunPtr a) | |
Eq (Ptr a) | Since: base-2.1 |
Eq a => Eq (Ratio a) | Since: base-2.1 |
Eq a => Eq (IntMap a) | |
Eq a => Eq (Seq a) | |
Eq a => Eq (ViewL a) | |
Eq a => Eq (ViewR a) | |
Eq a => Eq (Intersection a) | |
Defined in Data.Set.Internal Methods (==) :: Intersection a -> Intersection a -> Bool # (/=) :: Intersection a -> Intersection a -> Bool # | |
Eq a => Eq (Set a) | |
Eq a => Eq (Tree a) | |
Eq a => Eq (Hashed a) | Uses precomputed hash to detect inequality faster |
Eq a => Eq (AnnotDetails a) | |
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: AnnotDetails a -> AnnotDetails a -> Bool # (/=) :: AnnotDetails a -> AnnotDetails a -> Bool # | |
Eq (Doc a) | |
Eq a => Eq (Span a) | |
Eq (TBQueue a) | |
Eq (TChan a) | |
Eq (TMVar a) | |
Eq (TQueue a) | |
Eq flag => Eq (TyVarBndr flag) | |
Eq a => Eq (HashSet a) | Note that, in the presence of hash collisions, equal
In general, the lack of extensionality can be observed with any function that depends on the key ordering, such as folds and traversals. |
Eq a => Eq (Maybe a) | Since: base-2.1 |
Eq a => Eq (a) | |
Eq a => Eq [a] | |
(Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
Eq (TypeRep a) | Since: base-2.1 |
Eq (U1 p) | Since: base-4.9.0.0 |
Eq (V1 p) | Since: base-4.9.0.0 |
(Eq k, Eq a) => Eq (Map k a) | |
(Eq1 m, Eq a) => Eq (MaybeT m a) | |
(Eq k, Eq v) => Eq (HashMap k v) | Note that, in the presence of hash collisions, equal
In general, the lack of extensionality can be observed with any function that depends on the key ordering, such as folds and traversals. |
(Eq k, Eq v) => Eq (Leaf k v) | |
(Eq a, Eq b) => Eq (a, b) | |
Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
Eq (f a) => Eq (Ap f a) | Since: base-4.12.0.0 |
Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0 |
(Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a) | Since: base-4.18.0.0 |
Defined in GHC.Generics Methods (==) :: Generically1 f a -> Generically1 f a -> Bool # (/=) :: Generically1 f a -> Generically1 f a -> Bool # | |
Eq (f p) => Eq (Rec1 f p) | Since: base-4.7.0.0 |
Eq (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Eq (URec Char p) | Since: base-4.9.0.0 |
Eq (URec Double p) | Since: base-4.9.0.0 |
Eq (URec Float p) | |
Eq (URec Int p) | Since: base-4.9.0.0 |
Eq (URec Word p) | Since: base-4.9.0.0 |
(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a) | |
(Eq1 f, Eq a) => Eq (IdentityT f a) | |
(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) | |
(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) | |
(Eq a, Eq b, Eq c) => Eq (a, b, c) | |
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
Eq (f (g p)) => Eq ((f :.: g) p) | Since: base-4.7.0.0 |
Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
(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) | |
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 b
exp (fromInteger 0)
=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
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:*
)
recip
gives the multiplicative inversex * recip x
=recip x * x
=fromInteger 1
- Totality of
toRational
toRational
is total- Coherence with
toRational
- if the type also implements
Real
, thenfromRational
is a left inverse fortoRational
, i.e.fromRational (toRational i) = i
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
).
A floating literal stands for an application of Ratio
Integer
fromRational
to a value of type Rational
, so such literals have type
(
.Fractional
a) => a
Instances
Fractional CDouble | |
Fractional CFloat | |
Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
Basic numeric class.
The Haskell Report defines no laws for Num
. However, (
and +
)(
are
customarily expected to define a ring and have the following properties:*
)
- Associativity of
(
+
) (x + y) + z
=x + (y + z)
- Commutativity of
(
+
) x + y
=y + x
is the additive identityfromInteger
0x + fromInteger 0
=x
negate
gives the additive inversex + negate x
=fromInteger 0
- Associativity of
(
*
) (x * y) * z
=x * (y * z)
is the multiplicative identityfromInteger
1x * fromInteger 1
=x
andfromInteger 1 * x
=x
- Distributivity of
(
with respect to*
)(
+
) a * (b + c)
=(a * b) + (a * c)
and(b + c) * a
=(b * a) + (c * a)
- Coherence with
toInteger
- if the type also implements
Integral
, thenfromInteger
is a left inverse fortoInteger
, i.e.fromInteger (toInteger i) == i
Note that it isn't customarily expected that a type instance of both Num
and Ord
implement an ordered ring. Indeed, in base
only Integer
and
Rational
do.
