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
- data ID a
- runID :: ID a -> a
- 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 whereSource

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:

u`*>`

v =`pure`

(`const`

`id`

)`<*>`

u`<*>`

v u`<*`

v =`pure`

`const`

`<*>`

u`<*>`

v

As a consequence of these laws, the `Functor`

instance for `f`

will satisfy

`fmap`

f x =`pure`

f`<*>`

x

If `f`

is also a `Monad`

, it should satisfy

and
`pure`

= `return`

`(`

(which implies that `<*>`

) = `ap`

`pure`

and `<*>`

satisfy the
applicative functor laws).

Lift a value.

(<*>) :: f (a -> b) -> f a -> f bSource

Sequential application.

(*>) :: f a -> f b -> f bSource

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f aSource

Sequence actions, discarding the value of the second argument.

Applicative [] | |

Applicative IO | |

Applicative Maybe | |

Applicative Id | |

Applicative ZipList | |

Applicative STM | |

Applicative Id | |

Applicative UniqSM | |

Applicative Pair | |

Applicative CoreM | |

Applicative ((->) a) | |

Applicative (Either e) | |

Monoid a => Applicative ((,) a) | |

Applicative (ST s) | |

Applicative (StateL s) | |

Applicative (StateR s) | |

Monoid m => Applicative (Const m) | |

Monad m => Applicative (WrappedMonad m) | |

Applicative (ST s) | |

Applicative (State s) | |

Applicative (State s) | |

Applicative (IOEnv m) | |

Arrow a => Applicative (WrappedArrow a b) |

class Monad m => MonadFix m whereSource

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`

(`Control.Monad.liftM`

h . f) =`Control.Monad.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 bSource

Lift an `IO`

operation with 1 argument into another monad

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

Lift an `IO`

operation with 2 arguments into another monad

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

Lift an `IO`

operation with 3 arguments into another monad

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

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 BoolSource

Monadic version of `any`

, aborts the computation at the first `True`

value

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

Monad version of `all`

, aborts the computation at the first `False`

value