Copyright | (c) The University of Glasgow 2001 |
---|---|
License | BSD-style (see the file libraries/base/LICENSE) |
Maintainer | libraries@haskell.org |
Stability | provisional |
Portability | portable |
Safe Haskell | Trustworthy |
Language | Haskell2010 |
Synopsis
- class Functor f where
- fmap :: (a -> b) -> f a -> f b
- class Applicative m => Monad m where
- class Monad m => MonadFail m where
- class (Alternative m, Monad m) => MonadPlus m where
- mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b)
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
- forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
- sequence :: (Traversable t, Monad m) => t (m a) -> m (t a)
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- forever :: Applicative f => f a -> f b
- void :: Functor f => f a -> f ()
- join :: Monad m => m (m a) -> m a
- msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
- mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
- filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
- mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])
- zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]
- zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()
- foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
- replicateM :: Applicative m => Int -> m a -> m [a]
- replicateM_ :: Applicative m => Int -> m a -> m ()
- guard :: Alternative f => Bool -> f ()
- when :: Applicative f => Bool -> f () -> f ()
- unless :: Applicative f => Bool -> f () -> f ()
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
- liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
- liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
- ap :: Monad m => m (a -> b) -> m a -> m b
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
Functor and monad classes
A type f
is a Functor if it provides a function fmap
which, given any types a
and b
lets you apply any function from (a -> b)
to turn an f a
into an f b
, preserving the
structure of f
. Furthermore f
needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap
and
the first law, so you need only check that the former condition holds.
Instances
Functor [] # | Since: base-2.1 |
Functor Maybe # | Since: base-2.1 |
Functor IO # | Since: base-2.1 |
Functor Par1 # | Since: base-4.9.0.0 |
Functor NonEmpty # | Since: base-4.9.0.0 |
Functor NoIO # | Since: base-4.8.0.0 |
Functor ReadP # | Since: base-2.1 |
Functor ReadPrec # | Since: base-2.1 |
Functor Down # | Since: base-4.11.0.0 |
Functor Product # | Since: base-4.8.0.0 |
Functor Sum # | Since: base-4.8.0.0 |
Functor Dual # | Since: base-4.8.0.0 |
Functor Last # | Since: base-4.8.0.0 |
Functor First # | Since: base-4.8.0.0 |
Functor STM # | Since: base-4.3.0.0 |
Functor Handler # | Since: base-4.6.0.0 |
Functor Identity # | Since: base-4.8.0.0 |
Functor ZipList # | Since: base-2.1 |
Functor ArgDescr # | Since: base-4.6.0.0 |
Functor OptDescr # | Since: base-4.6.0.0 |
Functor ArgOrder # | Since: base-4.6.0.0 |
Functor Option # | Since: base-4.9.0.0 |
Functor Last # | Since: base-4.9.0.0 |
Functor First # | Since: base-4.9.0.0 |
Functor Max # | Since: base-4.9.0.0 |
Functor Min # | Since: base-4.9.0.0 |
Functor Complex # | Since: base-4.9.0.0 |
Functor (Either a) # | Since: base-3.0 |
Functor (V1 :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
Functor ((,) a) # | Since: base-2.1 |
Functor (ST s) # | Since: base-2.1 |
Functor (Array i) # | Since: base-2.1 |
Functor (Proxy :: Type -> Type) # | Since: base-4.7.0.0 |
Arrow a => Functor (ArrowMonad a) # | Since: base-4.6.0.0 |
Defined in Control.Arrow fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
Monad m => Functor (WrappedMonad m) # | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a # | |
Functor (ST s) # | Since: base-2.1 |
Functor (Arg a) # | Since: base-4.9.0.0 |
Functor f => Functor (Rec1 f) # | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) # | Since: base-4.9.0.0 |
Functor f => Functor (Alt f) # | Since: base-4.8.0.0 |
Functor f => Functor (Ap f) # | Since: base-4.12.0.0 |
Functor (Const m :: Type -> Type) # | Since: base-2.1 |
Arrow a => Functor (WrappedArrow a b) # | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Functor ((->) r :: Type -> Type) # | Since: base-2.1 |
Functor (K1 i c :: Type -> Type) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :*: g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Sum f g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Product f g) # | Since: base-4.9.0.0 |
Functor f => Functor (M1 i c f) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Compose f g) # | Since: base-4.9.0.0 |
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:
- Left identity
return
a>>=
k = k a- Right identity
m
>>=
return
= m- Associativity
m
>>=
(\x -> k x>>=
h) = (m>>=
k)>>=
h
Furthermore, the Monad
and Applicative
operations should relate as follows:
The above laws imply:
and that pure
and (<*>
) satisfy the applicative functor laws.
The instances of Monad
for lists, Maybe
and IO
defined in the Prelude satisfy these laws.
(>>=) :: forall a b. 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.
(>>) :: forall a b. 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.
