| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Language.Haskell.HGrep.Prelude
Contents
- data Bool :: *
- bool :: a -> a -> Bool -> a
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- otherwise :: Bool
- data Char :: *
- data Integer :: *
- data Int :: *
- data Int8 :: *
- data Int16 :: *
- data Int32 :: *
- data Int64 :: *
- data Word64 :: *
- fromIntegral :: (Integral a, Num b) => a -> b
- fromRational :: Fractional a => Rational -> a
- class Monoid a where
- (<>) :: Monoid m => m -> m -> m
- class Functor f where
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- ($>) :: Functor f => f a -> b -> f b
- void :: Functor f => f a -> f ()
- with :: Functor f => f a -> (a -> b) -> f b
- class Bifunctor p where
- class Functor f => Applicative f where
- (<**>) :: Applicative f => f a -> f (a -> b) -> f b
- class Applicative f => Alternative f where
- asum :: (Foldable t, Alternative f) => t (f a) -> f a
- class Applicative m => Monad m where
- join :: Monad m => m (m a) -> m a
- class (Alternative m, Monad m) => MonadPlus m where
- guard :: Alternative f => Bool -> f ()
- msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
- class MonadTrans t where
- class BifunctorTrans t where
- class Monad m => MonadIO m where
- data Either a b :: * -> * -> *
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- note :: a -> Maybe b -> Either a b
- type EitherT = ExceptT
- pattern EitherT :: forall m e a. m (Either e a) -> ExceptT e m a
- runEitherT :: EitherT e m a -> m (Either e a)
- left :: Monad m => x -> EitherT x m a
- right :: Monad m => a -> EitherT x m a
- data Maybe a :: * -> *
- fromMaybe :: a -> Maybe a -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- hush :: Either a b -> Maybe b
- newtype MaybeT m a :: (* -> *) -> * -> * = MaybeT {}
- nothing :: Monad m => MaybeT m a
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- curry :: ((a, b) -> c) -> a -> b -> c
- uncurry :: (a -> b -> c) -> (a, b) -> c
- class Enum a where
- class Eq a where
- class Read a where
- readEither :: Read a => String -> Either String a
- readMaybe :: Read a => String -> Maybe a
- class Show a where
- type ShowS = String -> String
- showString :: String -> ShowS
- class Foldable t where
- for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
- class Eq a => Ord a where
- data Ordering :: *
- comparing :: Ord a => (b -> a) -> b -> b -> Ordering
- class (Functor t, Foldable t) => Traversable t where
- for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
- traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
- id :: a -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- ($) :: (a -> b) -> a -> b
- ($!) :: (a -> b) -> a -> b
- (&) :: a -> (a -> b) -> b
- const :: a -> b -> a
- flip :: (a -> b -> c) -> b -> a -> c
- fix :: (a -> a) -> a
- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
- seq :: a -> b -> b
- data IO a :: * -> *
- type FilePath = String
- undefined :: HasCallStack => a
- error :: HasCallStack => [Char] -> a
- trace :: [Char] -> a -> a
- traceM :: Applicative f => [Char] -> f ()
- traceIO :: [Char] -> IO ()
Primitive types
Bool
Instances
| Bounded Bool | |
| Enum Bool | |
| Eq Bool | |
| Data Bool | |
| Ord Bool | |
| Read Bool | |
| Show Bool | |
| Ix Bool | |
| Generic Bool | |
| Lift Bool | |
| Storable Bool | |
| Outputable Bool | |
| Hashable Bool | |
| Unbox Bool | |
| IArray UArray Bool | |
| SingI Bool False | |
| SingI Bool True | |
| Vector Vector Bool | |
| MVector MVector Bool | |
| SingKind Bool (KProxy Bool) | |
| MArray (STUArray s) Bool (ST s) | |
| type Rep Bool | |
| data Sing Bool | |
| data Vector Bool | |
| data MVector s Bool | |
| type (==) Bool a b | |
| type DemoteRep Bool (KProxy 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
Char
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 | |
| Data Char | |
| Ord Char | |
| Read Char | |
| Show Char | |
| Ix Char | |
| Lift Char | |
| Storable Char | |
| Outputable Char | |
| Hashable Char | |
| Prim Char | |
