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/Haskell 8

Control.Monad.Instances

Copyright	(c) The University of Glasgow 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Description

Deprecated: This module now contains no instances and will be removed in the future

This module is DEPRECATED and will be removed in the future!

Functor and Monad instances for (->) r and Functor instances for (,) a and Either a.

class Functor f where Source

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

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

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Methods

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

(<$) :: 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

Functor []	Since: 2.1
Methods fmap :: (a -> b) -> [a] -> [b] Source (<$) :: a -> [b] -> [a] Source
Functor Maybe	Since: 2.1
Methods fmap :: (a -> b) -> Maybe a -> Maybe b Source (<$) :: a -> Maybe b -> Maybe a Source
Functor IO	Since: 2.1
Methods fmap :: (a -> b) -> IO a -> IO b Source (<$) :: a -> IO b -> IO a Source
Functor Par1
Methods fmap :: (a -> b) -> Par1 a -> Par1 b Source (<$) :: a -> Par1 b -> Par1 a Source
Functor ReadP	Since: 2.1
Methods fmap :: (a -> b) -> ReadP a -> ReadP b Source (<$) :: a -> ReadP b -> ReadP a Source
Functor ReadPrec	Since: 2.1
Methods fmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source (<$) :: a -> ReadPrec b -> ReadPrec a Source
Functor Last
Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
Functor First
Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
Functor Product	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Product a -> Product b Source (<$) :: a -> Product b -> Product a Source
Functor Sum	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Sum a -> Sum b Source (<$) :: a -> Sum b -> Sum a Source
Functor Dual	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Dual a -> Dual b Source (<$) :: a -> Dual b -> Dual a Source
Functor STM	Since: 4.3.0.0
Methods fmap :: (a -> b) -> STM a -> STM b Source (<$) :: a -> STM b -> STM a Source
Functor Handler	Since: 4.6.0.0
Methods fmap :: (a -> b) -> Handler a -> Handler b Source (<$) :: a -> Handler b -> Handler a Source
Functor Identity	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Identity a -> Identity b Source (<$) :: a -> Identity b -> Identity a Source
Functor ZipList
Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source (<$) :: a -> ZipList b -> ZipList a Source
Functor ArgDescr	Since: 4.6.0.0
Methods fmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source (<$) :: a -> ArgDescr b -> ArgDescr a Source
Functor OptDescr	Since: 4.6.0.0
Methods fmap :: (a -> b) -> OptDescr a -> OptDescr b Source (<$) :: a -> OptDescr b -> OptDescr a Source
Functor ArgOrder	Since: 4.6.0.0
Methods fmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source (<$) :: a -> ArgOrder b -> ArgOrder a Source
Functor NonEmpty	Since: 4.9.0.0
Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source (<$) :: a -> NonEmpty b -> NonEmpty a Source
Functor Option	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Option a -> Option b Source (<$) :: a -> Option b -> Option a Source
Functor Last	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
Functor First	Since: 4.9.0.0
Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
Functor Max	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Max a -> Max b Source (<$) :: a -> Max b -> Max a Source
Functor Min	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Min a -> Min b Source (<$) :: a -> Min b -> Min a Source
Functor Complex
Methods fmap :: (a -> b) -> Complex a -> Complex b Source (<$) :: a -> Complex b -> Complex a Source
Functor (Either a)	Since: 3.0
Methods fmap :: (a -> b) -> Either a a -> Either a b Source (<$) :: a -> Either a b -> Either a a Source
Functor (V1 *)
Methods fmap :: (a -> b) -> V1 * a -> V1 * b Source (<$) :: a -> V1 * b -> V1 * a Source
Functor (U1 *)	Since: 4.9.0.0
Methods fmap :: (a -> b) -> U1 * a -> U1 * b Source (<$) :: a -> U1 * b -> U1 * a Source
Functor ((,) a)	Since: 2.1
Methods fmap :: (a -> b) -> (a, a) -> (a, b) Source (<$) :: a -> (a, b) -> (a, a) Source
