| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
CorePrelude
Contents
- ($) :: (a -> b) -> a -> b
- ($!) :: (a -> b) -> a -> b
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- (.) :: Category k cat => forall b c a. cat b c -> cat a b -> cat a c
- not :: Bool -> Bool
- otherwise :: Bool
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- id :: Category k cat => forall a. cat a a
- maybe :: b -> (a -> b) -> Maybe a -> b
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- flip :: (a -> b -> c) -> b -> a -> c
- const :: a -> b -> a
- error :: HasCallStack => [Char] -> a
- putStr :: MonadIO m => Text -> m ()
- putStrLn :: MonadIO m => Text -> m ()
- print :: (MonadIO m, Show a) => a -> m ()
- getArgs :: MonadIO m => m [Text]
- terror :: HasCallStack => Text -> a
- odd :: Integral a => a -> Bool
- even :: Integral a => a -> Bool
- uncurry :: (a -> b -> c) -> (a, b) -> c
- curry :: ((a, b) -> c) -> a -> b -> c
- swap :: (a, b) -> (b, a)
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a -> a -> a
- undefined :: HasCallStack => a
- seq :: a -> b -> b
- class Eq a => Ord a where
- class Eq a where
- class Bounded a where
- class Enum a where
- class Show a
- class Read a
- class Functor f where
- class Applicative m => Monad m where
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- class IsString a where
- class Num a where
- class (Num a, Ord a) => Real a where
- class (Real a, Enum a) => Integral a where
- class Num a => Fractional a where
- class Fractional a => Floating a where
- class (Real a, Fractional a) => RealFrac a where
- class (RealFrac a, Floating a) => RealFloat a where
- data Maybe a :: * -> *
- data Ordering :: *
- data Bool :: *
- data Char :: *
- data IO a :: * -> *
- data Either a b :: * -> * -> *
- data ByteString :: *
- type LByteString = ByteString
- data Text :: *
- type LText = Text
- data Map k a :: * -> * -> *
- data HashMap k v :: * -> * -> *
- data IntMap a :: * -> *
- data Set a :: * -> *
- data HashSet a :: * -> *
- data IntSet :: *
- data Seq a :: * -> *
- data Vector a :: * -> *
- type UVector = Vector
- class (Vector Vector a, MVector MVector a) => Unbox a
- type SVector = Vector
- class Storable a
- class Hashable a where
- data Word :: *
- data Word8 :: *
- data Word32 :: *
- data Word64 :: *
- data Int :: *
- data Int32 :: *
- data Int64 :: *
- data Integer :: *
- type Rational = Ratio Integer
- data Float :: *
- data Double :: *
- (^) :: (Num a, Integral b) => a -> b -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- subtract :: Num a => a -> a -> a
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- class Monoid a where
- (<>) :: Monoid m => m -> m -> m
- class Foldable t
- asum :: (Foldable t, Alternative f) => t (f a) -> f a
- class (Functor t, Foldable t) => Traversable t
- first :: Arrow a => forall b c d. a b c -> a (b, d) (c, d)
- second :: Arrow a => forall b c d. a b c -> a (d, b) (d, c)
- (***) :: Arrow a => forall b c b' c'. a b c -> a b' c' -> a (b, b') (c, c')
- (&&&) :: Arrow a => forall b c c'. a b c -> a b c' -> a b (c, c')
- bool :: a -> a -> Bool -> a
- mapMaybe :: (a -> Maybe b) -> [a] -> [b]
- catMaybes :: [Maybe a] -> [a]
- fromMaybe :: a -> Maybe a -> a
- isJust :: Maybe a -> Bool
- isNothing :: Maybe a -> Bool
- listToMaybe :: [a] -> Maybe a
- maybeToList :: Maybe a -> [a]
- partitionEithers :: [Either a b] -> ([a], [b])
- lefts :: [Either a b] -> [a]
- rights :: [Either a b] -> [b]
- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
- comparing :: Ord a => (b -> a) -> b -> b -> Ordering
- equating :: Eq a => (b -> a) -> b -> b -> Bool
- newtype Down a :: * -> * = Down a
- class Functor f => Applicative f where
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- (<|>) :: Alternative f => forall a. f a -> f a -> f a
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- lift :: MonadTrans t => forall m a. Monad m => m a -> t m a
- class Monad m => MonadIO m where
- liftIO :: MonadIO m => forall a. IO a -> m a
- class (Typeable * e, Show e) => Exception e where
- class Typeable k a
- data SomeException :: *
- data IOException :: *
- module System.IO.Error
- type FilePath = String
- (</>) :: FilePath -> FilePath -> FilePath
- (<.>) :: FilePath -> String -> FilePath
- type String = [Char]
- hash :: Hashable a => a -> Int
- hashWithSalt :: Hashable a => Int -> a -> Int
Standard
Operators
($) :: (a -> b) -> a -> b infixr 0 #
Application operator. This operator is redundant, since ordinary
application (f x) means the same as (f . However, $ x)$ has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as map ($ 0) xszipWith ($) fs xs
($!) :: (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.
Functions
maybe :: b -> (a -> b) -> Maybe a -> b #
The maybe function takes a default value, a function, and a Maybe
value. If the Maybe value is Nothing, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just and returns the result.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed,
return twice the integer; that is, apply (*2) to it. If instead
we fail to parse an integer, return 0 by default:
>>>import Text.Read ( readMaybe )>>>maybe 0 (*2) (readMaybe "5")10>>>maybe 0 (*2) (readMaybe "")0
Apply show to a Maybe Int. If we have Just n, we want to show
the underlying Int n. But if we have Nothing, we return the
empty string instead of (for example) "Nothing":
>>>maybe "" show (Just 5)"5">>>maybe "" show Nothing""
either :: (a -> c) -> (b -> c) -> Either a b -> c #
Case analysis for the Either type.
If the value is Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft constructor and another using the Right constructor. Then
we apply "either" the length function (if we have a String)
or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
flip :: (a -> b -> c) -> b -> a -> c #
flip ff.
const x is a unary function which evaluates to x for all inputs.
For instance,
>>>map (const 42) [0..3][42,42,42,42]
error :: HasCallStack => [Char] -> a #
error stops execution and displays an error message.
terror :: HasCallStack => Text -> a Source #
error applied to Text
Since 0.4.1
uncurry :: (a -> b -> c) -> (a, b) -> c #
uncurry converts a curried function to a function on pairs.
until :: (a -> Bool) -> (a -> a) -> a -> a #
until p ff until p holds.
undefined :: HasCallStack => a #
The value of seq a b is bottom if a is bottom, and
otherwise equal to b. seq is usually introduced to
improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does
not guarantee that a will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
Type classes
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined
datatype whose constituent types are in Ord. The declared order
of the constructors in the data declaration determines the ordering
in derived Ord instances. The Ordering datatype allows a single
comparison to determine the precise ordering of two objects.
Minimal complete definition: either compare or <=.
