Safe Haskell | Safe-Inferred |
---|---|
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
- 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 :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- foldlM_ :: (Monad m, Foldable t) => (a -> b -> m a) -> a -> t b -> m ()
- foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
- 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 Source #
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 Source #
Sequential application.
A few functors support an implementation of <*>
that is more
efficient than the default one.
Using ApplicativeDo
: 'fs
' can be understood as
the <*>
asdo
expression
do f <- fs a <- as pure (f a)
liftA2 :: (a -> b -> c) -> f a -> f b -> f c Source #
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 <*>
.
This became a typeclass method in 4.10.0.0. Prior to that, it was
a function defined in terms of <*>
and fmap
.
Using ApplicativeDo
: '
' can be understood
as the liftA2
f as bsdo
expression
do a <- as b <- bs pure (f a b)
(*>) :: f a -> f b -> f b infixl 4 Source #
Sequence actions, discarding the value of the first argument.
'as
' can be understood as the *>
bsdo
expression
do as bs
This is a tad complicated for our ApplicativeDo
extension
which will give it a Monad
constraint. For an Applicative
constraint we write it of the form
do _ <- as b <- bs pure b
(<*) :: f a -> f b -> f a infixl 4 Source #
Sequence actions, discarding the value of the second argument.
Using ApplicativeDo
: 'as
' can be understood as
the <*
bsdo
expression
do a <- as bs pure a
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 |
Defined in Data.Functor.Identity | |
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 |
Defined in Data.Semigroup.Internal | |
Applicative Down | Since: base-4.11.0.0 |
Applicative ReadPrec | Since: base-4.6.0.0 |
Defined in Text.ParserCombinators.ReadPrec | |
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 Source # (<*>) :: Capability (a -> b) -> Capability a -> Capability b Source # liftA2 :: (a -> b -> c) -> Capability a -> Capability b -> Capability c Source # (*>) :: Capability a -> Capability b -> Capability b Source # (<*) :: Capability a -> Capability b -> Capability a Source # | |
Applicative P | Since: base-4.5.0.0 |
Applicative Pair # | |
Applicative UniqSM # | |
Applicative CoreM # | |
Applicative P # | |
Applicative PD # | |
Applicative UnifyResultM # | |
Defined in Unify pure :: a -> UnifyResultM a Source # (<*>) :: UnifyResultM (a -> b) -> UnifyResultM a -> UnifyResultM b Source # liftA2 :: (a -> b -> c) -> UnifyResultM a -> UnifyResultM b -> UnifyResultM c Source # (*>) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM b Source # (<*) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM a Source # | |
Applicative LiftM # | |
Applicative LlvmM # | |
Applicative FCode # | |
Applicative CmmParse # | |
Defined in GHC.StgToCmm.ExtCode | |
Applicative PV # | |
Applicative Hsc # | |
Applicative CompPipeline # | |
Defined in PipelineMonad pure :: a -> CompPipeline a Source # (<*>) :: CompPipeline (a -> b) -> CompPipeline a -> CompPipeline b Source # liftA2 :: (a -> b -> c) -> CompPipeline a -> CompPipeline b -> CompPipeline c Source # (*>) :: CompPipeline a -> CompPipeline b -> CompPipeline b Source # (<*) :: CompPipeline a -> CompPipeline b -> CompPipeline a Source # | |
Applicative Ghc # | |
Applicative SimplM # | |
Applicative TcPluginM # | |
Defined in TcRnTypes | |
Applicative CpsRn # | |
Applicative MetaTyVarUpdateResult # | |
Defined in TcUnify pure :: a -> MetaTyVarUpdateResult a Source # (<*>) :: MetaTyVarUpdateResult (a -> b) -> MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b Source # liftA2 :: (a -> b -> c) -> MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult c Source # (*>) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult b Source # (<*) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult a Source # | |
Applicative TcS # | |
Applicative NatM # | |
Applicative (Either e) | Since: base-3.0 |
Defined in Data.Either | |
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 Source # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source # | |
Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow pure :: a0 -> ArrowMonad a a0 Source # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
(Functor m, Monad m) => Applicative (MaybeT m) | |