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
Instances
Num CBool | |
Num CChar | |
Num CClock | |
Num CDouble | |
Num CFloat | |
Num CInt | |
Num CIntMax | |
Num CIntPtr | |
Num CLLong | |
Num CLong | |
Num CPtrdiff | |
Num CSChar | |
Num CSUSeconds | |
Defined in Foreign.C.Types Methods (+) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (-) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (*) :: CSUSeconds -> CSUSeconds -> CSUSeconds # negate :: CSUSeconds -> CSUSeconds # abs :: CSUSeconds -> CSUSeconds # signum :: CSUSeconds -> CSUSeconds # fromInteger :: Integer -> CSUSeconds # | |
Num CShort | |
Num CSigAtomic | |
Defined in Foreign.C.Types Methods (+) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (-) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (*) :: CSigAtomic -> CSigAtomic -> CSigAtomic # negate :: CSigAtomic -> CSigAtomic # abs :: CSigAtomic -> CSigAtomic # signum :: CSigAtomic -> CSigAtomic # fromInteger :: Integer -> CSigAtomic # | |
Num CSize | |
Num CTime | |
Num CUChar | |
Num CUInt | |
Num CUIntMax | |
Num CUIntPtr | |
Num CULLong | |
Num CULong | |
Num CUSeconds | |
Defined in Foreign.C.Types | |
Num CUShort | |
Num CWchar | |
Num Int16 | Since: base-2.1 |
Num Int32 | Since: base-2.1 |
Num Int64 | Since: base-2.1 |
Num Int8 | Since: base-2.1 |
Num Word16 | Since: base-2.1 |
Num Word32 | Since: base-2.1 |
Num Word64 | Since: base-2.1 |
Num Word8 | Since: base-2.1 |
Num Integer | Since: base-2.1 |
Num Natural | Note that Since: base-4.8.0.0 |
Num Int | Since: base-2.1 |
Num Word | Since: base-2.1 |
Num a => Num (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
Num a => Num (Down a) | Since: base-4.11.0.0 |
Num a => Num (Max a) | Since: base-4.9.0.0 |
Num a => Num (Min a) | Since: base-4.9.0.0 |
Num a => Num (Product a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
Num a => Num (Sum a) | Since: base-4.7.0.0 |
Integral a => Num (Ratio a) | Since: base-2.0.1 |
Num a => Num (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
(Applicative f, Num a) => Num (Ap f a) | Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base-4.12.0.0 |
Num (f a) => Num (Alt f a) | Since: base-4.8.0.0 |
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.
Ord
, as defined by the Haskell report, implements a total order and has the
following properties:
- Comparability
x <= y || y <= x
=True
- Transitivity
- if
x <= y && y <= z
=True
, thenx <= z
=True
- Reflexivity
x <= x
=True
- Antisymmetry
- if
x <= y && y <= x
=True
, thenx == y
=True
The following operator interactions are expected to hold:
x >= y
=y <= x
x < y
=x <= y && x /= y
x > y
=y < x
x < y
=compare x y == LT
x > y
=compare x y == GT
x == y
=compare x y == EQ
min x y == if x <= y then x else y
=True
max x y == if x >= y then x else y
=True
Note that (7.) and (8.) do not require min
and max
to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==)
.
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
class (Num a, Ord a) => Real a where #
Real numbers.
The Haskell report defines no laws for Real
, however Real
instances
are customarily expected to adhere to the following law:
- Coherence with
fromRational
- if the type also implements
Fractional
, thenfromRational
is a left inverse fortoRational
, i.e.fromRational (toRational i) = i
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
Instances
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
yields 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
.
In particular, floatDigits
x
. If the type
contains a negative zero, also decodeFloat
0 = (0,0)
.
The result of decodeFloat
(-0.0) = (0,0)
is unspecified if either of
decodeFloat
x
or isNaN
x
is isInfinite
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) = x
is one of the two closest representable
floating-point numbers to encodeFloat
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
.
and for finite nonzero exponent
0 = 0x
,
.
If exponent
x = snd (decodeFloat
x) + floatDigits
xx
is a finite floating-point number, it is equal in value to
, where 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
,
computes the angle
(from the positive x-axis) of the vector from the origin to the
point atan2
y x(x,y)
.
returns a value in the range [atan2
y x-pi
,
pi
]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported.
, with atan2
y 1y
in a type
that is RealFloat
, should return the same value as
.
A default definition of atan
yatan2
is provided, but implementors
can provide a more accurate implementation.
Instances
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) #
The function properFraction
takes a real fractional number x
and returns a pair (n,f)
such that x = n+f
, and:
n
is an integral number with the same sign asx
; andf
is a fraction with the same type and sign asx
, and with absolute value less than1
.
The default definitions of the ceiling
, floor
, truncate
and round
functions are in terms of properFraction
.
truncate :: Integral b => a -> b #
returns the integer nearest truncate
xx
between zero and x
round :: Integral b => a -> b #
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
ceiling :: Integral b => a -> b #
returns the least integer not less than ceiling
xx
floor :: Integral b => a -> b #
returns the greatest integer not greater than floor
xx
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.
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a #
error
stops execution and displays an error message.
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b infixr 0 #
The value of
is bottom if seq
a ba
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
does
not guarantee that seq
a ba
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.
fromIntegral :: (Integral a, Num b) => a -> b #
General coercion from Integral
types.
WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.
realToFrac :: (Real a, Fractional b) => a -> b #
General coercion to Fractional
types.
WARNING: This function goes through the Rational
type, which does not have values for NaN
for example.
This means it does not round-trip.
For Double
it also behaves differently with or without -O0:
Prelude> realToFrac nan -- With -O0 -Infinity Prelude> realToFrac nan NaN
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a #
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
utility function converting a Char
to a show function that
simply prepends the character unchanged.
showString :: String -> ShowS #
utility function converting a String
to a show function that
simply prepends the string unchanged.