Using compare can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering #
(<) :: a -> a -> Bool infix 4 #
(<=) :: a -> a -> Bool infix 4 #
(>) :: a -> a -> Bool infix 4 #
Instances
| Ord Bool | |
| Ord Char | |
| Ord Double | |
| Ord Float | |
| Ord Int | |
| Ord Int8 | |
| Ord Int16 | |
| Ord Int32 | |
| Ord Int64 | |
| Ord Integer | |
| Ord Ordering | |
| Ord Word | |
| Ord Word8 | |
| Ord Word16 | |
| Ord Word32 | |
| Ord Word64 | |
| Ord TypeRep | |
| Ord () | |
| Ord TyCon | |
| Ord BigNat | |
| Ord Void | |
| Ord Version | |
| Ord AsyncException | |
| Ord ArrayException | |
| Ord ExitCode | |
| Ord BufferMode | |
| Ord Newline | |
| Ord NewlineMode | |
| Ord CChar | |
| Ord CSChar | |
| Ord CUChar | |
| Ord CShort | |
| Ord CUShort | |
| Ord CInt | |
| Ord CUInt | |
| Ord CLong | |
| Ord CULong | |
| Ord CLLong | |
| Ord CULLong | |
| Ord CFloat | |
| Ord CDouble | |
| Ord CPtrdiff | |
| Ord CSize | |
| Ord CWchar | |
| Ord CSigAtomic | |
| Ord CClock | |
| Ord CTime | |
| Ord CUSeconds | |
| Ord CSUSeconds | |
| Ord CIntPtr | |
| Ord CUIntPtr | |
| Ord CIntMax | |
| Ord CUIntMax | |
| Ord All | |
| Ord Any | |
| Ord Fixity | |
| Ord Associativity | |
| Ord SourceUnpackedness | |
| Ord SourceStrictness | |
| Ord DecidedStrictness | |
| Ord ErrorCall | |
| Ord ArithException | |
| Ord SomeNat | |
| Ord SomeSymbol | |
| Ord ByteString | |
| Ord ByteString | |
| Ord IntSet | |
| Ord a => Ord [a] | |
| Ord a => Ord (Maybe a) | |
| Integral a => Ord (Ratio a) | |
| Ord (Ptr a) | |
| Ord (FunPtr a) | |
| Ord (V1 p) | |
| Ord (U1 p) | |
| Ord p => Ord (Par1 p) | |
| Ord (ForeignPtr a) | |
| Ord a => Ord (Identity a) | |
| Ord a => Ord (Min a) | |
| Ord a => Ord (Max a) | |
| Ord a => Ord (First a) | |
| Ord a => Ord (Last a) | |
| Ord m => Ord (WrappedMonoid m) | |
| Ord a => Ord (Option a) | |
| Ord a => Ord (NonEmpty a) | |
| Ord a => Ord (ZipList a) | |
| Ord a => Ord (Dual a) | |
| Ord a => Ord (Sum a) | |
| Ord a => Ord (Product a) | |
| Ord a => Ord (First a) | |
| Ord a => Ord (Last a) | |
| Ord a => Ord (Down a) | |
| Ord a => Ord (IntMap a) | |
| Ord a => Ord (Seq a) | |
| Ord a => Ord (ViewL a) | |
| Ord a => Ord (ViewR a) | |
| Ord a => Ord (Set a) | |
| Ord a => Ord (Hashed a) | |
| Ord a => Ord (Array a) | |
| Ord a => Ord (Vector a) | |
| (Storable a, Ord a) => Ord (Vector a) | |
| (Prim a, Ord a) => Ord (Vector a) | |
| (Ord b, Ord a) => Ord (Either a b) | |
| Ord (f p) => Ord (Rec1 f p) | |
| Ord (URec Char p) | |
| Ord (URec Double p) | |
| Ord (URec Float p) | |
| Ord (URec Int p) | |
| Ord (URec Word p) | |
| Ord (URec (Ptr ()) p) | |
| (Ord a, Ord b) => Ord (a, b) | |
| Ord a => Ord (Arg a b) | |
| Ord (Proxy k s) | |
| (Ord k, Ord v) => Ord (Map k v) | |
| (Ord1 m, Ord a) => Ord (MaybeT m a) | |
| (Ord1 m, Ord a) => Ord (ListT m a) | |
| Ord c => Ord (K1 i c p) | |
| (Ord (g p), Ord (f p)) => Ord ((:+:) f g p) | |
| (Ord (g p), Ord (f p)) => Ord ((:*:) f g p) | |
| Ord (f (g p)) => Ord ((:.:) f g p) | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
| Ord a => Ord (Const k a b) | |
| Ord (f a) => Ord (Alt k f a) | |
| Ord ((:~:) k a b) | |
| (Ord w, Ord1 m, Ord a) => Ord (WriterT w m a) | |
| (Ord w, Ord1 m, Ord a) => Ord (WriterT w m a) | |
| (Ord1 f, Ord a) => Ord (IdentityT * f a) | |
| (Ord e, Ord1 m, Ord a) => Ord (ExceptT e m a) | |
| (Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a) | |
| Ord (f p) => Ord (M1 i c f p) | |
| (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Sum * f g a) | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Product * f g a) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Compose * * f g a) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
The Eq class defines equality (==) and inequality (/=).
All the basic datatypes exported by the Prelude are instances of Eq,
and Eq may be derived for any datatype whose constituents are also
instances of Eq.
Instances
| Eq Bool | |
| Eq Char | |
| Eq Double | |
| Eq Float | |
| Eq Int | |
| Eq Int8 | |
| Eq Int16 | |
| Eq Int32 | |
| Eq Int64 | |
| Eq Integer | |
| Eq Ordering | |
| Eq Word | |
| Eq Word8 | |
| Eq Word16 | |
| Eq Word32 | |
| Eq Word64 | |
| Eq TypeRep | |
| Eq () | |
| Eq TyCon | |
| Eq Handle | |
| Eq BigNat | |
| Eq SpecConstrAnnotation | |
| Eq Void | |
| Eq Version | |
| Eq AsyncException | |
| Eq ArrayException | |
| Eq ExitCode | |
| Eq IOErrorType | |
| Eq BufferMode | |
| Eq Newline | |
| Eq NewlineMode | |
| Eq CChar | |
| Eq CSChar | |
| Eq CUChar | |
| Eq CShort | |
| Eq CUShort | |
| Eq CInt | |
| Eq CUInt | |
| Eq CLong | |
| Eq CULong | |
| Eq CLLong | |
| Eq CULLong | |
| Eq CFloat | |
| Eq CDouble | |
| Eq CPtrdiff | |
| Eq CSize | |
| Eq CWchar | |
| Eq CSigAtomic | |
| Eq CClock | |
| Eq CTime | |
| Eq CUSeconds | |
| Eq CSUSeconds | |
| Eq CIntPtr | |
| Eq CUIntPtr | |
| Eq CIntMax | |
| Eq CUIntMax | |
| Eq All | |
| Eq Any | |
| Eq Fixity | |
| Eq Associativity | |
| Eq SourceUnpackedness | |
| Eq SourceStrictness | |
| Eq DecidedStrictness | |
| Eq MaskingState | |
| Eq IOException | |
| Eq ErrorCall | |
| Eq ArithException | |
| Eq SomeNat | |
| Eq SomeSymbol | |
| Eq SrcLoc | |
| Eq ByteString | |
| Eq ByteString | |
| Eq IntSet | |
| Eq CodePoint | |
| Eq DecoderState | |
| Eq UnicodeException | |
| Eq a => Eq [a] | |
| Eq a => Eq (Maybe a) | |
| Eq a => Eq (Ratio a) | |
| Eq (Ptr a) | |
| Eq (FunPtr a) | |
| Eq (V1 p) | |
| Eq (U1 p) | |
| Eq p => Eq (Par1 p) | |
| Eq (ForeignPtr a) | |
| Eq a => Eq (Identity a) | |
| Eq a => Eq (Min a) | |
| Eq a => Eq (Max a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Last a) | |
| Eq m => Eq (WrappedMonoid m) | |
| Eq a => Eq (Option a) | |
| Eq a => Eq (NonEmpty a) | |
| Eq a => Eq (Complex a) | |
| Eq a => Eq (ZipList a) | |
| Eq a => Eq (Dual a) | |
| Eq a => Eq (Sum a) | |
| Eq a => Eq (Product a) | |
| Eq a => Eq (First a) | |
| Eq a => Eq (Last a) | |
| Eq a => Eq (Down a) | |
| Eq a => Eq (IntMap a) | |
| Eq a => Eq (Seq a) | |
| Eq a => Eq (ViewL a) | |
| Eq a => Eq (ViewR a) | |
| Eq a => Eq (Set a) | |
| Eq a => Eq (Hashed a) | Uses precomputed hash to detect inequality faster |
| Eq a => Eq (Array a) | |
| Eq a => Eq (HashSet a) | |
| Eq a => Eq (Vector a) | |
| (Storable a, Eq a) => Eq (Vector a) | |
| (Prim a, Eq a) => Eq (Vector a) | |
| (Eq b, Eq a) => Eq (Either a b) | |
| Eq (f p) => Eq (Rec1 f p) | |
| Eq (URec Char p) | |
| Eq (URec Double p) | |
| Eq (URec Float p) | |
| Eq (URec Int p) | |
| Eq (URec Word p) | |
| Eq (URec (Ptr ()) p) | |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq a => Eq (Arg a b) | |
| Eq (Proxy k s) | |
| (Eq k, Eq a) => Eq (Map k a) | |
| Eq (MutableArray s a) | |
| (Eq1 m, Eq a) => Eq (MaybeT m a) | |
| (Eq1 m, Eq a) => Eq (ListT m a) | |
| (Eq v, Eq k) => Eq (Leaf k v) | |
| (Eq k, Eq v) => Eq (HashMap k v) | |
| Eq c => Eq (K1 i c p) | |
| (Eq (g p), Eq (f p)) => Eq ((:+:) f g p) | |
| (Eq (g p), Eq (f p)) => Eq ((:*:) f g p) | |
| Eq (f (g p)) => Eq ((:.:) f g p) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| Eq a => Eq (Const k a b) | |
| Eq (f a) => Eq (Alt k f a) | |
| Eq ((:~:) k a b) | |
| (Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) | |
| (Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) | |
| (Eq1 f, Eq a) => Eq (IdentityT * f a) | |
| (Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a) | |
| (Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) | |
| Eq (f p) => Eq (M1 i c f p) | |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Sum * f g a) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Product * f g a) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Compose * * f g a) | |
| (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) | |
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
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..].