Defined in Control.Monad.Trans.Maybe | |
Applicative (State s) # | |
Applicative (MaybeErr err) # | |
Defined in Maybes pure :: a -> MaybeErr err a Source # (<*>) :: MaybeErr err (a -> b) -> MaybeErr err a -> MaybeErr err b Source # liftA2 :: (a -> b -> c) -> MaybeErr err a -> MaybeErr err b -> MaybeErr err c Source # (*>) :: MaybeErr err a -> MaybeErr err b -> MaybeErr err b Source # (<*) :: MaybeErr err a -> MaybeErr err b -> MaybeErr err a Source # | |
Applicative (SetM s) | |
Applicative (CmdLineP s) # | |
Defined in CmdLineParser pure :: a -> CmdLineP s a Source # (<*>) :: CmdLineP s (a -> b) -> CmdLineP s a -> CmdLineP s b Source # liftA2 :: (a -> b -> c) -> CmdLineP s a -> CmdLineP s b -> CmdLineP s c Source # (*>) :: CmdLineP s a -> CmdLineP s b -> CmdLineP s b Source # (<*) :: CmdLineP s a -> CmdLineP s b -> CmdLineP s a Source # | |
Monad m => Applicative (EwM m) # | |
Applicative (IOEnv m) # | |
Applicative (RegM freeRegs) # | |
Defined in RegAlloc.Linear.State pure :: a -> RegM freeRegs a Source # (<*>) :: RegM freeRegs (a -> b) -> RegM freeRegs a -> RegM freeRegs b Source # liftA2 :: (a -> b -> c) -> RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs c Source # (*>) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs b Source # (<*) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs a Source # | |
Applicative m => Applicative (GhcT m) # | |
Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
(Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative pure :: a0 -> WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in Control.Arrow pure :: a0 -> Kleisli m a a0 Source # (<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source # (*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source # | |
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 Source # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c Source # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b Source # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a Source # | |
(Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # | |
(Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # | |
(Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Lazy pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # | |
Applicative m => Applicative (ReaderT r m) | |
Defined in Control.Monad.Trans.Reader pure :: a -> ReaderT r m a Source # (<*>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b Source # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c Source # (*>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b Source # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a Source # | |
(Functor m, Monad m) => Applicative (ExceptT e m) | |
Defined in Control.Monad.Trans.Except pure :: a -> ExceptT e m a Source # (<*>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b Source # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c Source # (*>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b Source # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a Source # | |
Monad m => Applicative (Stream m a) # | |
Defined in Stream pure :: a0 -> Stream m a a0 Source # (<*>) :: Stream m a (a0 -> b) -> Stream m a a0 -> Stream m a b Source # liftA2 :: (a0 -> b -> c) -> Stream m a a0 -> Stream m a b -> Stream m a c Source # (*>) :: Stream m a a0 -> Stream m a b -> Stream m a b Source # (<*) :: Stream m a a0 -> Stream m a b -> Stream m a a0 Source # | |
Applicative ((->) r :: 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 |
Defined in GHC.Generics | |
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base pure :: a0 -> (a, b, c, a0) Source # (<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source # (*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source # | |
(Applicative f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product pure :: a -> Product f g a Source # (<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source # (*>) :: Product f g a -> Product f g b -> Product f g b Source # (<*) :: Product f g a -> Product f g b -> Product f g a Source # | |
(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 Source # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c Source # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b Source # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a Source # | |