| Unbox Char | |
| ErrorList Char | |
| IArray UArray Char | |
| Vector Vector Char | |
| MVector MVector Char | |
| KnownSymbol n => Reifies Symbol n String | |
| Functor (URec Char) | |
| IsString (Seq Char) | |
| Foldable (URec Char) | |
| Traversable (URec Char) | |
| Generic1 (URec Char) | |
| MArray (STUArray s) Char (ST s) | |
| Eq (URec Char p) | |
| Ord (URec Char p) | |
| Show (URec Char p) | |
| Generic (URec Char p) | |
| Annotate (SourceText, FastString) | |
| data URec Char | Used for marking occurrences of |
| data Vector Char | |
| data MVector s Char | |
| type Rep1 (URec Char) | |
| type Rep (URec Char p) | |
Int
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 | |
| Data Int | |
| Num Int | |
| Ord Int | |
| Read Int | |
| Real Int | |
| Show Int | |
| Ix Int | |
| Lift Int | |
| Storable Int | |
| Uniquable Int | |
| Outputable Int | |
| Hashable Int | |
| Prim Int | |
| Unbox Int | |
| IArray UArray Int | |
| Vector Vector Int | |
| MVector MVector Int | |
| Functor (URec Int) | |
| Foldable (URec Int) | |
| Traversable (URec Int) | |
| Generic1 (URec Int) | |
| Reifies * Z Int | |
| MArray (STUArray s) Int (ST s) | |
| Reifies * n Int => Reifies * (D n) Int | |
| Reifies * n Int => Reifies * (SD n) Int | |
| Reifies * n Int => Reifies * (PD n) 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) | |
8-bit signed integer type
Instances
| Bounded Int8 | |
| Enum Int8 | |
| Eq Int8 | |
| Integral Int8 | |
| Data Int8 | |
| Num Int8 | |
| Ord Int8 | |
| Read Int8 | |
| Real Int8 | |
| Show Int8 | |
| Ix Int8 | |
| Lift Int8 | |
| Storable Int8 | |
| Bits Int8 | |
| FiniteBits Int8 | |
| Hashable Int8 | |
| Prim Int8 | |
| Unbox Int8 | |
| IArray UArray Int8 | |
| Vector Vector Int8 | |
| MVector MVector Int8 | |
| MArray (STUArray s) Int8 (ST s) | |
| data Vector Int8 | |
| data MVector s Int8 | |
16-bit signed integer type
Instances
| Bounded Int16 | |
| Enum Int16 | |
| Eq Int16 | |
| Integral Int16 | |
| Data Int16 | |
| Num Int16 | |
| Ord Int16 | |
| Read Int16 | |
| Real Int16 | |
| Show Int16 | |
| Ix Int16 | |
| Lift Int16 | |
| Storable Int16 | |
| Bits Int16 | |
| FiniteBits Int16 | |
| Hashable Int16 | |
| Prim Int16 | |
| Unbox Int16 | |
| IArray UArray Int16 | |
| Vector Vector Int16 | |
| MVector MVector Int16 | |
| MArray (STUArray s) Int16 (ST s) | |
| data Vector Int16 | |
| data MVector s Int16 | |
32-bit signed integer type
Instances
| Bounded Int32 | |
| Enum Int32 | |
| Eq Int32 | |
| Integral Int32 | |
| Data Int32 | |
| Num Int32 | |
| Ord Int32 | |
| Read Int32 | |
| Real Int32 | |
| Show Int32 | |
| Ix Int32 | |
| Lift Int32 | |
| Storable Int32 | |
| Bits Int32 | |
| FiniteBits Int32 | |
| Outputable Int32 | |
| Hashable Int32 | |
| Prim Int32 | |
| Unbox Int32 | |
| IArray UArray Int32 | |
| Vector Vector Int32 | |
| MVector MVector Int32 | |
| MArray (STUArray s) Int32 (ST s) | |
| data Vector Int32 | |
| data MVector s Int32 | |
64-bit signed integer type
Instances
| Bounded Int64 | |
| Enum Int64 | |
| Eq Int64 | |
| Integral Int64 | |
| Data Int64 | |
| Num Int64 | |
| Ord Int64 | |
| Read Int64 | |
| Real Int64 | |
| Show Int64 | |
| Ix Int64 | |
| Lift Int64 | |
| Storable Int64 | |
| Bits Int64 | |
| FiniteBits Int64 | |
| Outputable Int64 | |
| Hashable Int64 | |
| Prim Int64 | |
| Unbox Int64 | |
| IArray UArray Int64 | |
| Vector Vector Int64 | |
| MVector MVector Int64 | |
| MArray (STUArray s) Int64 (ST s) | |
| data Vector Int64 | |
| data MVector s Int64 | |
Word
64-bit unsigned integer type
Instances
Real
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
fromRational :: Fractional a => Rational -> a #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Algebraic structures
Monoid
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
Functor
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
(<$>) :: 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 <$> (2,2)(2,True)
($>) :: Functor f => f a -> b -> f b infixl 4 #
Flipped version of <$.