enumFromThen :: a -> a -> [a] #
Used in Haskell's translation of [n,n'..].
enumFromTo :: a -> a -> [a] #
Used in Haskell's translation of [n..m].
enumFromThenTo :: a -> a -> a -> [a] #
Used in Haskell's translation of [n,n'..m].
Instances
| Enum Bool | |
| Enum Char | |
| Enum Int | |
| Enum Int8 | |
| Enum Int16 | |
| Enum Int32 | |
| Enum Int64 | |
| Enum Integer | |
| Enum Ordering | |
| Enum Word | |
| Enum Word8 | |
| Enum Word16 | |
| Enum Word32 | |
| Enum Word64 | |
| Enum () | |
| Enum CChar | |
| Enum CSChar | |
| Enum CUChar | |
| Enum CShort | |
| Enum CUShort | |
| Enum CInt | |
| Enum CUInt | |
| Enum CLong | |
| Enum CULong | |
| Enum CLLong | |
| Enum CULLong | |
| Enum CFloat | |
| Enum CDouble | |
| Enum CPtrdiff | |
| Enum CSize | |
| Enum CWchar | |
| Enum CSigAtomic | |
| Enum CClock | |
| Enum CTime | |
| Enum CUSeconds | |
| Enum CSUSeconds | |
| Enum CIntPtr | |
| Enum CUIntPtr | |
| Enum CIntMax | |
| Enum CUIntMax | |
| Enum Associativity | |
| Enum SourceUnpackedness | |
| Enum SourceStrictness | |
| Enum DecidedStrictness | |
| Integral a => Enum (Ratio a) | |
| Enum a => Enum (Identity a) | |
| Enum a => Enum (Min a) | |
| Enum a => Enum (Max a) | |
| Enum a => Enum (First a) | |
| Enum a => Enum (Last a) | |
| Enum a => Enum (WrappedMonoid a) | |
| Enum (Proxy k s) | |
| Enum a => Enum (Const k a b) | |
| Enum (f a) => Enum (Alt k f a) | |
| (~) k a b => Enum ((:~:) k a b) | |
Conversion of values to readable Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show is equivalent to
instance (Show a) => Show (Tree a) where
showsPrec d (Leaf m) = showParen (d > app_prec) $
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10
showsPrec d (u :^: v) = showParen (d > up_prec) $
showsPrec (up_prec+1) u .
showString " :^: " .
showsPrec (up_prec+1) v
where up_prec = 5Note that right-associativity of :^: is ignored. For example,
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Instances
Parsing of Strings, producing values.
Derived instances of Read make the following assumptions, which
derived instances of Show obey:
- If the constructor is defined to be an infix operator, then the
derived
Readinstance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Readinstance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where
readsPrec d r = readParen (d > app_prec)
(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r
++ readParen (d > up_prec)
(\r -> [(u:^:v,w) |
(u,s) <- readsPrec (up_prec+1) r,
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r
where app_prec = 10
up_prec = 5Note that right-associativity of :^: is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefaultInstances
| Read Bool | |
| Read Char | |
| Read Double | |
| Read Float | |
| Read Int | |
| Read Int8 | |
| Read Int16 | |
| Read Int32 | |
| Read Int64 | |
| Read Integer | |
| Read Ordering | |
| Read Word | |
| Read Word8 | |
| Read Word16 | |
| Read Word32 | |
| Read Word64 | |
| Read () | |
| Read Void | Reading a |
| Read Version | |
| Read ExitCode | |
| Read BufferMode | |
| Read Newline | |
| Read NewlineMode | |
| Read CChar | |
| Read CSChar | |
| Read CUChar | |
| Read CShort | |
| Read CUShort | |
| Read CInt | |
| Read CUInt | |
| Read CLong | |
| Read CULong | |
| Read CLLong | |
| Read CULLong | |
| Read CFloat | |
| Read CDouble | |
| Read CPtrdiff | |
| Read CSize | |
| Read CWchar | |
| Read CSigAtomic | |
| Read CClock | |
| Read CTime | |
| Read CUSeconds | |
| Read CSUSeconds | |
| Read CIntPtr | |
| Read CUIntPtr | |
| Read CIntMax | |
| Read CUIntMax | |
| Read All | |
| Read Any | |
| Read Fixity | |
| Read Associativity | |
| Read SourceUnpackedness | |
| Read SourceStrictness | |
| Read DecidedStrictness | |
| Read SomeNat | |
| Read SomeSymbol | |
| Read Lexeme | |
| Read GeneralCategory | |
| Read ByteString | |
| Read ByteString | |
| Read IntSet | |
| Read a => Read [a] | |
| Read a => Read (Maybe a) | |
| (Integral a, Read a) => Read (Ratio a) | |
| Read (V1 p) | |
| Read (U1 p) | |
| Read p => Read (Par1 p) | |
| Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
|
| Read a => Read (Min a) | |
| Read a => Read (Max a) | |
| Read a => Read (First a) | |
| Read a => Read (Last a) | |
| Read m => Read (WrappedMonoid m) | |
| Read a => Read (Option a) | |
| Read a => Read (NonEmpty a) | |
| Read a => Read (Complex a) | |
| Read a => Read (ZipList a) | |
| Read a => Read (Dual a) | |
| Read a => Read (Sum a) | |
| Read a => Read (Product a) | |
| Read a => Read (First a) | |
| Read a => Read (Last a) | |
| Read a => Read (Down a) | |
| 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 (Array a) | |
| (Eq a, Hashable a, Read a) => Read (HashSet a) | |
| Read a => Read (Vector a) | |
| (Read a, Storable a) => Read (Vector a) | |
| (Read a, Prim a) => Read (Vector a) | |
| (Read b, Read a) => Read (Either a b) | |
| Read (f p) => Read (Rec1 f p) | |
| (Read a, Read b) => Read (a, b) | |
| (Ix a, Read a, Read b) => Read (Array a b) | |
| (Read b, Read a) => Read (Arg a b) | |
| Read (Proxy k s) | |
| (Ord k, Read k, Read e) => Read (Map k e) | |
| (Read1 m, Read a) => Read (MaybeT m a) | |
| (Read1 m, Read a) => Read (ListT m a) | |
| (Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) | |
| Read c => Read (K1 i c p) | |
| (Read (g p), Read (f p)) => Read ((:+:) f g p) | |
| (Read (g p), Read (f p)) => Read ((:*:) f g p) | |
| Read (f (g p)) => Read ((:.:) f g p) | |
| (Read a, Read b, Read c) => Read (a, b, c) | |
| Read a => Read (Const k a b) | This instance would be equivalent to the derived instances of the
|
| Read (f a) => Read (Alt k f a) | |
| (~) k a b => Read ((:~:) k a b) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read1 f, Read a) => Read (IdentityT * f a) | |
| (Read e, Read1 m, Read a) => Read (ExceptT e m a) | |
| (Read e, Read1 m, Read a) => Read (ErrorT e m a) | |
| Read (f p) => Read (M1 i c f p) | |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | |
| (Read1 f, Read1 g, Read a) => Read (Sum * f g a) | |
| (Read1 f, Read1 g, Read a) => Read (Product * f g a) | |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | |
| (Read1 f, Read1 g, Read a) => Read (Compose * * f g a) | |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
The Functor class is used for types that can be mapped over.
