| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Imports
Description
Imports that are supposed to be used in all wire-server code.
Synopsis
- 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
- class Bounded a where
- class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
- class Eq a where
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class (Real a, Enum a) => Integral a where
- class Num a where
- class Eq a => Ord a where
- class Read a where
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
- atan2 :: a -> a -> a
- class (Real a, Fractional a) => RealFrac a where
- class Show a where
- data Double
- data Float
- data Integer
- type Rational = Ratio Integer
- data IO a
- type FilePath = String
- read :: Read a => String -> a
- reads :: Read a => ReadS a
- lex :: ReadS String
- readParen :: Bool -> ReadS a -> ReadS a
- type ReadS a = String -> [(a, String)]
- lcm :: Integral a => a -> a -> a
- gcd :: Integral a => a -> a -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- odd :: Integral a => a -> Bool
- even :: Integral a => a -> Bool
- showParen :: Bool -> ShowS -> ShowS
- showString :: String -> ShowS
- showChar :: Char -> ShowS
- shows :: Show a => a -> ShowS
- type ShowS = String -> String
- subtract :: Num a => a -> a -> a
- ($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
- error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
- (<$) :: Functor f => a -> f b -> f a
- class Functor f => Applicative (f :: Type -> Type) where
- newtype WrappedMonad (m :: Type -> Type) a = WrapMonad {
- unwrapMonad :: m a
- newtype WrappedArrow (a :: Type -> Type -> Type) b c = WrapArrow {
- unwrapArrow :: a b c
- newtype ZipList a = ZipList {
- getZipList :: [a]
- newtype Const a (b :: k) = Const {
- getConst :: a
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- liftA :: Applicative f => (a -> b) -> f a -> f b
- (<**>) :: Applicative f => f a -> f (a -> b) -> f b
- class Applicative f => Alternative (f :: Type -> Type) where
- (<|>) :: f a -> f a -> f a
- guard :: Alternative f => Bool -> f ()
- join :: Monad m => m (m a) -> m a
- class Applicative m => Monad (m :: Type -> Type) where
- class Functor (f :: Type -> Type) where
- class Monad m => MonadFail (m :: Type -> Type) where
- mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
- unless :: Applicative f => Bool -> f () -> f ()
- replicateM_ :: Applicative m => Int -> m a -> m ()
- replicateM :: Applicative m => Int -> m a -> m [a]
- foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
- foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()
- zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]
- mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])
- forever :: Applicative f => f a -> f b
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
- void :: Functor f => f a -> f ()
- ap :: Monad m => m (a -> b) -> m a -> m b
- liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
- liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
- liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- when :: Applicative f => Bool -> f () -> f ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- module Data.Functor
- class 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
- class Semigroup a where
- mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
- cycle1 :: Semigroup m => m -> m
- newtype Min a = Min {
- getMin :: a
- newtype Max a = Max {
- getMax :: a
- data Arg a b = Arg a b
- type ArgMin a b = Min (Arg a b)
- type ArgMax a b = Max (Arg a b)
- newtype First a = First {
- getFirst :: a
- newtype Last a = Last {
- getLast :: a
- newtype WrappedMonoid m = WrapMonoid {
- unwrapMonoid :: m
- getOption :: Option a -> Maybe a
- stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
- stimesIdempotent :: Integral b => b -> a -> a
- newtype Dual a = Dual {
- getDual :: a
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype All = All {}
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
- (<>) :: Semigroup a => a -> a -> a
- class Semigroup a => Monoid a where
- newtype Ap (f :: k -> Type) (a :: k) = Ap {
- getAp :: f a
- newtype Dual a = Dual {
- getDual :: a
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype All = All {}