Examples
Replace the contents of a Maybe IntString:
>>>Nothing $> "foo"Nothing>>>Just 90210 $> "foo"Just "foo"
Replace the contents of an Either Int IntString, resulting in an Either Int String
>>>Left 8675309 $> "foo"Left 8675309>>>Right 8675309 $> "foo"Right "foo"
Replace each element of a list with a constant String:
>>>[1,2,3] $> "foo"["foo","foo","foo"]
Replace the second element of a pair with a constant String:
>>>(1,2) $> "foo"(1,"foo")
Since: 4.7.0.0
void :: Functor f => f a -> f () #
void valueIO action.
Examples
Replace the contents of a Maybe Int
>>>void NothingNothing>>>void (Just 3)Just ()
Replace the contents of an Either Int IntEither Int '()'
>>>void (Left 8675309)Left 8675309>>>void (Right 8675309)Right ()
Replace every element of a list with unit:
>>>void [1,2,3][(),(),()]
Replace the second element of a pair with unit:
>>>void (1,2)(1,())
Discard the result of an IO action:
>>>mapM print [1,2]1 2 [(),()]>>>void $ mapM print [1,2]1 2
Bifunctor
Formally, the class Bifunctor represents a bifunctor
from Hask -> Hask.
Intuitively it is a bifunctor where both the first and second arguments are covariant.
You can define a Bifunctor by either defining bimap or by
defining both first and second.
If you supply bimap, you should ensure that:
bimapidid≡id
If you supply first and second, ensure:
firstid≡idsecondid≡id
If you supply both, you should also ensure:
bimapf g ≡firstf.secondg
These ensure by parametricity:
bimap(f.g) (h.i) ≡bimapf h.bimapg ifirst(f.g) ≡firstf.firstgsecond(f.g) ≡secondf.secondg
Since: 4.8.0.0
Instances
| Bifunctor Either | |
| Bifunctor (,) | |
| Bifunctor Arg | |
| Bifunctor (K1 i) | |
| Bifunctor ((,,) x1) | |
| Bifunctor (Const *) | |
| Functor f => Bifunctor (CofreeF f) | |
| Functor f => Bifunctor (FreeF f) | |
| Bifunctor (Tagged *) | |
| Bifunctor (Constant *) | |
| Bifunctor ((,,,) x1 x2) | |
| Bifunctor ((,,,,) x1 x2 x3) | |
| Bifunctor p => Bifunctor (WrappedBifunctor * * p) | |
| Functor g => Bifunctor (Joker * * g) | |
| Bifunctor p => Bifunctor (Flip * * p) | |
| Functor f => Bifunctor (Clown * * f) | |
| Bifunctor ((,,,,,) x1 x2 x3 x4) | |
| (Bifunctor f, Bifunctor g) => Bifunctor (Product * * f g) | |
| (Bifunctor p, Bifunctor q) => Bifunctor (Sum * * p q) | |
| Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) | |
| (Functor f, Bifunctor p) => Bifunctor (Tannen * * * f p) | |
| (Bifunctor p, Functor f, Functor g) => Bifunctor (Biff * * * * p f g) | |
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
(<**>) :: Applicative f => f a -> f (a -> b) -> f b infixl 4 #
A variant of <*> with the arguments reversed.
Alternative
class Applicative f => Alternative f where #
A monoid on applicative functors.
If defined, some and many should be the least solutions
of the equations:
Methods
The identity of <|>
(<|>) :: f a -> f a -> f a infixl 3 #
An associative binary operation
One or more.
Zero or more.
Instances
asum :: (Foldable t, Alternative f) => t (f a) -> f a #
The sum of a collection of actions, generalizing concat.
