base-4.20.0.0: Core data structures and operations
Copyright (c) The University of Glasgow 2001 BSD-style (see the file libraries/base/LICENSE) libraries@haskell.org provisional portable Safe Haskell2010

Control.Monad

Description

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

Synopsis

# Functor and monad classes

class Functor (f :: Type -> Type) where Source #

A type f is a Functor if it provides a function fmap which, given any types a and b lets you apply any function from (a -> b) to turn an f a into an f b, preserving the structure of f. Furthermore f needs to adhere to the following:

Identity
fmap id == id
Composition
fmap (f . g) == fmap f . fmap g

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds. See these articles by School of Haskell or David Luposchainsky for an explanation.

Minimal complete definition

fmap

Methods

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

fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in Either a b).

Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.

#### Examples

Expand

Convert from a Maybe Int to a Maybe String using show:

>>> fmap show Nothing
Nothing
>>> fmap show (Just 3)
Just "3"


Convert from an Either Int Int to an Either Int String using show:

>>> fmap show (Left 17)
Left 17
>>> fmap show (Right 17)
Right "17"


Double each element of a list:

>>> fmap (*2) [1,2,3]
[2,4,6]


Apply even to the second element of a pair:

>>> fmap even (2,2)
(2,True)


It may seem surprising that the function is only applied to the last element of the tuple compared to the list example above which applies it to every element in the list. To understand, remember that tuples are type constructors with multiple type parameters: a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over with fmap).

It explains why fmap can be used with tuples containing values of different types as in the following example:

>>> fmap even ("hello", 1.0, 4)
("hello",1.0,True)


