Portability  portable 

Stability  provisional 
Maintainer  Edward Kmett <ekmett@gmail.com> 
NB: The definitions exported through Data.Functor.Apply need to be included here because otherwise the instances for the transformers package have orphaned heads.
 class Functor f where
 (<$>) :: Functor f => (a > b) > f a > f b
 ($>) :: Functor f => f a > b > f b
 class Functor f => Apply f where
 (<..>) :: Apply w => w a > w (a > b) > w b
 liftF2 :: Apply w => (a > b > c) > w a > w b > w c
 liftF3 :: Apply w => (a > b > c > d) > w a > w b > w c > w d
 newtype WrappedApplicative f a = WrapApplicative {
 unwrapApplicative :: f a
 newtype MaybeApply f a = MaybeApply {
 runMaybeApply :: Either (f a) a
 class Apply m => Bind m where
 (<<) :: Bind m => (a > m b) > m a > m b
 (<) :: Bind m => (b > m c) > (a > m b) > a > m c
 (>) :: Bind m => (a > m b) > (b > m c) > a > m c
 apDefault :: Bind f => f (a > b) > f a > f b
 returning :: Functor f => f a > (a > b) > f b
Functors
class Functor f where
The Functor
class is used for types that can be mapped over.
Instances of Functor
should satisfy the following laws:
fmap id == id fmap (f . g) == fmap f . fmap g
The instances of Functor
for lists, Data.Maybe.Maybe
and System.IO.IO
satisfy these laws.
Applyable functors
class Functor f => Apply f whereSource
A strong lax semimonoidal endofunctor.
This is equivalent to an Applicative
without pure
.
Laws:
associative composition: (.) <$> u <.> v <.> w = u <.> (v <.> w)
(<.>) :: f (a > b) > f a > f bSource
(.>) :: f a > f b > f bSource
(<.) :: f a > f b > f aSource
a . b = const <$ a . b
liftF2 :: Apply w => (a > b > c) > w a > w b > w cSource
Lift a binary function into a comonad with zipping
liftF3 :: Apply w => (a > b > c > d) > w a > w b > w c > w dSource
Lift a ternary function into a comonad with zipping
Wrappers
newtype WrappedApplicative f a Source
Wrap an Applicative
to be used as a member of Apply
WrapApplicative  

Functor f => Functor (WrappedApplicative f)  
Applicative f => Applicative (WrappedApplicative f)  
Alternative f => Alternative (WrappedApplicative f)  
Applicative f => Apply (WrappedApplicative f)  
Alternative f => Alt (WrappedApplicative f)  
Alternative f => Plus (WrappedApplicative f) 
newtype MaybeApply f a Source
Transform a Apply into an Applicative by adding a unit.
MaybeApply  

Functor f => Functor (MaybeApply f)  
Apply f => Applicative (MaybeApply f)  
Comonad f => Comonad (MaybeApply f)  
Extend f => Extend (MaybeApply f)  
Apply f => Apply (MaybeApply f) 
Bindable functors
class Apply m => Bind m whereSource
Minimal definition: Either join
or >>
If defining both, then the following laws (the default definitions) must hold:
join = (>> id) m >> f = join (fmap f m)
Laws:
induced definition of <.>: f <.> x = f >> (<$> x)
Finally, there are two associativity conditions:
associativity of (>>): (m >> f) >> g == m >> (\x > f x >> g) associativity of join: join . join = join . fmap join
These can both be seen as special cases of the constraint that
associativity of (>): (f > g) > h = f > (g > h)
Bind []  
Bind IO  
Bind Maybe  
Bind Tree  
Bind Seq  
Bind IntMap  An 
Bind Option  
Bind Identity  
Bind ((>) m)  
Bind (Either a)  
Semigroup m => Bind ((,) m)  
Monad m => Bind (WrappedMonad m)  
Ord k => Bind (Map k)  
(Bind m, Monad m) => Bind (MaybeT m)  
(Bind m, Monad m) => Bind (ListT m)  
Bind m => Bind (IdentityT m)  
(Bind m, Semigroup w) => Bind (WriterT w m)  
(Bind m, Semigroup w) => Bind (WriterT w m)  
Bind m => Bind (StateT s m)  
Bind m => Bind (StateT s m)  
Bind m => Bind (ReaderT e m)  
(Bind m, Monad m) => Bind (ErrorT e m)  
Bind (ContT r m)  
(Bind f, Bind g) => Bind (Product f g)  
(Bind m, Semigroup w) => Bind (RWST r w s m)  
(Bind m, Semigroup w) => Bind (RWST r w s m) 