Safe Haskell | None |
---|---|
Language | Haskell2010 |
- ($) :: (a -> b) -> a -> b
- ($!) :: (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
,
or map
($
0) xs
.zipWith
($
) 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 Nothing
False
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
, apply the first function to Left
aa
;
if it is
, apply the second function to Right
bb
.
Examples
We create two values of type
, one using the
Either
String
Int
Left
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) s
3>>>
either length (*2) n
6
flip :: (a -> b -> c) -> b -> a -> c #
takes its (first) two arguments in the reverse order of 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 #
yields the result of applying 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.
compare :: a -> a -> Ordering #
(<) :: a -> a -> Bool infix 4 #
(<=) :: a -> a -> Bool infix 4 #
(>) :: a -> a -> Bool infix 4 #
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
.
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
.
Class Enum
defines operations on sequentially ordered types.
The enumFrom
... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum
may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum
from 0
through n-1
.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded
as well as Enum
,
the following should hold:
- The calls
andsucc
maxBound
should result in a runtime error.pred
minBound
fromEnum
andtoEnum
should give a runtime error if the result value is not representable in the result type. For example,
is an error.toEnum
7 ::Bool
enumFrom
andenumFromThen
should be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound enumFromThen x y = enumFromThenTo x y bound where bound | fromEnum y >= fromEnum x = maxBound | otherwise = minBound
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]
.
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 String
s.
Derived instances of Show
have the following properties, which
are compatible with derived instances of Read
:
- The result of
show
is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrec
will produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
x
is less thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
show
will produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show
is equivalent to
instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec) $ showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec) $ showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5
Note that right-associativity of :^:
is ignored. For example,
produces the stringshow
(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"
.
Parsing of String
s, producing values.
Derived instances of Read
make the following assumptions, which
derived instances of Show
obey:
- If the constructor is defined to be an infix operator, then the
derived
Read
instance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
Read
will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Read
instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read
in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5
Note that right-associativity of :^:
is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where readPrec = parens $ (prec app_prec $ do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec $ do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault
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.
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.
(>>=) :: 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.
(=<<) :: 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).
fromString :: String -> a #
Numeric type classes
Basic numeric class.
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
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 #
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
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.
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
class Num a => Fractional a where #
Fractional numbers, supporting real division.
fromRational, (recip | (/))
fractional division
reciprocal fraction
fromRational :: Rational -> a #
Conversion from a Rational
(that is
).
A floating literal stands for an application of Ratio
Integer
fromRational
to a value of type Rational
, so such literals have type
(
.Fractional
a) => a
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.
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
properFraction :: Integral b => a -> (b, a) #
The function properFraction
takes a real fractional number x
and returns a pair (n,f)
such that x = n+f
, and:
n
is an integral number with the same sign asx
; andf
is a fraction with the same type and sign asx
, and with absolute value less than1
.
The default definitions of the ceiling
, floor
, truncate
and round
functions are in terms of properFraction
.
truncate :: Integral b => a -> b #
returns the integer nearest truncate
xx
between zero and x
round :: Integral b => a -> b #
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
ceiling :: Integral b => a -> b #
returns the least integer not less than ceiling
xx
floor :: Integral b => a -> b #
returns the greatest integer not greater than floor
xx
class (RealFrac a, Floating a) => RealFloat a where #
Efficient, machine-independent access to the components of a floating-point number.
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
floatRadix :: a -> Integer #
a constant function, returning the radix of the representation
(often 2
)
floatDigits :: a -> Int #
a constant function, returning the number of digits of
floatRadix
in the significand
floatRange :: a -> (Int, Int) #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) #
The function decodeFloat
applied to a real floating-point
number returns the significand expressed as an Integer
and an
appropriately scaled exponent (an Int
). If
yields decodeFloat
x(m,n)
, then x
is equal in value to m*b^^n
, where b
is the floating-point radix, and furthermore, either m
and n
are both zero or else b^(d-1) <=
, where abs
m < b^dd
is
the value of
.
In particular, floatDigits
x
. If the type
contains a negative zero, also decodeFloat
0 = (0,0)
.
The result of decodeFloat
(-0.0) = (0,0)
is unspecified if either of
decodeFloat
x
or isNaN
x
is isInfinite
xTrue
.
encodeFloat :: Integer -> Int -> a #
encodeFloat
performs the inverse of decodeFloat
in the
sense that for finite x
with the exception of -0.0
,
.
uncurry
encodeFloat
(decodeFloat
x) = x
is one of the two closest representable
floating-point numbers to encodeFloat
m nm*b^^n
(or ±Infinity
if overflow
occurs); usually the closer, but if m
contains too many bits,
the result may be rounded in the wrong direction.
exponent
corresponds to the second component of decodeFloat
.
and for finite nonzero exponent
0 = 0x
,
.
If exponent
x = snd (decodeFloat
x) + floatDigits
xx
is a finite floating-point number, it is equal in value to
, where significand
x * b ^^ exponent
xb
is the
floating-point radix.
The behaviour is unspecified on infinite or NaN
values.
significand :: a -> a #
The first component of decodeFloat
, scaled to lie in the open
interval (-1
,1
), either 0.0
or of absolute value >= 1/b
,
where b
is the floating-point radix.