Instances of Functor should satisfy the following laws:
fmap id == id fmap (f . g) == fmap f . fmap g
The instances of Functor for lists, Maybe and IO
satisfy these laws.
Minimal complete definition
Instances
class Applicative m => Monad m where #
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad should satisfy the following laws:
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: m a -> m b -> m b infixl 1 #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
Inject a value into the monadic type.
Fail with a message. This operation is not part of the
mathematical definition of a monad, but is invoked on pattern-match
failure in a do expression.
As part of the MonadFail proposal (MFP), this function is moved
to its own class MonadFail (see Control.Monad.Fail for more
details). The definition here will be removed in a future
release.
Instances
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=, but with the arguments interchanged.
Class for string-like datastructures; used by the overloaded string extension (-XOverloadedStrings in GHC).
Minimal complete definition
Methods
fromString :: String -> a #
Numeric type classes
Basic numeric class.
Methods
Unary negation.
Absolute value.
Sign of a number.
The functions abs and signum should satisfy the law:
abs x * signum x == x
For real numbers, the signum is either -1 (negative), 0 (zero)
or 1 (positive).
fromInteger :: Integer -> a #
Conversion from an Integer.
An integer literal represents the application of the function
fromInteger to the appropriate value of type Integer,
so such literals have type (.Num a) => a
Instances
| Num Int | |
| Num Int8 | |
| Num Int16 | |
| Num Int32 | |
| Num Int64 | |
| Num Integer | |
| Num Word | |
| Num Word8 | |
| Num Word16 | |
| Num Word32 | |
| Num Word64 | |
| Num CChar | |
| Num CSChar | |
| Num CUChar | |
| Num CShort | |
| Num CUShort | |
| Num CInt | |
| Num CUInt | |
| Num CLong | |
| Num CULong | |
| Num CLLong | |
| Num CULLong | |
| Num CFloat | |
| Num CDouble | |
| Num CPtrdiff | |
| Num CSize | |
| Num CWchar | |
| Num CSigAtomic | |
| Num CClock | |
| Num CTime | |
| Num CUSeconds | |
| Num CSUSeconds | |
| Num CIntPtr | |
| Num CUIntPtr | |
| Num CIntMax | |
| Num CUIntMax | |
| Num CodePoint | |
| Num DecoderState | |
| Integral a => Num (Ratio a) | |
| Num a => Num (Identity a) | |
| Num a => Num (Min a) | |
| Num a => Num (Max a) | |
| RealFloat a => Num (Complex a) | |
| Num a => Num (Sum a) | |
| Num a => Num (Product a) | |
| Num a => Num (Const k a b) | |
| Num (f a) => Num (Alt k f a) | |
class (Num a, Ord a) => Real a where #
Minimal complete definition
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
Instances
| Real Int | |
| Real Int8 | |
| Real Int16 | |
| Real Int32 | |
| Real Int64 | |
| Real Integer | |
| Real Word | |
| Real Word8 | |
| Real Word16 | |
| Real Word32 | |
| Real Word64 | |
| Real CChar | |
| Real CSChar | |
| Real CUChar | |
| Real CShort | |
| Real CUShort | |
| Real CInt | |
| Real CUInt | |
| Real CLong | |
| Real CULong | |
| Real CLLong | |
| Real CULLong | |
| Real CFloat | |
| Real CDouble | |
| Real CPtrdiff | |
| Real CSize | |
| Real CWchar | |
| Real CSigAtomic | |
| Real CClock | |
| Real CTime | |
| Real CUSeconds | |
| Real CSUSeconds | |
| Real CIntPtr | |
| Real CUIntPtr | |
| Real CIntMax | |
| Real CUIntMax | |
| Integral a => Real (Ratio a) | |
| Real a => Real (Identity a) | |
| Real a => Real (Const k a b) | |
class (Real a, Enum a) => Integral a where #
Integral numbers, supporting integer division.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
conversion to Integer
Instances
class Num a => Fractional a where #
Fractional numbers, supporting real division.
Minimal complete definition
fromRational, (recip | (/))
Methods
fractional division
reciprocal fraction
fromRational :: Rational -> a #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional CFloat | |
| Fractional CDouble | |
| Integral a => Fractional (Ratio a) | |
| Fractional a => Fractional (Identity a) | |
| RealFloat a => Fractional (Complex a) | |
| Fractional a => Fractional (Const k a b) | |
class Fractional a => Floating a where #
Trigonometric and hyperbolic functions and related functions.
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) #
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> b #
truncate xx between zero and x
round :: Integral b => a -> b #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b #
ceiling xx
floor :: Integral b => a -> b #
floor xx
class (RealFrac a, Floating a) => RealFloat a where #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer #
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> Int #
a constant function, returning the number of digits of
floatRadix in the significand
floatRange :: a -> (Int, Int) #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) #
The function decodeFloat applied to a real floating-point
number returns the significand expressed as an Integer and an
appropriately scaled exponent (an Int). If decodeFloat x(m,n), then x is equal in value to m*b^^n, where b
is the floating-point radix, and furthermore, either m and n
are both zero or else b^(d-1) <= , where abs m < b^dd is
the value of floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite xTrue.
encodeFloat :: Integer -> Int -> a #
encodeFloat performs the inverse of decodeFloat in the
sense that for finite x with the exception of -0.0,
uncurry encodeFloat (decodeFloat x) = xencodeFloat m nm*b^^n (or ±Infinity if overflow
occurs); usually the closer, but if m contains too many bits,
the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
significand x * b ^^ exponent xb is the
floating-point radix.
The behaviour is unspecified on infinite or NaN values.
significand :: a -> a #
The first component of decodeFloat, scaled to lie in the open
interval (-1,1), either 0.0 or of absolute value >= 1/b,
where b is the floating-point radix.
The behaviour is unspecified on infinite or NaN values.
scaleFloat :: Int -> a -> a #
multiplies a floating-point number by an integer power of the radix
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool #
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool #
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool #
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloat, should return the same value as atan yatan2 is provided, but implementors
can provide a more accurate implementation.
Data types
The Maybe type encapsulates an optional value. A value of type
Maybe aa (represented as Just aNothing). Using Maybe is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as error.
The Maybe type is also a monad. It is a simple kind of error
monad, where all errors are represented by Nothing. A richer
error monad can be built using the Either type.
Instances
| Monad Maybe | |
| Functor Maybe | |
| Applicative Maybe | |
| Foldable Maybe | |
| Traversable Maybe | |
| Generic1 Maybe | |
| Alternative Maybe | |
| MonadPlus Maybe | |
| Hashable1 Maybe | |
| Eq a => Eq (Maybe a) | |
| Ord a => Ord (Maybe a) | |
| Read a => Read (Maybe a) | |
| Show a => Show (Maybe a) | |
| Generic (Maybe a) | |
| Semigroup a => Semigroup (Maybe a) | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| Hashable a => Hashable (Maybe a) | |
| SingI (Maybe a) (Nothing a) | |
| SingKind a (KProxy a) => SingKind (Maybe a) (KProxy (Maybe a)) | |
| SingI a a1 => SingI (Maybe a) (Just a a1) | |
| type Rep1 Maybe | |
| type Rep (Maybe a) | |
| data Sing (Maybe a) | |
| type (==) (Maybe k) a b | |
| type DemoteRep (Maybe a) (KProxy (Maybe a)) | |
Instances
| Bounded Bool | |
| Enum Bool | |
| Eq Bool | |
| Ord Bool | |
| Read Bool | |
| Show Bool | |
| Generic Bool | |
| Storable Bool | |
| Hashable Bool | |
| Unbox Bool | |
| SingI Bool False | |
| SingI Bool True | |
| Vector Vector Bool | |
| MVector MVector Bool | |
| SingKind Bool (KProxy Bool) | |
| type Rep Bool | |
| data Sing Bool | |
| data Vector Bool | |
| data MVector s Bool | |
| type (==) Bool a b | |
| type DemoteRep Bool (KProxy Bool) | |
The character type Char is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) characters (see
http://www.unicode.org/ for details). This set extends the ISO 8859-1
(Latin-1) character set (the first 256 characters), which is itself an extension
of the ASCII character set (the first 128 characters). A character literal in
Haskell has type Char.