Functor (ST s)	Since: 2.1
Methods fmap :: (a -> b) -> ST s a -> ST s b Source (<$) :: a -> ST s b -> ST s a Source
Functor (Proxy *)	Since: 4.7.0.0
Methods fmap :: (a -> b) -> Proxy * a -> Proxy * b Source (<$) :: a -> Proxy * b -> Proxy * a Source
Arrow a => Functor (ArrowMonad a)	Since: 4.6.0.0
Methods fmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b Source (<$) :: a -> ArrowMonad a b -> ArrowMonad a a Source
Monad m => Functor (WrappedMonad m)	Since: 2.1
Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source
Functor (ST s)	Since: 2.1
Methods fmap :: (a -> b) -> ST s a -> ST s b Source (<$) :: a -> ST s b -> ST s a Source
Functor (Arg a)	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Arg a a -> Arg a b Source (<$) :: a -> Arg a b -> Arg a a Source
Functor f => Functor (Rec1 * f)
Methods fmap :: (a -> b) -> Rec1 * f a -> Rec1 * f b Source (<$) :: a -> Rec1 * f b -> Rec1 * f a Source
Functor (URec * Char)
Methods fmap :: (a -> b) -> URec * Char a -> URec * Char b Source (<$) :: a -> URec * Char b -> URec * Char a Source
Functor (URec * Double)
Methods fmap :: (a -> b) -> URec * Double a -> URec * Double b Source (<$) :: a -> URec * Double b -> URec * Double a Source
Functor (URec * Float)
Methods fmap :: (a -> b) -> URec * Float a -> URec * Float b Source (<$) :: a -> URec * Float b -> URec * Float a Source
Functor (URec * Int)
Methods fmap :: (a -> b) -> URec * Int a -> URec * Int b Source (<$) :: a -> URec * Int b -> URec * Int a Source
Functor (URec * Word)
Methods fmap :: (a -> b) -> URec * Word a -> URec * Word b Source (<$) :: a -> URec * Word b -> URec * Word a Source
Functor (URec * (Ptr ()))
Methods fmap :: (a -> b) -> URec * (Ptr ()) a -> URec * (Ptr ()) b Source (<$) :: a -> URec * (Ptr ()) b -> URec * (Ptr ()) a Source
Functor f => Functor (Alt * f)
Methods fmap :: (a -> b) -> Alt * f a -> Alt * f b Source (<$) :: a -> Alt * f b -> Alt * f a Source
Functor (Const * m)	Since: 2.1
Methods fmap :: (a -> b) -> Const * m a -> Const * m b Source (<$) :: a -> Const * m b -> Const * m a Source
Arrow a => Functor (WrappedArrow a b)	Since: 2.1
Methods fmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source (<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a Source
Functor ((->) LiftedRep LiftedRep r)	Since: 2.1
Methods fmap :: (a -> b) -> (LiftedRep -> LiftedRep) r a -> (LiftedRep -> LiftedRep) r b Source (<$) :: a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r a Source
Functor (K1 * i c)
Methods fmap :: (a -> b) -> K1 * i c a -> K1 * i c b Source (<$) :: a -> K1 * i c b -> K1 * i c a Source
(Functor g, Functor f) => Functor ((:+:) * f g)
Methods fmap :: (a -> b) -> (* :+: f) g a -> (* :+: f) g b Source (<$) :: a -> (* :+: f) g b -> (* :+: f) g a Source
(Functor g, Functor f) => Functor ((::) f g)
Methods fmap :: (a -> b) -> (* :: f) g a -> ( :: f) g b Source (<$) :: a -> ( :: f) g b -> ( :*: f) g a Source
(Functor f, Functor g) => Functor (Sum * f g)	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Sum * f g a -> Sum * f g b Source (<$) :: a -> Sum * f g b -> Sum * f g a Source
(Functor f, Functor g) => Functor (Product * f g)	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Product * f g a -> Product * f g b Source (<$) :: a -> Product * f g b -> Product * f g a Source
Functor f => Functor (M1 * i c f)
Methods fmap :: (a -> b) -> M1 * i c f a -> M1 * i c f b Source (<$) :: a -> M1 * i c f b -> M1 * i c f a Source
(Functor g, Functor f) => Functor ((:.:) * * f g)
Methods fmap :: (a -> b) -> (* :.: ) f g a -> ( :.: ) f g b Source (<$) :: a -> ( :.: ) f g b -> ( :.: *) f g a Source
(Functor f, Functor g) => Functor (Compose * * f g)	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b Source (<$) :: a -> Compose * * f g b -> Compose * * f g a Source

class Applicative m => Monad m where Source

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

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

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

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

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

The above laws imply:

