Protolude.Monad

protolude-0.3.4: A small prelude.

Safe Haskell | Trustworthy
Language | Haskell2010

Protolude.Monad

Synopsis

- class Applicative m => Monad (m :: Type -> Type) where
  - (>>=) :: m a -> (a -> m b) -> m b
  - return :: a -> m a
- class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
  - mzero :: m a
  - mplus :: m a -> m a -> m a
- (=<<) :: 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:

-     pure = return

-     m1 <*> m2 = m1 >>= (\x1 -> m2 >>= (\x2 -> return (x1 x2)))

The above laws imply:

-     fmap f xs  =  xs >>= return . f

-     (>>) = (*>)

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 `>>=` bs`' can be understood as the `do` 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`.

return :: a -> m a #

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

Instances details

Monad Complex | Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b # (>>) :: Complex a -> Complex b -> Complex b # return :: a -> Complex a #
Monad First | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a #
Monad Last | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a #
Monad Max | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b # (>>) :: Max a -> Max b -> Max b # return :: a -> Max a #
Monad Min | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b # (>>) :: Min a -> Min b -> Min b # return :: a -> Min a #
Monad Put |
Instance details Defined in Data.ByteString.Builder.Internal Methods (>>=) :: Put a -> (a -> Put b) -> Put b # (>>) :: Put a -> Put b -> Put b # return :: a -> Put a #
Monad Seq |
Instance details Defined in Data.Sequence.Internal Methods (>>=) :: Seq a -> (a -> Seq b) -> Seq b # (>>) :: Seq a -> Seq b -> Seq b # return :: a -> Seq a #
Monad Tree |
Instance details Defined in Data.Tree Methods (>>=) :: Tree a -> (a -> Tree b) -> Tree b # (>>) :: Tree a -> Tree b -> Tree b # return :: a -> Tree a #
Monad NonEmpty | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b # (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b # return :: a -> NonEmpty a #
Monad STM | @since base-4.3.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods (>>=) :: STM a -> (a -> STM b) -> STM b # (>>) :: STM a -> STM b -> STM b # return :: a -> STM a #
Monad Identity | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b # (>>) :: Identity a -> Identity b -> Identity b # return :: a -> Identity a #
Monad First | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a #
Monad Last | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a #
Monad Down | @since base-4.11.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b # (>>) :: Down a -> Down b -> Down b # return :: a -> Down a #
Monad Dual | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b # (>>) :: Dual a -> Dual b -> Dual b # return :: a -> Dual a #
Monad Product | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a #
Monad Sum | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a #
Monad Par1 | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b # (>>) :: Par1 a -> Par1 b -> Par1 b # return :: a -> Par1 a #
Monad P | @since base-2.01
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods (>>=) :: P a -> (a -> P b) -> P b # (>>) :: P a -> P b -> P b # return :: a -> P a #
Monad ReadP | @since base-2.01
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b # (>>) :: ReadP a -> ReadP b -> ReadP b # return :: a -> ReadP a #
Monad IO | @since base-2.01
Instance details Defined in GHC.Internal.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b # (>>) :: IO a -> IO b -> IO b # return :: a -> IO a #
Monad Q |
Instance details Defined in Language.Haskell.TH.Syntax Methods (>>=) :: Q a -> (a -> Q b) -> Q b # (>>) :: Q a -> Q b -> Q b # return :: a -> Q a #
Monad Maybe | @since base-2.01
Instance details Defined in GHC.Internal.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b # (>>) :: Maybe a -> Maybe b -> Maybe b # return :: a -> Maybe a #
Monad Solo | @since base-4.15
Instance details Defined in GHC.Internal.Base Methods (>>=) :: Solo a -> (a -> Solo b) -> Solo b # (>>) :: Solo a -> Solo b -> Solo b # return :: a -> Solo a #
Monad [] | @since base-2.01
