Safe Haskell | Safe-Inferred |
---|---|

Language | Haskell98 |

Utilities related to Monad and Applicative classes Mostly for backwards compatability.

- class Functor f => Applicative f where
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- class Monad m => MonadFix m where
- mfix :: (a -> m a) -> m a

- class Monad m => MonadIO m where
- liftIO1 :: MonadIO m => (a -> IO b) -> a -> m b
- liftIO2 :: MonadIO m => (a -> b -> IO c) -> a -> b -> m c
- liftIO3 :: MonadIO m => (a -> b -> c -> IO d) -> a -> b -> c -> m d
- liftIO4 :: MonadIO m => (a -> b -> c -> d -> IO e) -> a -> b -> c -> d -> m e
- zipWith3M :: Monad m => (a -> b -> c -> m d) -> [a] -> [b] -> [c] -> m [d]
- mapAndUnzipM :: Monad m => (a -> m (b, c)) -> [a] -> m ([b], [c])
- mapAndUnzip3M :: Monad m => (a -> m (b, c, d)) -> [a] -> m ([b], [c], [d])
- mapAndUnzip4M :: Monad m => (a -> m (b, c, d, e)) -> [a] -> m ([b], [c], [d], [e])
- mapAccumLM :: Monad m => (acc -> x -> m (acc, y)) -> acc -> [x] -> m (acc, [y])
- mapSndM :: Monad m => (b -> m c) -> [(a, b)] -> m [(a, c)]
- concatMapM :: Monad m => (a -> m [b]) -> [a] -> m [b]
- mapMaybeM :: Monad m => (a -> m (Maybe b)) -> [a] -> m [b]
- fmapMaybeM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b)
- fmapEitherM :: Monad m => (a -> m b) -> (c -> m d) -> Either a c -> m (Either b d)
- anyM :: Monad m => (a -> m Bool) -> [a] -> m Bool
- allM :: Monad m => (a -> m Bool) -> [a] -> m Bool
- foldlM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a
- foldlM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m ()
- foldrM :: Monad m => (b -> a -> m a) -> a -> [b] -> m a
- maybeMapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b)

# Documentation

class Functor f => Applicative f where Source

A functor with application, providing operations to

A minimal complete definition must include implementations of these functions satisfying the following laws:

*identity*`pure`

`id`

`<*>`

v = v*composition*`pure`

(.)`<*>`

u`<*>`

v`<*>`

w = u`<*>`

(v`<*>`

w)*homomorphism*`pure`

f`<*>`

`pure`

x =`pure`

(f x)*interchange*u

`<*>`

`pure`

y =`pure`

(`$`

y)`<*>`

u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

As a consequence of these laws, the `Functor`

instance for `f`

will satisfy

If `f`

is also a `Monad`

, it should satisfy

(which implies that `pure`

and `<*>`

satisfy the applicative functor laws).

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source

Sequential application.

(*>) :: f a -> f b -> f b infixl 4 Source

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4 Source

Sequence actions, discarding the value of the second argument.

class Monad m => MonadFix m where Source

Monads having fixed points with a 'knot-tying' semantics.
Instances of `MonadFix`

should satisfy the following laws:

*purity*`mfix`

(`return`

. h) =`return`

(`fix`

h)*left shrinking*(or*tightening*)`mfix`

(\x -> a >>= \y -> f x y) = a >>= \y ->`mfix`

(\x -> f x y)*sliding*

, for strict`mfix`

(`liftM`

h . f) =`liftM`

h (`mfix`

(f . h))`h`

.*nesting*`mfix`

(\x ->`mfix`

(\y -> f x y)) =`mfix`

(\x -> f x x)

This class is used in the translation of the recursive `do`

notation
supported by GHC and Hugs.

liftIO1 :: MonadIO m => (a -> IO b) -> a -> m b Source

Lift an `IO`

operation with 1 argument into another monad

liftIO2 :: MonadIO m => (a -> b -> IO c) -> a -> b -> m c Source

Lift an `IO`

operation with 2 arguments into another monad

liftIO3 :: MonadIO m => (a -> b -> c -> IO d) -> a -> b -> c -> m d Source

Lift an `IO`

operation with 3 arguments into another monad

liftIO4 :: MonadIO m => (a -> b -> c -> d -> IO e) -> a -> b -> c -> d -> m e Source

Lift an `IO`

operation with 4 arguments into another monad

mapAndUnzipM :: Monad 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-transforming monad.

mapAndUnzip3M :: Monad m => (a -> m (b, c, d)) -> [a] -> m ([b], [c], [d]) Source

mapAndUnzipM for triples

mapAndUnzip4M :: Monad m => (a -> m (b, c, d, e)) -> [a] -> m ([b], [c], [d], [e]) Source

:: Monad m | |

=> (acc -> x -> m (acc, y)) | combining funcction |

-> acc | initial state |

-> [x] | inputs |

-> m (acc, [y]) | final state, outputs |

Monadic version of mapAccumL

concatMapM :: Monad m => (a -> m [b]) -> [a] -> m [b] Source

Monadic version of concatMap

fmapMaybeM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source

Monadic version of fmap

fmapEitherM :: Monad m => (a -> m b) -> (c -> m d) -> Either a c -> m (Either b d) Source

Monadic version of fmap

anyM :: Monad m => (a -> m Bool) -> [a] -> m Bool Source

Monadic version of `any`

, aborts the computation at the first `True`

value

allM :: Monad m => (a -> m Bool) -> [a] -> m Bool Source

Monad version of `all`

, aborts the computation at the first `False`

value