base-4.15.1.0: Basic libraries
Copyright (c) The University of Glasgow 2001 BSD-style (see the file libraries/base/LICENSE) libraries@haskell.org provisional portable Trustworthy Haskell2010

Description

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

Synopsis

# Functor and monad classes

class Functor f 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.

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

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)


(<$) :: a -> f b -> f a infixl 4 Source # Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version. #### Instances Instances details  Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> ZipList a -> ZipList b Source #(<$) :: a -> ZipList b -> ZipList a Source # Source # Since: base-4.6.0.0 Instance detailsDefined in Control.Exception Methodsfmap :: (a -> b) -> Handler a -> Handler b Source #(<$) :: a -> Handler b -> Handler a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Complex Methodsfmap :: (a -> b) -> Complex a -> Complex b Source #(<$) :: a -> Complex b -> Complex a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Functor.Identity Methodsfmap :: (a -> b) -> Identity a -> Identity b Source #(<$) :: a -> Identity b -> Identity a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # Source # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methodsfmap :: (a -> b) -> Down a -> Down b Source #(<$) :: a -> Down b -> Down 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-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Option a -> Option b Source #(<$) :: a -> Option b -> Option a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Dual a -> Dual b Source #(<$) :: a -> Dual b -> Dual a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Product a -> Product b Source #(<$) :: a -> Product b -> Product a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Sum a -> Sum b Source #(<$) :: a -> Sum b -> Sum a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source #(<$) :: a -> NonEmpty b -> NonEmpty a Source # Source # Since: base-4.3.0.0 Instance detailsDefined in GHC.Conc.Sync Methodsfmap :: (a -> b) -> STM a -> STM b Source #(<$) :: a -> STM b -> STM a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.GHCi Methodsfmap :: (a -> b) -> NoIO a -> NoIO b Source #(<$) :: a -> NoIO b -> NoIO a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> Par1 a -> Par1 b Source #(<$) :: a -> Par1 b -> Par1 a Source # Source # Since: base-4.6.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source #(<$) :: a -> ArgDescr b -> ArgDescr a Source # Source # Since: base-4.6.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source #(<$) :: a -> ArgOrder b -> ArgOrder a Source # Source # Since: base-4.6.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> OptDescr a -> OptDescr b Source #(<$) :: a -> OptDescr b -> OptDescr a Source # Source # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadP Methodsfmap :: (a -> b) -> ReadP a -> ReadP b Source #(<$) :: a -> ReadP b -> ReadP a Source # Source # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadPrec Methodsfmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source #(<$) :: a -> ReadPrec b -> ReadPrec a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> IO a -> IO b Source #(<$) :: a -> IO b -> IO a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> Maybe a -> Maybe b Source #(<$) :: a -> Maybe b -> Maybe a Source # Source # Since: base-4.15 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> Solo a -> Solo b Source #(<$) :: a -> Solo b -> Solo a Source # Functor [] Source # Since: base-2.1 Instance detailsDefined in GHC.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 # Arrow a => Functor (ArrowMonad a) Source # Since: base-4.6.0.0 Instance detailsDefined in Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source #(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # Functor (ST s) Source # Since: base-2.1 Instance detailsDefined in Control.Monad.ST.Lazy.Imp Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # Source # Since: base-3.0 Instance detailsDefined in Data.Either Methodsfmap :: (a0 -> b) -> Either a a0 -> Either a b Source #(<$) :: a0 -> Either a b -> Either a a0 Source # Functor (Proxy :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methodsfmap :: (a -> b) -> Proxy a -> Proxy b Source #(<$) :: a -> Proxy b -> Proxy 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 #(<$) :: a0 -> Arg a b -> Arg a a0 Source # Functor (Array i) Source # Since: base-2.1 Instance detailsDefined in GHC.Arr Methodsfmap :: (a -> b) -> Array i a -> Array i b Source #(<$) :: a -> Array i b -> Array i a Source # Functor (U1 :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> U1 a -> U1 b Source #(<$) :: a -> U1 b -> U1 a Source # Functor (V1 :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> V1 a -> V1 b Source #(<$) :: a -> V1 b -> V1 a Source # Functor (ST s) Source # Since: base-2.1 Instance detailsDefined in GHC.ST Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # Functor ((,) a) Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a0 -> b) -> (a, a0) -> (a, b) Source #(<$) :: 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 #(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # Functor m => Functor (Kleisli m a) Source # Since: base-4.14.0.0 Instance detailsDefined in Control.Arrow Methodsfmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source #(<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 Source # Functor (Const m :: Type -> Type) Source # Since: base-2.1 Instance detailsDefined in Data.Functor.Const Methodsfmap :: (a -> b) -> Const m a -> Const m b Source #(<$) :: a -> Const m b -> Const m a Source # Functor f => Functor (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> Ap f a -> Ap f b Source #(<$) :: a -> Ap f b -> Ap f a Source # Functor f => Functor (Alt f) Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Alt f a -> Alt f b Source #(<$) :: a -> Alt f b -> Alt f a Source # Functor