base-4.9.1.0: Basic libraries

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

Synopsis

# Documentation

class Functor f where #

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 #

(<$) :: a -> f b -> f a infixl 4 # Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version. Instances  Functor [] # Methodsfmap :: (a -> b) -> [a] -> [b] #(<$) :: a -> [b] -> [a] # # Methodsfmap :: (a -> b) -> Maybe a -> Maybe b #(<$) :: a -> Maybe b -> Maybe a # # Methodsfmap :: (a -> b) -> IO a -> IO b #(<$) :: a -> IO b -> IO a # # Methodsfmap :: (a -> b) -> V1 a -> V1 b #(<$) :: a -> V1 b -> V1 a # # Methodsfmap :: (a -> b) -> U1 a -> U1 b #(<$) :: a -> U1 b -> U1 a # # Methodsfmap :: (a -> b) -> Par1 a -> Par1 b #(<$) :: a -> Par1 b -> Par1 a # # Methodsfmap :: (a -> b) -> ReadP a -> ReadP b #(<$) :: a -> ReadP b -> ReadP a # # Methodsfmap :: (a -> b) -> ReadPrec a -> ReadPrec b #(<$) :: a -> ReadPrec b -> ReadPrec a # # Methodsfmap :: (a -> b) -> Last a -> Last b #(<$) :: a -> Last b -> Last a # # Methodsfmap :: (a -> b) -> First a -> First b #(<$) :: a -> First b -> First a # # Methodsfmap :: (a -> b) -> Product a -> Product b #(<$) :: a -> Product b -> Product a # # Methodsfmap :: (a -> b) -> Sum a -> Sum b #(<$) :: a -> Sum b -> Sum a # # Methodsfmap :: (a -> b) -> Dual a -> Dual b #(<$) :: a -> Dual b -> Dual a # # Methodsfmap :: (a -> b) -> STM a -> STM b #(<$) :: a -> STM b -> STM a # # Methodsfmap :: (a -> b) -> Handler a -> Handler b #(<$) :: a -> Handler b -> Handler a # # Methodsfmap :: (a -> b) -> ZipList a -> ZipList b #(<$) :: a -> ZipList b -> ZipList a # # Methodsfmap :: (a -> b) -> ArgDescr a -> ArgDescr b #(<$) :: a -> ArgDescr b -> ArgDescr a # # Methodsfmap :: (a -> b) -> OptDescr a -> OptDescr b #(<$) :: a -> OptDescr b -> OptDescr a # # Methodsfmap :: (a -> b) -> ArgOrder a -> ArgOrder b #(<$) :: a -> ArgOrder b -> ArgOrder a # # Methodsfmap :: (a -> b) -> Complex a -> Complex b #(<$) :: a -> Complex b -> Complex a # # Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b #(<$) :: a -> NonEmpty b -> NonEmpty a # # Methodsfmap :: (a -> b) -> Option a -> Option b #(<$) :: a -> Option b -> Option a # # Methodsfmap :: (a -> b) -> Last a -> Last b #(<$) :: a -> Last b -> Last a # # Methodsfmap :: (a -> b) -> First a -> First b #(<$) :: a -> First b -> First a # # Methodsfmap :: (a -> b) -> Max a -> Max b #(<$) :: a -> Max b -> Max a # # Methodsfmap :: (a -> b) -> Min a -> Min b #(<$) :: a -> Min b -> Min a # # Methodsfmap :: (a -> b) -> Identity a -> Identity b #(<$) :: a -> Identity b -> Identity a # Functor ((->) r) # Methodsfmap :: (a -> b) -> (r -> a) -> r -> b #(<$) :: a -> (r -> b) -> r -> a # # Methodsfmap :: (a -> b) -> Either a a -> Either a b #(<$) :: a -> Either a b -> Either a a # Functor f => Functor (Rec1 f) # Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b #(<$) :: a -> Rec1 f b -> Rec1 f a # # Methodsfmap :: (a -> b) -> URec Char a -> URec Char b #(<$) :: a -> URec Char b -> URec Char a # # Methodsfmap :: (a -> b) -> URec Double a -> URec Double b #(<$) :: a -> URec Double b -> URec Double a # # Methodsfmap :: (a -> b) -> URec Float a -> URec Float b #(<$) :: a -> URec Float b -> URec Float a # # Methodsfmap :: (a -> b) -> URec Int a -> URec Int b #(<$) :: a -> URec Int b -> URec Int a # # Methodsfmap :: (a -> b) -> URec Word a -> URec Word b #(<$) :: a -> URec Word b -> URec Word a # Functor (URec (Ptr ())) # Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a # Functor ((,) a) # Methodsfmap :: (a -> b) -> (a, a) -> (a, b) #(<$) :: a -> (a, b) -> (a, a) # Functor (ST s) # Methodsfmap :: (a -> b) -> ST s a -> ST s b #(<$) :: a -> ST s b -> ST s a # # Methodsfmap :: (a -> b) -> Proxy * a -> Proxy * b #(<$) :: a -> Proxy * b -> Proxy * a # Arrow a => Functor (ArrowMonad a) # Methodsfmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b #(<$) :: a -> ArrowMonad a b -> ArrowMonad a a # Monad m => Functor (WrappedMonad m) # Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b #(<$) :: a -> WrappedMonad m b -> WrappedMonad m a # Functor (ST s) # Methodsfmap :: (a -> b) -> ST s a -> ST s b #(<$) :: a -> ST s b -> ST s a # Functor (Arg a) # Methodsfmap :: (a -> b) -> Arg a a -> Arg a b #(<$) :: a -> Arg a b -> Arg a a # Functor (K1 i c) # Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b #(<$) :: a -> K1 i c b -> K1 i c a # (Functor g, Functor f) => Functor ((:+:) f g) # Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b #(<$) :: a -> (f :+: g) b -> (f :+: g) a # (Functor g, Functor f) => Functor ((:*:) f g) # Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b #(<$) :: a -> (f :*: g) b -> (f :*: g) a # (Functor g, Functor f) => Functor ((:.:) f g) # Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b #(<$) :: a -> (f :.: g) b -> (f :.: g) a # Functor f => Functor (Alt * f) # Methodsfmap :: (a -> b) -> Alt * f a -> Alt * f b #(<$) :: a -> Alt * f b -> Alt * f a # # Methodsfmap :: (a -> b) -> Const * m a -> Const * m b #(<$) :: a -> Const * m b -> Const * m a # Arrow a => Functor (WrappedArrow a b) # Methodsfmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b #(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a # Functor f => Functor (M1 i c f) # Methodsfmap :: (a -> b) -> M1 i c f a -> M1 i c f b #(<$) :: a -> M1 i c f b -> M1 i c f a # (Functor f, Functor g) => Functor (Product * f g) # Methodsfmap :: (a -> b) -> Product * f g a -> Product * f g b #(<$) :: a -> Product * f g b -> Product * f g a # (Functor f, Functor g) => Functor (Sum * f g) # Methodsfmap :: (a -> b) -> Sum * f g a -> Sum * f g b #(<$) :: a -> Sum * f g b -> Sum * f g a # (Functor f, Functor g) => Functor (Compose * * f g) # Methodsfmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b #(<\$) :: a -> Compose * * f g b -> Compose * * f g a #

class Applicative m => Monad m where #

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 #

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 #

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 #

Inject a value into the monadic type.

fail :: String -> m a #

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