Monad
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
join :: Monad m => m (m a) -> m a #
The join function is the conventional monad join operator. It
is used to remove one level of monadic structure, projecting its
bound argument into the outer level.
MonadPlus
class (Alternative m, Monad m) => MonadPlus m where #
Monads that also support choice and failure.
Methods
the identity of mplus. It should also satisfy the equations
mzero >>= f = mzero v >> mzero = mzero
an associative operation
Instances
MonadTrans
class MonadTrans t where #
The class of monad transformers. Instances should satisfy the
following laws, which state that lift is a monad transformation:
Minimal complete definition
Methods
lift :: Monad m => m a -> t m a #
Lift a computation from the argument monad to the constructed monad.
Instances
| MonadTrans CatchT | |
| MonadTrans IterT | |
| MonadTrans MaybeT | |
| MonadTrans Yoneda | |
| MonadTrans ListT | |
| MonadTrans (IdentityT *) | |
| Alternative f => MonadTrans (CofreeT f) | |
| MonadTrans (FreeT f) | |
| MonadTrans (ErrorT e) | |
| MonadTrans (ExceptT e) | |
| MonadTrans (StateT s) | |
| MonadTrans (StateT s) | |
| Monoid w => MonadTrans (WriterT w) | |
| Monoid w => MonadTrans (WriterT w) | |
| MonadTrans (ContT * r) | |
| MonadTrans (ReaderT * r) | |
| Monoid w => MonadTrans (RWST r w s) | |
| Monoid w => MonadTrans (RWST r w s) | |
BifunctorTrans
class BifunctorTrans t where #
Class of monad transformers which are bifunctors.
You can implement a BifunctorTrans by either defining bimapT or by
defining both firstT and secondT.
If you supply bimapT, you should ensure that:
bimapTidid≡id
If you supply first and second, ensure:
firstTid≡idsecondTid≡id
If you supply both, you should also ensure:
bimapTf g ≡firstTf.secondTg
These ensure by parametricity:
bimapT(f.g) (h.i) ≡bimapTf h.bimapTg ifirstT(f.g) ≡firstTf.firstTgsecondT(f.g) ≡secondTf.secondTg
Methods
bimapT :: Functor f => (x -> y) -> (a -> b) -> t x f a -> t y f b #
Map over both arguments at the same time.
bimapf g ≡firstf.secondg
firstT :: Functor f => (x -> y) -> t x f a -> t y f a #
secondT :: Functor f => (a -> b) -> t x f a -> t x f b #
Map covariantly over the second argument.
second≡bimapid
MonadIO
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 (CatchT m) | |
| MonadIO m => MonadIO (IterT m) | |
| MonadIO m => MonadIO (MaybeT m) | |
| MonadIO m => MonadIO (ListT m) | |
| MonadIO m => MonadIO (IdentityT * m) | |
| (Functor f, MonadIO m) => MonadIO (FreeT f m) | |
| (Error e, MonadIO m) => MonadIO (ErrorT e m) | |
| MonadIO m => MonadIO (ExceptT e m) | |
| MonadIO m => MonadIO (StateT s m) | |
| MonadIO m => MonadIO (StateT s m) | |
| (Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
| (Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
| MonadIO m => MonadIO (ContT * r 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) | |
Data structures
Either
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
| Bifunctor Either | |
| Hashable2 Either | |
| Swapped Either | |
| Monad (Either e) | |
| Functor (Either a) | |
| Applicative (Either e) | |
| Foldable (Either a) | |
| Traversable (Either a) | |
| Generic1 (Either a) | |
| Hashable a => Hashable1 (Either a) | |
| Apply (Either a) | |
| Bind (Either a) | |
| (Eq b, Eq a) => Eq (Either a b) | |
| (Data a, Data b) => Data (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) | |
| (Lift a, Lift b) => Lift (Either a b) | |
| (Outputable a, Outputable b) => Outputable (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 | |
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
EitherT
runEitherT :: EitherT e m a -> m (Either e a) Source #
Maybe
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 | |
| Apply Maybe | |
| Bind Maybe | |
| Eq a => Eq (Maybe a) | |
| Data a => Data (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 |
| Lift a => Lift (Maybe a) | |
| Outputable a => Outputable (Maybe a) | |
| Annotate (Maybe Role) | |
| Hashable a => Hashable (Maybe a) | |
| Ixed (Maybe a) | |
| At (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 Index (Maybe a) | |
| type IxValue (Maybe a) | |
| type (==) (Maybe k) a b | |
| type DemoteRep (Maybe a) (KProxy (Maybe a)) | |
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
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""
MaybeT
newtype MaybeT m a :: (* -> *) -> * -> * #
The parameterizable maybe monad, obtained by composing an arbitrary
monad with the Maybe monad.