f => Functor (Rec1 f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source #(<$) :: a -> Rec1 f b -> Rec1 f a Source # Functor (URec (Ptr ()) :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source # Functor (URec Char :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Char a -> URec Char b Source #(<$) :: a -> URec Char b -> URec Char a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Double a -> URec Double b Source #(<$) :: a -> URec Double b -> URec Double a Source # Functor (URec Float :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Float a -> URec Float b Source #(<$) :: a -> URec Float b -> URec Float a Source # Functor (URec Int :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Int a -> URec Int b Source #(<$) :: a -> URec Int b -> URec Int a Source # Functor (URec Word :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Word a -> URec Word b Source #(<$) :: a -> URec Word b -> URec Word a Source # Functor ((,,) a b) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.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 #(<$) :: a -> Sum f g b -> Sum f g a Source # (Functor f, Functor g) => Functor (f :*: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b Source #(<$) :: a -> (f :*: g) b -> (f :*: g) a Source # (Functor f, Functor g) => Functor (f :+: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source #(<$) :: a -> (f :+: g) b -> (f :+: g) a Source # Functor (K1 i c :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b Source #(<$) :: a -> K1 i c b -> K1 i c a Source # Functor ((,,,) a b c) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source #(<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) Source # Functor ((->) r) Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> (r -> a) -> r -> b Source #(<$) :: 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 #(<$) :: a -> Compose f g b -> Compose f g a Source # (Functor f, Functor g) => Functor (f :.: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source #(<$) :: a -> (f :.: g) b -> (f :.: g) a Source # Functor f => Functor (M1 i c f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.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 # 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: 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 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. 'as >>= bs' can be understood as the do expression do a <- as bs a  (>>) :: 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. 'as >> bs' can be understood as the do expression do as bs  return :: a -> m a Source # Inject a value into the monadic type. #### 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-4.8.0.0 Instance detailsDefined 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methods(>>=) :: First a -> (a -> First b) -> First b Source #(>>) :: First a -> First b -> First b Source #return :: a -> First a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methods(>>=) :: Last a -> (a -> Last b) -> Last b Source #(>>) :: Last a -> Last b -> Last b Source #return :: a -> Last a Source # Source # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methods(>>=) :: Down a -> (a -> Down b) -> Down b Source #(>>) :: Down a -> Down b -> Down b Source #return :: a -> Down 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Option a -> (a -> Option b) -> Option b Source #(>>) :: Option a -> Option b -> Option b Source #return :: a -> Option a Source # Source # Since: base-4.8.0.0 Instance detailsDefined 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 # Source # Since: base-4.8.0.0 Instance detailsDefined 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 # Source # Since: base-4.8.0.0 Instance detailsDefined 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source #(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source #return :: a -> NonEmpty a Source # Source # Since: base-4.3.0.0 Instance detailsDefined 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 # Source # Since: base-4.4.0.0 Instance detailsDefined in GHC.GHCi Methods(>>=) :: NoIO a -> (a -> NoIO b) -> NoIO b Source #(>>) :: NoIO a -> NoIO b -> NoIO b Source #return :: a -> NoIO a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source #(>>) :: Par1 a -> Par1 b -> Par1 b Source #return :: a -> Par1 a Source # Source # Since: base-2.1 Instance detailsDefined 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 # Source # Since: base-2.1 Instance detailsDefined 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 # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: IO a -> (a -> IO b) -> IO b Source #(>>) :: IO a -> IO b -> IO b Source #return :: a -> IO a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source #(>>) :: Maybe a -> Maybe b -> Maybe b Source #return :: a -> Maybe a Source # Source # Since: base-4.15 Instance detailsDefined in GHC.Base Methods(>>=) :: Solo a -> (a -> Solo b) -> Solo b Source #(>>) :: Solo a -> Solo b -> Solo b Source #return :: a -> Solo a Source # Monad [] Source # Since: base-2.1 Instance detailsDefined in GHC.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) Source # Since: base-2.1 Instance detailsDefined 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 # Monad (ST s) Source # Since: base-2.1 Instance detailsDefined 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 # Monad (Either e) Source # Since: base-4.4.0.0 Instance detailsDefined 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 # Monad (Proxy :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in 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) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.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) Source # Since: base-2.1 Instance detailsDefined 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 # Monoid a => Monad ((,) a) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.