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype Alt (f :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
- module Data.Maybe
- module Data.Either
- module Data.Foldable
- module Data.Traversable
- module Data.Tuple
- module Data.String
- (++) :: [a] -> [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- map :: (a -> b) -> [a] -> [b]
- elem :: (Foldable t, Eq a) => a -> t a -> Bool
- minimum :: (Foldable t, Ord a) => t a -> a
- maximum :: (Foldable t, Ord a) => t a -> a
- foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
- product :: (Foldable t, Num a) => t a -> a
- sum :: (Foldable t, Num a) => t a -> a
- foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
- foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b
- null :: Foldable t => t a -> Bool
- length :: Foldable t => t a -> Int
- foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
- isSubsequenceOf :: Eq a => [a] -> [a] -> Bool
- mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
- mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
- find :: Foldable t => (a -> Bool) -> t a -> Maybe a
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- or :: Foldable t => t Bool -> Bool
- and :: Foldable t => t Bool -> Bool
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- unwords :: [String] -> String
- words :: String -> [String]
- unlines :: [String] -> String
- lines :: String -> [String]
- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- sort :: Ord a => [a] -> [a]
- permutations :: [a] -> [[a]]
- subsequences :: [a] -> [[a]]
- tails :: [a] -> [[a]]
- inits :: [a] -> [[a]]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- group :: Eq a => [a] -> [[a]]
- deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])
- unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])
- unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])
- unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
- zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]
- zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]
- zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]
- zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
- zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]
- zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]
- zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]
- zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
- genericReplicate :: Integral i => i -> a -> [a]
- genericIndex :: Integral i => [a] -> i -> a
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericDrop :: Integral i => i -> [a] -> [a]
- genericTake :: Integral i => i -> [a] -> [a]
- genericLength :: Num i => [a] -> i
- insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
- partition :: (a -> Bool) -> [a] -> ([a], [a])
- transpose :: [[a]] -> [[a]]
- intercalate :: [a] -> [[a]] -> [a]
- intersperse :: a -> [a] -> [a]
- intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersect :: Eq a => [a] -> [a] -> [a]
- unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- union :: Eq a => [a] -> [a] -> [a]
- (\\) :: Eq a => [a] -> [a] -> [a]
- deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- nub :: Eq a => [a] -> [a]
- isInfixOf :: Eq a => [a] -> [a] -> Bool
- isSuffixOf :: Eq a => [a] -> [a] -> Bool
- isPrefixOf :: Eq a => [a] -> [a] -> Bool
- findIndices :: (a -> Bool) -> [a] -> [Int]
- findIndex :: (a -> Bool) -> [a] -> Maybe Int
- elemIndices :: Eq a => a -> [a] -> [Int]
- elemIndex :: Eq a => a -> [a] -> Maybe Int
- stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
- dropWhileEnd :: (a -> Bool) -> [a] -> [a]
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip :: [(a, b)] -> ([a], [b])
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- (!!) :: [a] -> Int -> a
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- reverse :: [a] -> [a]
- break :: (a -> Bool) -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- splitAt :: Int -> [a] -> ([a], [a])
- drop :: Int -> [a] -> [a]
- take :: Int -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- cycle :: [a] -> [a]
- replicate :: Int -> a -> [a]
- repeat :: a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- iterate :: (a -> a) -> a -> [a]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- foldl1' :: (a -> a -> a) -> [a] -> a
- init :: [a] -> [a]
- last :: [a] -> a
