
Control.Applicative  Portability  portable  Stability  experimental  Maintainer  libraries@haskell.org 





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
Data.Traversable.Traversable class.


Synopsis 




Applicative functors



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
 ignore left value

u *> v = pure (const id) <*> u <*> v
 ignore right value

u <* v = pure const <*> u <*> v
The Functor instance should satisfy
fmap f x = pure f <*> x
If f is also a Monad, define pure = return and (<*>) = ap.
Minimal complete definition: pure and <*>.
  Methods   Lift a value.
  (<*>) :: f (a > b) > f a > f b  Source 
 Sequential application.
  (*>) :: f a > f b > f b  Source 
 Sequence actions, discarding the value of the first argument.
  (<*) :: f a > f b > f a  Source 
 Sequence actions, discarding the value of the second argument.

  Instances  


Alternatives



A monoid on applicative functors.
Minimal complete definition: empty and <>.
some and many should be the least solutions of the equations:
  Methods   The identity of <>
  (<>) :: f a > f a > f a  Source 
 An associative binary operation
   One or more.
   Zero or more.

  Instances  


Instances



Constructors   Instances  


newtype WrappedMonad m a  Source 

Constructors   Instances  


newtype WrappedArrow a b c  Source 

Constructors   Instances  





Utility functions



An infix synonym for fmap.



Replace all locations in the input with the same value.
The default definition is fmap . const, but this may be
overridden with a more efficient version.



A variant of <*> with the arguments reversed.



Lift a function to actions.
This function may be used as a value for fmap in a Functor instance.



Lift a binary function to actions.



Lift a ternary function to actions.



One or none.


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