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

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

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

Minimal complete definition

(>>=)

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1 Source

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: forall a b. m a -> m b -> m b infixl 1 Source

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a Source

Inject a value into the monadic type.

fail :: String -> m a Source

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

Instances

Monad []	Since: 2.1
Methods (>>=) :: [a] -> (a -> [b]) -> [b] Source (>>) :: [a] -> [b] -> [b] Source return :: a -> [a] Source fail :: String -> [a] Source
Monad Maybe	Since: 2.1
Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source (>>) :: Maybe a -> Maybe b -> Maybe b Source return :: a -> Maybe a Source fail :: String -> Maybe a Source
Monad IO	Since: 2.1
Methods (>>=) :: IO a -> (a -> IO b) -> IO b Source (>>) :: IO a -> IO b -> IO b Source return :: a -> IO a Source fail :: String -> IO a Source
Monad Par1	Since: 4.9.0.0
Methods (>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source (>>) :: Par1 a -> Par1 b -> Par1 b Source return :: a -> Par1 a Source fail :: String -> Par1 a Source
Monad ReadP	Since: 2.1
Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source (>>) :: ReadP a -> ReadP b -> ReadP b Source return :: a -> ReadP a Source fail :: String -> ReadP a Source
Monad ReadPrec	Since: 2.1
Methods (>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b Source (>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source return :: a -> ReadPrec a Source fail :: String -> ReadPrec a Source
Monad Last
Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source fail :: String -> Last a Source
Monad First
Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source fail :: String -> First a Source
Monad Product	Since: 4.8.0.0
Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source (>>) :: Product a -> Product b -> Product b Source return :: a -> Product a Source fail :: String -> Product a Source
Monad Sum	Since: 4.8.0.0
Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source (>>) :: Sum a -> Sum b -> Sum b Source return :: a -> Sum a Source fail :: String -> Sum a Source
Monad Dual	Since: 4.8.0.0
Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source (>>) :: Dual a -> Dual b -> Dual b Source return :: a -> Dual a Source fail :: String -> Dual a Source
Monad STM	Since: 4.3.0.0
Methods (>>=) :: STM a -> (a -> STM b) -> STM b Source (>>) :: STM a -> STM b -> STM b Source return :: a -> STM a Source fail :: String -> STM a Source
Monad Identity	Since: 4.8.0.0
Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b Source (>>) :: Identity a -> Identity b -> Identity b Source return :: a -> Identity a Source fail :: String -> Identity a Source
Monad NonEmpty	Since: 4.9.0.0
Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source return :: a -> NonEmpty a Source fail :: String -> NonEmpty a Source
Monad Option	Since: 4.9.0.0
Methods (>>=) :: Option a -> (a -> Option b) -> Option b Source (>>) :: Option a -> Option b -> Option b Source return :: a -> Option a Source fail :: String -> Option a Source
Monad Last	Since: 4.9.0.0
Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source fail :: String -> Last a Source
Monad First	Since: 4.9.0.0
Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source fail :: String -> First a Source
Monad Max	Since: 4.9.0.0
Methods (>>=) :: Max a -> (a -> Max b) -> Max b Source (>>) :: Max a -> Max b -> Max b Source return :: a -> Max a Source fail :: String -> Max a Source
Monad Min	Since: 4.9.0.0