(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 Source # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c Source # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b Source # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a Source # | |
Applicative (ContT r m) | |
Defined in Control.Monad.Trans.Cont | |
Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
(Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
(Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose pure :: a -> Compose f g a Source # (<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source # (*>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source # | |
(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 Source # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c Source # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b Source # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a Source # | |
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Strict pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # | |
(Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.CPS pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # |
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #
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 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 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
MonadFix [] | Since: base-2.1 |
Defined in Control.Monad.Fix | |
MonadFix Maybe | Since: base-2.1 |
MonadFix IO | Since: base-2.1 |
MonadFix Par1 | Since: base-4.9.0.0 |
MonadFix Min | Since: base-4.9.0.0 |
MonadFix Max | Since: base-4.9.0.0 |
MonadFix First | Since: base-4.9.0.0 |
MonadFix Last | Since: base-4.9.0.0 |
MonadFix Option | Since: base-4.9.0.0 |
MonadFix Identity | Since: base-4.8.0.0 |
MonadFix First | Since: base-4.8.0.0 |
MonadFix Last | Since: base-4.8.0.0 |
MonadFix Dual | Since: base-4.8.0.0 |
MonadFix Sum | Since: base-4.8.0.0 |
MonadFix Product | Since: base-4.8.0.0 |
MonadFix Down | Since: base-4.12.0.0 |
MonadFix NonEmpty | Since: base-4.9.0.0 |
MonadFix Tree | Since: containers-0.5.11 |
MonadFix Seq | Since: containers-0.5.11 |
MonadFix UniqSM # | |
MonadFix Ghc # | |
MonadFix (Either e) | Since: base-4.3.0.0 |
MonadFix (ST s) | Since: base-2.1 |
MonadFix m => MonadFix (MaybeT m) | |
MonadFix f => MonadFix (Rec1 f) | Since: base-4.9.0.0 |
MonadFix f => MonadFix (Ap f) | Since: base-4.12.0.0 |
MonadFix f => MonadFix (Alt f) | Since: base-4.8.0.0 |
(Monoid w, MonadFix m) => MonadFix (WriterT w m) | |
MonadFix m => MonadFix (StateT s m) | |
MonadFix m => MonadFix (StateT s m) | |
MonadFix m => MonadFix (ReaderT r m) | |
MonadFix m => MonadFix (ExceptT e m) | |
MonadFix ((->) r :: Type -> Type) | Since: base-2.1 |
Defined in Control.Monad.Fix | |
(MonadFix f, MonadFix g) => MonadFix (f :*: g) | Since: base-4.9.0.0 |
(MonadFix f, MonadFix g) => MonadFix (Product f g) | Since: base-4.9.0.0 |
MonadFix f => MonadFix (M1 i c f) | Since: base-4.9.0.0 |
(Monoid w, MonadFix m) => MonadFix (RWST r w s m) | |
MonadFix m => MonadFix (RWST r w s m) | |
class Monad m => MonadIO (m :: Type -> Type) where Source #
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 |
MonadIO Q | |
MonadIO CoreM # | |
MonadIO Hsc # | |
MonadIO CompPipeline # | |
Defined in PipelineMonad liftIO :: IO a -> CompPipeline a Source # | |
MonadIO Ghc # | |
MonadIO SimplM # | |
MonadIO m => MonadIO (MaybeT m) | |
MonadIO (IOEnv env) # | |
MonadIO m => MonadIO (GhcT m) # | |
(Monoid w, MonadIO m) => MonadIO (WriterT w m) | |
MonadIO m => MonadIO (StateT s m) | |
MonadIO m => MonadIO (StateT s m) | |
MonadIO m => MonadIO (ReaderT r m) | |
MonadIO m => MonadIO (ExceptT e m) | |
MonadIO m => MonadIO (ContT r m) | |
(Monoid w, MonadIO m) => MonadIO (RWST r w s m) | |
MonadIO m => MonadIO (RWST r w s m) | |
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]) 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 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 :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b Source #
Monadic fold over the elements of a structure, associating to the left, i.e. from left to right.
foldlM_ :: (Monad m, Foldable t) => (a -> b -> m a) -> a -> t b -> m () Source #
Monadic version of foldl that discards its result
foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b Source #
Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.
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.