Computations are actions that may produce a value or exit.
The return function yields a computation that produces that
value, while >>= sequences two subcomputations, exiting if either
computation does.
Instances
Tuple
uncurry :: (a -> b -> c) -> (a, b) -> c #
uncurry converts a curried function to a function on pairs.
Typeclasses
Enum
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
Eq
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
Read
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 = readListPrecDefaultMethods
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that
showsPrec started with.
The method readList is provided to allow the programmer to
give a specialised way of parsing lists of values.
For example, this is used by the predefined Read instance of
the Char type, where values of type String should be are
expected to use double quotes, rather than square brackets.
Proposed replacement for readsPrec using new-style parsers (GHC only).
readListPrec :: ReadPrec [a] #
Proposed replacement for readList using new-style parsers (GHC only).
The default definition uses readList. Instances that define readPrec
should also define readListPrec as readListPrecDefault.
Instances
| 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 Color | |
| Read ColorIntensity | |
| Read ConsoleLayer | |
| Read BlinkSpeed | |
| Read Underlining | |
| Read ConsoleIntensity | |
| Read SGR | |
| Read Void | Reading a |
| Read Version | |
| Read CDev | |
| Read CIno | |
| Read CMode | |
| Read COff | |
| Read CPid | |
| Read CSsize | |
| Read CGid | |
| Read CNlink | |
| Read CUid | |
| Read CCc | |
| Read CSpeed | |
| Read CTcflag | |
| Read CRLim | |
| Read Fd | |
| 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 Lexeme | |
| Read GeneralCategory | |
| Read ByteString | |
| Read ByteString | |
| Read IntSet | |
| Read ColourPrefs | |
| Read DatatypeVariant | |
| 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 (Tree a) | |
| 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 (Vector a) | |
| (Read a, Prim a) => Read (Vector a) | |
| (Read a, Storable a) => Read (Vector a) | |
| (Eq a, Hashable a, Read a) => Read (HashSet a) | |
| Read a => Read (Array 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) | |
| (Read (f (Cofree f a)), Read a) => Read (Cofree f a) | |
| Read (w (a, CoiterT w a)) => Read (CoiterT w a) | |
| Read (m (Either a (IterT m a))) => Read (IterT m a) | |
| (Read1 m, Read a) => Read (MaybeT m a) | |
| (Functor f, Read (f a)) => Read (Yoneda f a) | |
| (Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) | |
| (Read1 m, Read a) => Read (ListT m a) | |
| 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) | |
| Coercible k a b => Read (Coercion k a b) | |
| (~) k a b => Read ((:~:) k a b) | |
| Read (p a a) => Read (Join k p a) | |
| Read (p (Fix k p a) a) => Read (Fix k p a) | |
| (Read1 f, Read a) => Read (IdentityT * f a) | |
| (Read (f b), Read a) => Read (CofreeF f a b) | |
| Read (w (CofreeF f a (CofreeT f w a))) => Read (CofreeT f w a) | |
| (Read (f b), Read a) => Read (FreeF f a b) | |
| Read (m (FreeF f a (FreeT f m a))) => Read (FreeT f m a) | |
| (Read1 f, Read a) => Read (Backwards * f a) | |
| (Read e, Read1 m, Read a) => Read (ErrorT e m a) | |
| (Read e, Read1 m, Read a) => Read (ExceptT e m a) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| Read b => Read (Tagged k s b) | |
| (Read1 f, Read a) => Read (Reverse * f a) | |
| Read a => Read (Constant k a b) | |
| 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 (p a b) => Read (WrappedBifunctor k1 k p a b) | |
| Read (g b) => Read (Joker k1 k g a b) | |
| Read (p b a) => Read (Flip k k1 p a b) | |
| Read (f a) => Read (Clown k1 k f a b) | |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | |
| (Read (g a b), Read (f a b)) => Read (Product k1 k f g a b) | |
| (Read (q a b), Read (p a b)) => Read (Sum k1 k p q a b) | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | |
| Read (f (p a b)) => Read (Tannen k2 k1 k f p a b) | |
| (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 (p (f a) (g b)) => Read (Biff k3 k2 k1 k p f g a b) | |
| (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) | |
readMaybe :: Read a => String -> Maybe a #
Parse a string using the Read instance.
