
Control.Applicative  Portability  portable  Stability  experimental  Maintainer  ross@soi.city.ac.uk 





Description 
This module describes a structure intermediate between a functor and
a monad: it provides pure expressions and sequencing, but no binding.
(Technically, a strong lax monoidal functor.) For more details, see
Applicative Programming with Effects,
by Conor McBride and Ross Paterson, online at
http://www.soi.city.ac.uk/~ross/papers/Applicative.html.
This interface was introduced for parsers by Niklas Röjemo, because
it admits more sharing than the monadic interface. The names here are
mostly based on recent parsing work by Doaitse Swierstra.
This class is also useful with instances of the
Traversable class.


Synopsis 




Applicative functors


class Functor f => Applicative f where 
A functor with application.
Instances should satisfy 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
If f is also a Monad, define pure = return and (<*>) = ap.
  Methods  pure :: a > f a  Lift a value.
  (<*>) :: f (a > b) > f a > f b  Sequential application.

  Instances  


Instances


newtype WrappedMonad m a 
Constructors   Instances  


newtype Const a b 
Constructors   Instances  


newtype ZipList a 


Utility functions


(<$>) :: Functor f => (a > b) > f a > f b 
A synonym for fmap.


(<$) :: Functor f => a > f b > f a 
Replace the value.


(*>) :: Applicative f => f a > f b > f b 
Sequence actions, discarding the value of the first argument.


(<*) :: Applicative f => f a > f b > f a 
Sequence actions, discarding the value of the second argument.


(<**>) :: Applicative f => f a > f (a > b) > f b 
A variant of <*> with the arguments reversed.


liftA :: Applicative f => (a > b) > f a > f b 
Lift a function to actions.
This function may be used as a value for fmap in a Functor instance.


liftA2 :: Applicative f => (a > b > c) > f a > f b > f c 
Lift a binary function to actions.


liftA3 :: Applicative f => (a > b > c > d) > f a > f b > f c > f d 
Lift a ternary function to actions.


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