The behaviour is unspecified on infinite or NaN
values.
scaleFloat :: Int -> a -> a #
multiplies a floating-point number by an integer power of the radix
True
if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool #
True
if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool #
True
if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool #
True
if the argument is an IEEE negative zero
True
if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x
and y
,
computes the angle
(from the positive x-axis) of the vector from the origin to the
point atan2
y x(x,y)
.
returns a value in the range [atan2
y x-pi
,
pi
]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported.
, with atan2
y 1y
in a type
that is RealFloat
, should return the same value as
.
A default definition of atan
yatan2
is provided, but implementors
can provide a more accurate implementation.
Data types
The Maybe
type encapsulates an optional value. A value of type
either contains a value of type Maybe
aa
(represented as
),
or it is empty (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.
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)) | |
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
).
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
is a computation which, when performed,
does some I/O before returning a value of type IO
aa
.
There is really only one way to "perform" an I/O action: bind it to
Main.main
in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the IO
monad and called
at some point, directly or indirectly, from Main.main
.
IO
is a monad, so IO
actions can be combined using either the do-notation
or the >>
and >>=
operations from the Monad
class.
data Either a b :: * -> * -> * #
The Either
type represents values with two possibilities: a value of
type
is either Either
a b
or Left
a
.Right
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
is the type of values which can be either
a Either
String
Int
String
or an Int
. The Left
constructor can be used only on
String
s, and the Right
constructor can be used only on Int
s:
>>>
let s = Left "foo" :: Either String Int
>>>
s
Left "foo">>>
let n = Right 3 :: Either String Int
>>>
n
Right 3>>>
:type s
s :: Either String Int>>>
:type n
n :: 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) s
Left "foo">>>
fmap (*2) n
Right 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 Int
s.
>>>
:{
let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>
:}
>>>
parseMultiple
Right 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)>>>
:}
>>>
parseMultiple
Left "parse error"
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 #
Containers
A Map from keys k
to values a
.
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.
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.
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.
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.
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 #
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
, for some
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
.
sizeOf, alignment, (peek | peekElemOff | peekByteOff), (poke | pokeElemOff | pokeByteOff)
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
.
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 thehashWithSalt
method 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 thehashWithSalt
method 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
hashWithSalt
must 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.
Numbers
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.
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.
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.
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 =
foldr
mappend 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 newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
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.
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)
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 transformationtraverse
f =traverse
(t . f)t
- identity
traverse
Identity = Identity- composition
traverse
(Compose .fmap
g . f) = Compose .fmap
(traverse
g) .traverse
f
A definition of sequenceA
must satisfy the following laws:
- naturality
t .
for every applicative transformationsequenceA
=sequenceA
.fmap
tt
- identity
sequenceA
.fmap
Identity = Identity- composition
sequenceA
.fmap
Compose = Compose .fmap
sequenceA
.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
Functor
instance,fmap
should be equivalent to traversal with the identity applicative functor (fmapDefault
). - In the
Foldable
instance,foldMap
should be equivalent to traversal with a constant applicative functor (foldMapDefault
).
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.
evaluates to 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
and 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 x
True>>>
let p = False
>>>
bool x y p == if p then y else x
True
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
. If this is Maybe
bNothing
, no element
is added on to the result list. If it is
, then Just
bb
is
included in the result list.
Examples
Using
is a shortcut for mapMaybe
f x
in most cases:catMaybes
$ 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 Maybe
s 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
where 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
should be the same
pair as 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
contains a value of type Down
aa
(represented as
).
If Down
aa
has an
instance associated with it then comparing two
values thus wrapped will give you the opposite of their normal sort order.
This is particularly useful when sorting in generalised list comprehensions,
as in: Ord
then sortWith by
Down
x
Provides Show
and Read
instances (since: 4.7.0.0).
Since: 4.6.0.0
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
pure
id
<*>
v = v- composition
pure
(.)<*>
u<*>
v<*>
w = u<*>
(v<*>
w)- homomorphism
pure
f<*>
pure
x =pure
(f x)- interchange
u
<*>
pure
y =pure
($
y)<*>
u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor
instance for f
will satisfy
If f
is also a Monad
, it should satisfy
(which implies that pure
and <*>
satisfy the applicative functor laws).
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.
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
An infix synonym for fmap
.
The name of this operator is an allusion to $
.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $
is function application, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> Left 17
Left 17>>>
show <$> Right 17
Right "17"
Double each element of a list:
>>>
(*2) <$> [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
even <$> (2,2)
(2,True)
(<|>) :: 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:
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 MyException
The 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 = frontendExceptionFromException
We can now catch a MismatchedParentheses
exception as
MismatchedParentheses
, SomeFrontendException
or
SomeCompilerException
, but not other types, e.g. IOException
:
*Main> throw MismatchedParenthesescatch
e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatch
e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatch
e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException)) Caught MismatchedParentheses *Main> throw MismatchedParenthesescatch
e -> putStrLn ("Caught " ++ show (e :: IOException)) *** Exception: MismatchedParentheses
toException :: e -> SomeException #
fromException :: SomeException -> Maybe e #
displayException :: e -> String #
The class Typeable
allows a concrete representation of a type to
be calculated.
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
.
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.
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` x
Combined:
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 thehashWithSalt
method 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 thehashWithSalt
method 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
hashWithSalt
must make use of the salt in its implementation.