Instance details Defined in GHC.Internal.Base Methods (>>=) :: [a] -> (a -> [b]) -> [b] # (>>) :: [a] -> [b] -> [b] # return :: a -> [a] #
Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0
Instance details 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) |
Instance details Defined in Data.Graph Methods (>>=) :: SetM s a -> (a -> SetM s b) -> SetM s b # (>>) :: SetM s a -> SetM s b -> SetM s b # return :: a -> SetM s a #
ArrowApply a => Monad (ArrowMonad a) | @since base-2.01
Instance details 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
Instance details Defined in GHC.Internal.Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b # (>>) :: Either e a -> Either e b -> Either e b # return :: a -> Either e a #
Monad (Proxy :: Type -> Type) | @since base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b # (>>) :: Proxy a -> Proxy b -> Proxy b # return :: a -> Proxy a #
Monad (U1 :: Type -> Type) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b # (>>) :: U1 a -> U1 b -> U1 b # return :: a -> U1 a #
Monad (ST s) | @since base-2.01
Instance details Defined in GHC.Internal.ST Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b # (>>) :: ST s a -> ST s b -> ST s b # return :: a -> ST s a #
Monad (IParser t) |
Instance details Defined in Data.Text.Internal.Read Methods (>>=) :: IParser t a -> (a -> IParser t b) -> IParser t b # (>>) :: IParser t a -> IParser t b -> IParser t b # return :: a -> IParser t a #
Monad m => Monad (MaybeT m) |
Instance details Defined in Control.Monad.Trans.Maybe Methods (>>=) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b # (>>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # return :: a -> MaybeT m a #
Monoid a => Monad ((,) a) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) # (>>) :: (a, a0) -> (a, b) -> (a, b) # return :: a0 -> (a, a0) #
(Applicative f, Monad f) => Monad (WhenMissing f x) | Equivalent to `ReaderT k (ReaderT x (MaybeT f))`. Since: containers-0.5.9
Instance details 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
Instance details Defined in GHC.Internal.Control.Arrow Methods (>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b # (>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b # return :: a0 -> Kleisli m a a0 #
Monad f => Monad (Ap f) | @since base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b # (>>) :: Ap f a -> Ap f b -> Ap f b # return :: a -> Ap f a #
Monad f => Monad (Alt f) | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b # (>>) :: Alt f a -> Alt f b -> Alt f b # return :: a -> Alt f a #
Monad f => Monad (Rec1 f) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b # (>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # return :: a -> Rec1 f a #
Monad (t m) => Monad (LiftingAccum t m) | Since: mtl-2.3
Instance details 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
Instance details 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) |
Instance details Defined in Control.Monad.Trans.Accum Methods (>>=) :: AccumT w m a -> (a -> AccumT w m b) -> AccumT w m b # (>>) :: AccumT w m a -> AccumT w m b -> AccumT w m b # return :: a -> AccumT w m a #
Monad m => Monad (ExceptT e m) |
Instance details Defined in Control.Monad.Trans.Except Methods (>>=) :: ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b # (>>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # return :: a -> ExceptT e m a #
Monad m => Monad (IdentityT m) |
Instance details Defined in Control.Monad.Trans.Identity Methods (>>=) :: IdentityT m a -> (a -> IdentityT m b) -> IdentityT m b # (>>) :: IdentityT m a -> IdentityT m b -> IdentityT m b # return :: a -> IdentityT m a #
Monad m => Monad (ReaderT r m) |
Instance details Defined in Control.Monad.Trans.Reader Methods (>>=) :: ReaderT r m a -> (a -> ReaderT r m b) -> ReaderT r m b # (>>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # return :: a -> ReaderT r m a #
Monad m => Monad (SelectT r m) |
Instance details Defined in Control.Monad.Trans.Select Methods (>>=) :: SelectT r m a -> (a -> SelectT r m b) -> SelectT r m b # (>>) :: SelectT r m a -> SelectT r m b -> SelectT r m b # return :: a -> SelectT r m a #
Monad m => Monad (StateT s m) |
