Copyright | (c) Hans Hoglund 2012 |
---|---|
License | BSD-style |
Maintainer | hans@hanshoglund.se |
Stability | experimental |
Portability | non-portable (TF,GNTD) |
Safe Haskell | None |
Language | Haskell98 |
Control.Monad.Plus
Description
Partial maps and filters over MonadPlus
instances. The basic idea here is that
the monad interface together with the monoidal structure of MonadPlus
is enough
to implement partial maps and filters (i.e. mmapMaybe
and mfilter
).
This is especially useful for sequential structures such as event lists, tracks etc.
Inspired by the following blog post:
Synopsis
- guard :: Alternative f => Bool -> f ()
- join :: Monad m => m (m a) -> m a
- class Applicative m => Monad (m :: Type -> Type) where
- class Functor (f :: Type -> Type) where
- fmap :: (a -> b) -> f a -> f b
- mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b)
- sequence :: (Traversable t, Monad m) => t (m a) -> m (t a)
- mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
- unless :: Applicative f => Bool -> f () -> f ()
- replicateM_ :: Applicative m => Int -> m a -> m ()
- replicateM :: Applicative m => Int -> m a -> m [a]
- foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
- foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()
- zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]
- mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])
- forever :: Applicative f => f a -> f b
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
- forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- void :: Functor f => f a -> f ()
- ap :: Monad m => m (a -> b) -> m a -> m b
- liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
- liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
- liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- when :: Applicative f => Bool -> f () -> f ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
- msum' :: (MonadPlus m, Foldable t) => t (m a) -> m a
- mfold :: (MonadPlus m, Foldable t) => t a -> m a
- mfromList :: MonadPlus m => [a] -> m a
- mfromMaybe :: MonadPlus m => Maybe a -> m a
- mreturn :: MonadPlus m => (a -> Maybe b) -> a -> m b
- mpartition :: MonadPlus m => (a -> Bool) -> m a -> (m a, m a)
- mscatter :: MonadPlus m => m [b] -> m b
- mscatter' :: (MonadPlus m, Foldable t) => m (t b) -> m b
- mcatMaybes :: MonadPlus m => m (Maybe a) -> m a
- mlefts :: MonadPlus m => m (Either a b) -> m a
- mrights :: MonadPlus m => m (Either a b) -> m b
- mpartitionEithers :: MonadPlus m => m (Either a b) -> (m a, m b)
- mmapMaybe :: MonadPlus m => (a -> Maybe b) -> m a -> m b
- mconcatMap :: MonadPlus m => (a -> [b]) -> m a -> m b
- mconcatMap' :: (MonadPlus m, Foldable t) => (a -> t b) -> m a -> m b
- newtype Partial a b = Partial {
- getPartial :: a -> Maybe b
- partial :: (a -> Bool) -> a -> Maybe a
- predicate :: (a -> Maybe a) -> a -> Bool
- always :: (a -> b) -> a -> Maybe b
- never :: a -> Maybe c
Basics
guard :: Alternative f => Bool -> f () Source #
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)
join :: Monad m => m (m a) -> m a Source #
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
class Applicative m => Monad (m :: Type -> Type) where Source #
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 Source #
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 Source #
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 :: String -> m a Source #
Fail with a message. This operation is not part of the
mathematical definition of a monad, but is invoked on pattern-match
failure in a do
expression.
As part of the MonadFail proposal (MFP), this function is moved
to its own class MonadFail
(see Control.Monad.Fail for more
details). The definition here will be removed in a future
release.
Instances
Monad [] | 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 First | Since: base-4.8.0.0 |
Monad Last | Since: base-4.8.0.0 |
Monad Dual | Since: base-4.8.0.0 |
Monad Sum | Since: base-4.8.0.0 |
Monad Product | Since: base-4.8.0.0 |
Monad Down | Since: base-4.11.0.0 |
Monad ReadP | Since: base-2.1 |
Monad NonEmpty | Since: base-4.9.0.0 |
Monad P | Since: base-2.1 |
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 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 Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source # fail :: String -> WrappedMonad m a Source # | |
ArrowApply a => Monad (ArrowMonad a) | Since: base-2.1 |
Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source # fail :: String -> ArrowMonad a a0 Source # | |
Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Monad (Partial r) Source # | |
Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
Monad ((->) r :: Type -> Type) | Since: base-2.1 |
(Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
class Functor (f :: Type -> Type) where Source #
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.