To convert a Char to or from the corresponding Int value defined
by Unicode, use toEnum and fromEnum from the
Enum class respectively (or equivalently ord and chr).
Instances
| Bounded Char | |
| Enum Char | |
| Eq Char | |
| Ord Char | |
| Read Char | |
| Show Char | |
| Storable Char | |
| Hashable Char | |
| ErrorList Char | |
| Unbox Char | |
| Vector Vector Char | |
| MVector MVector Char | |
| Functor (URec Char) | |
| IsString (Seq Char) | |
| Foldable (URec Char) | |
| Traversable (URec Char) | |
| Generic1 (URec Char) | |
| Eq (URec Char p) | |
| Ord (URec Char p) | |
| Show (URec Char p) | |
| Generic (URec Char p) | |
| data URec Char | Used for marking occurrences of |
| data Vector Char | |
| data MVector s Char | |
| type Rep1 (URec Char) | |
| type Rep (URec Char p) | |
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.
data Either a b :: * -> * -> * #
The Either type represents values with two possibilities: a value of
type Either a bLeft aRight b
The Either type is sometimes used to represent a value which is
either correct or an error; by convention, the Left constructor is
used to hold an error value and the Right constructor is used to
hold a correct value (mnemonic: "right" also means "correct").
Examples
The type Either String IntString or an Int. The Left constructor can be used only on
Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: Either String Int
The fmap from our Functor instance will ignore Left values, but
will apply the supplied function to values contained in a Right:
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>fmap (*2) sLeft "foo">>>fmap (*2) nRight 6
The Monad instance for Either allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int from a Char, or fail.
>>>import Data.Char ( digitToInt, isDigit )>>>:{let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>:}
The following should work, since both '1' and '2' can be
parsed as Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 3
But the following should fail overall, since the first operation where
we attempt to parse 'm' as an Int will fail:
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleLeft "parse error"
Instances
| Hashable2 Either | |
| Monad (Either e) | |
| Functor (Either a) | |
| Applicative (Either e) | |
| Foldable (Either a) | |
| Traversable (Either a) | |
| Generic1 (Either a) | |
| Hashable a => Hashable1 (Either a) | |
| (Eq b, Eq a) => Eq (Either a b) | |
| (Ord b, Ord a) => Ord (Either a b) | |
| (Read b, Read a) => Read (Either a b) | |
| (Show b, Show a) => Show (Either a b) | |
| Generic (Either a b) | |
| Semigroup (Either a b) | |
| (Hashable a, Hashable b) => Hashable (Either a b) | |
| type Rep1 (Either a) | |
| type Rep (Either a b) | |
| type (==) (Either k k1) a b | |
Re-exports
Packed reps
data ByteString :: * #
A space-efficient representation of a Word8 vector, supporting many
efficient operations.
A ByteString contains 8-bit bytes, or by using the operations from
Data.ByteString.Char8 it can be interpreted as containing 8-bit
characters.
type LByteString = ByteString Source #
A space efficient, packed, unboxed Unicode text type.
Containers
A Map from keys k to values a.
Instances
| Functor (Map k) | |
| Foldable (Map k) | |
| Traversable (Map k) | |
| Ord k => IsList (Map k v) | |
| (Eq k, Eq a) => Eq (Map k a) | |
| (Data k, Data a, Ord k) => Data (Map k a) | |
| (Ord k, Ord v) => Ord (Map k v) | |
| (Ord k, Read k, Read e) => Read (Map k e) | |
| (Show k, Show a) => Show (Map k a) | |
| Ord k => Semigroup (Map k v) | |
| Ord k => Monoid (Map k v) | |
| (NFData k, NFData a) => NFData (Map k a) | |
| type Item (Map k v) | |
data HashMap k v :: * -> * -> * #
A map from keys to values. A map cannot contain duplicate keys; each key can map to at most one value.
Instances
| Eq2 HashMap | |
| Show2 HashMap | |
| Hashable2 HashMap | |
| Functor (HashMap k) | |
| Foldable (HashMap k) | |
| Traversable (HashMap k) | |
| Eq k => Eq1 (HashMap k) | |
| (Eq k, Hashable k, Read k) => Read1 (HashMap k) | |
| Show k => Show1 (HashMap k) | |
| Hashable k => Hashable1 (HashMap k) | |
| (Eq k, Hashable k) => IsList (HashMap k v) | |
| (Eq k, Eq v) => Eq (HashMap k v) | |
| (Data k, Data v, Eq k, Hashable k) => Data (HashMap k v) | |
| (Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) | |
| (Show k, Show v) => Show (HashMap k v) | |
| (Eq k, Hashable k) => Semigroup (HashMap k v) | |
| (Eq k, Hashable k) => Monoid (HashMap k v) | |
| (NFData k, NFData v) => NFData (HashMap k v) | |
| (Hashable k, Hashable v) => Hashable (HashMap k v) | |
| type Item (HashMap k v) | |
A map of integers to values a.
A set of values a.
A set of values. A set cannot contain duplicate values.
Instances
| Foldable HashSet | |
| Eq1 HashSet | |
| Show1 HashSet | |
| Hashable1 HashSet | |
| (Eq a, Hashable a) => IsList (HashSet a) | |
| Eq a => Eq (HashSet a) | |
| (Data a, Eq a, Hashable a) => Data (HashSet a) | |
| (Eq a, Hashable a, Read a) => Read (HashSet a) | |
| Show a => Show (HashSet a) | |
| (Hashable a, Eq a) => Semigroup (HashSet a) | |
| (Hashable a, Eq a) => Monoid (HashSet a) | |
| NFData a => NFData (HashSet a) | |
| Hashable a => Hashable (HashSet a) | |
| type Item (HashSet a) | |
A set of integers.
General-purpose finite sequences.
Instances
| Monad Seq | |
| Functor Seq | |
| Applicative Seq | |
| Foldable Seq | |
| Traversable Seq | |
| Alternative Seq | |
| MonadPlus Seq | |
| IsList (Seq a) | |
| Eq a => Eq (Seq a) | |
| Data a => Data (Seq a) | |
| Ord a => Ord (Seq a) | |
| Read a => Read (Seq a) | |
| Show a => Show (Seq a) | |
| IsString (Seq Char) | |
| Semigroup (Seq a) | |
| Monoid (Seq a) | |
| NFData a => NFData (Seq a) | |
| type Item (Seq a) | |
Boxed vectors, supporting efficient slicing.