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) Source # Since: base-4.14.0.0 Instance detailsDefined in 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 f => Monad (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined 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 # Monad f => Monad (Alt f) Source # Since: base-4.8.0.0 Instance detailsDefined 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 # Monad f => Monad (Rec1 f) Source # Since: base-4.9.0.0 Instance detailsDefined 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 # (Monoid a, Monoid b) => Monad ((,,) a b) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.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) Source # Since: base-4.9.0.0 Instance detailsDefined 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 # (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.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) Source # Since: base-2.1 Instance detailsDefined in GHC.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) Source # Since: base-4.9.0.0 Instance detailsDefined 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 # class Monad m => MonadFail m 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  Since: base-4.9.0.0 Methods fail :: String -> m a Source # #### Instances Instances details  Source # Since: base-4.9.0.0 Instance detailsDefined in Text.ParserCombinators.ReadP Methods Source # Since: base-4.9.0.0 Instance detailsDefined in Text.ParserCombinators.ReadPrec Methods Source # Since: base-4.9.0.0 Instance detailsDefined in Control.Monad.Fail Methodsfail :: String -> IO a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Control.Monad.Fail Methods Source # Since: base-4.9.0.0 Instance detailsDefined in Control.Monad.Fail Methodsfail :: String -> [a] Source # MonadFail (ST s) Source # Since: base-4.10 Instance detailsDefined in Control.Monad.ST.Lazy.Imp Methodsfail :: String -> ST s a Source # MonadFail (ST s) Source # Since: base-4.11.0.0 Instance detailsDefined in GHC.ST Methodsfail :: String -> ST s a Source # MonadFail f => MonadFail (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodsfail :: String -> Ap 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 Instances details  Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmplus :: Option a -> Option a -> Option a Source # Source # Since: base-4.3.0.0 Instance detailsDefined in GHC.Conc.Sync Methodsmplus :: STM a -> STM a -> STM a Source # Source # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadP Methodsmplus :: ReadP a -> ReadP a -> ReadP a Source # Source # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadPrec Methodsmplus :: ReadPrec a -> ReadPrec a -> ReadPrec a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsmplus :: IO a -> IO a -> IO a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsmplus :: Maybe a -> Maybe a -> Maybe a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsmzero :: [a] Source #mplus :: [a] -> [a] -> [a] Source # (ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) Source # Since: base-4.6.0.0 Instance detailsDefined in Control.Arrow Methodsmzero :: ArrowMonad a a0 Source #mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source # MonadPlus (Proxy :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Proxy Methodsmplus :: Proxy a -> Proxy a -> Proxy a Source # MonadPlus (U1 :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsmplus :: U1 a -> U1 a -> U1 a Source # MonadPlus m => MonadPlus (Kleisli m a) Source # Since: base-4.14.0.0 Instance detailsDefined in 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) Source # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodsmzero :: Ap f a Source #mplus :: Ap f a -> Ap f a -> Ap f a Source # MonadPlus f => MonadPlus (Alt f) Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsmzero :: Alt f a Source #mplus :: Alt f a -> Alt f a -> Alt f a Source # MonadPlus f => MonadPlus (Rec1 f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.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) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsmzero :: (f :*: g) a Source #mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a Source # MonadPlus f => MonadPlus (M1 i c f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.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 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_. #### 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 $[Left 0, Right 1,Right 2,Right 3,Right 4] Left 0  sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source # Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence. sequence_ is just like sequenceA_, but specialised to monadic actions. (=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source # Same as >>=, but with the arguments interchanged. (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 Source # Left-to-right composition of Kleisli arrows. '(bs >=> cs) a' can be understood as the do expression do b <- bs a cs b  (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c infixr 1 Source # Right-to-left composition of Kleisli arrows. (>=>), with the arguments flipped. Note how this operator resembles function composition (.): (.) :: (b -> c) -> (a -> b) -> a -> c (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c forever :: Applicative f => f a -> f b Source # Repeat an action indefinitely. #### Examples Expand A common use of forever is to process input from network sockets, Handles, and channels (e.g. MVar and Chan). For example, here is how we might implement an echo server, using forever both to listen for client connections on a network socket and to echo client input on client connection handles: echoServer :: Socket -> IO () echoServer socket = forever$ 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

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.

msum is just like asum, but specialised 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 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:

#### Examples

Expand
>>> replicateM 3 (putStrLn "a")
a
a
a


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