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
gcd :: Integral a => a -> a -> a #
is the non-negative factor of both gcd
x yx
and y
of which
every common factor of x
and y
is also a factor; for example
, gcd
4 2 = 2
, gcd
(-4) 6 = 2
= gcd
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,
,
the result may be negative if one of the arguments is abs
minBound
< 0
(and
necessarily is if the other is minBound
0
or
) for such types.minBound
lcm :: Integral a => a -> a -> a #
is the smallest positive integer that both lcm
x yx
and y
divide.
The lex
function reads a single lexeme from the input, discarding
initial white space, and returning the characters that constitute the
lexeme. If the input string contains only white space, lex
returns a
single successful `lexeme' consisting of the empty string. (Thus
.) If there is no legal lexeme at the
beginning of the input string, lex
"" = [("","")]lex
fails (i.e. returns []
).
This lexer is not completely faithful to the Haskell lexical syntax in the following respects:
- Qualified names are not handled properly
- Octal and hexadecimal numerics are not recognized as a single token
- Comments are not treated properly
read :: Read a => String -> a #
The read
function reads input from a string, which must be
completely consumed by the input process. read
fails with an error
if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use readMaybe
or readEither
for safe alternatives.
>>>
read "123" :: Int
123
>>>
read "hello" :: Int
*** Exception: Prelude.read: no parse
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*>
or liftA2
. If it defines both, then they must behave
the same as their default definitions:
(<*>
) =liftA2
id
liftA2
f x y = f<$>
x<*>
y
Further, any definition must satisfy the following:
- Identity
pure
id
<*>
v = v- Composition
pure
(.)<*>
u<*>
v<*>
w = u<*>
(v<*>
w)- Homomorphism
pure
f<*>
pure
x =pure
(f x)- Interchange
u
<*>
pure
y =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
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2
p (liftA2
q u v) =liftA2
f u .liftA2
g v
If f
is also a Monad
, it should satisfy
(which implies that pure
and <*>
satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 #
Sequential application.
A few functors support an implementation of <*>
that is more
efficient than the default one.
Example
Used in combination with (
, <$>
)(
can be used to build a record.<*>
)
>>>
data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>>
produceFoo :: Applicative f => f Foo
>>>
produceBar :: Applicative f => f Bar
>>>
produceBaz :: Applicative f => f Baz
>>>
mkState :: Applicative f => f MyState
>>>
mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
liftA2 :: (a -> b -> c) -> f a -> f b -> f c #
Lift a binary function to actions.
Some functors support an implementation of liftA2
that is more
efficient than the default one. In particular, if fmap
is an
expensive operation, it is likely better to use liftA2
than to
fmap
over the structure and then use <*>
.
This became a typeclass method in 4.10.0.0. Prior to that, it was
a function defined in terms of <*>
and fmap
.
Example
>>>
liftA2 (,) (Just 3) (Just 5)
Just (3,5)
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
Examples
If used in conjunction with the Applicative instance for Maybe
,
you can chain Maybe computations, with a possible "early return"
in case of Nothing
.
>>>
Just 2 *> Just 3
Just 3
>>>
Nothing *> Just 3
Nothing
Of course a more interesting use case would be to have effectful computations instead of just returning pure values.
>>>
import Data.Char
>>>
import Text.ParserCombinators.ReadP
>>>
let p = string "my name is " *> munch1 isAlpha <* eof
>>>
readP_to_S p "my name is Simon"
[("Simon","")]
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1 |
Applicative Identity | Since: base-4.8.0.0 |
Applicative First | Since: base-4.8.0.0 |
Applicative Last | Since: base-4.8.0.0 |
Applicative Down | Since: base-4.11.0.0 |
Applicative First | Since: base-4.9.0.0 |
Applicative Last | Since: base-4.9.0.0 |
Applicative Max | Since: base-4.9.0.0 |
Applicative Min | Since: base-4.9.0.0 |
Applicative Dual | Since: base-4.8.0.0 |
Applicative Product | Since: base-4.8.0.0 |
Applicative Sum | Since: base-4.8.0.0 |
Applicative NonEmpty | Since: base-4.9.0.0 |
Applicative STM | Since: base-4.8.0.0 |
Applicative Par1 | Since: base-4.9.0.0 |
Applicative P | Since: base-4.5.0.0 |
Applicative ReadP | Since: base-4.6.0.0 |
Applicative Seq | Since: containers-0.5.4 |
Applicative Tree | |
Applicative IO | Since: base-2.1 |
Applicative Q | |
Applicative Maybe | Since: base-2.1 |
Applicative Solo | Since: base-4.15 |
Applicative List | Since: base-2.1 |
Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a # | |
Applicative (Either e) | Since: base-3.0 |
Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
(Functor m, Monad m) => Applicative (MaybeT m) | |
Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) Since: base-2.1 |
Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods pure :: a -> Generically1 f a # (<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b # liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c # (*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b # (<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a # | |
Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
(Applicative f, Monad f) => Applicative (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a # | |
(Monoid w, Functor m, Monad m) => Applicative (AccumT w m) | |
Defined in Control.Monad.Trans.Accum | |
(Functor m, Monad m) => Applicative (ExceptT e m) | |
Defined in Control.Monad.Trans.Except | |
Applicative m => Applicative (IdentityT m) | |
Defined in Control.Monad.Trans.Identity | |
Applicative m => Applicative (ReaderT r m) | |
Defined in Control.Monad.Trans.Reader | |
(Functor m, Monad m) => Applicative (SelectT r m) | |
Defined in Control.Monad.Trans.Select | |
(Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Lazy | |
(Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict | |
(Functor m, Monad m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.CPS | |
(Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
(Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Strict | |
(Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
(Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
(Monad f, Applicative f) => Applicative (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Applicative (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a # | |
Applicative (ContT r m) | |
Defined in Control.Monad.Trans.Cont | |
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
Applicative ((->) r) | Since: base-2.1 |
(Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Applicative (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a # | |
(Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.CPS | |
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Lazy | |
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Strict |
class Applicative f => Alternative (f :: Type -> Type) where #
A monoid on applicative functors.