Instances
| Monad Vector | |
| Functor Vector | |
| Applicative Vector | |
| Foldable Vector | |
| Traversable Vector | |
| Eq1 Vector | |
| Ord1 Vector | |
| Read1 Vector | |
| Show1 Vector | |
| MonadZip Vector | |
| Alternative Vector | |
| MonadPlus Vector | |
| Vector Vector a | |
| IsList (Vector a) | |
| Eq a => Eq (Vector a) | |
| Data a => Data (Vector a) | |
| Ord a => Ord (Vector a) | |
| Read a => Read (Vector a) | |
| Show a => Show (Vector a) | |
| Semigroup (Vector a) | |
| Monoid (Vector a) | |
| NFData a => NFData (Vector a) | |
| type Mutable Vector | |
| type Item (Vector a) | |
class (Vector Vector a, MVector MVector a) => Unbox a #
Instances
| Unbox Bool | |
| Unbox Char | |
| Unbox Double | |
| Unbox Float | |
| Unbox Int | |
| Unbox Int8 | |
| Unbox Int16 | |
| Unbox Int32 | |
| Unbox Int64 | |
| Unbox Word | |
| Unbox Word8 | |
| Unbox Word16 | |
| Unbox Word32 | |
| Unbox Word64 | |
| Unbox () | |
| Unbox a => Unbox (Complex a) | |
| (Unbox a, Unbox b) => Unbox (a, b) | |
| (Unbox a, Unbox b, Unbox c) => Unbox (a, b, c) | |
| (Unbox a, Unbox b, Unbox c, Unbox d) => Unbox (a, b, c, d) | |
| (Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Unbox (a, b, c, d, e) | |
| (Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Unbox (a, b, c, d, e, f) | |
The member functions of this class facilitate writing values of primitive types to raw memory (which may have been allocated with the above mentioned routines) and reading values from blocks of raw memory. The class, furthermore, includes support for computing the storage requirements and alignment restrictions of storable types.
Memory addresses are represented as values of type Ptr aa which is an instance of class Storable. The type argument to
Ptr helps provide some valuable type safety in FFI code (you can't
mix pointers of different types without an explicit cast), while
helping the Haskell type system figure out which marshalling method is
needed for a given pointer.
All marshalling between Haskell and a foreign language ultimately
boils down to translating Haskell data structures into the binary
representation of a corresponding data structure of the foreign
language and vice versa. To code this marshalling in Haskell, it is
necessary to manipulate primitive data types stored in unstructured
memory blocks. The class Storable facilitates this manipulation on
all types for which it is instantiated, which are the standard basic
types of Haskell, the fixed size Int types (Int8, Int16,
Int32, Int64), the fixed size Word types (Word8, Word16,
Word32, Word64), StablePtr, all types from Foreign.C.Types,
as well as Ptr.
Minimal complete definition
sizeOf, alignment, (peek | peekElemOff | peekByteOff), (poke | pokeElemOff | pokeByteOff)
Instances
| Storable Bool | |
| Storable Char | |
| Storable Double | |
| Storable Float | |
| Storable Int | |
| Storable Int8 | |
| Storable Int16 | |
| Storable Int32 | |
| Storable Int64 | |
| Storable Word | |
| Storable Word8 | |
| Storable Word16 | |
| Storable Word32 | |
| Storable Word64 | |
| Storable () | |
| Storable CChar | |
| Storable CSChar | |
| Storable CUChar | |
| Storable CShort | |
| Storable CUShort | |
| Storable CInt | |
| Storable CUInt | |
| Storable CLong | |
| Storable CULong | |
| Storable CLLong | |
| Storable CULLong | |
| Storable CFloat | |
| Storable CDouble | |
| Storable CPtrdiff | |
| Storable CSize | |
| Storable CWchar | |
| Storable CSigAtomic | |
| Storable CClock | |
| Storable CTime | |
| Storable CUSeconds | |
| Storable CSUSeconds | |
| Storable CIntPtr | |
| Storable CUIntPtr | |
| Storable CIntMax | |
| Storable CUIntMax | |
| Storable Fingerprint | |
| Storable CodePoint | |
| Storable DecoderState | |
| (Storable a, Integral a) => Storable (Ratio a) | |
| Storable (StablePtr a) | |
| Storable (Ptr a) | |
| Storable (FunPtr a) | |
| Storable a => Storable (Identity a) | |
| Storable a => Storable (Complex a) | |
| Storable a => Storable (Const k a b) | |
The class of types that can be converted to a hash value.
Minimal implementation: hashWithSalt.
Methods
hashWithSalt :: Int -> a -> Int infixl 0 #
Return a hash value for the argument, using the given salt.
The general contract of hashWithSalt is:
- If two values are equal according to the
==method, then applying thehashWithSaltmethod on each of the two values must produce the same integer result if the same salt is used in each case. - It is not required that if two values are unequal
according to the
==method, then applying thehashWithSaltmethod on each of the two values must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal values may improve the performance of hashing-based data structures. - This method can be used to compute different hash values for
the same input by providing a different salt in each
application of the method. This implies that any instance
that defines
hashWithSaltmust make use of the salt in its implementation.
Like hashWithSalt, but no salt is used. The default
implementation uses hashWithSalt with some default salt.
Instances might want to implement this method to provide a more
efficient implementation than the default implementation.
Instances
Numbers
Instances
| Bounded Word | |
| Enum Word | |
| Eq Word | |
| Integral Word | |
| Num Word | |
| Ord Word | |
| Read Word | |
| Real Word | |
| Show Word | |
| Storable Word | |
| Hashable Word | |
| Unbox Word | |
| Vector Vector Word | |
| MVector MVector Word | |
| Functor (URec Word) | |
| Foldable (URec Word) | |
| Traversable (URec Word) | |
| Generic1 (URec Word) | |
| Eq (URec Word p) | |
| Ord (URec Word p) | |
| Show (URec Word p) | |
| Generic (URec Word p) | |
| data URec Word | Used for marking occurrences of |
| data Vector Word | |
| data MVector s Word | |
| type Rep1 (URec Word) | |
| type Rep (URec Word p) | |
8-bit unsigned integer type
32-bit unsigned integer type
64-bit unsigned integer type
A fixed-precision integer type with at least the range [-2^29 .. 2^29-1].
The exact range for a given implementation can be determined by using
minBound and maxBound from the Bounded class.
Instances
| Bounded Int | |
| Enum Int | |
| Eq Int | |
| Integral Int | |
| Num Int | |
| Ord Int | |
| Read Int | |
| Real Int | |
| Show Int | |
| Storable Int | |
| Hashable Int | |
| Unbox Int | |
| Vector Vector Int | |
| MVector MVector Int | |
| Functor (URec Int) | |
| Foldable (URec Int) | |
| Traversable (URec Int) | |
| Generic1 (URec Int) | |
| Eq (URec Int p) | |
| Ord (URec Int p) | |
| Show (URec Int p) | |
| Generic (URec Int p) | |
| data URec Int | Used for marking occurrences of |
| data Vector Int | |
| data MVector s Int | |
| type Rep1 (URec Int) | |
| type Rep (URec Int p) | |
32-bit signed integer type
64-bit signed integer type
Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.
Instances
| Eq Float | |
| Floating Float | |
| Ord Float | |
| Read Float | |
| RealFloat Float | |
| Storable Float | |
| Hashable Float | |
| Unbox Float | |
| Vector Vector Float | |
| MVector MVector Float | |
| Functor (URec Float) | |
| Foldable (URec Float) | |
| Traversable (URec Float) | |
| Generic1 (URec Float) | |
| Eq (URec Float p) | |
| Ord (URec Float p) | |
| Show (URec Float p) | |
| Generic (URec Float p) | |
| data URec Float | Used for marking occurrences of |
| data Vector Float | |
| data MVector s Float | |
| type Rep1 (URec Float) | |
| type Rep (URec Float p) | |
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
Instances
| Eq Double | |
| Floating Double | |
| Ord Double | |
| Read Double | |
| RealFloat Double | |
| Storable Double | |
| Hashable Double | |
| Unbox Double | |
| Vector Vector Double | |
| MVector MVector Double | |
| Functor (URec Double) | |
| Foldable (URec Double) | |
| Traversable (URec Double) | |
| Generic1 (URec Double) | |
| Eq (URec Double p) | |
| Ord (URec Double p) | |
| Show (URec Double p) | |
| Generic (URec Double p) | |
| data URec Double | Used for marking occurrences of |
| data Vector Double | |
| data MVector s Double | |
| type Rep1 (URec Double) | |
| type Rep (URec Double p) | |
Numeric functions
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
Monoids
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
mappend mempty x = x
mappend x mempty = x
mappend x (mappend y z) = mappend (mappend x y) z
mconcat =
foldrmappend mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtypes and make those instances
of Monoid, e.g. Sum and Product.