(<$) :: a -> f b -> f a infixl 4 Source # Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version. #### Examples Expand Perform a computation with Maybe and replace the result with a constant value if it is Just: >>> 'a' <$ Just 2
Just 'a'
>>> 'a' <$Nothing Nothing  #### Instances Instances details  Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Complex Methodsfmap :: (a -> b) -> Complex a -> Complex b Source #(<$) :: a -> Complex b -> Complex a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Max a -> Max b Source #(<$) :: a -> Max b -> Max a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Min a -> Min b Source #(<$) :: a -> Min b -> Min a Source # Source # Since: base-4.7.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source #(<$) :: a -> ArgDescr b -> ArgDescr a Source # Source # Since: base-4.7.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source #(<$) :: a -> ArgOrder b -> ArgOrder a Source # Source # Since: base-4.7.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> OptDescr a -> OptDescr b Source #(<$) :: a -> OptDescr b -> OptDescr a Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source #(<$) :: a -> NonEmpty b -> NonEmpty a Source # @since base-4.3.0.0 Instance detailsDefined in GHC.Internal.Conc.Sync Methodsfmap :: (a -> b) -> STM a -> STM b Source #(<$) :: a -> STM b -> STM a Source # @since base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Exception Methodsfmap :: (a -> b) -> Handler a -> Handler b Source #(<$) :: a -> Handler b -> Handler a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Identity Methodsfmap :: (a -> b) -> Identity a -> Identity b Source #(<$) :: a -> Identity b -> Identity a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # @since base-4.11.0.0 Instance detailsDefined in GHC.Internal.Data.Ord Methodsfmap :: (a -> b) -> Down a -> Down b Source #(<$) :: a -> Down b -> Down a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Dual a -> Dual b Source #(<$) :: a -> Dual b -> Dual a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Product a -> Product b Source #(<$) :: a -> Product b -> Product a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Sum a -> Sum b Source #(<$) :: a -> Sum b -> Sum a Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Functor.ZipList Methodsfmap :: (a -> b) -> ZipList a -> ZipList b Source #(<$) :: a -> ZipList b -> ZipList a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.GHCi Methodsfmap :: (a -> b) -> NoIO a -> NoIO b Source #(<$) :: a -> NoIO b -> NoIO a Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> Par1 a -> Par1 b Source #(<$) :: a -> Par1 b -> Par1 a Source # @since base-4.8.0.0 Instance details Methodsfmap :: (a -> b) -> P a -> P b Source #(<$) :: a -> P b -> P a Source # @since base-2.01 Instance details Methodsfmap :: (a -> b) -> ReadP a -> ReadP b Source #(<$) :: a -> ReadP b -> ReadP a Source # @since base-2.01 Instance details Methodsfmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source #(<$) :: a -> ReadPrec b -> ReadPrec a Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> IO a -> IO b Source #(<$) :: a -> IO b -> IO a Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> Maybe a -> Maybe b Source #(<$) :: a -> Maybe b -> Maybe a Source # @since base-4.15 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> Solo a -> Solo b Source #(<$) :: a -> Solo b -> Solo a Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> [a] -> [b] Source #(<$) :: a -> [b] -> [a] Source # Monad m => Functor (WrappedMonad m) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #(<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # Functor (Arg a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source #(<$) :: a0 -> Arg a b -> Arg a a0 Source # Functor (Array i) @since base-2.01 Instance detailsDefined in GHC.Internal.Arr Methodsfmap :: (a -> b) -> Array i a -> Array i b Source #(<$) :: a -> Array i b -> Array i a Source # Arrow a => Functor (ArrowMonad a) @since base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source #(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # Functor (ST s) @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Monad.ST.Lazy.Imp Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # @since base-3.0 Instance detailsDefined in GHC.Internal.Data.Either Methodsfmap :: (a0 -> b) -> Either a a0 -> Either a b Source #(<$) :: a0 -> Either a b -> Either a a0 Source # @since base-4.0 Instance detailsDefined in GHC.Internal.Data.Functor.Utils Methodsfmap :: (a -> b) -> StateL s a -> StateL s b Source #(<$) :: a -> StateL s b -> StateL s a Source # @since base-4.0 Instance detailsDefined in GHC.Internal.Data.Functor.Utils Methodsfmap :: (a -> b) -> StateR s a -> StateR s b Source #(<$) :: a -> StateR s b -> StateR s a Source # Functor (Proxy :: Type -> Type) @since base-4.7.0.0 Instance detailsDefined in GHC.Internal.Data.Proxy Methodsfmap :: (a -> b) -> Proxy a -> Proxy b Source #(<$) :: a -> Proxy b -> Proxy a Source # Functor (U1 :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> U1 a -> U1 b Source #(<$) :: a -> U1 b -> U1 a Source # Functor (V1 :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> V1 a -> V1 b Source #(<$) :: a -> V1 b -> V1 a Source # Functor (ST s) @since base-2.01 Instance detailsDefined in GHC.Internal.ST Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # Functor ((,) a) @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b) -> (a, a0) -> (a, b) Source #(<$) :: a0 -> (a, b) -> (a, a0) Source # Arrow a => Functor (WrappedArrow a b) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source #(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # Functor m => Functor (Kleisli m a) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsfmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source #(<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 Source # Functor (Const m :: Type -> Type) @since base-2.01 Instance detailsDefined in GHC.Internal.Data.Functor.Const Methodsfmap :: (a -> b) -> Const m a -> Const m b Source #(<$) :: a -> Const m b -> Const m a Source # Monad m => Functor (StateT s m) @since base-4.18.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Utils Methodsfmap :: (a -> b) -> StateT s m a -> StateT s m b Source #(<$) :: a -> StateT s m b -> StateT s m a Source # Functor f => Functor (Ap f) @since base-4.12.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsfmap :: (a -> b) -> Ap f a -> Ap f b Source #(<$) :: a -> Ap f b -> Ap f a Source # Functor f => Functor (Alt f) @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Alt f a -> Alt f b Source #(<$) :: a -> Alt f b -> Alt f a Source # (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) @since base-4.17.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source #(<$) :: a -> Generically1 f b -> Generically1 f a Source # Functor f => Functor (Rec1 f) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source #(<$) :: a -> Rec1 f b -> Rec1 f a Source # Functor (URec (Ptr ()) :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source # Functor (URec Char :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Char a -> URec Char b Source #(<$) :: a -> URec Char b -> URec Char a Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Double a -> URec Double b Source #(<$) :: a -> URec Double b -> URec Double a Source # Functor (URec Float :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Float a -> URec Float b Source #(<$) :: a -> URec Float b -> URec Float a Source # Functor (URec Int :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Int a -> URec Int b Source #(<$) :: a -> URec Int b -> URec Int a Source # Functor (URec Word :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Word a -> URec Word b Source #(<$) :: a -> URec Word b -> URec Word a Source # Functor ((,,) a b) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source #(<$) :: a0 -> (a, b, b0) -> (a, b, a0) Source # (Functor f, Functor g) => Functor (Product f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Product Methodsfmap :: (a -> b) -> Product f g a -> Product f g b Source #(<$) :: a -> Product f g b -> Product f g a Source # (Functor f, Functor g) => Functor (Sum f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Sum Methodsfmap :: (a -> b) -> Sum f g a -> Sum f g b Source #(<$) :: a -> Sum f g b -> Sum f g a Source # (Functor f, Functor g) => Functor (f :*: g) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b Source #(<$) :: a -> (f :*: g) b -> (f :*: g) a Source # (Functor f, Functor g) => Functor (f :+: g) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source #(<$) :: a -> (f :+: g) b -> (f :+: g) a Source # Functor (K1 i c :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b Source #(<$) :: a -> K1 i c b -> K1 i c a Source # Functor ((,,,) a b c) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source #(<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) Source # Functor ((->) r) @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> (r -> a) -> r -> b Source #(<$) :: a -> (r -> b) -> r -> a Source # (Functor f, Functor g) => Functor (Compose f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Compose Methodsfmap :: (a -> b) -> Compose f g a -> Compose f g b Source #(<$) :: a -> Compose f g b -> Compose f g a Source # (Functor f, Functor g) => Functor (f :.: g) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source #(<$) :: a -> (f :.: g) b -> (f :.: g) a Source # Functor f => Functor (M1 i c f) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source #(<$) :: a -> M1 i c f b -> M1 i c f a Source # Functor ((,,,,) a b c d) @since base-4.18.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, d, a0) -> (a, b, c, d, b0) Source #(<$) :: a0 -> (a, b, c, d, b0) -> (a, b, c, d, a0) Source # Functor ((,,,,,) a b c d e) @since base-4.18.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, d, e, a0) -> (a, b, c, d, e, b0) Source #(<$) :: a0 -> (a, b, c, d, e, b0) -> (a, b, c, d, e, a0) Source # Functor ((,,,,,,) a b c d e f) @since base-4.18.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, d, e, f, a0) -> (a, b, c, d, e, f, b0) Source #(<$) :: a0 -> (a, b, c, d, e, f, b0) -> (a, b, c, d, e, f, a0) Source #