- tail :: [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- head :: [a] -> a
- 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
- deepseq :: NFData a => a -> b -> b
- class NFData a where
- rnf :: a -> ()
- stderr :: Handle
- stdin :: Handle
- stdout :: Handle
- data BufferMode
- data SeekMode
- data IOMode
- hReady :: MonadIO m => Handle -> m Bool
- hWaitForInput :: MonadIO m => Handle -> Int -> m Bool
- hGetEcho :: MonadIO m => Handle -> m Bool
- hSetEcho :: MonadIO m => Handle -> Bool -> m ()
- hIsTerminalDevice :: MonadIO m => Handle -> m Bool
- hIsSeekable :: MonadIO m => Handle -> m Bool
- hIsWritable :: MonadIO m => Handle -> m Bool
- hIsReadable :: MonadIO m => Handle -> m Bool
- hIsClosed :: MonadIO m => Handle -> m Bool
- hIsOpen :: MonadIO m => Handle -> m Bool
- hTell :: MonadIO m => Handle -> m Integer
- hSeek :: MonadIO m => Handle -> SeekMode -> Integer -> m ()
- hGetBuffering :: MonadIO m => Handle -> m BufferMode
- hSetBuffering :: MonadIO m => Handle -> BufferMode -> m ()
- hIsEOF :: MonadIO m => Handle -> m Bool
- hSetFileSize :: MonadIO m => Handle -> Integer -> m ()
- hFileSize :: MonadIO m => Handle -> m Integer
- hFlush :: MonadIO m => Handle -> m ()
- hClose :: MonadIO m => Handle -> m ()
- openFile :: MonadIO m => FilePath -> IOMode -> m Handle
- withBinaryFile :: MonadUnliftIO m => FilePath -> IOMode -> (Handle -> m a) -> m a
- withFile :: MonadUnliftIO m => FilePath -> IOMode -> (Handle -> m a) -> m a
- exeExtension :: String
- setOwnerSearchable :: Bool -> Permissions -> Permissions
- setOwnerExecutable :: Bool -> Permissions -> Permissions
- setOwnerWritable :: Bool -> Permissions -> Permissions
- setOwnerReadable :: Bool -> Permissions -> Permissions
- emptyPermissions :: Permissions
- searchable :: Permissions -> Bool
- executable :: Permissions -> Bool
- readable :: Permissions -> Bool
- writable :: Permissions -> Bool
- data XdgDirectory
- setModificationTime :: MonadIO m => FilePath -> UTCTime -> m ()
- setAccessTime :: MonadIO m => FilePath -> UTCTime -> m ()
- getModificationTime :: MonadIO m => FilePath -> m UTCTime
- getAccessTime :: MonadIO m => FilePath -> m UTCTime
- copyPermissions :: MonadIO m => FilePath -> FilePath -> m ()
- setPermissions :: MonadIO m => FilePath -> Permissions -> m ()
- getPermissions :: MonadIO m => FilePath -> m Permissions
- pathIsSymbolicLink :: MonadIO m => FilePath -> m Bool
- doesDirectoryExist :: MonadIO m => FilePath -> m Bool
- doesFileExist :: MonadIO m => FilePath -> m Bool
- doesPathExist :: MonadIO m => FilePath -> m Bool
- getFileSize :: MonadIO m => FilePath -> m Integer
- findFilesWith :: MonadUnliftIO m => (FilePath -> m Bool) -> [FilePath] -> String -> m [FilePath]
- findFileWith :: MonadUnliftIO m => (FilePath -> m Bool) -> [FilePath] -> String -> m (Maybe FilePath)
- findFiles :: MonadIO m => [FilePath] -> String -> m [FilePath]
- findFile :: MonadIO m => [FilePath] -> String -> m (Maybe FilePath)
- findExecutablesInDirectories :: MonadIO m => [FilePath] -> String -> m [FilePath]
- findExecutables :: MonadIO m => String -> m [FilePath]
- findExecutable :: MonadIO m => String -> m (Maybe FilePath)
- makeRelativeToCurrentDirectory :: MonadIO m => FilePath -> m FilePath
- makeAbsolute :: MonadIO m => FilePath -> m FilePath
- canonicalizePath :: MonadIO m => FilePath -> m FilePath
- copyFileWithMetadata :: MonadIO m => FilePath -> FilePath -> m ()
- copyFile :: MonadIO m => FilePath -> FilePath -> m ()
- renamePath :: MonadIO m => FilePath -> FilePath -> m ()
- renameFile :: MonadIO m => FilePath -> FilePath -> m ()
- removeFile :: MonadIO m => FilePath -> m ()
- getTemporaryDirectory :: MonadIO m => m FilePath
- getUserDocumentsDirectory :: MonadIO m => m FilePath
- getAppUserDataDirectory :: MonadIO m => FilePath -> m FilePath
- getXdgDirectory :: MonadIO m => XdgDirectory -> FilePath -> m FilePath
- getHomeDirectory :: MonadIO m => m FilePath
- withCurrentDirectory :: MonadUnliftIO m => FilePath -> m a -> m a
- setCurrentDirectory :: MonadIO m => FilePath -> m ()
- getCurrentDirectory :: MonadIO m => m FilePath
- getDirectoryContents :: MonadIO m => FilePath -> m [FilePath]
- listDirectory :: MonadIO m => FilePath -> m [FilePath]
- renameDirectory :: MonadIO m => FilePath -> FilePath -> m ()