Methods
Identity of mappend
An associative operation
Fold a list using the monoid.
For most types, the default definition for mconcat will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
Instances
| Monoid Ordering | |
| Monoid () | |
| Monoid All | |
| Monoid Any | |
| Monoid ByteString | |
| Monoid ByteString | |
| Monoid IntSet | |
| Monoid [a] | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| Monoid a => Monoid (IO a) | |
| Ord a => Monoid (Max a) | |
| Ord a => Monoid (Min a) | |
| Monoid a => Monoid (Identity a) | |
| (Ord a, Bounded a) => Monoid (Min a) | |
| (Ord a, Bounded a) => Monoid (Max a) | |
| Monoid m => Monoid (WrappedMonoid m) | |
| Semigroup a => Monoid (Option a) | |
| Monoid a => Monoid (Dual a) | |
| Monoid (Endo a) | |
| Num a => Monoid (Sum a) | |
| Num a => Monoid (Product a) | |
| Monoid (First a) | |
| Monoid (Last a) | |
| Monoid (IntMap a) | |
| Monoid (Seq a) | |
| Ord a => Monoid (Set a) | |
| Monoid (Array a) | |
| (Hashable a, Eq a) => Monoid (HashSet a) | |
| Monoid (Vector a) | |
| Storable a => Monoid (Vector a) | |
| Prim a => Monoid (Vector a) | |
| Monoid b => Monoid (a -> b) | |
| (Monoid a, Monoid b) => Monoid (a, b) | |
| Monoid (Proxy k s) | |
| Ord k => Monoid (Map k v) | |
| (Eq k, Hashable k) => Monoid (HashMap k v) | |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |
| Monoid a => Monoid (Const k a b) | |
| Alternative f => Monoid (Alt * f a) | |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | |
Folds and traversals
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed
to satisfy the monoid laws. Alternatively, one could define foldr:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
sum, product, maximum, and minimum should all be essentially
equivalent to foldMap forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a Functor instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
Instances
asum :: (Foldable t, Alternative f) => t (f a) -> f a #
The sum of a collection of actions, generalizing concat.
class (Functor t, Foldable t) => Traversable t #
Functors representing data structures that can be traversed from left to right.
A definition of traverse must satisfy the following laws:
- naturality
t .for every applicative transformationtraversef =traverse(t . f)t- identity
traverseIdentity = Identity- composition
traverse(Compose .fmapg . f) = Compose .fmap(traverseg) .traversef
A definition of sequenceA must satisfy the following laws:
- naturality
t .for every applicative transformationsequenceA=sequenceA.fmaptt- identity
sequenceA.fmapIdentity = Identity- composition
sequenceA.fmapCompose = Compose .fmapsequenceA.sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative operations, i.e.
and the identity functor Identity and composition of functors Compose
are defined as
newtype Identity a = Identity a
instance Functor Identity where
fmap f (Identity x) = Identity (f x)
instance Applicative Identity where
pure x = Identity x
Identity f <*> Identity x = Identity (f x)
newtype Compose f g a = Compose (f (g a))
instance (Functor f, Functor g) => Functor (Compose f g) where
fmap f (Compose x) = Compose (fmap (fmap f) x)
instance (Applicative f, Applicative g) => Applicative (Compose f g) where
pure x = Compose (pure (pure x))
Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)(The naturality law is implied by parametricity.)
Instances are similar to Functor, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*>
imply a form of associativity.
The superclass instances should satisfy the following:
- In the
Functorinstance,fmapshould be equivalent to traversal with the identity applicative functor (fmapDefault). - In the
Foldableinstance,foldMapshould be equivalent to traversal with a constant applicative functor (foldMapDefault).
Instances
arrow
first :: Arrow a => forall b c d. a b c -> a (b, d) (c, d) #
Send the first component of the input through the argument arrow, and copy the rest unchanged to the output.
second :: Arrow a => forall b c d. a b c -> a (d, b) (d, c) #
A mirror image of first.
The default definition may be overridden with a more efficient version if desired.
(***) :: Arrow a => forall b c b' c'. a b c -> a b' c' -> a (b, b') (c, c') #
Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.
The default definition may be overridden with a more efficient version if desired.
(&&&) :: Arrow a => forall b c c'. a b c -> a b c' -> a b (c, c') #
Fanout: send the input to both argument arrows and combine their output.
The default definition may be overridden with a more efficient version if desired.
Bool
Case analysis for the Bool type. bool x y px
when p is False, and evaluates to y when p is True.
This is equivalent to if p then y else x; that is, one can
think of it as an if-then-else construct with its arguments
reordered.
Examples
Basic usage:
>>>bool "foo" "bar" True"bar">>>bool "foo" "bar" False"foo"
Confirm that bool x y pif p then y else x are
equivalent:
>>>let p = True; x = "bar"; y = "foo">>>bool x y p == if p then y else xTrue>>>let p = False>>>bool x y p == if p then y else xTrue
Since: 4.7.0.0
Maybe
mapMaybe :: (a -> Maybe b) -> [a] -> [b] #
The mapMaybe function is a version of map which can throw
out elements. In particular, the functional argument returns
something of type Maybe bNothing, no element
is added on to the result list. If it is Just bb is
included in the result list.
Examples
Using mapMaybe f xcatMaybes $ map f x
>>>import Text.Read ( readMaybe )>>>let readMaybeInt = readMaybe :: String -> Maybe Int>>>mapMaybe readMaybeInt ["1", "Foo", "3"][1,3]>>>catMaybes $ map readMaybeInt ["1", "Foo", "3"][1,3]
If we map the Just constructor, the entire list should be returned:
>>>mapMaybe Just [1,2,3][1,2,3]
catMaybes :: [Maybe a] -> [a] #
The catMaybes function takes a list of Maybes and returns
a list of all the Just values.
Examples
Basic usage:
>>>catMaybes [Just 1, Nothing, Just 3][1,3]
When constructing a list of Maybe values, catMaybes can be used
to return all of the "success" results (if the list is the result
of a map, then mapMaybe would be more appropriate):
>>>import Text.Read ( readMaybe )>>>[readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ][Just 1,Nothing,Just 3]>>>catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ][1,3]
fromMaybe :: a -> Maybe a -> a #
The fromMaybe function takes a default value and and Maybe
value. If the Maybe is Nothing, it returns the default values;
otherwise, it returns the value contained in the Maybe.
Examples
Basic usage:
>>>fromMaybe "" (Just "Hello, World!")"Hello, World!"
>>>fromMaybe "" Nothing""
Read an integer from a string using readMaybe. If we fail to
parse an integer, we want to return 0 by default:
>>>import Text.Read ( readMaybe )>>>fromMaybe 0 (readMaybe "5")5>>>fromMaybe 0 (readMaybe "")0
listToMaybe :: [a] -> Maybe a #
The listToMaybe function returns Nothing on an empty list
or Just aa is the first element of the list.
Examples
Basic usage:
>>>listToMaybe []Nothing
>>>listToMaybe [9]Just 9
>>>listToMaybe [1,2,3]Just 1
Composing maybeToList with listToMaybe should be the identity
on singleton/empty lists:
>>>maybeToList $ listToMaybe [5][5]>>>maybeToList $ listToMaybe [][]
But not on lists with more than one element:
>>>maybeToList $ listToMaybe [1,2,3][1]
maybeToList :: Maybe a -> [a] #
The maybeToList function returns an empty list when given
Nothing or a singleton list when not given Nothing.
Examples
Basic usage:
>>>maybeToList (Just 7)[7]
>>>maybeToList Nothing[]
One can use maybeToList to avoid pattern matching when combined
with a function that (safely) works on lists:
>>>import Text.Read ( readMaybe )>>>sum $ maybeToList (readMaybe "3")3>>>sum $ maybeToList (readMaybe "")0
Either
partitionEithers :: [Either a b] -> ([a], [b]) #
Partitions a list of Either into two lists.
