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Control.Monad

Portability | portable
Stability | provisional
Maintainer | libraries@haskell.org

Contents

Functor and monad classes
Functions
  Naming conventions
  Basic functions from the Prelude
  Generalisations of list functions
  Conditional execution of monadic expressions
  Monadic lifting operators

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

class Functor f where

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

class Monad m where

(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
fail :: String -> m a

class Monad m => MonadPlus m where

mzero :: m a
mplus :: m a -> m a -> m a

mapM :: Monad m => (a -> m b) -> [a] -> m [b]
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
sequence :: Monad m => [m a] -> m [a]
sequence_ :: Monad m => [m a] -> m ()
(=<<) :: Monad m => (a -> m b) -> m a -> m b
join :: Monad m => m (m a) -> m a
msum :: MonadPlus m => [m a] -> m a
filterM :: Monad m => (a -> m Bool) -> [a] -> m [a]
mapAndUnzipM :: Monad m => (a -> m (b, c)) -> [a] -> m ([b], [c])
zipWithM :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m [c]
zipWithM_ :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m ()
foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a
foldM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m ()
replicateM :: Monad m => Int -> m a -> m [a]
replicateM_ :: Monad m => Int -> m a -> m ()
guard :: MonadPlus m => Bool -> m ()
when :: Monad m => Bool -> m () -> m ()
unless :: Monad m => Bool -> m () -> m ()
liftM :: Monad m => (a1 -> r) -> m a1 -> m r
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
ap :: Monad m => m (a -> b) -> m a -> m b

Functor and monad classes
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 defined in the Prelude satisfy these laws.

Methods

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

Instances

Functor (Cont r)
Monad m => Functor (ContT r m)
Functor (Either e)
Monad m => Functor (ErrorT e m)
Functor Identity
Monad m => Functor (ListT m)
Functor (RWS r w s)
Monad m => Functor (RWST r w s m)
Functor ((->) r)
Functor (Reader r)
Monad m => Functor (ReaderT r m)
Functor (ST s)
Functor (State s)
Monad m => Functor (StateT s m)
Functor (Writer w)
Monad m => Functor (WriterT w m)
Functor Maybe
Ix i => Functor (Array i)
Functor []
Functor IO
Functor (ST s)
Functor ReadP
Functor ReadPrec

class Monad m where

The `Monad` class defines the basic operations over a monad. Instances of `Monad` should satisfy the following laws:

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

Instances of both `Monad` and `Functor` should additionally satisfy the law:

     fmap f xs  ==  xs >>= return . f

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

Methods

(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
fail :: String -> m a

Instances

ArrowApply a => Monad (ArrowMonad a)
Monad (Cont r)
Monad m => Monad (ContT r m)
Error e => Monad (Either e)
(Monad m, Error e) => Monad (ErrorT e m)
Monad Identity
Monad m => Monad (ListT m)
Monoid w => Monad (RWS r w s)
(Monoid w, Monad m) => Monad (RWST r w s m)
Monad ((->) r)
Monad (Reader r)
Monad m => Monad (ReaderT r m)
Monad (ST s)
Monad (State s)
Monad m => Monad (StateT s m)
Monoid w => Monad (Writer w)
(Monoid w, Monad m) => Monad (WriterT w m)
Monad Maybe
Monad []
Monad IO
Monad (ST s)
Monad P
Monad ReadP
Monad ReadPrec

class Monad m => MonadPlus m where

The MonadPlus class definition
Methods

mzero :: m a
mplus :: m a -> m a -> m a

Instances

MonadPlus []
MonadPlus Maybe
MonadPlus IO
Error e => MonadPlus (Either e)
(Monad m, Error e) => MonadPlus (ErrorT e m)
Monad m => MonadPlus (ListT m)
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m)
MonadPlus m => MonadPlus (ReaderT r m)
MonadPlus m => MonadPlus (StateT s m)
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m)
MonadPlus P
MonadPlus ReadP
MonadPlus ReadPrec

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: `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 (in the Prelude):

      sequence  :: Monad m => [m a] -> m [a]
      sequence_ :: Monad m => [m a] -> m ()

- A prefix `m' generalises an existing function to a monadic form. Thus, for example:

      sum  :: Num a       => [a]   -> a
      msum :: MonadPlus m => [m a] -> m a

Basic functions from the Prelude
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
sequence :: Monad m => [m a] -> m [a]
sequence_ :: Monad m => [m a] -> m ()
(=<<) :: Monad m => (a -> m b) -> m a -> m b
Generalisations of list functions
join :: Monad m => m (m a) -> m a
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.
msum :: MonadPlus m => [m a] -> m a
filterM :: Monad m => (a -> m Bool) -> [a] -> m [a]
mapAndUnzipM :: Monad m => (a -> m (b, c)) -> [a] -> m ([b], [c])
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-transforming monad.
zipWithM :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m [c]
The `zipWithM` function generalises `zipWith` to arbitrary monads.
zipWithM_ :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m ()
`zipWithM_` is the extension of `zipWithM` which ignores the final result.
foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a

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.

foldM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m ()
replicateM :: Monad m => Int -> m a -> m [a]
replicateM_ :: Monad m => Int -> m a -> m ()
Conditional execution of monadic expressions
guard :: MonadPlus m => Bool -> m ()
when :: Monad m => Bool -> m () -> m ()

Conditional execution of monadic expressions. For example,

    	when debug (putStr "Debugging\n")

will output the string `Debugging\n` if the Boolean value `debug` is `True`, and otherwise do nothing.

unless :: Monad m => Bool -> m () -> m ()
The reverse of `when`.
Monadic lifting operators

The monadic lifting operators promote a function to a monad. The function arguments are scanned left to right. For example,

    	liftM2 (+) [0,1] [0,2] = [0,2,1,3]
    	liftM2 (+) (Just 1) Nothing = Nothing

liftM :: Monad m => (a1 -> r) -> m a1 -> m r
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
ap :: Monad m => m (a -> b) -> m a -> m b

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

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