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:

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 Source #

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.

(>>) :: 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.

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

do as
bs


or in terms of (>>=) as

as >>= const bs

return :: a -> m a Source #

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
 Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Complex Methods(>>=) :: Complex a -> (a -> Complex b) -> Complex b Source #(>>) :: Complex a -> Complex b -> Complex b Source #return :: a -> Complex a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: First a -> (a -> First b) -> First b Source #(>>) :: First a -> First b -> First b Source #return :: a -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Last a -> (a -> Last b) -> Last b Source #(>>) :: Last a -> Last b -> Last b Source #return :: a -> Last a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Max a -> (a -> Max b) -> Max b Source #(>>) :: Max a -> Max b -> Max b Source #return :: a -> Max a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Min a -> (a -> Min b) -> Min b Source #(>>) :: Min a -> Min b -> Min b Source #return :: a -> Min a Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source #(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source #return :: a -> NonEmpty a Source # @since base-4.3.0.0 Instance detailsDefined in GHC.Internal.Conc.Sync Methods(>>=) :: STM a -> (a -> STM b) -> STM b Source #(>>) :: STM a -> STM b -> STM b Source #return :: a -> STM a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Identity Methods(>>=) :: Identity a -> (a -> Identity b) -> Identity b Source #(>>) :: Identity a -> Identity b -> Identity b Source #return :: a -> Identity a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methods(>>=) :: First a -> (a -> First b) -> First b Source #(>>) :: First a -> First b -> First b Source #return :: a -> First a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methods(>>=) :: Last a -> (a -> Last b) -> Last b Source #(>>) :: Last a -> Last b -> Last b Source #return :: a -> Last a Source # @since base-4.11.0.0 Instance detailsDefined in GHC.Internal.Data.Ord Methods(>>=) :: Down a -> (a -> Down b) -> Down b Source #(>>) :: Down a -> Down b -> Down b Source #return :: a -> Down a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methods(>>=) :: Dual a -> (a -> Dual b) -> Dual b Source #(>>) :: Dual a -> Dual b -> Dual b Source #return :: a -> Dual a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methods(>>=) :: Product a -> (a -> Product b) -> Product b Source #(>>) :: Product a -> Product b -> Product b Source #return :: a -> Product a Source # @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methods(>>=) :: Sum a -> (a -> Sum b) -> Sum b Source #(>>) :: Sum a -> Sum b -> Sum b Source #return :: a -> Sum a Source # @since base-4.4.0.0 Instance detailsDefined in GHC.Internal.GHCi Methods(>>=) :: NoIO a -> (a -> NoIO b) -> NoIO b Source #(>>) :: NoIO a -> NoIO b -> NoIO b Source #return :: a -> NoIO a Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methods(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source #(>>) :: Par1 a -> Par1 b -> Par1 b Source #return :: a -> Par1 a Source # @since base-2.01 Instance details Methods(>>=) :: P a -> (a -> P b) -> P b Source #(>>) :: P a -> P b -> P b Source #return :: a -> P a Source # @since base-2.01 Instance details Methods(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source #(>>) :: ReadP a -> ReadP b -> ReadP b Source #return :: a -> ReadP a Source # @since base-2.01 Instance details Methods(>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b Source #(>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source #return :: a -> ReadPrec a Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: IO a -> (a -> IO b) -> IO b Source #(>>) :: IO a -> IO b -> IO b Source #return :: a -> IO a Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source #(>>) :: Maybe a -> Maybe b -> Maybe b Source #return :: a -> Maybe a Source # @since base-4.15 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: Solo a -> (a -> Solo b) -> Solo b Source #(>>) :: Solo a -> Solo b -> Solo b Source #return :: a -> Solo a Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: [a] -> (a -> [b]) -> [b] Source #(>>) :: [a] -> [b] -> [b] Source #return :: a -> [a] Source # Monad m => Monad (WrappedMonad m) Source # Since: base-4.7.0.0 Instance detailsDefined 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 # ArrowApply a => Monad (ArrowMonad a) @since base-2.01 Instance detailsDefined in GHC.Internal.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 # Monad (ST s) @since base-2.01 Instance detailsDefined in GHC.Internal.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 # Monad (Either e) @since base-4.4.0.0 Instance detailsDefined in GHC.Internal.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 # Monad (Proxy :: Type -> Type) @since base-4.7.0.0 Instance detailsDefined in GHC.Internal.Data.Proxy Methods(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b Source #(>>) :: Proxy a -> Proxy b -> Proxy b Source #return :: a -> Proxy a Source # Monad (U1 :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methods(>>=) :: U1 a -> (a -> U1 b) -> U1 b Source #(>>) :: U1 a -> U1 b -> U1 b Source #return :: a -> U1 a Source # Monad (ST s) @since base-2.01 Instance detailsDefined in GHC.Internal.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 # Monoid a => Monad ((,) a) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) Source #(>>) :: (a, a0) -> (a, b) -> (a, b) Source #return :: a0 -> (a, a0) Source # Monad m => Monad (Kleisli m a) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methods(>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b Source #(>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source #return :: a0 -> Kleisli m a a0 Source # Monad m => Monad (StateT s m) @since base-4.18.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Utils Methods(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b Source #(>>) :: StateT s m a -> StateT s m b -> StateT s m b Source #return :: a -> StateT s m a Source # Monad f => Monad (Ap f) @since base-4.12.0.0 Instance detailsDefined in GHC.Internal.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 # Monad f => Monad (Alt f) @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.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 # Monad f => Monad (Rec1 f) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.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 # (Monoid a, Monoid b) => Monad ((,,) a b) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) Source #(>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source #return :: a0 -> (a, b, a0) Source # (Monad f, Monad g) => Monad (Product f g) Source # Since: base-4.9.0.0 Instance detailsDefined 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 # (Monad f, Monad g) => Monad (f :*: g) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.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 # (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) Source #(>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source #return :: a0 -> (a, b, c, a0) Source # Monad ((->) r) @since base-2.01 Instance detailsDefined in GHC.Internal.Base Methods(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b Source #(>>) :: (r -> a) -> (r -> b) -> r -> b Source #return :: a -> r -> a Source # Monad f => Monad (M1 i c f) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.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 #

class Monad m => MonadFail (m :: Type -> Type) where Source #

When a value is bound in do-notation, the pattern on the left hand side of <- might not match. In this case, this class provides a function to recover.

A Monad without a MonadFail instance may only be used in conjunction with pattern that always match, such as newtypes, tuples, data types with only a single data constructor, and irrefutable patterns (~pat).

Instances of MonadFail should satisfy the following law: fail s should be a left zero for >>=,

fail s >>= f  =  fail s


If your Monad is also MonadPlus, a popular definition is

fail _ = mzero


fail s should be an action that runs in the monad itself, not an exception (except in instances of MonadIO). In particular, fail should not be implemented in terms of error.