Instance details Defined in Control.Monad.Trans.State.Lazy Methods (>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b # (>>) :: StateT s m a -> StateT s m b -> StateT s m b # return :: a -> StateT s m a #
Monad m => Monad (StateT s m) |
Instance details Defined in Control.Monad.Trans.State.Strict Methods (>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b # (>>) :: StateT s m a -> StateT s m b -> StateT s m b # return :: a -> StateT s m a #
Monad m => Monad (WriterT w m) |
Instance details Defined in Control.Monad.Trans.Writer.CPS Methods (>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b # (>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # return :: a -> WriterT w m a #
(Monoid w, Monad m) => Monad (WriterT w m) |
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods (>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b # (>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # return :: a -> WriterT w m a #
(Monoid w, Monad m) => Monad (WriterT w m) |
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods (>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b # (>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # return :: a -> WriterT w m a #
Monad m => Monad (Reverse m) | Derived instance.
Instance details Defined in Data.Functor.Reverse Methods (>>=) :: Reverse m a -> (a -> Reverse m b) -> Reverse m b # (>>) :: Reverse m a -> Reverse m b -> Reverse m b # return :: a -> Reverse m a #
(Monoid a, Monoid b) => Monad ((,,) a b) | @since base-4.14.0.0
Instance details Defined in GHC.Internal.Base Methods (>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) # (>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) # return :: a0 -> (a, b, a0) #
(Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b # (>>) :: Product f g a -> Product f g b -> Product f g b # return :: a -> Product f g a #
(Monad f, Applicative f) => Monad (WhenMatched f x y) | Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details 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 `ReaderT k (ReaderT x (MaybeT f))` . Since: containers-0.5.9
Instance details 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
Instance details Defined in GHC.Internal.Generics Methods (>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b # (>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b # return :: a -> (f :*: g) a #
Monad (ContT r m) |
Instance details Defined in Control.Monad.Trans.Cont Methods (>>=) :: ContT r m a -> (a -> ContT r m b) -> ContT r m b # (>>) :: ContT r m a -> ContT r m b -> ContT r m b # return :: a -> ContT r m a #
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | @since base-4.14.0.0
Instance details Defined in GHC.Internal.Base Methods (>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) # (>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) # return :: a0 -> (a, b, c, a0) #
Monad ((->) r) | @since base-2.01
Instance details Defined in GHC.Internal.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b # (>>) :: (r -> a) -> (r -> b) -> r -> b # return :: a -> r -> a #
(Monad f, Applicative f) => Monad (WhenMatched f k x y) | Equivalent to `ReaderT k (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details 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
Instance details Defined in GHC.Internal.Generics Methods (>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b # (>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # return :: a -> M1 i c f a #
Monad m => Monad (RWST r w s m) |
Instance details Defined in Control.Monad.Trans.RWS.CPS Methods (>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b # (>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # return :: a -> RWST r w s m a #
(Monoid w, Monad m) => Monad (RWST r w s m) |
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods (>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b # (>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # return :: a -> RWST r w s m a #
(Monoid w, Monad m) => Monad (RWST r w s m) |
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods (>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b # (>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # return :: a -> RWST r w s m a #

class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where #

Monads that also support choice and failure.

Minimal complete definition

Nothing

Methods

mzero :: m a #

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 #

An associative operation. The default definition is

    mplus = (<|>)

#### Instances

Instances details

MonadPlus Seq |
Instance details Defined in Data.Sequence.Internal Methods mzero :: Seq a # mplus :: Seq a -> Seq a -> Seq a #
MonadPlus STM | Takes the first non-`retry`ing `STM` action. @since base-4.3.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods mzero :: STM a # mplus :: STM a -> STM a -> STM a #
MonadPlus P | @since base-2.01
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods mzero :: P a # mplus :: P a -> P a -> P a #
MonadPlus ReadP | @since base-2.01
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods mzero :: ReadP a # mplus :: ReadP a -> ReadP a -> ReadP a #
MonadPlus IO | Takes the first non-throwing `IO` action's result. `mzero` throws an exception. @since base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods mzero :: IO a # mplus :: IO a -> IO a -> IO a #
MonadPlus Maybe | Picks the leftmost `Just` value, or, alternatively, `Nothing`. @since base-2.01
Instance details Defined in GHC.Internal.Base Methods mzero :: Maybe a # mplus :: Maybe a -> Maybe a -> Maybe a #
MonadPlus [] | Combines lists by concatenation, starting from the empty list. @since base-2.01
Instance details Defined in GHC.Internal.Base Methods mzero :: [a] # mplus :: [a] -> [a] -> [a] #
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) | @since base-4.6.0.0
Instance details Defined in GHC.Internal.Control.Arrow Methods mzero :: ArrowMonad a a0 # mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 #
MonadPlus (Proxy :: Type -> Type) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods mzero :: Proxy a # mplus :: Proxy a -> Proxy a -> Proxy a #
MonadPlus (U1 :: Type -> Type) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods mzero :: U1 a # mplus :: U1 a -> U1 a -> U1 a #
Monad m => MonadPlus (MaybeT m) |
Instance details Defined in Control.Monad.Trans.Maybe Methods mzero :: MaybeT m a # mplus :: MaybeT m a -> MaybeT m a -> MaybeT m a #
MonadPlus m => MonadPlus (Kleisli m a) | @since base-4.14.0.0
Instance details Defined in GHC.Internal.Control.Arrow Methods mzero :: Kleisli m a a0 # mplus :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 #
MonadPlus f => MonadPlus (Ap f) | @since base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods mzero :: Ap f a # mplus :: Ap f a -> Ap f a -> Ap f a #
MonadPlus f => MonadPlus (Alt f) | @since base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods mzero :: Alt f a # mplus :: Alt f a -> Alt f a -> Alt f a #
MonadPlus f => MonadPlus (Rec1 f) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods mzero :: Rec1 f a # mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a #
(Monoid w, Functor m, MonadPlus m) => MonadPlus (AccumT w m) |
Instance details Defined in Control.Monad.Trans.Accum Methods mzero :: AccumT w m a # mplus :: AccumT w m a -> AccumT w m a -> AccumT w m a #
(Monad m, Monoid e) => MonadPlus (ExceptT e m) |
Instance details Defined in Control.Monad.Trans.Except Methods mzero :: ExceptT e m a # mplus :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a #
MonadPlus m => MonadPlus (IdentityT m) |
Instance details Defined in Control.Monad.Trans.Identity Methods mzero :: IdentityT m a # mplus :: IdentityT m a -> IdentityT m a -> IdentityT m a #
MonadPlus m => MonadPlus (ReaderT r m) |
Instance details Defined in Control.Monad.Trans.Reader Methods mzero :: ReaderT r m a # mplus :: ReaderT r m a -> ReaderT r m a -> ReaderT r m a #
MonadPlus m => MonadPlus (SelectT r m) |
Instance details Defined in Control.Monad.Trans.Select Methods mzero :: SelectT r m a # mplus :: SelectT r m a -> SelectT r m a -> SelectT r m a #
MonadPlus m => MonadPlus (StateT s m) |
Instance details Defined in Control.Monad.Trans.State.Lazy Methods mzero :: StateT s m a # mplus :: StateT s m a -> StateT s m a -> StateT s m a #
MonadPlus m => MonadPlus (StateT s m) |
Instance details Defined in Control.Monad.Trans.State.Strict Methods mzero :: StateT s m a # mplus :: StateT s m a -> StateT s m a -> StateT s m a #
(Functor m, MonadPlus m) => MonadPlus (WriterT w m) |
Instance details Defined in Control.Monad.Trans.Writer.CPS Methods mzero :: WriterT w m a # mplus :: WriterT w m a -> WriterT w m a -> WriterT w m a #
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) |
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods mzero :: WriterT w m a # mplus :: WriterT w m a -> WriterT w m a -> WriterT w m a #
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m) |
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods mzero :: WriterT w m a # mplus :: WriterT w m a -> WriterT w m a -> WriterT w m a #
MonadPlus m => MonadPlus (Reverse m) | Derived instance.
Instance details Defined in Data.Functor.Reverse Methods mzero :: Reverse m a # mplus :: Reverse m a -> Reverse m a -> Reverse m a #
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzero :: Product f g a # mplus :: Product f g a -> Product f g a -> Product f g a #
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods mzero :: (f :*: g) a # mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a #
MonadPlus f => MonadPlus (M1 i c f) | @since base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods mzero :: M1 i c f a # mplus :: M1 i c f a -> M1 i c f a -> M1 i c f a #
(Functor m, MonadPlus m) => MonadPlus (RWST r w s m) |
Instance details Defined in Control.Monad.Trans.RWS.CPS Methods mzero :: RWST r w s m a # mplus :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a #
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) |
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods mzero :: RWST r w s m a # mplus :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a #
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m) |
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods mzero :: RWST r w s m a # mplus :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a #

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as `>>=`, but with the arguments interchanged.

    as >>= f == f =<< as

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #

Left-to-right composition of `Kleisli` arrows.

'`(bs `>=>` cs) a`' can be understood as the `do` expression

    do b <- bs a
       cs b

or in terms of ``(>>=)`` as

    bs a >>= cs

(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c infixr 1 #

Right-to-left composition of Kleisli arrows. `(`>=>`)`, with the arguments flipped.

Note how this operator resembles function composition `(`.`)`:

    (.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
    (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c

(>>) :: Monad m => 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.

'`as `>>` bs`' can be understood as the `do` expression

    do as
       bs

or in terms of ``(>>=)`` as

    as >>= const bs

forever :: Applicative f => f a -> f b #

Repeat an action indefinitely.

#### Examples

Expand

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 socket
      forkFinally (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 ``MonadPlus`` and short-circuits after some number of iterations. then ``forever`` actually returns `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.

'``join` bss`' can be understood as the `do` expression

    do bs <- bss
       bs

#### Examples

Expand

    >>> 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

to run an `STM` transaction and the `IO` action it returns.

mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a #

Direct `MonadPlus` equivalent of `filter`.

#### Examples

Expand

The `filter` function is just `mfilter` specialized to the list monad:

    filter = ( mfilter :: (a -> Bool) -> [a] -> [a] )

An example using `mfilter` with the `Maybe` monad:

    >>> mfilter odd (Just 1)
    Just 1
    >>> mfilter odd (Just 2)
    Nothing

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

Expand

    >>> 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] #

The `zipWithM` function generalizes `zipWith` to arbitrary applicative functors.

zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () #

`zipWithM_` is the extension of `zipWithM` which ignores the final result.

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.

Note: `foldM` is the same as `foldlM`

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] #

``replicateM` n act` performs the action `act` `n` times, and then returns the list of results.

    replicateM n (pure x) == replicate n x

#### Examples

Expand

    >>> 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 () #

Like `replicateM`, but discards the result.

#### Examples

Expand

    >>> replicateM_ 3 (putStr "a")
    aaa

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

Expand

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 ``Just` (x `div` y)` otherwise. For example:

    >>> 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

Expand

    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

Expand

    >>> 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

Expand

    >>> 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`).

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 #

In many situations, the `liftM` operations can be replaced by uses of `ap`, which promotes function application.

    return f `ap` x1 `ap` ... `ap` xn

is equivalent to

    liftM<n> f x1 x2 ... xn

#### Examples

Expand

    >>> pure (\x y z -> x + y * z) `ap` Just 1 `ap` Just 5 `ap` Just 10
    Just 51

(<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4 #

Strict version of `<$>`.

@since base-4.8.0.0