package preface

An Applicative is a functor with lifting and sequencing capabilities. Applicative is more general (and by extension weaker) than a Monad. An Applicative is also a Functor.

Laws

To have a predictable behaviour, the instance of Applicative must obey some laws.

1. apply = lift2 id
2. lift2 f x y = f <$> x <*> y
3. pure id <*> v = v
4. pure (%) <*> u <*> v <*> w = u <*> (v <*> w)
5. pure f <*> pure x = pure (f x)
6. u <*> pure y = pure ((|>) y) <*> u
7. u *> v = (id <$ u) <*> v
8. u <* v = lift2 const u v
9. fmap f x = pure f <*> x
10. lift2 p (lift2 q u v) = lift2 f u % lift2 g v

Minimal definition

Structure anatomy

Complete API

Additional references

• Haskell's documentation of an Applicative Functor
• Applicative Programming with Effects