Instances
Monad [] # | Since: base-2.1 |
Monad Maybe # | Since: base-2.1 |
Monad IO # | Since: base-2.1 |
Monad Par1 # | Since: base-4.9.0.0 |
Monad NonEmpty # | Since: base-4.9.0.0 |
Monad NoIO # | Since: base-4.4.0.0 |
Monad ReadP # | Since: base-2.1 |
Monad ReadPrec # | Since: base-2.1 |
Monad Down # | Since: base-4.11.0.0 |
Monad Product # | Since: base-4.8.0.0 |
Monad Sum # | Since: base-4.8.0.0 |
Monad Dual # | Since: base-4.8.0.0 |
Monad Last # | Since: base-4.8.0.0 |
Monad First # | Since: base-4.8.0.0 |
Monad STM # | Since: base-4.3.0.0 |
Monad Identity # | Since: base-4.8.0.0 |
Monad Option # | Since: base-4.9.0.0 |
Monad Last # | Since: base-4.9.0.0 |
Monad First # | Since: base-4.9.0.0 |
Monad Max # | Since: base-4.9.0.0 |
Monad Min # | Since: base-4.9.0.0 |
Monad Complex # | Since: base-4.9.0.0 |
Monad (Either e) # | Since: base-4.4.0.0 |
Monad (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
Monoid a => Monad ((,) a) # | Since: base-4.9.0.0 |
Monad (ST s) # | Since: base-2.1 |
Monad (Proxy :: Type -> Type) # | Since: base-4.7.0.0 |
ArrowApply a => Monad (ArrowMonad a) # | Since: base-2.1 |
Defined in Control.Arrow (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # return :: a0 -> ArrowMonad a a0 # | |
Monad m => Monad (WrappedMonad m) # | Since: base-4.7.0.0 |
Defined in Control.Applicative (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a # | |
Monad (ST s) # | Since: base-2.1 |
Monad f => Monad (Rec1 f) # | Since: base-4.9.0.0 |
Monad f => Monad (Alt f) # | Since: base-4.8.0.0 |
Monad f => Monad (Ap f) # | Since: base-4.12.0.0 |
Monad ((->) r :: Type -> Type) # | Since: base-2.1 |
(Monad f, Monad g) => Monad (f :*: g) # | Since: base-4.9.0.0 |
(Monad f, Monad g) => Monad (Product f g) # | Since: base-4.9.0.0 |
Monad f => Monad (M1 i c f) # | Since: base-4.9.0.0 |
class Monad m => MonadFail m where #
When a value is bound in do
-notation, the pattern on the left
hand side of <-
might not match. In this case, this class
provides a function to recover.
A Monad
without a MonadFail
instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat
).
Instances of MonadFail
should satisfy the following law: fail s
should
be a left zero for >>=
,
fail s >>= f = fail s
If your Monad
is also MonadPlus
, a popular definition is
fail _ = mzero
Since: base-4.9.0.0
Instances
MonadFail [] # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
MonadFail Maybe # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
MonadFail IO # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
MonadFail ReadP # | Since: base-4.9.0.0 |
Defined in Text.ParserCombinators.ReadP | |
MonadFail ReadPrec # | Since: base-4.9.0.0 |
Defined in Text.ParserCombinators.ReadPrec | |
MonadFail (ST s) # | Since: base-4.11.0.0 |
MonadFail (ST s) # | Since: base-4.10 |
Defined in Control.Monad.ST.Lazy.Imp | |
MonadFail f => MonadFail (Ap f) # | Since: base-4.12.0.0 |
Defined in Data.Monoid |
class (Alternative m, Monad m) => MonadPlus m where #
Monads that also support choice and failure.
Nothing
The identity of mplus
. It should also satisfy the equations
mzero >>= f = mzero v >> mzero = mzero
The default definition is
mzero = empty
An associative operation. The default definition is
mplus = (<|>
)
Instances
MonadPlus [] # | Since: base-2.1 |
MonadPlus Maybe # | Since: base-2.1 |
MonadPlus IO # | Since: base-4.9.0.0 |
MonadPlus ReadP # | Since: base-2.1 |
MonadPlus ReadPrec # | Since: base-2.1 |
MonadPlus STM # | Since: base-4.3.0.0 |
MonadPlus Option # | Since: base-4.9.0.0 |
MonadPlus (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
MonadPlus (Proxy :: Type -> Type) # | Since: base-4.9.0.0 |
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) # | Since: base-4.6.0.0 |
Defined in Control.Arrow mzero :: ArrowMonad a a0 # mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 # | |
MonadPlus f => MonadPlus (Rec1 f) # | Since: base-4.9.0.0 |
MonadPlus f => MonadPlus (Alt f) # | Since: base-4.8.0.0 |
MonadPlus f => MonadPlus (Ap f) # | Since: base-4.12.0.0 |
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) # | Since: base-4.9.0.0 |
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g) # | Since: base-4.9.0.0 |
MonadPlus f => MonadPlus (M1 i c f) # | Since: base-4.9.0.0 |
Functions
Naming conventions
The functions in this library use the following naming conventions:
- A postfix '
M
' always stands for a function in the Kleisli category: The monad type constructorm
is added to function results (modulo currying) and nowhere else. So, for example,
filter :: (a -> Bool) -> [a] -> [a] filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a]
- A postfix '
_
' changes the result type from(m a)
to(m ())
. Thus, for example:
sequence :: Monad m => [m a] -> m [a] sequence_ :: Monad m => [m a] -> m ()
- A prefix '
m
' generalizes an existing function to a monadic form. Thus, for example:
filter :: (a -> Bool) -> [a] -> [a] mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
Basic Monad
functions
mapM :: (Traversable t, 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_
.
