Copyright  Conor McBride and Ross Paterson 2005 

License  Conor McBride and Ross Paterson 2005 
Maintainer  libraries@haskell.org 
Stability  experimental 
Portability  portable 
Safe Haskell  Trustworthy 
This module describes a structure intermediate between a functor and
a monad (technically, a strong lax monoidal functor). Compared with
monads, this interface lacks the full power of the binding operation
>>=
, but
 it has more instances.
 it is sufficient for many uses, e.g. contextfree parsing, or the
Traversable
class.  instances can perform analysis of computations before they are executed, and thus produce shared optimizations.
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 parsing work by Doaitse Swierstra.
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.
 class Functor f => Applicative f where
 class Applicative f => Alternative f where
 newtype Const a b = Const {
 getConst :: a
 newtype WrappedMonad m a = WrapMonad {
 unwrapMonad :: m a
 newtype WrappedArrow a b c = WrapArrow {
 unwrapArrow :: a b c
 newtype ZipList a = ZipList {
 getZipList :: [a]
 (<$>) :: Functor f => (a > b) > f a > f b
 (<$) :: Functor f => a > f b > f a
 (<**>) :: Applicative f => f a > f (a > b) > f b
 liftA :: Applicative f => (a > b) > f a > f b
 liftA2 :: Applicative f => (a > b > c) > f a > f b > f c
 liftA3 :: Applicative f => (a > b > c > d) > f a > f b > f c > f d
 optional :: Alternative f => f a > f (Maybe a)
Applicative functors
class Functor f => Applicative f whereSource
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying 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
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
u*>
v =pure
(const
id
)<*>
u<*>
v u<*
v =pure
const
<*>
u<*>
v
As a consequence of these laws, the Functor
instance for f
will satisfy
fmap
f x =pure
f<*>
x
If f
is also a Monad
, it should satisfy
and
pure
= return
(
(which implies that <*>
) = ap
pure
and <*>
satisfy the
applicative functor laws).
Lift a value.
(<*>) :: f (a > b) > f a > f bSource
Sequential application.
(*>) :: f a > f b > f bSource
Sequence actions, discarding the value of the first argument.
(<*) :: f a > f b > f aSource
Sequence actions, discarding the value of the second argument.
Applicative []  
Applicative IO  
Applicative Maybe  
Applicative ReadP  
Applicative ReadPrec  
Applicative STM  
Applicative ZipList  
Applicative ((>) a)  
Applicative (Either e)  
Monoid a => Applicative ((,) a)  
Applicative (ST s)  
Applicative (Proxy *)  
Arrow a => Applicative (ArrowMonad a)  
Applicative (ST s)  
Monad m => Applicative (WrappedMonad m)  
Monoid m => Applicative (Const m)  
Arrow a => Applicative (WrappedArrow a b) 
Alternatives
class Applicative f => Alternative f whereSource
A monoid on applicative functors.
Minimal complete definition: empty
and <>
.
If defined, some
and many
should be the least solutions
of the equations:
The identity of <>
(<>) :: f a > f a > f aSource
An associative binary operation
One or more.
Zero or more.
Alternative []  
Alternative Maybe  
Alternative ReadP  
Alternative ReadPrec  
Alternative STM  
ArrowPlus a => Alternative (ArrowMonad a)  
MonadPlus m => Alternative (WrappedMonad m)  
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) 
Instances
newtype WrappedMonad m a Source
WrapMonad  

Monad m => Functor (WrappedMonad m)  
Monad m => Applicative (WrappedMonad m)  
MonadPlus m => Alternative (WrappedMonad m) 
newtype WrappedArrow a b c Source
WrapArrow  

Arrow a => Functor (WrappedArrow a b)  
Arrow a => Applicative (WrappedArrow a b)  
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) 
Lists, but with an Applicative
functor based on zipping, so that
f<$>
ZipList
xs1<*>
...<*>
ZipList
xsn =ZipList
(zipWithn f xs1 ... xsn)
ZipList  

Utility functions
(<**>) :: Applicative f => f a > f (a > b) > f bSource
A variant of <*>
with the arguments reversed.
liftA :: Applicative f => (a > b) > f a > f bSource
liftA2 :: Applicative f => (a > b > c) > f a > f b > f cSource
Lift a binary function to actions.
liftA3 :: Applicative f => (a > b > c > d) > f a > f b > f c > f dSource
Lift a ternary function to actions.
optional :: Alternative f => f a > f (Maybe a)Source
One or none.