If defined, some
and many
should be the least solutions
of the equations:
Instances
The Const
functor.
Instances
Generic1 (Const a :: k -> Type) | |
Bifunctor (Const :: Type -> Type -> Type) | Since: base-4.8.0.0 |
NFData2 (Const :: Type -> Type -> Type) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Hashable2 (Const :: Type -> Type -> Type) | |
Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
Traversable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
Functor (Const m :: Type -> Type) | Since: base-2.1 |
NFData a => NFData1 (Const a :: Type -> Type) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Hashable a => Hashable1 (Const a :: Type -> Type) | |
Defined in Data.Hashable.Class | |
IsString a => IsString (Const a b) | Since: base-4.9.0.0 |
Defined in Data.String Methods fromString :: String -> Const a b # | |
Storable a => Storable (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
Bits a => Bits (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods (.&.) :: Const a b -> Const a b -> Const a b # (.|.) :: Const a b -> Const a b -> Const a b # xor :: Const a b -> Const a b -> Const a b # complement :: Const a b -> Const a b # shift :: Const a b -> Int -> Const a b # rotate :: Const a b -> Int -> Const a b # setBit :: Const a b -> Int -> Const a b # clearBit :: Const a b -> Int -> Const a b # complementBit :: Const a b -> Int -> Const a b # testBit :: Const a b -> Int -> Bool # bitSizeMaybe :: Const a b -> Maybe Int # isSigned :: Const a b -> Bool # shiftL :: Const a b -> Int -> Const a b # unsafeShiftL :: Const a b -> Int -> Const a b # shiftR :: Const a b -> Int -> Const a b # unsafeShiftR :: Const a b -> Int -> Const a b # rotateL :: Const a b -> Int -> Const a b # | |
FiniteBits a => FiniteBits (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int # countLeadingZeros :: Const a b -> Int # countTrailingZeros :: Const a b -> Int # | |
Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
Enum a => Enum (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] # | |
Floating a => Floating (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # | |
RealFloat a => RealFloat (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # | |
Generic (Const a b) | |
Ix a => Ix (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] # index :: (Const a b, Const a b) -> Const a b -> Int # unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int # inRange :: (Const a b, Const a b) -> Const a b -> Bool # rangeSize :: (Const a b, Const a b) -> Int # unsafeRangeSize :: (Const a b, Const a b) -> Int # | |
Num a => Num (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
Integral a => Integral (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # | |
Real a => Real (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational # | |
RealFrac a => RealFrac (Const a b) | Since: base-4.9.0.0 |
Show a => Show (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
NFData a => NFData (Const a b) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
Ord a => Ord (Const a b) | Since: base-4.9.0.0 |
Hashable a => Hashable (Const a b) | |
type Rep1 (Const a :: k -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
type Rep (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const |
Lists, but with an Applicative
functor based on zipping.
Constructors
ZipList | |
Fields
|
Instances
Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
Traversable ZipList | Since: base-4.9.0.0 |
Alternative ZipList | Since: base-4.11.0.0 |
Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1 |
Functor ZipList | Since: base-2.1 |
NFData1 ZipList | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Generic1 ZipList | |
Generic (ZipList a) | |
IsList (ZipList a) | Since: base-4.15.0.0 |
Read a => Read (ZipList a) | Since: base-4.7.0.0 |
Show a => Show (ZipList a) | Since: base-4.7.0.0 |
NFData a => NFData (ZipList a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
Ord a => Ord (ZipList a) | Since: base-4.7.0.0 |
type Rep1 ZipList | Since: base-4.7.0.0 |
Defined in Control.Applicative | |
type Rep (ZipList a) | Since: base-4.7.0.0 |
Defined in Control.Applicative | |
type Item (ZipList a) | |
Defined in GHC.IsList |
newtype WrappedArrow (a :: Type -> Type -> Type) b c #
Constructors
WrapArrow | |
Fields
|
Instances
Generic1 (WrappedArrow a b :: Type -> Type) | |
Defined in Control.Applicative Associated Types type Rep1 (WrappedArrow a b) :: k -> Type # Methods from1 :: forall (a0 :: k). WrappedArrow a b a0 -> Rep1 (WrappedArrow a b) a0 # to1 :: forall (a0 :: k). Rep1 (WrappedArrow a b) a0 -> WrappedArrow a b a0 # | |
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods empty :: WrappedArrow a b a0 # (<|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 # some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] # many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] # | |
Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Generic (WrappedArrow a b c) | |
Defined in Control.Applicative Associated Types type Rep (WrappedArrow a b c) :: Type -> Type # Methods from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x # to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c # | |
type Rep1 (WrappedArrow a b :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Control.Applicative type Rep1 (WrappedArrow a b :: Type -> Type) = D1 ('MetaData "WrappedArrow" "Control.Applicative" "base" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (a b)))) | |
type Rep (WrappedArrow a b c) | Since: base-4.7.0.0 |
Defined in Control.Applicative type Rep (WrappedArrow a b c) = D1 ('MetaData "WrappedArrow" "Control.Applicative" "base" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a b c)))) |
newtype WrappedMonad (m :: Type -> Type) a #
Constructors
WrapMonad | |
Fields
|
Instances
(<$>) :: 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, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an
Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> Left 17
Left 17>>>
show <$> Right 17
Right "17"
Double each element of a list:
>>>
(*2) <$> [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
even <$> (2,2)
(2,True)
(<**>) :: Applicative f => f a -> f (a -> b) -> f b infixl 4 #
A variant of <*>
with the arguments reversed.