- removePathForcibly :: MonadIO m => FilePath -> m ()
- removeDirectoryRecursive :: MonadIO m => FilePath -> m ()
- removeDirectory :: MonadIO m => FilePath -> m ()
- createFileLink :: MonadIO m => FilePath -> FilePath -> m ()
- createDirectoryIfMissing :: MonadIO m => Bool -> FilePath -> m ()
- createDirectory :: MonadIO m => FilePath -> m ()
- putChar :: MonadIO m => Char -> m ()
- putStr :: MonadIO m => String -> m ()
- putStrLn :: MonadIO m => String -> m ()
- print :: (Show a, MonadIO m) => a -> m ()
- getChar :: MonadIO m => m Char
- getLine :: MonadIO m => m String
- getContents :: MonadIO m => m String
- interact :: MonadIO m => (String -> String) -> m ()
- readFile :: MonadIO m => FilePath -> m String
- writeFile :: MonadIO m => FilePath -> String -> m ()
- appendFile :: MonadIO m => FilePath -> String -> m ()
- readIO :: (Read a, MonadIO m) => String -> m a
- readLn :: (Read a, MonadIO m) => m a
- 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))
Base
seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b infixr 0 Source #
The value of seq a b is bottom if a is bottom, and
otherwise equal to b. In other words, it evaluates the first
argument a to weak head normal form (WHNF). seq is usually
introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does
not guarantee that a will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
fromIntegral :: (Integral a, Num b) => a -> b Source #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b Source #
general coercion to fractional types
class Bounded a where Source #
The Bounded class is used to name the upper and lower limits of a
type. Ord is not a superclass of Bounded since types that are not
totally ordered may also have upper and lower bounds.
The Bounded class may be derived for any enumeration type;
minBound is the first constructor listed in the data declaration
and maxBound is the last.
Bounded may also be derived for single-constructor datatypes whose
constituent types are in Bounded.
Instances
| Bounded Bool | Since: base-2.1 |
| Bounded Char | Since: base-2.1 |
| Bounded Int | Since: base-2.1 |
| Bounded Int8 | Since: base-2.1 |
| Bounded Int16 | Since: base-2.1 |
| Bounded Int32 | Since: base-2.1 |
| Bounded Int64 | Since: base-2.1 |
| Bounded Ordering | Since: base-2.1 |
| Bounded Word | Since: base-2.1 |
| Bounded Word8 | Since: base-2.1 |
| Bounded Word16 | Since: base-2.1 |
| Bounded Word32 | Since: base-2.1 |
| Bounded Word64 | Since: base-2.1 |
| Bounded VecCount | Since: base-4.10.0.0 |
| Bounded VecElem | Since: base-4.10.0.0 |
| Bounded () | Since: base-2.1 |
| Bounded All | Since: base-2.1 |
| Bounded Any | Since: base-2.1 |
| Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded CChar | |
| Bounded CSChar | |
| Bounded CUChar | |
| Bounded CShort | |
| Bounded CUShort | |
| Bounded CInt | |
| Bounded CUInt | |
| Bounded CLong | |
| Bounded CULong | |
| Bounded CLLong | |
| Bounded CULLong | |
| Bounded CBool | |
| Bounded CPtrdiff | |
| Bounded CSize | |
| Bounded CWchar | |
| Bounded CSigAtomic | |
Defined in Foreign.C.Types | |
| Bounded CIntPtr | |
| Bounded CUIntPtr | |
| Bounded CIntMax | |
| Bounded CUIntMax | |
| Bounded GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode | |
| Bounded FileType | |
| Bounded XdgDirectory | |
Defined in System.Directory.Internal.Common | |
| Bounded XdgDirectoryList | |
Defined in System.Directory.Internal.Common | |
| Bounded a => Bounded (Min a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Max a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Last a) | Since: base-4.9.0.0 |
| Bounded m => Bounded (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Dual a) | Since: base-2.1 |
| Bounded a => Bounded (Sum a) | Since: base-2.1 |
| Bounded a => Bounded (Product a) | Since: base-2.1 |
| Bounded a => Bounded (Down a) | Since: base-4.14.0.0 |
| (Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | 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 d) => Bounded (a, b, c, d) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum from 0 through n-1.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum,
the following should hold:
- The calls
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBoundMethods
the successor of a value. For numeric types, succ adds 1.
