applicative

Applicative

Haskell class

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.

Reference

Parents

Subset of

Functor . Haskell