liftA :: Applicative f => (a -> b) -> f a -> f b #
Lift a function to actions.
Equivalent to Functor's fmap
but implemented using only Applicative
's methods:
liftA
f a = pure
f <*>
a
As such this function may be used to implement a Functor
instance from an Applicative
one.
Examples
Using the Applicative instance for Lists:
>>>
liftA (+1) [1, 2]
[2,3]
Or the Applicative instance for Maybe
>>>
liftA (+1) (Just 3)
Just 4
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d #
Lift a ternary function to actions.
asum :: (Foldable t, Alternative f) => t (f a) -> f a #
The sum of a collection of actions using (<|>)
, generalizing concat
.
asum
is just like msum
, but generalised to Alternative
.
Examples
Basic usage:
>>>
asum [Just "Hello", Nothing, Just "World"]
Just "Hello"
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.
See https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or
https://github.com/quchen/articles/blob/master/second_functor_law.md
for an explanation.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b #
fmap
is used to apply a function of type (a -> b)
to a value of type f a
,
where f is a functor, to produce a value of type f b
.
Note that for any type constructor with more than one parameter (e.g., Either
),
only the last type parameter can be modified with fmap
(e.g., b
in `Either a b`).
Some type constructors with two parameters or more have a
instance that allows
both the last and the penultimate parameters to be mapped over.Bifunctor
Examples
Convert from a
to a Maybe
IntMaybe String
using show
:
>>>
fmap show Nothing
Nothing>>>
fmap show (Just 3)
Just "3"
Convert from an
to an
Either
Int IntEither Int String
using show
:
>>>
fmap show (Left 17)
Left 17>>>
fmap show (Right 17)
Right "17"
Double each element of a list:
>>>
fmap (*2) [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
fmap even (2,2)
(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c)
can also be written (,,) a b c
and its Functor
instance
is defined for Functor ((,,) a b)
(i.e., only the third parameter is free to be mapped over
with fmap
).
It explains why fmap
can be used with tuples containing values of different types as in the
following example:
>>>
fmap even ("hello", 1.0, 4)
("hello",1.0,True)
Instances
Functor ZipList | Since: base-2.1 |
Functor Handler | Since: base-4.6.0.0 |
Functor Identity | Since: base-4.8.0.0 |
Functor First | Since: base-4.8.0.0 |
Functor Last | Since: base-4.8.0.0 |
Functor Down | Since: base-4.11.0.0 |
Functor First | Since: base-4.9.0.0 |
Functor Last | Since: base-4.9.0.0 |
Functor Max | Since: base-4.9.0.0 |
Functor Min | Since: base-4.9.0.0 |
Functor Dual | Since: base-4.8.0.0 |
Functor Product | Since: base-4.8.0.0 |
Functor Sum | Since: base-4.8.0.0 |
Functor NonEmpty | Since: base-4.9.0.0 |
Functor STM | Since: base-4.3.0.0 |
Functor Par1 | Since: base-4.9.0.0 |
Functor P | Since: base-4.8.0.0 |
Defined in Text.ParserCombinators.ReadP | |
Functor ReadP | Since: base-2.1 |
Functor IntMap | |
Functor Digit | |
Functor Elem | |
Functor FingerTree | |
Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> FingerTree a -> FingerTree b # (<$) :: a -> FingerTree b -> FingerTree a # | |
Functor Node | |
Functor Seq | |
Functor ViewL | |
Functor ViewR | |
Functor Tree | |
Functor IO | Since: base-2.1 |
Functor AnnotDetails | |
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> AnnotDetails a -> AnnotDetails b # (<$) :: a -> AnnotDetails b -> AnnotDetails a # | |
Functor Doc | |
Functor Span | |
Functor Q | |
Functor TyVarBndr | |
Functor Maybe | Since: base-2.1 |
Functor Solo | Since: base-4.15 |
Functor List | Since: base-2.1 |
Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a # | |
Functor (Either a) | Since: base-3.0 |
Functor (Arg a) | Since: base-4.9.0.0 |
Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor (Map k) | |
Monad m => Functor (Handler m) | |
Functor m => Functor (MaybeT m) | |
Functor (HashMap k) | |
Functor ((,) a) | Since: base-2.1 |
Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Functor (Const m :: Type -> Type) | Since: base-2.1 |
Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b # (<$) :: a -> Generically1 f b -> Generically1 f a # | |
Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
(Applicative f, Monad f) => Functor (WhenMissing f x) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a # | |
Functor m => Functor (AccumT w m) | |
Functor m => Functor (ExceptT e m) | |
Functor m => Functor (IdentityT m) | |
Functor m => Functor (ReaderT r m) | |
Functor m => Functor (SelectT r m) | |
Functor m => Functor (StateT s m) | |
Functor m => Functor (StateT s m) | |
Functor m => Functor (WriterT w m) | |
Functor m => Functor (WriterT w m) | |
Functor m => Functor (WriterT w m) | |
Functor ((,,) a b) | Since: base-4.14.0.0 |
(Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Functor f => Functor (WhenMatched f x y) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Functor (WhenMissing f k x) | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a # | |
