Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
Utilities related to Monad and Applicative classes Mostly for backwards compatibility.
Synopsis
- class Functor f => Applicative (f :: Type -> Type) where
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- class Monad m => MonadFix (m :: Type -> Type) where
- mfix :: (a -> m a) -> m a
- class Monad m => MonadIO (m :: Type -> Type) 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]
- zipWith3M_ :: Monad m => (a -> b -> c -> m d) -> [a] -> [b] -> [c] -> m ()
- zipWith4M :: Monad m => (a -> b -> c -> d -> m e) -> [a] -> [b] -> [c] -> [d] -> m [e]
- zipWithAndUnzipM :: Monad m => (a -> b -> m (c, d)) -> [a] -> [b] -> m ([c], [d])
- mapAndUnzipM :: Applicative 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])
- mapAndUnzip5M :: Monad m => (a -> m (b, c, d, e, f)) -> [a] -> m ([b], [c], [d], [e], [f])
- 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 :: Applicative 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
- orM :: Monad m => m Bool -> m Bool -> 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)
- whenM :: Monad m => m Bool -> m () -> m ()
- unlessM :: Monad m => m Bool -> m () -> m ()
- filterOutM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
Documentation
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*>
or liftA2
. If it defines both, then they must behave
the same as their default definitions:
(<*>
) =liftA2
id
liftA2
f x y = f<$>
x<*>
y
Further, any definition must satisfy the following:
- 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
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2
p (liftA2
q u v) =liftA2
f u .liftA2
g v
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 #
Sequential application.
A few functors support an implementation of <*>
that is more
efficient than the default one.
liftA2 :: (a -> b -> c) -> f a -> f b -> f c #
Lift a binary function to actions.
Some functors support an implementation of liftA2
that is more
efficient than the default one. In particular, if fmap
is an
expensive operation, it is likely better to use liftA2
than to
fmap
over the structure and then use <*>
.
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
Applicative [] | Since: base-2.1 |
Applicative Maybe | Since: base-2.1 |
Applicative IO | Since: base-2.1 |
Applicative Par1 | Since: base-4.9.0.0 |
Applicative Complex | Since: base-4.9.0.0 |
Applicative Min | Since: base-4.9.0.0 |
Applicative Max | Since: base-4.9.0.0 |
Applicative First | Since: base-4.9.0.0 |
Applicative Last | Since: base-4.9.0.0 |
Applicative Option | Since: base-4.9.0.0 |
Applicative ZipList | f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1 |
Applicative Identity | Since: base-4.8.0.0 |
Applicative STM | Since: base-4.8.0.0 |
Applicative First | Since: base-4.8.0.0 |
Applicative Last | Since: base-4.8.0.0 |
Applicative Dual | Since: base-4.8.0.0 |
Applicative Sum | Since: base-4.8.0.0 |
Applicative Product | Since: base-4.8.0.0 |
Applicative Down | Since: base-4.11.0.0 |
Applicative ReadPrec | Since: base-4.6.0.0 |
Applicative ReadP | Since: base-4.6.0.0 |
Applicative NonEmpty | Since: base-4.9.0.0 |
Applicative PutM | |
Applicative Get | |
Applicative Put | |
Applicative Tree | |
Applicative Seq | Since: containers-0.5.4 |
Applicative P | Since: base-4.5.0.0 |
Applicative Q Source # | |
Applicative PprM Source # | |
Applicative Pair Source # | |
Applicative UniqSM Source # | |
Applicative CoreM Source # | |
Applicative P Source # | |
Applicative UnifyResultM Source # | |
Defined in Unify pure :: a -> UnifyResultM a # (<*>) :: UnifyResultM (a -> b) -> UnifyResultM a -> UnifyResultM b # liftA2 :: (a -> b -> c) -> UnifyResultM a -> UnifyResultM b -> UnifyResultM c # (*>) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM b # (<*) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM a # | |
Applicative PV Source # | |
Applicative Hsc Source # | |
Applicative TcPluginM Source # | |
Applicative CompPipeline Source # | |
Defined in PipelineMonad pure :: a -> CompPipeline a # (<*>) :: CompPipeline (a -> b) -> CompPipeline a -> CompPipeline b # liftA2 :: (a -> b -> c) -> CompPipeline a -> CompPipeline b -> CompPipeline c # (*>) :: CompPipeline a -> CompPipeline b -> CompPipeline b # (<*) :: CompPipeline a -> CompPipeline b -> CompPipeline a # | |
Applicative Ghc Source # | |
Applicative (Either e) | Since: base-3.0 |
Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) Since: base-2.1 |
Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative pure :: a -> WrappedMonad m a # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a # | |
Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow pure :: a0 -> ArrowMonad a a0 # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
(Functor m, Monad m) => Applicative (MaybeT m) | |
