# W3cubDocs

Copyright (c) The University of Glasgow 2001 BSD-style (see the file libraries/base/LICENSE) [email protected] provisional portable Trustworthy 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

Since: base-2.1

Instance details

#### Methods

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

(<\$) :: a -> ReadP b -> ReadP a Source

Since: base-2.1

Instance details

#### 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

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

#### 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:

• `pure = return`
• `(<*>) = ap`

The above laws imply:

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

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

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

(>>=)

#### 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

Since: base-2.1

Instance details

Defined in GHC.Base

#### Methods

(>>=) :: [a] -> (a -> [b]) -> [b] Source

(>>) :: [a] -> [b] -> [b] Source

return :: a -> [a] Source

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

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

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

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

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

Since: base-2.1

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-2.1

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-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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Since: base-2.1

Instance details

#### 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

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

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

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

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

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

Since: base-4.9.0.0

Instance details

#### Methods

fail :: String -> [a] Source

Since: base-4.9.0.0

Instance details

#### Methods

Since: base-4.9.0.0

Instance details

#### Methods

fail :: String -> IO a Source

Since: base-4.9.0.0

Instance details

#### Methods

Since: base-4.9.0.0

Instance details

#### Methods

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

#### Methods

fail :: String -> ST s a Source

Since: base-4.10

Instance details

#### Methods

fail :: String -> ST s a Source

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.

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

Since: base-2.1

Instance details

Defined in GHC.Base

#### Methods

mzero :: [a] Source

mplus :: [a] -> [a] -> [a] Source

Since: base-2.1

Instance details

Defined in GHC.Base

#### Methods

mplus :: Maybe a -> Maybe a -> Maybe a Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

#### Methods

mplus :: IO a -> IO a -> IO a Source

Since: base-2.1

Instance details

#### Methods

mplus :: ReadP a -> ReadP a -> ReadP a Source

Since: base-2.1

Instance details

#### Methods

mplus :: ReadPrec a -> ReadPrec a -> ReadPrec a Source

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

#### Methods

mplus :: STM a -> STM a -> STM a Source

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

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

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

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

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

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

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

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

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, `Handle`s, and channels (e.g. `MVar` and `Chan`).

For example, here is how we might implement an echo server, using `forever` both to listen for client connections on a network socket and to echo client input on client connection handles:

```echoServer :: Socket -> IO ()
echoServer socket = forever \$ do
client <- accept socket
forkFinally (echo client) (\_ -> hClose client)
where
echo :: Handle -> IO ()
echo client = forever \$
hGetLine client >>= hPutStrLn client
```

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).