Functor (ContT r m) | |
Functor ((,,,) a b c) | Since: base-4.14.0.0 |
Functor ((->) r) | Since: base-2.1 |
(Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
Functor f => Functor (WhenMatched f k x y) | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a # | |
Functor m => Functor (RWST r w s m) | |
Functor m => Functor (RWST r w s m) | |
Functor m => Functor (RWST r w s m) | |
Functor ((,,,,) a b c d) | Since: base-4.18.0.0 |
Functor ((,,,,,) a b c d e) | Since: base-4.18.0.0 |
Functor ((,,,,,,) a b c d e f) | Since: base-4.18.0.0 |
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
return
a>>=
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 Identity | Since: base-4.8.0.0 |
Monad First | Since: base-4.8.0.0 |
Monad Last | Since: base-4.8.0.0 |
Monad Down | Since: base-4.11.0.0 |
Monad First | Since: base-4.9.0.0 |
Monad Last | Since: base-4.9.0.0 |
Monad Max | Since: base-4.9.0.0 |
Monad Min | Since: base-4.9.0.0 |
Monad Dual | Since: base-4.8.0.0 |
Monad Product | Since: base-4.8.0.0 |
Monad Sum | Since: base-4.8.0.0 |
Monad NonEmpty | Since: base-4.9.0.0 |
Monad STM | Since: base-4.3.0.0 |
Monad Par1 | Since: base-4.9.0.0 |
Monad P | Since: base-2.1 |
Monad ReadP | Since: base-2.1 |
Monad Seq | |
Monad Tree | |
Monad IO | Since: base-2.1 |
Monad Q | |
Monad Maybe | Since: base-2.1 |
Monad Solo | Since: base-4.15 |
Monad List | Since: base-2.1 |
Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a # | |
Monad (Either e) | Since: base-4.4.0.0 |
Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Monad m => Monad (MaybeT m) | |
Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
(Applicative f, Monad f) => Monad (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # return :: a -> WhenMissing f x a # | |
(Monoid w, Functor m, Monad m) => Monad (AccumT w m) | |
Monad m => Monad (ExceptT e m) | |
Monad m => Monad (IdentityT m) | |
Monad m => Monad (ReaderT r m) | |
Monad m => Monad (SelectT r m) | |
Monad m => Monad (StateT s m) | |
Monad m => Monad (StateT s m) | |
Monad m => Monad (WriterT w m) | |
(Monoid w, Monad m) => Monad (WriterT w m) | |
(Monoid w, Monad m) => Monad (WriterT w m) | |
(Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
(Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Monad (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # return :: a -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Monad (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a # | |
Monad (ContT r m) | |
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
Monad ((->) r) | Since: base-2.1 |
Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Monad (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a # | |
Monad m => Monad (RWST r w s m) | |
(Monoid w, Monad m) => Monad (RWST r w s m) | |
(Monoid w, Monad m) => Monad (RWST r w s m) | |
class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where #
Monads that also support choice and failure.
Minimal complete definition
Nothing
Methods
The identity of mplus
. It should also satisfy the equations
mzero >>= f = mzero v >> mzero = mzero
The default definition is
mzero = empty
An associative operation. The default definition is
mplus = (<|>
)
Instances
MonadPlus STM | Takes the first non- Since: base-4.3.0.0 |
MonadPlus P | Since: base-2.1 |
Defined in Text.ParserCombinators.ReadP | |
MonadPlus ReadP | Since: base-2.1 |
MonadPlus Seq | |
MonadPlus IO | Takes the first non-throwing Since: base-4.9.0.0 |
MonadPlus Maybe | Picks the leftmost Since: base-2.1 |
MonadPlus List | Combines lists by concatenation, starting from the empty list. Since: base-2.1 |
MonadPlus (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Monad m => MonadPlus (MaybeT m) | |
MonadPlus f => MonadPlus (Ap f) | Since: base-4.12.0.0 |
MonadPlus f => MonadPlus (Alt f) | Since: base-4.8.0.0 |
MonadPlus f => MonadPlus (Rec1 f) | Since: base-4.9.0.0 |
(Monoid w, Functor m, MonadPlus m) => MonadPlus (AccumT w m) | |
(Monad m, Monoid e) => MonadPlus (ExceptT e m) | |
MonadPlus m => MonadPlus (IdentityT m) | |
MonadPlus m => MonadPlus (ReaderT r m) | |
MonadPlus m => MonadPlus (SelectT r m) | |
MonadPlus m => MonadPlus (StateT s m) | |
MonadPlus m => MonadPlus (StateT s m) | |
(Functor m, MonadPlus m) => MonadPlus (WriterT w m) | |
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) | |
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) | |
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) | Since: base-4.9.0.0 |
MonadPlus f => MonadPlus (M1 i c f) | Since: base-4.9.0.0 |
(Functor m, MonadPlus m) => MonadPlus (RWST r w s m) | |
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) | |
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) | |
class Monad m => MonadFail (m :: Type -> Type) where #
When a value is bound in do
-notation, the pattern on the left
hand side of <-
might not match. In this case, this class
provides a function to recover.