Applicative (MaybeErr err) Source # | |
Defined in Maybes | |
Applicative (SetM s) | |
Applicative (CmdLineP s) Source # | |
Monad m => Applicative (EwM m) Source # | |
Applicative (IOEnv m) Source # | |
Applicative m => Applicative (GhcT m) Source # | |
Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
(Applicative f, Monad f) => Applicative (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal pure :: a -> WhenMissing f x a # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a # | |
(Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
(Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Lazy | |
(Functor m, Monad m) => Applicative (ExceptT e m) | |
Defined in Control.Monad.Trans.Except | |
Applicative ((->) a :: Type -> Type) | Since: base-2.1 |
Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
(Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
(Applicative f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product | |
(Monad f, Applicative f) => Applicative (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal pure :: a -> WhenMatched f x y a # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Applicative (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal pure :: a -> WhenMissing f k x a # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a # | |
Applicative m => Applicative (ReaderT r m) | |
Defined in Control.Monad.Trans.Reader | |
Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
(Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
(Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
(Monad f, Applicative f) => Applicative (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal pure :: a -> WhenMatched f k x y a # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a # |
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
An infix synonym for fmap
.
The name of this operator is an allusion to $
.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $
is function application, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> Left 17
Left 17>>>
show <$> Right 17
Right "17"
Double each element of a list:
>>>
(*2) <$> [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
even <$> (2,2)
(2,True)
class Monad m => MonadFix (m :: Type -> Type) where #
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 strictmfix
(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.
Instances
class Monad m => MonadIO (m :: Type -> Type) where #
Monads in which IO
computations may be embedded.
Any monad built by applying a sequence of monad transformers to the
IO
monad will be an instance of this class.
Instances should satisfy the following laws, which state that liftIO
is a transformer of monads:
Instances
MonadIO IO | Since: base-4.9.0.0 |
Defined in Control.Monad.IO.Class | |
MonadIO Q Source # | |
Defined in Language.Haskell.TH.Syntax | |
MonadIO CoreM Source # | |
MonadIO Hsc Source # | |
MonadIO CompPipeline Source # | |
Defined in PipelineMonad liftIO :: IO a -> CompPipeline a # | |
MonadIO Ghc Source # | |
MonadIO m => MonadIO (MaybeT m) | |
Defined in Control.Monad.Trans.Maybe | |
MonadIO (IOEnv env) Source # | |
MonadIO m => MonadIO (GhcT m) Source # | |
(Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
MonadIO m => MonadIO (StateT s m) | |
Defined in Control.Monad.Trans.State.Lazy | |
MonadIO m => MonadIO (ExceptT e m) | |
Defined in Control.Monad.Trans.Except | |
MonadIO m => MonadIO (ReaderT r m) | |
Defined in Control.Monad.Trans.Reader |
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
zipWith3M_ :: Monad m => (a -> b -> c -> m d) -> [a] -> [b] -> [c] -> m () Source #
zipWithAndUnzipM :: Monad m => (a -> b -> m (c, d)) -> [a] -> [b] -> m ([c], [d]) Source #
mapAndUnzipM :: Applicative 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.
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 #
mapAndUnzip5M :: Monad m => (a -> m (b, c, d, e, f)) -> [a] -> m ([b], [c], [d], [e], [f]) Source #
:: Monad m | |
=> (acc -> x -> m (acc, y)) | combining function |
-> 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
mapMaybeM :: Applicative m => (a -> m (Maybe b)) -> [a] -> m [b] Source #
Applicative version of mapMaybe
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
foldlM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m () Source #
Monadic version of foldl that discards its result
maybeMapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source #
Monadic version of fmap specialised for Maybe
whenM :: Monad m => m Bool -> m () -> m () Source #
Monadic version of when
, taking the condition in the monad
unlessM :: Monad m => m Bool -> m () -> m () Source #
Monadic version of unless
, taking the condition in the monad
filterOutM :: Applicative m => (a -> m Bool) -> [a] -> m [a] Source #
Like filterM
, only it reverses the sense of the test.