## Applicative

#### Definition

-- definition
class Functor f => Applicative f where
pure  :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b
 pure id <*> v $\ \leftrightsquigarrow\$ v pure f <*> pure x $\ \leftrightsquigarrow\$ pure (f x) u <*> pure y $\ \leftrightsquigarrow\$ pure ($y) <*> u u <*> (v <*> w)$\ \leftrightsquigarrow\ \$ pure (.) <*> u <*> v <*> w

### Discussion

Applicative is a functor together with a polymorphic function 'pure' lifting terms, as well as a function '(<*>)' which applies terms in the lifted function type to lifted terms. Note that 'f (a → b)' is generally not a function space. E.g. the term 'Nothing' of 'Maybe (a→b)' isn't a function.