A Monad
without a MonadFail
instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat
).
Instances of MonadFail
should satisfy the following law: fail s
should
be a left zero for >>=
,
fail s >>= f = fail s
If your Monad
is also MonadPlus
, a popular definition is
fail _ = mzero
fail s
should be an action that runs in the monad itself, not an
exception (except in instances of MonadIO
). In particular,
fail
should not be implemented in terms of error
.
Since: base-4.9.0.0
Instances
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.
'
' can be understood as the 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
forever :: Applicative f => f a -> f b #
Repeat an action indefinitely.
Examples
A common use of forever
is to process input from network sockets,
Handle
s, and channels
(e.g. MVar
and
Chan
).
For example, here is how we might implement an echo
server, using
forever
both to listen for client connections on a network socket
and to echo client input on client connection handles:
echoServer :: Socket -> IO () echoServer socket =forever
$ do client <- accept socketforkFinally
(echo client) (\_ -> hClose client) where echo :: Handle -> IO () echo client =forever
$ hGetLine client >>= hPutStrLn client
Note that "forever" isn't necessarily non-terminating.
If the action is in a
and short-circuits after some number of iterations.
then MonadPlus
actually returns forever
mzero
, effectively short-circuiting its caller.
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
otherwise. For example: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)
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=
, but with the arguments interchanged.
when :: Applicative f => Bool -> f () -> f () #
Conditional execution of Applicative
expressions. For example,
when debug (putStrLn "Debugging")
will output the string Debugging
if the Boolean value debug
is True
, and otherwise do nothing.
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r #
Promote a function to a monad, scanning the monadic arguments from left to right. For example,
liftM2 (+) [0,1] [0,2] = [0,2,1,3] liftM2 (+) (Just 1) Nothing = Nothing
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
void :: Functor f => f a -> f () #
discards or ignores the result of evaluation, such
as the return value of an void
valueIO
action.
Examples
Replace the contents of a
with unit:Maybe
Int
>>>
void Nothing
Nothing>>>
void (Just 3)
Just ()
Replace the contents of an
with unit, resulting in an Either
Int
Int
:Either
Int
()
>>>
void (Left 8675309)
Left 8675309>>>
void (Right 8675309)
Right ()
Replace every element of a list with unit:
>>>
void [1,2,3]
[(),(),()]
Replace the second element of a pair with unit:
>>>
void (1,2)
(1,())
Discard the result of an IO
action:
>>>
mapM print [1,2]
1 2 [(),()]>>>
void $ mapM print [1,2]
1 2
filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a] #
This generalizes the list-based filter
function.
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #
Left-to-right composition of Kleisli arrows.
'(bs
' can be understood as the >=>
cs) ado
expression
do b <- bs a cs b
mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) #
The mapAndUnzipM
function maps its first argument over a list, returning
the result as a pair of lists. This function is mainly used with complicated
data structures or a state monad.
zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] #
zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () #
foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #
The foldM
function is analogous to foldl
, except that its result is
encapsulated in a monad. Note that foldM
works from left-to-right over
the list arguments. This could be an issue where (
and the `folded
function' are not commutative.>>
)
foldM f a1 [x1, x2, ..., xm] == do a2 <- f a1 x1 a3 <- f a2 x2 ... f am xm
If right-to-left evaluation is required, the input list should be reversed.
foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () #
Like foldM
, but discards the result.
replicateM :: Applicative m => Int -> m a -> m [a] #
performs the action replicateM
n actact
n
times,
and then returns the list of results:
Examples
>>>
import Control.Monad.State
>>>
runState (replicateM 3 $ state $ \s -> (s, s + 1)) 1
([1,2,3],4)
replicateM_ :: Applicative m => Int -> m a -> m () #
unless :: Applicative f => Bool -> f () -> f () #
The reverse of when
.
module Data.Functor
class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where #
A bifunctor is a type constructor that takes
two type arguments and is a functor in both arguments. That
is, unlike with Functor
, a type constructor such as Either
does not need to be partially applied for a Bifunctor
instance, and the methods in this class permit mapping
functions over the Left
value or the Right
value,
or both at the same time.
Formally, the class Bifunctor
represents a bifunctor
from Hask
-> Hask
.
Intuitively it is a bifunctor where both the first and second arguments are covariant.
You can define a Bifunctor
by either defining bimap
or by
defining both first
and second
. A partially applied Bifunctor
must be a Functor
and the second
method must agree with fmap
.