Methods (>>=) :: Min a -> (a -> Min b) -> Min b Source (>>) :: Min a -> Min b -> Min b Source return :: a -> Min a Source fail :: String -> Min a Source
Monad Complex	Since: 4.9.0.0
Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b Source (>>) :: Complex a -> Complex b -> Complex b Source return :: a -> Complex a Source fail :: String -> Complex a Source
Monad (Either e)	Since: 4.4.0.0
Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b Source (>>) :: Either e a -> Either e b -> Either e b Source return :: a -> Either e a Source fail :: String -> Either e a Source
Monad (U1 *)	Since: 4.9.0.0
Methods (>>=) :: U1 * a -> (a -> U1 * b) -> U1 * b Source (>>) :: U1 * a -> U1 * b -> U1 * b Source return :: a -> U1 * a Source fail :: String -> U1 * a Source
Monoid a => Monad ((,) a)	Since: 4.9.0.0
Methods (>>=) :: (a, a) -> (a -> (a, b)) -> (a, b) Source (>>) :: (a, a) -> (a, b) -> (a, b) Source return :: a -> (a, a) Source fail :: String -> (a, a) Source
Monad (ST s)	Since: 2.1
Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source (>>) :: ST s a -> ST s b -> ST s b Source return :: a -> ST s a Source fail :: String -> ST s a Source
Monad (Proxy *)	Since: 4.7.0.0
Methods (>>=) :: Proxy * a -> (a -> Proxy * b) -> Proxy * b Source (>>) :: Proxy * a -> Proxy * b -> Proxy * b Source return :: a -> Proxy * a Source fail :: String -> Proxy * a Source
ArrowApply a => Monad (ArrowMonad a)	Since: 2.1
Methods (>>=) :: ArrowMonad a a -> (a -> ArrowMonad a b) -> ArrowMonad a b Source (>>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b Source return :: a -> ArrowMonad a a Source fail :: String -> ArrowMonad a a Source
Monad m => Monad (WrappedMonad m)
Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source return :: a -> WrappedMonad m a Source fail :: String -> WrappedMonad m a Source
Monad (ST s)	Since: 2.1
Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source (>>) :: ST s a -> ST s b -> ST s b Source return :: a -> ST s a Source fail :: String -> ST s a Source
Monad f => Monad (Rec1 * f)	Since: 4.9.0.0
Methods (>>=) :: Rec1 * f a -> (a -> Rec1 * f b) -> Rec1 * f b Source (>>) :: Rec1 * f a -> Rec1 * f b -> Rec1 * f b Source return :: a -> Rec1 * f a Source fail :: String -> Rec1 * f a Source
Monad f => Monad (Alt * f)
Methods (>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b Source (>>) :: Alt * f a -> Alt * f b -> Alt * f b Source return :: a -> Alt * f a Source fail :: String -> Alt * f a Source
Monad ((->) LiftedRep LiftedRep r)	Since: 2.1
Methods (>>=) :: (LiftedRep -> LiftedRep) r a -> (a -> (LiftedRep -> LiftedRep) r b) -> (LiftedRep -> LiftedRep) r b Source (>>) :: (LiftedRep -> LiftedRep) r a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r b Source return :: a -> (LiftedRep -> LiftedRep) r a Source fail :: String -> (LiftedRep -> LiftedRep) r a Source
(Monad f, Monad g) => Monad ((::) f g)	Since: 4.9.0.0
Methods (>>=) :: (* :: f) g a -> (a -> ( :: f) g b) -> ( :: f) g b Source (>>) :: ( :: f) g a -> ( :: f) g b -> ( :: f) g b Source return :: a -> ( :: f) g a Source fail :: String -> ( :*: f) g a Source
(Monad f, Monad g) => Monad (Product * f g)	Since: 4.9.0.0
Methods (>>=) :: Product * f g a -> (a -> Product * f g b) -> Product * f g b Source (>>) :: Product * f g a -> Product * f g b -> Product * f g b Source return :: a -> Product * f g a Source fail :: String -> Product * f g a Source
Monad f => Monad (M1 * i c f)	Since: 4.9.0.0
Methods (>>=) :: M1 * i c f a -> (a -> M1 * i c f b) -> M1 * i c f b Source (>>) :: M1 * i c f a -> M1 * i c f b -> M1 * i c f b Source return :: a -> M1 * i c f a Source fail :: String -> M1 * i c f a Source

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Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.2.1/docs/html/libraries/base-4.10.0.0/Control-Monad-Instances.html