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) #
sequence :: (Traversable t, 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_
.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence
.
As of base 4.8.0.0, sequence_
is just sequenceA_
, specialized
to Monad
.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=
, but with the arguments interchanged.
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #
Left-to-right composition of Kleisli arrows.
forever :: Applicative f => f a -> f b #
Repeat an action indefinitely.
Examples
A common use of forever
is to process input from network sockets,
Handle
s, and channels
(e.g. MVar
and
Chan
).
For example, here is how we might implement an echo
server, using
forever
both to listen for client connections on a network socket
and to echo client input on client connection handles:
echoServer :: Socket -> IO () echoServer socket =forever
$ do client <- accept socketforkFinally
(echo client) (\_ -> hClose client) where echo :: Handle -> IO () echo client =forever
$ hGetLine client >>= hPutStrLn client
void :: Functor f => f a -> f () #
discards or ignores the result of evaluation, such
as the return value of an void
valueIO
action.
Examples
Replace the contents of a
with unit:Maybe
Int
>>>
void Nothing
Nothing>>>
void (Just 3)
Just ()
Replace the contents of an
with unit, resulting in an Either
Int
Int
:Either
Int
()
>>>
void (Left 8675309)
Left 8675309>>>
void (Right 8675309)
Right ()
Replace every element of a list with unit:
>>>
void [1,2,3]
[(),(),()]
Replace the second element of a pair with unit:
>>>
void (1,2)
(1,())
Discard the result of an IO
action:
>>>
mapM print [1,2]
1 2 [(),()]>>>
void $ mapM print [1,2]
1 2
Generalisations of list functions
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.
Examples
A common use of join
is to run an IO
computation returned from
an STM
transaction, since STM
transactions
can't perform IO
directly. Recall that
atomically
:: STM a -> IO a
is used to run STM
transactions atomically. So, by
specializing the types of atomically
and join
to
atomically
:: STM (IO b) -> IO (IO b)join
:: IO (IO b) -> IO b
we can compose them as
join
.atomically
:: STM (IO b) -> IO b
filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a] #
This generalizes the list-based filter
function.
mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) #
The mapAndUnzipM
function maps its first argument over a list, returning
the result as a pair of lists. This function is mainly used with complicated
data structures or a state monad.
zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] #
zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () #
foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #
The foldM
function is analogous to foldl
, except that its result is
encapsulated in a monad. Note that foldM
works from left-to-right over
the list arguments. This could be an issue where (
and the `folded
function' are not commutative.>>
)
foldM f a1 [x1, x2, ..., xm] == do a2 <- f a1 x1 a3 <- f a2 x2 ... f am xm
If right-to-left evaluation is required, the input list should be reversed.
foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () #
Like foldM
, but discards the result.
replicateM :: Applicative m => Int -> m a -> m [a] #
performs the action replicateM
n actn
times,
gathering the results.
replicateM_ :: Applicative m => Int -> m a -> m () #
Like replicateM
, but discards the result.
Conditional execution of monadic expressions
guard :: Alternative f => Bool -> f () #
Conditional failure of Alternative
computations. Defined by
guard True =pure
() guard False =empty
Examples
Common uses of guard
include conditionally signaling an error in
an error monad and conditionally rejecting the current choice in an
Alternative
-based parser.
As an example of signaling an error in the error monad Maybe
,
consider a safe division function safeDiv x y
that returns
Nothing
when the denominator y
is zero and
otherwise. For example:Just
(x `div`
y)
>>> safeDiv 4 0 Nothing >>> safeDiv 4 2 Just 2
A definition of safeDiv
using guards, but not guard
:
safeDiv :: Int -> Int -> Maybe Int safeDiv x y | y /= 0 = Just (x `div` y) | otherwise = Nothing
A definition of safeDiv
using guard
and Monad
do
-notation:
safeDiv :: Int -> Int -> Maybe Int safeDiv x y = do guard (y /= 0) return (x `div` y)
when :: Applicative f => Bool -> f () -> f () #
Conditional execution of Applicative
expressions. For example,
when debug (putStrLn "Debugging")
will output the string Debugging
if the Boolean value debug
is True
, and otherwise do nothing.
unless :: Applicative f => Bool -> f () -> f () #
The reverse of when
.
Monadic lifting operators
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r #
Promote a function to a monad, scanning the monadic arguments from left to right. For example,
liftM2 (+) [0,1] [0,2] = [0,2,1,3] liftM2 (+) (Just 1) Nothing = Nothing
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).