Safe Haskell | Trustworthy |
---|---|
Language | Haskell2010 |
Protolude.Monad
Synopsis
- class Applicative m => Monad (m :: Type -> Type) where
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- (=<<) :: 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
- (>>) :: Monad m => m a -> m b -> m b
- forever :: Applicative f => f a -> f b
- join :: Monad m => m (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 ()
- concatMapM :: Monad m => (a -> m [b]) -> [a] -> m [b]
- 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
- liftM' :: Monad m => (a -> b) -> m a -> m b
- liftM2' :: Monad m => (a -> b -> c) -> m a -> m b -> m c
- ap :: Monad m => m (a -> b) -> m a -> m b
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
Documentation
class Applicative m => Monad (m :: Type -> Type) 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 List
, 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.
'as
' can be understood as the >>=
bsdo
expression
do a <- as bs a
An alternative name for this function is 'bind', but some people may refer to it as 'flatMap', which results from it being equivialent to
\x f ->join
(fmap
f x) :: Monad m => m a -> (a -> m b) -> m b
which can be seen as mapping a value with
Monad m => m a -> m (m b)
and then 'flattening' m (m b)
to m b
using join
.
Inject a value into the monadic type.
This function should not be different from its default implementation
as pure
. The justification for the existence of this function is
merely historic.
Instances
Monad Complex | Since: base-4.9.0.0 |
Monad First | Since: base-4.9.0.0 |
Monad Last | Since: base-4.9.0.0 |
Monad Max | Since: base-4.9.0.0 |
Monad Min | Since: base-4.9.0.0 |
Monad Put | |
Monad Seq | |
Monad Tree | |
Monad NonEmpty | @since base-4.9.0.0 |
Monad STM | @since base-4.3.0.0 |
Monad Identity | @since base-4.8.0.0 |
Monad First | @since base-4.8.0.0 |
Monad Last | @since base-4.8.0.0 |
Monad Down | @since base-4.11.0.0 |
Monad Dual | @since base-4.8.0.0 |
Monad Product | @since base-4.8.0.0 |
Monad Sum | @since base-4.8.0.0 |
Monad Par1 | @since base-4.9.0.0 |
Monad P | @since base-2.01 |
Monad ReadP | @since base-2.01 |
Monad IO | @since base-2.01 |
Monad Q | |
Monad Maybe | @since base-2.01 |
Monad Solo | @since base-4.15 |
Monad [] | @since base-2.01 |
Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods (>>=) :: 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 (SetM s) | |
ArrowApply a => Monad (ArrowMonad a) | @since base-2.01 |
Defined in GHC.Internal.Control.Arrow Methods (>>=) :: 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 (Either e) | @since base-4.4.0.0 |
Monad (Proxy :: Type -> Type) | @since base-4.7.0.0 |
Monad (U1 :: Type -> Type) | @since base-4.9.0.0 |
Monad (ST s) | @since base-2.01 |
Monad (IParser t) | |
Monad m => Monad (MaybeT m) | |
Monoid a => Monad ((,) a) | @since base-4.9.0.0 |
(Applicative f, Monad f) => Monad (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # return :: a -> WhenMissing f x a # | |
Monad m => Monad (Kleisli m a) | @since base-4.14.0.0 |
Monad f => Monad (Ap f) | @since base-4.12.0.0 |
Monad f => Monad (Alt f) | @since base-4.8.0.0 |
Monad f => Monad (Rec1 f) | @since base-4.9.0.0 |
Monad (t m) => Monad (LiftingAccum t m) | Since: mtl-2.3 |
Defined in Control.Monad.Accum Methods (>>=) :: LiftingAccum t m a -> (a -> LiftingAccum t m b) -> LiftingAccum t m b # (>>) :: LiftingAccum t m a -> LiftingAccum t m b -> LiftingAccum t m b # return :: a -> LiftingAccum t m a # | |
Monad (t m) => Monad (LiftingSelect t m) | Since: mtl-2.3 |
Defined in Control.Monad.Select Methods (>>=) :: LiftingSelect t m a -> (a -> LiftingSelect t m b) -> LiftingSelect t m b # (>>) :: LiftingSelect t m a -> LiftingSelect t m b -> LiftingSelect t m b # return :: a -> LiftingSelect t m a # | |
(Monoid w, Functor m, Monad m) => Monad (AccumT w m) | |
Monad m => Monad (ExceptT e m) | |
Monad m => Monad (IdentityT m) | |
Monad m => Monad (ReaderT r m) | |
Monad m => Monad (SelectT r m) | |
Monad m => Monad (StateT s m) | |
Monad m => Monad (StateT s m) | |
Monad m => Monad (WriterT w m) | |
(Monoid w, Monad m) => Monad (WriterT w m) | |
(Monoid w, Monad m) => Monad (WriterT w m) | |
Monad m => Monad (Reverse m) | Derived instance. |
(Monoid a, Monoid b) => Monad ((,,) a b) | @since base-4.14.0.0 |
(Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
(Monad f, Applicative f) => Monad (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # return :: a -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Monad (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a # | |
(Monad f, Monad g) => Monad (f :*: g) | @since base-4.9.0.0 |
Monad (ContT r m) | |
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | @since base-4.14.0.0 |
Monad ((->) r) | @since base-2.01 |
(Monad f, Applicative f) => Monad (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a # | |
Monad f => Monad (M1 i c f) | @since base-4.9.0.0 |
Monad m => Monad (RWST r w s m) | |
(Monoid w, Monad m) => Monad (RWST r w s m) | |
(Monoid w, Monad m) => Monad (RWST r w s m) | |
class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where #
Monads that also support choice and failure.