Succeeds if there is exactly one valid result.
Since: 4.6.0.0
Show
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)".
Methods
showsPrec :: Int -> a -> ShowS #
Convert a value to a readable String.
showsPrec should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that showsPrec started with.
Instances
ShowS
showString :: String -> ShowS #
utility function converting a String to a show function that
simply prepends the string unchanged.
Foldable
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)
Methods
fold :: Monoid m => t m -> m #
Combine the elements of a structure using a monoid.
foldMap :: Monoid m => (a -> m) -> t a -> m #
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure.
In the case of lists, foldr, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that, since the head of the resulting expression is produced by
an application of the operator to the first element of the list,
foldr can produce a terminating expression from an infinite list.
For a general Foldable structure this should be semantically identical
to,
foldr f z =foldrf z .toList
foldr' :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure, but with strict application of the operator.
foldl :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure.
In the case of lists, foldl, when applied to a binary
operator, a starting value (typically the left-identity of the operator),
and a list, reduces the list using the binary operator, from left to
right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. This means that foldl' will
diverge if given an infinite list.
Also note that if you want an efficient left-fold, you probably want to
use foldl' instead of foldl. The reason for this is that latter does
not force the "inner" results (e.g. z in the above example)
before applying them to the operator (e.g. to f x1(). This results
in a thunk chain f x2)O(n) elements long, which then must be evaluated from
the outside-in.
For a general Foldable structure this should be semantically identical
to,
foldl f z =foldlf z .toList
foldl' :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure but with strict application of the operator.
This ensures that each step of the fold is forced to weak head normal
form before being applied, avoiding the collection of thunks that would
otherwise occur. This is often what you want to strictly reduce a finite
list to a single, monolithic result (e.g. length).
For a general Foldable structure this should be semantically identical
to,
foldl f z =foldl'f z .toList
foldr1 :: (a -> a -> a) -> t a -> a #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
foldr1f =foldr1f .toList
foldl1 :: (a -> a -> a) -> t a -> a #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
foldl1f =foldl1f .toList
List of elements of a structure, from left to right.
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
Returns the size/length of a finite structure as an Int. The
default implementation is optimized for structures that are similar to
cons-lists, because there is no general way to do better.
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
maximum :: Ord a => t a -> a #
The largest element of a non-empty structure.
minimum :: Ord a => t a -> a #
The least element of a non-empty structure.
The sum function computes the sum of the numbers of a structure.
product :: Num a => t a -> a #
The product function computes the product of the numbers of a
structure.
Instances
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () #
Ord
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
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) ...
Traversable
class (Functor t, Foldable t) => Traversable t where #
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 <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*>
imply a form of associativity.
The superclass instances should satisfy the following:
- In the
Functorinstance,fmapshould be equivalent to traversal with the identity applicative functor (fmapDefault). - In the
Foldableinstance,foldMapshould be equivalent to traversal with a constant applicative functor (foldMapDefault).
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_.
sequenceA :: Applicative f => t (f a) -> f (t a) #
Evaluate each action in the structure from left to right, and
and collect the results. For a version that ignores the results
see sequenceA_.
mapM :: Monad m => (a -> m b) -> t a -> m (t b) #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_.
sequence :: Monad m => t (m a) -> m (t a) #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_.
Instances
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b) #
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () #
Map each element of a structure to an action, evaluate these
actions from left to right, and ignore the results. For a version
that doesn't ignore the results see traverse.
Combinators
($) :: (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.
const x is a unary function which evaluates to x for all inputs.
For instance,
>>>map (const 42) [0..3][42,42,42,42]
flip :: (a -> b -> c) -> b -> a -> c #
flip ff.
fix ff,
i.e. the least defined x such that f x = x.
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.
System
IO
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.
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.
Partial functions
undefined :: HasCallStack => a Source #
Warning: undefined is unsafe