Safe Haskell | None |
---|---|
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 :: 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
- 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 ()
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.
(*>) :: 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 Q | |
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 Capability | |
Defined in System.Console.Terminfo.Base pure :: a -> Capability a # (<*>) :: Capability (a -> b) -> Capability a -> Capability b # liftA2 :: (a -> b -> c) -> Capability a -> Capability b -> Capability c # (*>) :: Capability a -> Capability b -> Capability b # (<*) :: Capability a -> Capability b -> Capability a # | |
Applicative P | Since: base-4.5.0.0 |
Applicative Pair Source # | |
Applicative UniqSM Source # | |
Applicative CoreM Source # | |
Applicative P Source # | |
Applicative PD 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 LlvmM Source # | |
Applicative FCode Source # | |
Applicative CmmParse 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 SimplM Source # | |
Applicative CpsRn Source # | |
Applicative OccCheckResult Source # | |
Defined in TcUnify pure :: a -> OccCheckResult a # (<*>) :: OccCheckResult (a -> b) -> OccCheckResult a -> OccCheckResult b # liftA2 :: (a -> b -> c) -> OccCheckResult a -> OccCheckResult b -> OccCheckResult c # (*>) :: OccCheckResult a -> OccCheckResult b -> OccCheckResult b # (<*) :: OccCheckResult a -> OccCheckResult b -> OccCheckResult a # | |
Applicative TcS Source # | |
Applicative NatM 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 |
Applicative (ST s) | Since: base-4.4.0.0 |
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 (ListT f) Source # | |
Applicative (State s) Source # | |
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 (RegM freeRegs) Source # | |
Defined in RegAlloc.Linear.State pure :: a -> RegM freeRegs a # (<*>) :: RegM freeRegs (a -> b) -> RegM freeRegs a -> RegM freeRegs b # liftA2 :: (a -> b -> c) -> RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs c # (*>) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs b # (<*) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs a # | |
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.Strict | |
(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 | |
Monad m => Applicative (Stream m a) Source # | |
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 | |
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 SimplM Source # | |
Defined in SimplMonad | |
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.Strict | |
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
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