Minimal complete definition
Nothing
Methods
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 Seq | |
MonadPlus STM | Takes the first non- @since base-4.3.0.0 |
MonadPlus P | @since base-2.01 |
Defined in GHC.Internal.Text.ParserCombinators.ReadP | |
MonadPlus ReadP | @since base-2.01 |
MonadPlus IO | Takes the first non-throwing @since base-4.9.0.0 |
MonadPlus Maybe | Picks the leftmost @since base-2.01 |
MonadPlus [] | Combines lists by concatenation, starting from the empty list. @since base-2.01 |
Defined in GHC.Internal.Base | |
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) | @since base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow | |
MonadPlus (Proxy :: Type -> Type) | @since base-4.9.0.0 |
MonadPlus (U1 :: Type -> Type) | @since base-4.9.0.0 |
Monad m => MonadPlus (MaybeT m) | |
MonadPlus m => MonadPlus (Kleisli m a) | @since base-4.14.0.0 |
MonadPlus f => MonadPlus (Ap f) | @since base-4.12.0.0 |
MonadPlus f => MonadPlus (Alt f) | @since base-4.8.0.0 |
MonadPlus f => MonadPlus (Rec1 f) | @since base-4.9.0.0 |
(Monoid w, Functor m, MonadPlus m) => MonadPlus (AccumT w m) | |
(Monad m, Monoid e) => MonadPlus (ExceptT e m) | |
MonadPlus m => MonadPlus (IdentityT m) | |
MonadPlus m => MonadPlus (ReaderT r m) | |
MonadPlus m => MonadPlus (SelectT r m) | |
MonadPlus m => MonadPlus (StateT s m) | |
MonadPlus m => MonadPlus (StateT s m) | |
(Functor m, MonadPlus m) => MonadPlus (WriterT w m) | |
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) | |
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) | |
MonadPlus m => MonadPlus (Reverse m) | Derived instance. |
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g) | Since: base-4.9.0.0 |
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) | @since base-4.9.0.0 |
MonadPlus f => MonadPlus (M1 i c f) | @since base-4.9.0.0 |
(Functor m, MonadPlus m) => MonadPlus (RWST r w s m) | |
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) | |
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) | |
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=
, but with the arguments interchanged.
as >>= f == f =<< as
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
Note that "forever" isn't necessarily non-terminating.
If the action is in a
and short-circuits after some number of iterations.
then MonadPlus
actually returns forever
mzero
, effectively short-circuiting its caller.
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.
'
' can be understood as the join
bssdo
expression
do bs <- bss bs
Examples
>>>
join [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
[1,2,3,4,5,6,7,8,9]
>>>
join (Just (Just 3))
Just 3
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.
runIdentity (filterM (Identity . p) xs) == filter p xs
Examples
>>>
filterM (\x -> do
putStrLn ("Keep: " ++ show x ++ "?") answer <- getLine pure (answer == "y")) [1, 2, 3] Keep: 1? y Keep: 2? n Keep: 3? y [1,3]
>>>
filterM (\x -> do
putStr (show x) x' <- readLn pure (x == x')) [1, 2, 3] 12 22 33 [2,3]
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 actact
n
times,
and then returns the list of results.
replicateM n (pure x) == replicate
n x
Examples
>>>
replicateM 3 getLine
hi heya hiya ["hi","heya","hiya"]
>>>
import Control.Monad.State
>>>
runState (replicateM 3 $ state $ \s -> (s, s + 1)) 1
([1,2,3],4)
replicateM_ :: Applicative m => Int -> m a -> m () #
concatMapM :: Monad m => (a -> m [b]) -> [a] -> m [b] #
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 signalling an error in
an error monad and conditionally rejecting the current choice in an
Alternative
-based parser.
As an example of signalling 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,
Examples
when debug (putStrLn "Debugging")
will output the string Debugging
if the Boolean value debug
is True
, and otherwise do nothing.
>>>
putStr "pi:" >> when False (print 3.14159)
pi:
unless :: Applicative f => Bool -> f () -> f () #
The reverse of when
.
Examples
>>>
do x <- getLine
unless (x == "hi") (putStrLn "hi!") comingupwithexamplesisdifficult hi!
>>>
unless (pi > exp 1) Nothing
Just ()
liftM :: Monad m => (a1 -> r) -> m a1 -> m r #
Promote a function to a monad.
This is equivalent to fmap
but specialised to Monads.
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.
Examples
>>>
liftM2 (+) [0,1] [0,2]
[0,2,1,3]
>>>
liftM2 (+) (Just 1) Nothing
Nothing
>>>
liftM2 (+) (+ 3) (* 2) 5
18
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
).