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 ZipList | Since: base-2.1 |
Functor First | Since: base-4.8.0.0 |
Functor Last | Since: base-4.8.0.0 |
Functor Dual | Since: base-4.8.0.0 |
Functor Sum | Since: base-4.8.0.0 |
Functor Product | Since: base-4.8.0.0 |
Functor Down | Since: base-4.11.0.0 |
Functor ReadP | Since: base-2.1 |
Functor NonEmpty | Since: base-4.9.0.0 |
Functor P | Since: base-4.8.0.0 |
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 (Array i) | Since: base-2.1 |
Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Functor (Partial r) Source # | |
Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
Functor (Const m :: Type -> Type) | Since: base-2.1 |
Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
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 (M1 i c f) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b) Source #
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 :: (Traversable t, Monad m) => t (m a) -> m (t a) Source #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_
.
(<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4 Source #
Strict version of <$>
.
Since: base-4.8.0.0
replicateM_ :: Applicative m => Int -> m a -> m () Source #
Like replicateM
, but discards the result.
replicateM :: Applicative m => Int -> m a -> m [a] Source #
performs the action replicateM
n actn
times,
gathering the results.
foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () Source #
Like foldM
, but discards the result.
foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b Source #
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.
zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () Source #
zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] Source #
mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) Source #
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-transforming monad.
forever :: Applicative f => f a -> f b Source #
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
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 Source #
Left-to-right composition of Kleisli arrows.
filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a] Source #
This generalizes the list-based filter
function.
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) Source #
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source #
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
.
void :: Functor f => f a -> f () Source #
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
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r Source #
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 Source #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r Source #
Promote a function to a monad, scanning the monadic arguments from
left to right (cf. liftM2
).
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r Source #
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
when :: Applicative f => Bool -> f () -> f () Source #
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.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #
Same as >>=
, but with the arguments interchanged.
class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where Source #
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
mplus :: m a -> m a -> m a Source #
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 P | Since: base-2.1 |
MonadPlus (U1 :: 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 Methods mzero :: ArrowMonad a a0 Source # mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source # | |
MonadPlus (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
MonadPlus (Partial r) Source # | |
MonadPlus f => MonadPlus (Rec1 f) | Since: base-4.9.0.0 |
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 g) => MonadPlus (f :*: g) | Since: base-4.9.0.0 |
MonadPlus f => MonadPlus (M1 i c f) | Since: base-4.9.0.0 |
msum' :: (MonadPlus m, Foldable t) => t (m a) -> m a Source #
This generalizes the list-based concat
function.
Constructing
mfromList :: MonadPlus m => [a] -> m a Source #
Translate a list to an arbitrary MonadPlus
type.
This function generalizes the listToMaybe
function.
mfromMaybe :: MonadPlus m => Maybe a -> m a Source #
Translate maybe to an arbitrary MonadPlus
type.
This function generalizes the maybeToList
function.
mreturn :: MonadPlus m => (a -> Maybe b) -> a -> m b Source #
Convert a partial function to a function returning an arbitrary
MonadPlus
type.
Filtering
mpartition :: MonadPlus m => (a -> Bool) -> m a -> (m a, m a) Source #
Special filters
mscatter :: MonadPlus m => m [b] -> m b Source #
Join list elements together.
This function generalizes the catMaybes
function.
mscatter' :: (MonadPlus m, Foldable t) => m (t b) -> m b Source #
Join foldable elements together.
This function generalizes the catMaybes
function.
mcatMaybes :: MonadPlus m => m (Maybe a) -> m a Source #
Pass through Just
elements.
This function generalizes the catMaybes
function.
mlefts :: MonadPlus m => m (Either a b) -> m a Source #
Pass through Left
elements.
This function generalizes the lefts
function.
mrights :: MonadPlus m => m (Either a b) -> m b Source #
Pass through Right
elements.
This function generalizes the rights
function.
mpartitionEithers :: MonadPlus m => m (Either a b) -> (m a, m b) Source #
Separate Left
and Right
elements.
This function generalizes the partitionEithers
function.
Special maps
mmapMaybe :: MonadPlus m => (a -> Maybe b) -> m a -> m b Source #
Modify or discard a value.
This function generalizes the mapMaybe
function.
mconcatMap :: MonadPlus m => (a -> [b]) -> m a -> m b Source #
Modify, discard or spawn values.
This function generalizes the concatMap
function.
mconcatMap' :: (MonadPlus m, Foldable t) => (a -> t b) -> m a -> m b Source #
Modify, discard or spawn values.
This function generalizes the concatMap
function.
Utility
Wrapper for partial functions with MonadPlus
instance.
Constructors
Partial | |
Fields
|