the predecessor of a value. For numeric types, pred subtracts 1.
Convert from an Int.
Convert to an Int.
It is implementation-dependent what fromEnum returns when
applied to a value that is too large to fit in an Int.
Used in Haskell's translation of [n..] with [n..] = enumFrom n,
a possible implementation being enumFrom n = n : enumFrom (succ n).
For example:
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] Source #
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] Source #
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] Source #
Used in Haskell's translation of [n,n'..m] with
[n,n'..m] = enumFromThenTo n n' m, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m,
x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
For example:
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
The Eq class defines equality (==) and inequality (/=).
All the basic datatypes exported by the Prelude are instances of Eq,
and Eq may be derived for any datatype whose constituents are also
instances of Eq.
The Haskell Report defines no laws for Eq. However, == is customarily
expected to implement an equivalence relationship where two values comparing
equal are indistinguishable by "public" functions, with a "public" function
being one not allowing to see implementation details. For example, for a
type representing non-normalised natural numbers modulo 100, a "public"
function doesn't make the difference between 1 and 201. It is expected to
have the following properties:
Instances
| 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 Int8 | Since: base-2.1 |
| Eq Int16 | Since: base-2.1 |
| Eq Int32 | Since: base-2.1 |
| Eq Int64 | Since: base-2.1 |
| Eq Integer | |
| Eq Natural | Since: base-4.8.0.0 |
| Eq Ordering | |
| Eq Word | |
| Eq Word8 | Since: base-2.1 |
| Eq Word16 | Since: base-2.1 |
| Eq Word32 | Since: base-2.1 |
| Eq Word64 | Since: base-2.1 |
| Eq SomeTypeRep | |
Defined in Data.Typeable.Internal Methods (==) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # | |
| Eq () | |
| Eq TyCon | |
| Eq Module | |
| Eq TrName | |
| Eq Handle | Since: base-4.1.0.0 |
| Eq ThreadId | Since: base-4.2.0.0 |
| Eq Void | Since: base-4.8.0.0 |
| Eq SpecConstrAnnotation | Since: base-4.3.0.0 |
Defined in GHC.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source # | |
| Eq Version | Since: base-2.1 |
| Eq BlockReason | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methods (==) :: BlockReason -> BlockReason -> Bool Source # (/=) :: BlockReason -> BlockReason -> Bool Source # | |
| Eq ThreadStatus | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methods (==) :: ThreadStatus -> ThreadStatus -> Bool Source # (/=) :: ThreadStatus -> ThreadStatus -> Bool Source # | |
| Eq AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool Source # (/=) :: AsyncException -> AsyncException -> Bool Source # | |
| Eq ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool Source # (/=) :: ArrayException -> ArrayException -> Bool Source # | |
| Eq ExitCode | |
| Eq IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool Source # (/=) :: IOErrorType -> IOErrorType -> Bool Source # | |
| Eq BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods (==) :: BufferMode -> BufferMode -> Bool Source # (/=) :: BufferMode -> BufferMode -> Bool Source # | |
| Eq Newline | Since: base-4.2.0.0 |
| Eq NewlineMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods (==) :: NewlineMode -> NewlineMode -> Bool Source # (/=) :: NewlineMode -> NewlineMode -> Bool Source # | |
| Eq IODeviceType | Since: base-4.2.0.0 |
Defined in GHC.IO.Device Methods (==) :: IODeviceType -> IODeviceType -> Bool Source # (/=) :: IODeviceType -> IODeviceType -> Bool Source # | |