@since base-4.9.0.0

Methods

fail :: String -> m a Source #

#### Instances

Instances details
 @since base-4.9.0.0 Instance details Methodsfail :: String -> P a Source # @since base-4.9.0.0 Instance details Methods @since base-4.9.0.0 Instance details Methods @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fail Methodsfail :: String -> IO a Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fail Methods @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fail Methodsfail :: String -> [a] Source # MonadFail f => MonadFail (Ap f) @since base-4.12.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsfail :: String -> Ap f a Source #

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

Instances details
 Takes the first non-retrying STM action.@since base-4.3.0.0 Instance detailsDefined in GHC.Internal.Conc.Sync Methodsmplus :: STM a -> STM a -> STM a Source # @since base-2.01 Instance details Methodsmzero :: P a Source #mplus :: P a -> P a -> P a Source # @since base-2.01 Instance details Methodsmplus :: ReadP a -> ReadP a -> ReadP a Source # @since base-2.01 Instance details Methodsmplus :: ReadPrec a -> ReadPrec a -> ReadPrec a Source # Takes the first non-throwing IO action's result. mzero throws an exception.@since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Base Methodsmplus :: IO a -> IO a -> IO a Source # Picks the leftmost Just value, or, alternatively, Nothing.@since base-2.01 Instance detailsDefined in GHC.Internal.Base Methodsmplus :: Maybe a -> Maybe a -> Maybe a Source # Combines lists by concatenation, starting from the empty list.@since base-2.01 Instance detailsDefined in GHC.Internal.Base Methodsmzero :: [a] Source #mplus :: [a] -> [a] -> [a] Source # (ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) @since base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsmzero :: 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 Instance detailsDefined in GHC.Internal.Data.Proxy Methodsmplus :: Proxy a -> Proxy a -> Proxy a Source # MonadPlus (U1 :: Type -> Type) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsmplus :: U1 a -> U1 a -> U1 a Source # MonadPlus m => MonadPlus (Kleisli m a) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsmzero :: Kleisli m a a0 Source #mplus :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source # MonadPlus f => MonadPlus (Ap f) @since base-4.12.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsmzero :: Ap f a Source #mplus :: Ap f a -> Ap f a -> Ap f a Source # MonadPlus f => MonadPlus (Alt f) @since base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsmzero :: Alt f a Source #mplus :: Alt f a -> Alt f a -> Alt f a Source # MonadPlus f => MonadPlus (Rec1 f) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsmzero :: Rec1 f a Source #mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a Source # (MonadPlus f, MonadPlus g) => MonadPlus (Product f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Product Methodsmzero :: Product f g a Source #mplus :: Product f g a -> Product f g a -> Product f g a Source # (MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsmzero :: (f :*: g) a Source #mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a Source # MonadPlus f => MonadPlus (M1 i c f) @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsmzero :: 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 module 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

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_.

#### Examples

Expand

mapM is literally a traverse with a type signature restricted to Monad. Its implementation may be more efficient due to additional power of Monad.

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.

mapM_ is just like traverse_, but specialised to monadic actions.

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.

forM_ is just like for_, but specialised to monadic actions.

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_.

#### Examples

Expand

Basic usage:

The first two examples are instances where the input and and output of sequence are isomorphic.

>>> sequence $Right [1,2,3,4] [Right 1,Right 2,Right 3,Right 4]  >>> sequence$ [Right 1,Right 2,Right 3,Right 4]
Right [1,2,3,4]


The following examples demonstrate short circuit behavior for sequence.

>>> sequence $Left [1,2,3,4] Left [1,2,3,4]  >>> sequence$ [Left 0, Right 1,Right 2,Right 3,Right 4]
Left 0


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.

sequence_ is just like sequenceA_, but specialised to monadic actions.

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

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

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

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

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 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


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.

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. '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. msum :: (Foldable t, MonadPlus m) => t (m a) -> m a Source # The sum of a collection of actions using (<|>), generalizing concat. msum is just like asum, but specialised to MonadPlus. #### Examples Expand Basic usage, using the MonadPlus instance for Maybe: >>> msum [Just "Hello", Nothing, Just "World"] Just "Hello"  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. 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]) 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 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 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 () Source # Like replicateM, but discards the result. #### Examples Expand >>> replicateM_ 3 (putStr "a") aaa  ## 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 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 () Source # 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 () Source # The reverse of when. #### Examples Expand >>> do x <- getLine  unless (x == "hi") (putStrLn "hi!") comingupwithexamplesisdifficult hi!  >>> unless (pi > exp 1) Nothing Just ()  ## Monadic lifting operators liftM :: Monad m => (a1 -> r) -> m a1 -> m r Source # 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 Source # 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 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 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  ## Strict monadic functions (<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4 Source #

Strict version of <\$>`.

@since base-4.8.0.0