All the Left elements are extracted, in order, to the first
component of the output. Similarly the Right elements are extracted
to the second component of the output.
Examples
Basic usage:
>>>let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]>>>partitionEithers list(["foo","bar","baz"],[3,7])
The pair returned by partitionEithers x(:lefts x, rights x)
>>>let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]>>>partitionEithers list == (lefts list, rights list)True
Ord
comparing :: Ord a => (b -> a) -> b -> b -> Ordering #
comparing p x y = compare (p x) (p y)
Useful combinator for use in conjunction with the xxxBy family
of functions from Data.List, for example:
... sortBy (comparing fst) ...
The Down type allows you to reverse sort order conveniently. A value of type
Down aa (represented as Down aa has an Ordthen sortWith by Down x
Provides Show and Read instances (since: 4.7.0.0).
Since: 4.6.0.0
Constructors
| Down a |
Applicative
class Functor f => Applicative f where #
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying the following laws:
- identity
pureid<*>v = v- composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- homomorphism
puref<*>purex =pure(f x)- interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 #
Sequential application.
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
(<$>) :: 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, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
(<|>) :: Alternative f => forall a. f a -> f a -> f a #
An associative binary operation
Monad
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #
Left-to-right Kleisli composition of monads.
Transformers
lift :: MonadTrans t => forall m a. Monad m => m a -> t m a #
Lift a computation from the argument monad to the constructed monad.
class Monad m => MonadIO m where #
Monads in which IO computations may be embedded.
Any monad built by applying a sequence of monad transformers to the
IO monad will be an instance of this class.
Instances should satisfy the following laws, which state that liftIO
is a transformer of monads:
Minimal complete definition
Instances
| MonadIO IO | |
| MonadIO m => MonadIO (MaybeT m) | |
| MonadIO m => MonadIO (ListT m) | |
| (Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
| (Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
| MonadIO m => MonadIO (StateT s m) | |
| MonadIO m => MonadIO (StateT s m) | |
| MonadIO m => MonadIO (IdentityT * m) | |
| MonadIO m => MonadIO (ExceptT e m) | |
| (Error e, MonadIO m) => MonadIO (ErrorT e m) | |
| MonadIO m => MonadIO (ReaderT * r m) | |
| (Monoid w, MonadIO m) => MonadIO (RWST r w s m) | |
| (Monoid w, MonadIO m) => MonadIO (RWST r w s m) | |
Exceptions
class (Typeable * e, Show e) => Exception e where #
Any type that you wish to throw or catch as an exception must be an
instance of the Exception class. The simplest case is a new exception
type directly below the root:
data MyException = ThisException | ThatException
deriving (Show, Typeable)
instance Exception MyExceptionThe default method definitions in the Exception class do what we need
in this case. You can now throw and catch ThisException and
ThatException as exceptions:
*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
Caught ThisException
In more complicated examples, you may wish to define a whole hierarchy of exceptions:
---------------------------------------------------------------------
-- Make the root exception type for all the exceptions in a compiler
data SomeCompilerException = forall e . Exception e => SomeCompilerException e
deriving Typeable
instance Show SomeCompilerException where
show (SomeCompilerException e) = show e
instance Exception SomeCompilerException
compilerExceptionToException :: Exception e => e -> SomeException
compilerExceptionToException = toException . SomeCompilerException
compilerExceptionFromException :: Exception e => SomeException -> Maybe e
compilerExceptionFromException x = do
SomeCompilerException a <- fromException x
cast a
---------------------------------------------------------------------
-- Make a subhierarchy for exceptions in the frontend of the compiler
data SomeFrontendException = forall e . Exception e => SomeFrontendException e
deriving Typeable
instance Show SomeFrontendException where
show (SomeFrontendException e) = show e
instance Exception SomeFrontendException where
toException = compilerExceptionToException
fromException = compilerExceptionFromException
frontendExceptionToException :: Exception e => e -> SomeException
frontendExceptionToException = toException . SomeFrontendException
frontendExceptionFromException :: Exception e => SomeException -> Maybe e
frontendExceptionFromException x = do
SomeFrontendException a <- fromException x
cast a
---------------------------------------------------------------------
-- Make an exception type for a particular frontend compiler exception
data MismatchedParentheses = MismatchedParentheses
deriving (Typeable, Show)
instance Exception MismatchedParentheses where
toException = frontendExceptionToException
fromException = frontendExceptionFromExceptionWe can now catch a MismatchedParentheses exception as
MismatchedParentheses, SomeFrontendException or
SomeCompilerException, but not other types, e.g. IOException:
*Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: SomeFrontendException)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: SomeCompilerException)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatche -> putStrLn ("Caught " ++ show (e :: IOException)) *** Exception: MismatchedParentheses
Methods
toException :: e -> SomeException #
fromException :: SomeException -> Maybe e #
displayException :: e -> String #
Instances
The class Typeable allows a concrete representation of a type to
be calculated.
Minimal complete definition
data SomeException :: * #
The SomeException type is the root of the exception type hierarchy.
When an exception of type e is thrown, behind the scenes it is
encapsulated in a SomeException.
Instances
data IOException :: * #
Exceptions that occur in the IO monad.
An IOException records a more specific error type, a descriptive
string and maybe the handle that was used when the error was
flagged.
Instances
module System.IO.Error
Files
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.
(</>) :: FilePath -> FilePath -> FilePath infixr 5 #
Combine two paths with a path separator.
If the second path starts with a path separator or a drive letter, then it returns the second.
The intention is that readFile (dir will access the same file as
</> file)setCurrentDirectory dir; readFile file.
Posix: "/directory" </> "file.ext" == "/directory/file.ext"
Windows: "/directory" </> "file.ext" == "/directory\\file.ext"
"directory" </> "/file.ext" == "/file.ext"
Valid x => (takeDirectory x </> takeFileName x) `equalFilePath` xCombined:
Posix: "/" </> "test" == "/test" Posix: "home" </> "bob" == "home/bob" Posix: "x:" </> "foo" == "x:/foo" Windows: "C:\\foo" </> "bar" == "C:\\foo\\bar" Windows: "home" </> "bob" == "home\\bob"
Not combined:
Posix: "home" </> "/bob" == "/bob" Windows: "home" </> "C:\\bob" == "C:\\bob"
Not combined (tricky):
On Windows, if a filepath starts with a single slash, it is relative to the
root of the current drive. In [1], this is (confusingly) referred to as an
absolute path.
The current behavior of </> is to never combine these forms.
Windows: "home" </> "/bob" == "/bob" Windows: "home" </> "\\bob" == "\\bob" Windows: "C:\\home" </> "\\bob" == "\\bob"
On Windows, from [1]: "If a file name begins with only a disk designator
but not the backslash after the colon, it is interpreted as a relative path
to the current directory on the drive with the specified letter."
The current behavior of </> is to never combine these forms.
Windows: "D:\\foo" </> "C:bar" == "C:bar" Windows: "C:\\foo" </> "C:bar" == "C:bar"
(<.>) :: FilePath -> String -> FilePath infixr 7 #
Add an extension, even if there is already one there, equivalent to addExtension.
"/directory/path" <.> "ext" == "/directory/path.ext" "/directory/path" <.> ".ext" == "/directory/path.ext"
Strings
Hashing
hash :: Hashable a => a -> Int #
Like hashWithSalt, but no salt is used. The default
implementation uses hashWithSalt with some default salt.
Instances might want to implement this method to provide a more
efficient implementation than the default implementation.
hashWithSalt :: Hashable a => Int -> a -> Int #
Return a hash value for the argument, using the given salt.
The general contract of hashWithSalt is:
- If two values are equal according to the
==method, then applying thehashWithSaltmethod on each of the two values must produce the same integer result if the same salt is used in each case. - It is not required that if two values are unequal
according to the
==method, then applying thehashWithSaltmethod on each of the two values must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal values may improve the performance of hashing-based data structures. - This method can be used to compute different hash values for
the same input by providing a different salt in each
application of the method. This implies that any instance
that defines
hashWithSaltmust make use of the salt in its implementation.