| Eq SeekMode | Since: base-4.2.0.0 |
| Eq MaskingState | Since: base-4.3.0.0 |
Defined in GHC.IO Methods (==) :: MaskingState -> MaskingState -> Bool Source # (/=) :: MaskingState -> MaskingState -> Bool Source # | |
| Eq IOException | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception Methods (==) :: IOException -> IOException -> Bool Source # (/=) :: IOException -> IOException -> Bool Source # | |
| Eq ArithException | Since: base-3.0 |
Defined in GHC.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool Source # (/=) :: ArithException -> ArithException -> Bool Source # | |
| Eq All | Since: base-2.1 |
| Eq Any | Since: base-2.1 |
| Eq Fixity | Since: base-4.6.0.0 |
| Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods (==) :: Associativity -> Associativity -> Bool Source # (/=) :: Associativity -> Associativity -> Bool Source # | |
| Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # | |
| Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool Source # (/=) :: SourceStrictness -> SourceStrictness -> Bool Source # | |
| Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # | |
| Eq CChar | |
| Eq CSChar | |
| Eq CUChar | |
| Eq CShort | |
| Eq CUShort | |
| Eq CInt | |
| Eq CUInt | |
| Eq CLong | |
| Eq CULong | |
| Eq CLLong | |
| Eq CULLong | |
| Eq CBool | |
| Eq CFloat | |
| Eq CDouble | |
| Eq CPtrdiff | |
| Eq CSize | |
| Eq CWchar | |
| Eq CSigAtomic | |
Defined in Foreign.C.Types Methods (==) :: CSigAtomic -> CSigAtomic -> Bool Source # (/=) :: CSigAtomic -> CSigAtomic -> Bool Source # | |
| Eq CClock | |
| Eq CTime | |
| Eq CUSeconds | |
| Eq CSUSeconds | |
Defined in Foreign.C.Types Methods (==) :: CSUSeconds -> CSUSeconds -> Bool Source # (/=) :: CSUSeconds -> CSUSeconds -> Bool Source # | |
| Eq CIntPtr | |
| Eq CUIntPtr | |
| Eq CIntMax | |
| Eq CUIntMax | |
| Eq IOMode | Since: base-4.2.0.0 |
| Eq GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode Methods (==) :: GeneralCategory -> GeneralCategory -> Bool Source # (/=) :: GeneralCategory -> GeneralCategory -> Bool Source # | |
| Eq SrcLoc | Since: base-4.9.0.0 |
| Eq ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods (==) :: ByteString -> ByteString -> Bool Source # (/=) :: ByteString -> ByteString -> Bool Source # | |
| Eq ByteString | |
Defined in Data.ByteString.Internal Methods (==) :: ByteString -> ByteString -> Bool Source # (/=) :: ByteString -> ByteString -> Bool Source # | |
| Eq FileType | |
| Eq Permissions | |
Defined in System.Directory.Internal.Common Methods (==) :: Permissions -> Permissions -> Bool Source # (/=) :: Permissions -> Permissions -> Bool Source # | |
| Eq XdgDirectory | |
Defined in System.Directory.Internal.Common Methods (==) :: XdgDirectory -> XdgDirectory -> Bool Source # (/=) :: XdgDirectory -> XdgDirectory -> Bool Source # | |
| Eq XdgDirectoryList | |
Defined in System.Directory.Internal.Common Methods (==) :: XdgDirectoryList -> XdgDirectoryList -> Bool Source # (/=) :: XdgDirectoryList -> XdgDirectoryList -> Bool Source # | |
| Eq BigNat | |
| Eq LocalTime | |
| Eq UTCTime | |
| Eq StringException | Since: unliftio-0.2.19 |
Defined in UnliftIO.Exception Methods (==) :: StringException -> StringException -> Bool Source # (/=) :: StringException -> StringException -> Bool Source # | |
| Eq a => Eq [a] | |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Eq a => Eq (Ratio a) | Since: base-2.1 |
| Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
| Eq a => Eq (Min a) | Since: base-4.9.0.0 |
| Eq a => Eq (Max a) | Since: base-4.9.0.0 |
| Eq a => Eq (First a) | Since: base-4.9.0.0 |
| Eq a => Eq (Last a) | Since: base-4.9.0.0 |
| Eq m => Eq (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # | |
| Eq a => Eq (Option a) | Since: base-4.9.0.0 |
| Eq (Chan a) | Since: base-4.4.0.0 |
| Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
| Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
| Eq (TVar a) | Since: base-4.8.0.0 |
| Eq (IORef a) | Pointer equality. Since: base-4.0.0.0 |
| Eq a => Eq (First a) | Since: base-2.1 |
| Eq a => Eq (Last a) | Since: base-2.1 |
| Eq a => Eq (Dual a) | Since: base-2.1 |
| Eq a => Eq (Sum a) | Since: base-2.1 |
| Eq a => Eq (Product a) | Since: base-2.1 |
| Eq a => Eq (Down a) | Since: base-4.6.0.0 |
| Eq (MVar a) | Since: base-4.1.0.0 |
| Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
| Eq a => Eq (Set a) | |
| Eq (TQueue a) | |
| Eq (TMVar a) | |
| Eq (TChan a) | |
| Eq (TBQueue a) | |
| Eq a => Eq (HashSet a) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| Eq (V1 p) | Since: base-4.9.0.0 |
| Eq (U1 p) | Since: base-4.9.0.0 |
| Eq (TypeRep a) | Since: base-2.1 |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
| (Eq k, Eq a) => Eq (Map k a) | |
| (Eq k, Eq v) => Eq (Leaf k v) | |
| (Eq k, Eq v) => Eq (HashMap k v) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
| 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 a, Eq b, Eq c) => Eq (a, b, c) | |
| 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 |
| (Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) | |
| Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
| (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 a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
| Eq (f (g p)) => Eq ((f :.: g) 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 Source #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (, +)(
and *)exp are customarily expected to define an exponential field and have
the following properties:
exp (a + b)=exp a * exp bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class Num a => Fractional a where Source #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, ( and
+)( are customarily expected to define a division ring and have the
following properties:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1
Note that it isn't customarily expected that a type instance of
Fractional implement a field. However, all instances in base do.
Minimal complete definition
fromRational, (recip | (/))
Methods
(/) :: a -> a -> a infixl 7 Source #
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a Source #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional CFloat | |
| Fractional CDouble | |
| Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
| Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
| Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
| Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
class (Real a, Enum a) => Integral a where Source #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div/mod and quot/rem pairs, given
suitable Euclidean functions f and g:
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for Integer's instance, is
abs.
Methods
quot :: a -> a -> a infixl 7 Source #
integer division truncated toward zero
rem :: a -> a -> a infixl 7 Source #
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7 Source #
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7 Source #
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a) Source #
divMod :: a -> a -> (a, a) Source #
toInteger :: a -> Integer Source #
conversion to Integer
Instances
| Integral Int | Since: base-2.0.1 |
| Integral Int8 | Since: base-2.1 |
Defined in GHC.Int | |
| Integral Int16 | Since: base-2.1 |
| Integral Int32 | Since: base-2.1 |
| Integral Int64 | Since: base-2.1 |
| Integral Integer | Since: |