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/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

Description

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

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.

Methods

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

Instances
Instances details
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 NoIO

Since: base-4.8.0.0

Instance details

Defined in GHC.GHCi

Methods

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

(<$) :: a -> NoIO b -> NoIO 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 (Array i)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b Source

(<$) :: a -> Array i b -> Array i 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:

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:

The above laws imply:

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: 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.

Instances
Instances details
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

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

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

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

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

Monad NoIO

Since: base-4.4.0.0

Instance details

Defined in GHC.GHCi

Methods

(>>=) :: NoIO a -> (a -> NoIO b) -> NoIO b Source

(>>) :: NoIO a -> NoIO b -> NoIO b Source

return :: a -> NoIO 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(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

(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

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

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
MonadFail []

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Fail

Methods

fail :: String -> [a] Source

MonadFail Maybe

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Fail

Methods

fail :: String -> Maybe a Source

MonadFail IO

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Fail

Methods

fail :: String -> IO a Source

MonadFail ReadP

Since: base-4.9.0.0

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

fail :: String -> ReadP a Source

MonadFail ReadPrec

Since: base-4.9.0.0

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

fail :: String -> ReadPrec a Source

MonadFail (ST s)

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

fail :: String -> ST s a Source

MonadFail (ST s)

Since: base-4.10

Instance details

Defined in Control.Monad.ST.Lazy.Imp

Methods

fail :: String -> ST s a Source

MonadFail f => MonadFail (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

fail :: 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
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 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/8.8.3/docs/html/libraries/base-4.13.0.0/Control-Monad.html