From this it follows that:
second
id
=id
If you supply bimap
, you should ensure that:
bimap
id
id
≡id
If you supply first
and second
, ensure:
first
id
≡id
second
id
≡id
If you supply both, you should also ensure:
bimap
f g ≡first
f.
second
g
These ensure by parametricity:
bimap
(f.
g) (h.
i) ≡bimap
f h.
bimap
g ifirst
(f.
g) ≡first
f.
first
gsecond
(f.
g) ≡second
f.
second
g
Since 4.18.0.0 Functor
is a superclass of 'Bifunctor.
Since: base-4.8.0.0
Methods
Instances
Bifunctor Either | Since: base-4.8.0.0 |
Bifunctor Arg | Since: base-4.9.0.0 |
Bifunctor (,) | Class laws for tuples hold only up to laziness. Both
Since: base-4.8.0.0 |
Bifunctor (Const :: Type -> Type -> Type) | Since: base-4.8.0.0 |
Bifunctor ((,,) x1) | Since: base-4.8.0.0 |
Bifunctor (K1 i :: Type -> Type -> Type) | Since: base-4.9.0.0 |
Bifunctor ((,,,) x1 x2) | Since: base-4.8.0.0 |
Bifunctor ((,,,,) x1 x2 x3) | Since: base-4.8.0.0 |
Bifunctor ((,,,,,) x1 x2 x3 x4) | Since: base-4.8.0.0 |
Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) | Since: base-4.8.0.0 |
module Data.Function
module Data.Functor.Identity
module Data.Int
module Data.Word
module Data.Void
module Data.Bool
module Data.Char
module Data.Ord
Boolean monoid under disjunction (||)
.
Any x <> Any y = Any (x || y)
Examples
>>>
Any True <> mempty <> Any False
Any {getAny = True}
>>>
mconcat (map (\x -> Any (even x)) [2,4,6,7,8])
Any {getAny = True}
>>>
Any False <> mempty
Any {getAny = False}
Instances
Monoid Any | Since: base-2.1 |
Semigroup Any | Since: base-4.9.0.0 |
Bounded Any | Since: base-2.1 |
Generic Any | |
Read Any | Since: base-2.1 |
Show Any | Since: base-2.1 |
NFData Any | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq Any | Since: base-2.1 |
Ord Any | Since: base-2.1 |
type Rep Any | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
You can alternatively define sconcat
instead of (<>
), in which case the
laws are:
Since: base-4.9.0.0
Methods
(<>) :: a -> a -> a infixr 6 #
An associative operation.
Examples
>>>
[1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
>>>
Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]
>>>
putStr "Hello, " <> putStrLn "World!"
Hello, World!
Reduce a non-empty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
Examples
For the following examples, we will assume that we have:
>>>
import Data.List.NonEmpty (NonEmpty (..))
>>>
sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"
>>>
sconcat $ Just [1, 2, 3] :| [Nothing, Just [4, 5, 6]]
Just [1,2,3,4,5,6]
>>>
sconcat $ Left 1 :| [Right 2, Left 3, Right 4]
Right 2
stimes :: Integral b => b -> a -> a #
Repeat a value n
times.
The default definition will raise an exception for a multiplier that is <= 0
.
This may be overridden with an implementation that is total. For monoids
it is preferred to use stimesMonoid
.
By making this a member of the class, idempotent semigroups
and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by
picking stimes =
or stimesIdempotent
stimes =
respectively.stimesIdempotentMonoid
Examples
>>>
stimes 4 [1]
[1,1,1,1]
>>>
stimes 5 (putStr "hi!")
hi!hi!hi!hi!hi!
>>>
stimes 3 (Right ":)")
Right ":)"
Instances
Monoid under addition.
Sum a <> Sum b = Sum (a + b)
Examples
>>>
Sum 1 <> Sum 2 <> mempty
Sum {getSum = 3}
>>>
mconcat [ Sum n | n <- [3 .. 9]]
Sum {getSum = 42}
Instances
Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
Traversable Sum | Since: base-4.8.0.0 |
Applicative Sum | Since: base-4.8.0.0 |
Functor Sum | Since: base-4.8.0.0 |
Monad Sum | Since: base-4.8.0.0 |
NFData1 Sum | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Generic1 Sum | |
Num a => Monoid (Sum a) | Since: base-2.1 |
Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Sum a) | Since: base-2.1 |
Generic (Sum a) | |
Num a => Num (Sum a) | Since: base-4.7.0.0 |
Read a => Read (Sum a) | Since: base-2.1 |
Show a => Show (Sum a) | Since: base-2.1 |
NFData a => NFData (Sum a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (Sum a) | Since: base-2.1 |
Ord a => Ord (Sum a) | Since: base-2.1 |
type Rep1 Sum | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
type Rep (Sum a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
Monoid under multiplication.
Product x <> Product y == Product (x * y)
Examples
>>>
Product 3 <> Product 4 <> mempty
Product {getProduct = 12}
>>>
mconcat [ Product n | n <- [2 .. 10]]
Product {getProduct = 3628800}
Constructors
Product | |
Fields
|
Instances
Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
Traversable Product | Since: base-4.8.0.0 |
Applicative Product | Since: base-4.8.0.0 |
Functor Product | Since: base-4.8.0.0 |
Monad Product | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal |