W3cubDocs

/Haskell 8

Control.Monad

Copyright	(c) The University of Glasgow 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	[email protected]
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Functor and monad classes
Functions

Description

The Functor, Monad and MonadPlus classes, with some useful operations on monads.

Functor and monad classes

class Functor f 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.

Methods

fmap :: (a -> b) -> f a -> f b Source

Instances

Functor []	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] Source (<$) :: a -> [b] -> [a] Source
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b Source (<$) :: a -> Maybe b -> Maybe a Source
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b Source (<$) :: a -> IO b -> IO a Source
Functor Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b Source (<$) :: a -> Par1 b -> Par1 a Source
Functor NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source (<$) :: a -> NonEmpty b -> NonEmpty a Source
Functor ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b Source (<$) :: a -> ReadP b -> ReadP a Source
Functor ReadPrec	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods fmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source (<$) :: a -> ReadPrec b -> ReadPrec a Source
Functor Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b Source (<$) :: a -> Down b -> Down a Source
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b Source (<$) :: a -> Product b -> Product a Source
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b Source (<$) :: a -> Sum b -> Sum a Source
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source (<$) :: a -> Dual b -> Dual a Source
Functor Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
Functor First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
Functor STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods fmap :: (a -> b) -> STM a -> STM b Source (<$) :: a -> STM b -> STM a Source
Functor Handler	Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b Source (<$) :: a -> Handler b -> Handler a Source
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b Source (<$) :: a -> Identity b -> Identity a Source
Functor ZipList	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source (<$) :: a -> ZipList b -> ZipList a Source
Functor ArgDescr	Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source (<$) :: a -> ArgDescr b -> ArgDescr a Source
Functor OptDescr	Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> OptDescr a -> OptDescr b Source (<$) :: a -> OptDescr b -> OptDescr a Source
Functor ArgOrder	Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source (<$) :: a -> ArgOrder b -> ArgOrder a Source
Functor Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Option a -> Option b Source (<$) :: a -> Option b -> Option a Source
Functor Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
Functor First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
Functor Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b Source (<$) :: a -> Max b -> Max a Source
Functor Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b Source (<$) :: a -> Min b -> Min a Source
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b Source (<$) :: a -> Complex b -> Complex a Source
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b Source (<$) :: a0 -> Either a b -> Either a a0 Source
Functor (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b Source (<$) :: a -> V1 b -> V1 a Source
Functor (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b Source (<$) :: a -> U1 b -> U1 a Source
Functor ((,) a)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) Source (<$) :: a0 -> (a, b) -> (a, a0) Source
Functor (ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods fmap :: (a -> b) -> ST s a -> ST s b Source (<$) :: a -> ST s b -> ST s a Source
Functor (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b Source (<$) :: a -> Proxy b -> Proxy a Source
Arrow a => Functor (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source
Monad m => Functor (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source
Functor (ST s)	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods fmap :: (a -> b) -> ST s a -> ST s b Source (<$) :: a -> ST s b -> ST s a Source
Functor (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source (<$) :: a0 -> Arg a b -> Arg a a0 Source
Functor f => Functor (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source (<$) :: a -> Rec1 f b -> Rec1 f a Source
Functor (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b Source (<$) :: a -> URec Char b -> URec Char a Source
Functor (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b Source (<$) :: a -> URec Double b -> URec Double a Source
Functor (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b Source (<$) :: a -> URec Float b -> URec Float a Source
Functor (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b Source (<$) :: a -> URec Int b -> URec Int a Source
Functor (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b Source (<$) :: a -> URec Word b -> URec Word a Source
Functor (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source (<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source
Functor f => Functor (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b Source (<$) :: a -> Alt f b -> Alt f a Source
Functor f => Functor (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b Source (<$) :: a -> Ap f b -> Ap f a Source
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b Source (<$) :: a -> Const m b -> Const m a Source
Arrow a => Functor (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source
Functor ((->) r :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b Source (<$) :: a -> (r -> b) -> r -> a Source
Functor (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> K1 i c a -> K1 i c b Source (<$) :: a -> K1 i c b -> K1 i c a Source
(Functor f, Functor g) => Functor (f :+: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source (<$) :: a -> (f :+: g) b -> (f :+: g) a Source
(Functor f, Functor g) => Functor (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b Source (<$) :: a -> (f :: g) b -> (f :: g) a Source
(Functor f, Functor g) => Functor (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b Source (<$) :: a -> Sum f g b -> Sum f g a Source
(Functor f, Functor g) => Functor (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b Source (<$) :: a -> Product f g b -> Product f g a Source
Functor f => Functor (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source (<$) :: a -> M1 i c f b -> M1 i c f a Source
(Functor f, Functor g) => Functor (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source (<$) :: a -> (f :.: g) b -> (f :.: g) a Source
(Functor f, Functor g) => Functor (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b Source (<$) :: a -> Compose f g b -> Compose f g a Source

class Applicative m => Monad m 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:

```
return a >>= k  =  k a
```
```
m >>= return  =  m
```

m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

```
pure = return
```
```
(<*>) = ap
```

The above laws imply:

```
fmap f xs  =  xs >>= return . f
```
```
(>>) = (*>)
```

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

(>>=) :: forall a b. 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.

(>>) :: forall a b. 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.

return :: a -> m a Source

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
Instance details Defined in GHC.Base Methods (>>=) :: [a] -> (a -> [b]) -> [b] Source (>>) :: [a] -> [b] -> [b] Source return :: a -> [a] Source fail :: String -> [a] Source
Monad Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source (>>) :: Maybe a -> Maybe b -> Maybe b Source return :: a -> Maybe a Source fail :: String -> Maybe a Source
Monad IO	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b Source (>>) :: IO a -> IO b -> IO b Source return :: a -> IO a Source fail :: String -> IO a Source
Monad Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source (>>) :: Par1 a -> Par1 b -> Par1 b Source return :: a -> Par1 a Source fail :: String -> Par1 a Source
Monad NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source return :: a -> NonEmpty a Source fail :: String -> NonEmpty a Source
Monad ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source (>>) :: ReadP a -> ReadP b -> ReadP b Source return :: a -> ReadP a Source fail :: String -> ReadP a Source
Monad ReadPrec	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods (>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b Source (>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source return :: a -> ReadPrec a Source fail :: String -> ReadPrec a Source
Monad Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b Source (>>) :: Down a -> Down b -> Down b Source return :: a -> Down a Source fail :: String -> Down a Source
Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source (>>) :: Product a -> Product b -> Product b Source return :: a -> Product a Source fail :: String -> Product a Source
Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source (>>) :: Sum a -> Sum b -> Sum b Source return :: a -> Sum a Source fail :: String -> Sum a Source
Monad Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source (>>) :: Dual a -> Dual b -> Dual b Source return :: a -> Dual a Source fail :: String -> Dual a Source
Monad Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source fail :: String -> Last a Source
Monad First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source fail :: String -> First a Source
Monad STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (>>=) :: STM a -> (a -> STM b) -> STM b Source (>>) :: STM a -> STM b -> STM b Source return :: a -> STM a Source fail :: String -> STM a Source
Monad Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b Source (>>) :: Identity a -> Identity b -> Identity b Source return :: a -> Identity a Source fail :: String -> Identity a Source
Monad Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Option a -> (a -> Option b) -> Option b Source (>>) :: Option a -> Option b -> Option b Source return :: a -> Option a Source fail :: String -> Option a Source
Monad Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source fail :: String -> Last a Source
Monad First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source fail :: String -> First a Source
Monad Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b Source (>>) :: Max a -> Max b -> Max b Source return :: a -> Max a Source fail :: String -> Max a Source
Monad Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b Source (>>) :: Min a -> Min b -> Min b Source return :: a -> Min a Source fail :: String -> Min a Source
Monad Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b Source (>>) :: Complex a -> Complex b -> Complex b Source return :: a -> Complex a Source fail :: String -> Complex a Source
Monad (Either e)	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b Source (>>) :: Either e a -> Either e b -> Either e b Source return :: a -> Either e a Source fail :: String -> Either e a Source
Monad (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b Source (>>) :: U1 a -> U1 b -> U1 b Source return :: a -> U1 a Source fail :: String -> U1 a Source
Monoid a => Monad ((,) a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) Source (>>) :: (a, a0) -> (a, b) -> (a, b) Source return :: a0 -> (a, a0) Source fail :: String -> (a, a0) Source
Monad (ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source (>>) :: ST s a -> ST s b -> ST s b Source return :: a -> ST s a Source fail :: String -> ST s a Source
Monad (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b Source (>>) :: Proxy a -> Proxy b -> Proxy b Source return :: a -> Proxy a Source fail :: String -> Proxy a Source
ArrowApply a => Monad (ArrowMonad a)	Since: base-2.1
Instance details 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 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 Source (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source return :: a -> WrappedMonad m a Source fail :: String -> WrappedMonad m a Source
Monad (ST s)	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source (>>) :: ST s a -> ST s b -> ST s b Source return :: a -> ST s a Source fail :: String -> ST s a Source
Monad f => Monad (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b Source (>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source return :: a -> Rec1 f a Source fail :: String -> Rec1 f a Source
Monad f => Monad (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source (>>) :: Alt f a -> Alt f b -> Alt f b Source return :: a -> Alt f a Source fail :: String -> Alt f a Source
Monad f => Monad (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source (>>) :: Ap f a -> Ap f b -> Ap f b Source return :: a -> Ap f a Source fail :: String -> Ap f a Source
Monad ((->) r :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b Source (>>) :: (r -> a) -> (r -> b) -> r -> b Source return :: a -> r -> a Source fail :: String -> r -> a Source
(Monad f, Monad g) => Monad (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: (f :: g) a -> (a -> (f :: g) b) -> (f :: g) b Source (>>) :: (f :: g) a -> (f :: g) b -> (f :: g) b Source return :: a -> (f :: g) a Source fail :: String -> (f :: g) a Source
(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 Source (>>) :: Product f g a -> Product f g b -> Product f g b Source return :: a -> Product f g a Source fail :: String -> Product f g a Source
Monad f => Monad (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b Source (>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source return :: a -> M1 i c f a Source fail :: String -> M1 i c f a Source

class (Alternative m, Monad m) => MonadPlus m where Source

Monads that also support choice and failure.

Minimal complete definition

Nothing

Methods

mzero :: m a Source

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
Instance details Defined in GHC.Base Methods mzero :: [a] Source mplus :: [a] -> [a] -> [a] Source
MonadPlus Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: Maybe a Source mplus :: Maybe a -> Maybe a -> Maybe a Source
MonadPlus IO	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mzero :: IO a Source mplus :: IO a -> IO a -> IO a Source
MonadPlus ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods mzero :: ReadP a Source mplus :: ReadP a -> ReadP a -> ReadP a Source
MonadPlus ReadPrec	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods mzero :: ReadPrec a Source mplus :: ReadPrec a -> ReadPrec a -> ReadPrec a Source
MonadPlus STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods mzero :: STM a Source mplus :: STM a -> STM a -> STM a Source
MonadPlus Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mzero :: Option a Source mplus :: Option a -> Option a -> Option a Source
MonadPlus (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: U1 a Source mplus :: U1 a -> U1 a -> U1 a Source
MonadPlus (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods mzero :: Proxy a Source mplus :: Proxy a -> Proxy a -> Proxy a Source
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods mzero :: ArrowMonad a a0 Source mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source
MonadPlus f => MonadPlus (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: Rec1 f a Source mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a Source
MonadPlus f => MonadPlus (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a Source mplus :: Alt f a -> Alt f a -> Alt f a Source
MonadPlus f => MonadPlus (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a Source mplus :: Ap f a -> Ap f a -> Ap f a Source
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: (f :: g) a Source mplus :: (f :: g) a -> (f :: g) a -> (f :: g) a Source
(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 Source mplus :: Product f g a -> Product f g a -> Product f g a Source
MonadPlus f => MonadPlus (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: M1 i c f a Source mplus :: M1 i c f a -> M1 i c f a -> M1 i c f a Source

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 constructor m 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) 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_.

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () Source

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) Source

forM is mapM with its arguments flipped. For a version that ignores the results see forM_.

forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m () Source

forM_ is mapM_ with its arguments flipped. For a version that doesn't ignore the results see forM.

As of base 4.8.0.0, forM_ is just for_, specialized to Monad.

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_.

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.

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

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

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

Left-to-right composition of Kleisli arrows.

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

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

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

Repeat an action indefinitely.

Examples

Expand

A common use of forever is to process input from network sockets, Handles, 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

void :: Functor f => f a -> f () Source

void value discards or ignores the result of evaluation, such as the return value of an IO action.

Examples

Expand

Replace the contents of a Maybe Int with unit:

>>> void Nothing
Nothing
>>> void (Just 3)
Just ()

Replace the contents of an Either Int Int with unit, resulting in an 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 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

Expand

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.

msum :: (Foldable t, MonadPlus m) => t (m a) -> m a Source

The sum of a collection of actions, generalizing concat. As of base 4.8.0.0, msum is just asum, specialized to MonadPlus.

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

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] Source

This generalizes the list-based filter function.

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.

zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] Source

The zipWithM function generalizes zipWith to arbitrary applicative functors.

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

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 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.

Note: foldM is the same as foldlM

foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () Source

Like foldM, but discards the result.

replicateM :: Applicative m => Int -> m a -> m [a] Source

replicateM n act performs the action n times, gathering the results.

replicateM_ :: Applicative m => Int -> m a -> m () Source

Like replicateM, but discards the result.

Conditional execution of monadic expressions

guard :: Alternative f => Bool -> f () Source

Conditional failure of Alternative computations. Defined by

guard True  = pure ()
guard False = empty

Examples

Expand

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 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 () 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.

unless :: Applicative f => Bool -> f () -> f () Source

The reverse of when.

Monadic lifting operators

liftM :: Monad m => (a1 -> r) -> m a1 -> m r Source

Promote a function to a monad.

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

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).

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).

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).

ap :: Monad m => m (a -> b) -> m a -> m b Source

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

liftMn f x1 x2 ... xn

Strict monadic functions

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

Strict version of <$>.

Since: base-4.8.0.0

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.6.1/docs/html/libraries/base-4.12.0.0/Control-Monad.html

Control.Monad

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Functor and monad classes

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Basic `Monad` functions